Lumen Game Creation

Let me analyze the task. I need to create a brand new game that hasn't been done before. The last game was "Bridge Lab" - a Verlet physics bridge builder. Let me think about what kind of game would be fresh, interesting, and useful to the audience.

Let me first check what games already exist in the arcade to avoid repetition, and then come up with a creative new game idea.

Let me install the shell tools and check the existing games.

Let me think about what kind of game to create. I have 56 games already. Let me look at the genres covered:

• Physics/puzzle: bridge-lab, gravity-golf, gravity-wells, box-pusher, powder-lab
• Grid/puzzle: 2048, picross-quest, sudoku-sage, harmony-grid, neon-flip
• Word games: word-forge, word-hunt, code-quest
• Rhythm/music: beat-drop, pulse, harmony-grid
• Strategy: battleship, mancala, mastermind, stock-tycoon, realm-guard
• Arcade/action: snake, neon-breakout, type-storm, nova-pop, block-cascade, gem-cascade
• Physics simulation: lunar-lander, stellar-pinball, murmuration
• Creative/building: biome-builder, cosmic-forge, pixel-painter, forge-master
• Logic/circuit: circuit-breaker, quantum-circuit, gear-works, loop-lab
• Card/board: dungeon-deck
• Adventure/RPG: dungeon-delver, aether-spire, echo-maze
• Color/visual: chroma-shift, color-clash, prism, neon-flow
• Other: mine-sweeper, tower-of-hanoi, math-blitz, synapse, reaction-chain, orbit-weaver, starweave, deep-cast, hive, gridlock

I need something fresh. Let me think about what's NOT covered:

1. Conway's Game of Life / cellular automata - not covered, but could be educational
2. Tangram / shape puzzle - not covered
3. Nonogram - covered by picross-quest
4. Tower defense - realm-guard is similar
5. Idle/incremental game - stock-tycoon is somewhat similar
6. Roguelike - dungeon-delver is similar
7. Music sequencer / beat maker - beat-drop and harmony-grid cover this
8. Sorting algorithm visualizer game - not covered, could be educational
9. Tetris - block-cascade might be similar
10. Sokoban - box-pusher is similar
11. Pipe/connect puzzle - neon-flow is similar
12. Memory game - not explicitly covered
13. Typing game - type-storm covers this
14. Drawing/art game - pixel-painter covers this
15. Chemistry/element game - alchemy-lab covers this
16. Farming/garden game - not covered
17. Weather simulation - not covered
18. DNA/genetics game - not covered
19. Ecosystem simulation - biome-builder is similar
20. Optical illusion game - not covered
21. Knot tying puzzle - not covered
22. Origami/folding puzzle - not covered
23. Shadow/light puzzle - not covered
24. Magnetic field simulation - not covered
25. Sorting/organizing game - not covered
26. Log sorting / lumberjack game - not covered
27. Constellation/astronomy game - not covered (orbit-weaver is orbital mechanics)
28. Fruit/produce sorting game - not covered
29. Traffic control game - gridlock might be similar
30. Plumber/pipe game - neon-flow is similar
31. Rubik's cube - not covered
32. Sliding puzzle (15-puzzle) - not covered
33. Match-3 - gem-cascade, nova-pop might be similar
34. Bubble shooter - not covered explicitly
35. Pinball - stellar-pinball covers this
36. Doodle/quick draw - not covered
37. Geography/map game - not covered
38. Anagram/word scramble - word-forge might cover this
39. Simon Says / memory sequence - not covered explicitly
40. Reflexes/reaction time game - reaction-chain covers this
41. Stacking game - not covered (like Stack by Ketchapp)
42. One-button game - not covered
43. Idle/clicker game - not covered
44. Pet/virtual pet - not covered
45. Cooking game - not covered
46. Restaurant management - not covered
47. Factory/production line game - not covered
48. Logistics/supply chain game - not covered
49. Robot programming game - not covered (code-quest is coding but different)
50. Light/laser puzzle - not covered
51. Mirror/reflection puzzle - not covered
52. Color mixing puzzle - chroma-shift, color-clash, prism cover color
53. Folding/origami - not covered
54. Paper airplane game - not covered
55. Wind/airflow simulation - not covered
56. Sailing game - not covered
57. Fishing game - not covered
58. Mining/excavation game - not covered
59. Archaeology/dig game - not covered
60. Genealogy/family tree - not covered

Let me think about what would be both unique and useful/educational...

I think a Light/Laser Puzzle Game would be great! The concept: you place mirrors and prisms on a grid to direct a laser beam from a source to a target, hitting all the required nodes along the way. This is mechanically distinct from anything in the arcade, visually striking (neon laser beams), and educational (teaches reflection, refraction, color mixing).

Actually, let me think more creatively. What about a Constellation Builder game? You connect stars to form constellations based on patterns. That's different from anything there.

Or what about a Robot Programming Puzzle - where you program a robot with a sequence of commands to navigate through a grid, avoiding obstacles and collecting items. This is educational (teaches basic programming concepts) and mechanically different from code-quest (which seems to be a typing/coding game).

Actually, let me think about what's truly unique and engaging...

How about a Terraforming / Climate Simulation Game? You manage a planet's climate by adjusting atmospheric composition, placing terraforming machines, and trying to make it habitable. This combines simulation, strategy, and education about climate science.

Or a Sound Wave / Frequency Puzzle - where you manipulate wave frequencies to match patterns. But beat-drop and harmony-grid cover audio.

Let me go with something really fresh: A "Circuit Scramble" style logic puzzle game - but wait, circuit-breaker and quantum-circuit already exist.

How about "Hex Hive" - a hexagonal territory control puzzle? No, hive already exists.

Let me think about this differently. What about a "Paper Plane" flight game where you fold and throw paper planes, adjusting fold angles to navigate through obstacles? That's unique - combines origami/folding mechanics with physics-based flight.

Or a "Sort It" - a sorting puzzle game where you sort colored balls/liquids into containers (like the water sort puzzle). This is a popular mobile game genre that's not represented.

Actually, let me go with something really creative and educational: "Signal Tower" - an air traffic control game. You manage incoming planes by drawing flight paths to runways, avoiding collisions, and managing landing sequences. This is:

• Mechanically unique (path-drawing + time management)
• Visually distinct (radar/ATC aesthetic with sweeping radar line)
• Educational (teaches about air traffic management)
• Engaging (increasing difficulty with more planes)

Wait, gridlock might be similar (traffic). Let me think of something else.

How about "Prism Path" - a light/laser puzzle game? You place mirrors, splitters, and prisms on a grid to guide laser beams from emitters to receivers, with color mixing mechanics. This is:

• Mechanically unique (light propagation puzzle)
• Visually stunning (neon laser beams, glowing prisms)
• Educational (teaches reflection, refraction, color theory)
• Deep gameplay (multiple beam colors, mixing, splitting)

Actually, I realize I should check if there's something similar. Let me look at what neon-flow is about.

Actually, let me just go with a really cool idea: "Terraform" - a planet terraforming simulation/puzzle game. You're given a barren planet and must strategically place terraforming devices (atmosphere generators, water pumps, seed bombs, etc.) to transform it into a habitable world. The challenge is managing limited resources while dealing with planetary conditions (temperature, atmosphere, water, life).

Hmm, but biome-builder might be similar. Let me think of something else.

OK, I'll go with "Lumen" - a light/laser puzzle game. This is a grid-based puzzle where you direct light beams using mirrors, prisms, and filters to light up all targets. It's:

• Completely unique in the arcade
• Visually gorgeous with glowing neon beams
• Educational (optics, reflection, color mixing)
• Deep puzzle mechanics

Let me design this game:

Game: Lumen

• Grid-based puzzle (like 8x8 or 10x10)
• Light emitters (sources) that shoot beams in a direction
• Mirrors (reflect beams 90°)
• Prisms (split white light into colors)
• Color filters (only let certain colors through)
• Targets (need to be hit by the right color light)
• Walls/obstacles
• Multiple levels with increasing complexity
• Beautiful neon aesthetic with glowing beams

Actually, let me reconsider. I want to make something that's really polished and fun. Let me think about what would be most engaging...

You know what, let me go with a "Constellation" game - a star-mapping puzzle where you connect stars to recreate ancient constellations. The twist: you're given a sky full of stars and must figure out which stars form each constellation based on clues (distances, angles, brightness). It's:

• Unique (no similar game in arcade)
• Beautiful (night sky aesthetic)
• Educational (actual constellations)
• Relaxing yet challenging

Hmm, but the gameplay might be too simple. Let me think more...

Actually, I'll go with the light/laser puzzle idea but make it really polished. Let me call it "Lumen".

Wait, actually, let me think about what would be most useful to the audience. The task says "something that is useful to the audience." Educational games are useful. Let me think about what educational topic hasn't been covered:

• Math: math-blitz
• Words: word-forge, word-hunt, code-quest
• Logic: circuit-breaker, quantum-circuit, gear-works
• Music: beat-drop, harmony-grid, pulse
• Chemistry: alchemy-lab, powder-lab
• Physics: bridge-lab, gravity-golf, gravity-wells, lunar-lander
• Biology: biome-builder
• Geography: not covered
• History: not covered
• Programming: code-quest
• Art: pixel-painter
• Strategy/Logic: mastermind, sudoku-sage, picross-quest, tower-of-hanoi

What about a geography/country game? Or a periodic table game? Or a typing/keyboard learning game?

Actually, let me go with something fun and unique: "Sort Tower" - a water sort puzzle. This is a very popular puzzle genre where you have tubes with colored liquids and you need to sort them so each tube has only one color. It's:

• Simple to understand but challenging
• Unique in the arcade
• Visually appealing with liquid physics
• Great for all ages
• Many levels possible

Actually, I think I should go with something more ambitious and creative. Let me think about what would really stand out...

How about "Garden Guardian" - a plant growing/garden management puzzle game? You place seeds, water them, manage sunlight, and deal with pests to grow a beautiful garden. It combines resource management with puzzle elements.

Or "Echo" - a sound-based navigation game where you navigate through a dark cave using only sound echoes to "see" your surroundings. Bats and obstacles reflect sound waves, and you must navigate to the exit. This is:

• Unique (echolocation mechanic)
• Educational (teaches about sound waves and echolocation)
• Atmospheric (dark cave with sound visualization)
• Innovative (using sound as the primary game mechanic)

Hmm, but echo-maze might be similar. Let me check what echo-maze is about.

Actually, I don't need to check every game. Let me just pick a strong concept and build it well.

I'll go with "Lumen" - a light/laser puzzle game. Here's my design:

Lumen - Light Puzzle Game

Core mechanic: Place and rotate mirrors on a grid to direct light beams from emitters to targets.

Features:

• Grid-based puzzle (various sizes)
• Light emitters that shoot beams in cardinal directions
• Mirrors that can be placed and rotated (45° angles: / and )
• Prisms that split white light into RGB components
• Color filters
• Colored targets (must be hit by matching color)
• Walls/obstacles
• Multiple beam colors (red, green, blue, and white = all three)
• Color mixing (red + green = yellow, etc.)
• 15+ progressive levels
• Beautiful neon aesthetic
• Click to place, click to rotate
• Undo functionality
• Level select
• Progress saving via localStorage
• Web Audio API sound effects

Visual style: Dark background with glowing neon beams, particle effects where beams hit targets, smooth animations.

Let me build this. I'll create a comprehensive, polished game.

Actually, wait. Let me reconsider the complexity. Light beam puzzles with color mixing can get very complex to implement correctly. Let me simplify but still make it engaging:

Simplified design:

• Grid-based puzzle
• Light emitters (fixed position, fixed direction, fixed color)
• Mirrors (player places on grid, can rotate between / and )
• Beam splitters (split beam into two perpendicular directions)
• Targets (must be hit by any beam to complete level)
• Walls (block beams)
• 20+ levels
• Clean neon aesthetic

This is more manageable while still being unique and fun.

Let me start building this game now. I'll create it in /space/games/lumen/.

Actually, let me reconsider one more time. I want to make sure this is really good and polished. Let me think about the implementation:

1. Grid system - 2D array
2. Light propagation - ray casting from emitters, following mirrors
3. Rendering - Canvas 2D with glow effects
4. Interaction - click to place/rotate mirrors
5. Level system - JSON-like level definitions
6. Win condition - all targets lit

The light propagation is the trickiest part. I need to:

• Start from each emitter
• Cast a ray in the emitter's direction
• When hitting a mirror, reflect 90°
• When hitting a splitter, create two new rays
• When hitting a target, mark it as lit
• When hitting a wall or grid edge, stop
• Need to handle beam loops (visited cells to prevent infinite loops)

Let me code this up. I'll make it really polished with:

• Beautiful glowing beam rendering
• Particle effects
• Smooth animations
• Sound effects
• Multiple level themes
• Star rating system

Let me start coding!

Actually, I just realized I should think about what makes this game truly special and not just a basic light puzzle. Let me add some unique twists:

1. Color mixing: Some targets require specific colors. White light can be split by prisms into RGB, and beams can be combined.
2. Beam intensity: Beams lose intensity when split, so some targets need direct hits.
3. Moving elements: Some levels have rotating mirrors or moving targets.
4. Portal mirrors: Mirrors that teleport beams to another location.

Actually, let me keep it focused but polished. The core mechanic of placing mirrors to direct light is already engaging. Let me add:

• Multiple beam colors with color mixing
• Prisms that split white light
• Filters that only pass certain colors
• Colored targets

This gives enough depth without being overwhelming.

Let me start building. I'll write the complete game in a single HTML file for simplicity.

Let me plan the code structure:

Let me write this now. I'll aim for a really polished, complete game.

Actually, I want to make sure the light propagation is correct. Let me think through the algorithm:

1. For each emitter, create a beam with: position, direction, color
2. Process beams in a queue: a. Move beam one cell in its direction b. If out of bounds → beam ends c. If hits wall → beam ends d. If hits mirror → change direction (90° rotation based on mirror orientation) e. If hits prism → if white light, split into R, G, B beams in different directions; if colored, pass through f. If hits filter → if matching color, pass through; else beam ends g. If hits target → mark target as lit (with beam color), beam continues h. If hits splitter → create two beams (original direction + perpendicular) i. If empty cell → beam continues
3. Track visited (cell, direction, color) to prevent infinite loops
4. After processing all beams, check if all targets are lit

For rendering:

• Draw the grid
• Draw placed items (mirrors, prisms, etc.)
• Draw beams as glowing lines
• Draw targets with glow when lit
• Draw emitters

For the beam rendering, I'll use:

• Canvas 2D context
• Shadow blur for glow effect
• Multiple passes for stronger glow
• Gradient along beam for intensity

Let me code this up now!

Actually, I realize I should think about the mirror mechanics more carefully. In a grid-based system:

• A mirror at position (x, y) with orientation "/" reflects:

  • Beam going right → up
  • Beam going left → down
  • Beam going up → right
  • Beam going down → left

• A mirror with orientation "" reflects:

  • Beam going right → down
  • Beam going left → up
  • Beam going up → left
  • Beam going down → right

This is the standard mirror reflection in grid puzzles. Let me implement this.

For the beam splitting (prism), when white light hits a prism:

• The beam continues straight (as white light? or stops?)
• Actually, let me make it simpler: a prism splits white light into 3 colored beams going in 3 different directions (e.g., straight, left, right)

Hmm, that's a bit arbitrary. Let me think about this differently.

Actually, for a cleaner design, let me simplify:

• Emitters produce colored light (red, green, blue, or white)
• Mirrors reflect light 90°
• Prisms split white light into R, G, B going in 3 directions (forward, left-perpendicular, right-perpendicular)
• Colored light passes through prisms unchanged
• Targets need specific colors
• Some targets accept any color, some need specific colors

Wait, this is getting complex. Let me simplify even further for the first version:

Simplified Lumen:

• Emitters produce light (single color per emitter)
• Mirrors reflect light (/ and \ orientations)
• Beam splitters split light into two perpendicular beams
• Targets need to be hit by light
• Walls block light
• Player places mirrors and splitters on the grid
• Some cells are pre-placed (emitters, targets, walls, fixed mirrors)
• Player has a limited number of mirrors/splitters to place

This is clean, understandable, and fun. Color mixing can be a later addition if needed.

Actually, you know what, let me add colors because it makes the game much more interesting and visually stunning. Here's my final design:

Lumen - Light Direction Puzzle

Grid elements:

• Emitter: Fixed position, direction, and color. Shoots a beam.
• Target: Fixed position. Must be hit by matching color beam. Some targets are white (accept any color), some are colored (need specific color).
• Wall: Blocks all beams.
• Mirror: Player-placeable. Rotates between / and . Reflects beams 90°.
• Prism: Player-placeable or fixed. Splits white light into R, G, B. Colored light passes through.
• Filter: Fixed. Only lets matching color through.

Colors:

• Red, Green, Blue (primary)
• White = R + G + B combined
• When white beam hits prism → splits into R (one direction), G (another), B (another)

Actually, the prism splitting into 3 directions is weird in a 2D grid. Let me think...

In 2D, a prism could split white light into two beams: one continues straight, one deflects 90°. But which color goes which way?

OK, let me simplify the color system:

• Beams are either white or colored (R, G, B)
• A prism splits white light into R, G, B, each going in a different direction:
  • R goes right
  • G goes straight
  • B goes left (relative to the incoming beam direction)
• Colored beams pass through prisms unchanged
• Colored beams can be combined: if R and G beams enter the same cell from different directions, they create a yellow beam? No, this is getting too complex.

Let me just go with a simpler approach:

• All beams are the same "color" (white light)
• Prisms split beams into two (straight + perpendicular)
• No color mixing
• All targets accept any light

This is clean, fun, and still unique. The puzzle depth comes from:

• Limited mirrors to place
• Splitters creating multiple beams
• Complex grid layouts
• Multiple targets to hit
• Obstacles to navigate around

OK wait, I keep going back and forth. Let me just commit to a design and build it.

FINAL DESIGN: Lumen

A light direction puzzle game where you place mirrors on a grid to direct light beams from emitters to all targets.

Elements:

1. Emitter (▣): Fixed. Shoots a beam in one direction. Can be different colors.
2. Target (◎): Fixed. Must be hit by a beam of matching color. White targets accept any color.
3. Wall (█): Fixed. Blocks beams.
4. Mirror (╱ or ╲): Player-placeable. Click to place, click again to rotate. Reflects beams 90°.
5. Splitter (◇): Fixed or player-placeable. Splits beam into two perpendicular beams.

Colors: Red, Green, Blue, White

• White beam through splitter → two white beams
• Colored beam through splitter → two colored beams
• White target accepts any color
• Colored target needs matching color

Player tools:

• Place mirror (limited count per level)
• Rotate mirror
• Remove mirror
• Undo

Levels: 20+ progressive levels with increasing complexity

Visual: Dark background, glowing neon beams, particle effects, smooth animations

OK, I'm going with this. Let me also add color mixing to make it more interesting:

• When two different colored beams cross paths, they mix (R+G=Yellow, R+B=Magenta, G+B=Cyan, R+G+B=White)
• Some targets need mixed colors

Actually no, color mixing at beam crossings is complex to implement and visualize. Let me keep it simple:

• Beams have colors
• Targets have colors
• A target is "lit" if a beam of matching color hits it
• White targets accept any color
• White beams can be split by prisms into colored beams

Let me just build it now. I'll start with a simpler version and add complexity as needed.

Let me go with this final simplified design:

Lumen - Light Puzzle Game

Grid elements:

• Emitter: Fixed position, direction, color. Shoots beam.
• Target: Fixed position, color. Must be hit by matching color (white = any).
• Wall: Fixed. Blocks beams.
• Mirror: Player-placeable. / or \ orientation. Reflects 90°.
• Prism: Fixed. Splits white light into R (right), G (straight), B (left) relative to incoming direction. Colored light passes through.

Player interaction:

• Click empty cell to place mirror (if mirrors remaining)
• Click mirror to rotate (/ ↔ )
• Right-click or shift-click mirror to remove
• Undo button

Win condition: All targets lit with correct color.

Levels: 20 progressive levels.

Let me code this now!

Actually, I realize the prism mechanic (splitting into 3 directions) is a bit unusual for a 2D grid. Let me reconsider...

In most light puzzle games, a prism splits a beam into two: one continues straight, one deflects at an angle. But in a grid, "at an angle" doesn't work well.

Let me use a different approach:

• Beam Splitter: Splits beam into two beams going perpendicular (left and right relative to incoming direction). The original beam stops.
  • E.g., beam going right hits splitter → one beam goes up, one goes down
• This is cleaner for a grid system.

And for colors:

• Color Prism: Splits white light into R, G, B going in 3 directions (left, straight, right relative to incoming). Colored light passes through unchanged.

Actually, let me just go with beam splitters (no color splitting) for simplicity, and add colored emitters/targets for puzzle variety. The color matching adds enough depth.

FINAL FINAL DESIGN:

Elements:

1. Emitter: Fixed. Direction + color. Shoots beam.
2. Target: Fixed. Color. Must be hit by matching color (white = any).
3. Wall: Fixed. Blocks beams.
4. Mirror: Player-placeable. / or . Reflects 90°.
5. Splitter: Fixed. Splits beam into two perpendicular beams (left + right relative to incoming direction). Original beam stops.

Colors: Red, Green, Blue, White

• White beam + splitter → two white beams
• Colored beam + splitter → two colored beams
• White target accepts any color
• Colored target needs matching color

This is clean, implementable, and fun. Let me build it now!

Let me write the code. I'll create a comprehensive single-file game.

Actually, I want to make this really good. Let me think about the visual design:

• Dark navy/black background (#0a0a14)
• Grid lines: subtle dark blue (#1a1a2e)
• Beams: glowing colored lines with shadow blur
  • Red: #ff3366
  • Green: #33ff99
  • Blue: #3399ff
  • White: #ffffff
• Emitters: glowing circles with directional arrow
• Targets: ring shapes that glow when lit
• Mirrors: diagonal lines with subtle glow
• Splitters: diamond shapes
• Walls: solid blocks
• UI: clean, modern, with neon accents

For the beam rendering, I'll use:

• Multiple canvas passes for glow effect
• Line segments along the beam path
• Shadow blur for glow
• Animated dash effect for energy flow

Let me also add:

• Particle effects when targets are lit
• Smooth mirror rotation animation
• Beam animation (flowing energy)
• Background subtle grid pulse
• Sound effects (Web Audio API)
• Level transition animations

OK, let me start writing the code now. This will be a substantial single HTML file.

Let me think about the level design too. I need 20 levels that progressively introduce mechanics:

Level 1: Simple - one emitter, one target, place one mirror Level 2: Two mirrors needed Level 3: Introduce walls Level 4: Multiple targets Level 5: Introduce colored emitters/targets Level 6: Color matching required Level 7: Introduce splitters Level 8: Splitter + mirrors Level 9: Multiple emitters Level 10: Complex layout ... and so on, increasing in difficulty

Let me design these levels as I code.

OK, I'm going to start writing the game now. Let me create the file.

Let me think about the data structure for levels:

Directions: "up", "down", "left", "right"

For the beam propagation, I'll use a queue-based approach:

1. Start with beams from all emitters
2. For each beam, step through the grid cell by cell
3. At each cell, check what's there and react accordingly
4. Track visited (cell, direction, color) to prevent loops
5. Mark targets as hit when beams pass through them

Let me code this up now!

I'll write the complete game in one go. Let me structure the code:

1. HTML structure
2. CSS styles
3. JavaScript: a. Constants and configuration b. Level definitions c. Game state d. Light propagation engine e. Rendering engine f. Input handling g. UI management h. Audio system i. Save/load system j. Main game loop

Let me write this now. I'll aim for around 1500-2000 lines of well-structured code.

Actually, let me think about the beam propagation more carefully. The beam should be a continuous line from the emitter, through mirrors, to its endpoint. I need to track the path for rendering.

Beam path representation:

• Array of points (x, y) that the beam passes through
• Each beam has: color, path (array of {x, y}), and whether it hit a target

Algorithm:

1. Start at emitter position, direction = emitter direction, color = emitter color
2. Current position = emitter position
3. Path = [{x: emitter.x, y: emitter.y}]
4. Loop: a. Calculate next position (current + direction) b. If next is out of bounds → beam ends, add last point to path c. If next is wall → beam ends, add wall position to path d. If next is mirror → change direction, add mirror position to path, continue e. If next is splitter → create two new beams (perpendicular directions), add splitter position to path, original beam ends f. If next is target → mark target as hit (if color matches), add target position to path, continue (beam passes through target) g. If next is empty → move to next position, continue h. Check for loops: if we've been at this position with this direction and color before → beam ends

Wait, I need to be more careful. The beam should pass through empty cells and targets, but stop/transform at mirrors, walls, and splitters.

Let me refine:

This looks right. Let me implement it.

For the mirror reflection:

• "/" mirror:

  • right → up
  • left → down
  • up → right
  • down → left

• "" mirror:

  • right → down
  • left → up
  • up → left
  • down → right

For the splitter:

• Beam going right → splits into up and down
• Beam going left → splits into up and down
• Beam going up → splits into left and right
• Beam going down → splits into left and right

OK, let me code this now. I'll write the complete game.

Let me also think about the color matching logic:

• Target color "white" → accepts any beam color
• Beam color "white" → matches any target color
• Otherwise → beam color must equal target color

Wait, should a white beam match a colored target? In real optics, white light contains all colors, so yes. But for gameplay, it might be more interesting if white beams DON'T match colored targets (you need to use prisms to split white light into colors).

Let me go with:

• White target → accepts any beam color
• Colored target → only accepts matching colored beam (white beam does NOT match)
• This creates the need for prisms to split white light

But wait, I removed prisms from the design. Let me add them back:

• Prism: Fixed. Splits white beam into R, G, B going in 3 directions (left, straight, right relative to incoming). Colored beams pass through unchanged.

Hmm, 3-way split in a 2D grid is awkward. Let me think...

When a beam going RIGHT hits a prism:

• Red beam goes UP
• Green beam goes RIGHT (continues straight)
• Blue beam goes DOWN

When a beam going UP hits a prism:

• Red beam goes LEFT
• Green beam goes UP (continues straight)
• Blue beam goes RIGHT

This actually works! The prism splits white light into 3 colored beams: one continues straight, two go perpendicular. The colors are assigned to specific perpendicular directions.

But this is a bit arbitrary (why red=up, blue=down?). Let me make it simpler:

Prism: Splits white beam into 3 colored beams:

• One continues straight (green)
• One goes left-perpendicular (red)
• One goes right-perpendicular (blue)

Colored beams pass through unchanged.

This is clean and implementable. Let me go with this.

So my final element list:

1. Emitter: Fixed. Direction + color. Shoots beam.
2. Target: Fixed. Color. Must be hit by matching color (white = any).
3. Wall: Fixed. Blocks beams.
4. Mirror: Player-placeable. / or . Reflects 90°.
5. Splitter: Fixed. Splits any beam into two perpendicular beams (same color).
6. Prism: Fixed. Splits white beam into R (left-perp), G (straight), B (right-perp). Colored beams pass through.

Color matching:

• White target → accepts any beam
• Colored target → only accepts exact matching color (white beam does NOT match)

This gives nice puzzle depth: you might need to split white light with a prism to get the right colors for targets.

OK, NOW let me actually code this. I've spent too long planning. Let me write the game!

Let me think about the level designs:

Level 1: "First Light" - 7x7 grid, one white emitter on left, one white target on right, one wall in between. Place 1 mirror to redirect. Actually, if emitter is on left shooting right and target is on right, they're in a straight line. No mirror needed. Let me redesign.

Level 1: "First Light" - 7x7 grid, white emitter at (0,3) shooting right, white target at (6,1). Place 1 mirror to redirect beam upward.

Level 2: "Double Bounce" - Need 2 mirrors to redirect beam around walls.

Level 3: "Obstacles" - More walls, need 3 mirrors.

Level 4: "Multiple Targets" - 2 targets, need to hit both. Use a splitter.

Level 5: "Color Code" - Red emitter, red target. Green emitter, green target. Need to route both.

Level 6: "Prism" - White emitter, red and blue targets. Use prism to split.

Level 7: "Maze" - Complex layout with many walls.

Level 8: "Crossfire" - Multiple emitters and targets, colors must not cross-contaminate.

... and so on.

Let me design 20 levels. I'll do this as I code.

OK, let me start writing the actual code now. I'll create the file in one go.

Let me think about the canvas size and grid rendering:

• Canvas: responsive, max 600x600
• Grid cells: square, calculated based on canvas size and grid dimensions
• Each cell: drawn with subtle border
• Elements drawn centered in cells

For the beam rendering:

• Draw beam path as connected line segments
• Use shadowBlur for glow effect
• Draw multiple passes: wide low-opacity, medium medium-opacity, thin high-opacity
• Animate with a flowing dash pattern

Let me code this now!

I'll write the complete HTML file. Let me structure it carefully.

Actually, I realize I should also think about the UI:

• Top bar: level name, level number, mirrors remaining
• Game area: canvas
• Bottom bar: undo button, reset button, hint button
• Level select: grid of level buttons
• Win screen: stars, next level button

Let me also add:

• Tutorial overlay for first-time players
• Settings (sound toggle)
• Progress tracking (completed levels, stars)

OK, I'm going to write the code now. Let me create the file.

Let me think about the overall structure of the JavaScript code:

OK, let me write this now. I'll create the complete game file.

Let me think about one more thing: the beam animation. I want the beams to look like flowing energy, not just static lines. I'll use:

• A time-based offset for dash patterns
• Pulsing glow intensity
• Particle effects at beam endpoints and targets

For the mirror rotation animation:

• When a mirror is rotated, animate the rotation over ~200ms
• Use easing for smooth motion

Let me also think about the color palette for the UI:

• Background: #0a0a14 (very dark blue-black)
• Grid: #141420 (slightly lighter)
• Grid lines: #1e1e30
• UI background: #0f0f1a
• UI accent: #00d4ff (cyan)
• Text: #e0e0f0
• Muted text: #606080
• Beam colors:
  • Red: #ff3366
  • Green: #33ff99
  • Blue: #3399ff
  • White: #ffffff
• Target colors: same as beam colors
• Mirror: #8080a0 with white glow
• Splitter: #c0c0e0 with cyan glow
• Prism: rainbow gradient
• Wall: #2a2a3e

OK, let me write the code now!

I'll write it in sections and combine them. Let me start with the HTML structure and CSS, then the JavaScript.

Actually, let me just write the whole thing at once. It'll be a big file but that's fine.

Let me think about the level data format more carefully:

Wait, I need to think about whether the emitter is AT position (0,3) or if it's on the edge. Let me make emitters be grid cells, not edges. So an emitter at (0,3) shooting right means the beam starts at cell (0,3) and moves right.

Actually, let me make the emitter occupy a cell and the beam starts from that cell going in the specified direction. The first cell the beam enters is (0+1, 3) = (1, 3).

Hmm, but then the emitter cell itself is occupied. Let me think...

In most light puzzle games, the emitter is a cell that emits light in a direction. The light starts from the emitter cell and goes in that direction. So:

• Emitter at (0, 3) shooting right
• Beam starts at (0, 3), next cell is (1, 3), then (2, 3), etc.

The emitter cell itself is not passable by other beams (it's a solid object). Same for targets - they're cells that beams can pass through (or stop at?).

Let me make targets passable - beams go through targets. This allows hitting multiple targets with one beam.

OK, let me finalize the cell behavior:

• Empty: beam passes through
• Wall: beam stops
• Emitter: beam stops (solid object, but this shouldn't happen in normal gameplay)
• Target: beam passes through, target gets marked as hit
• Mirror: beam reflects, continues in new direction
• Splitter: beam splits into two perpendicular beams, original stops
• Prism: white beam splits into R/G/B, colored beam passes through

For player-placed mirrors, they occupy empty cells. The player can place mirrors on empty cells only.

Let me code this now. I'll write the complete game.

Let me also think about the grid coordinate system:

• (0, 0) is top-left
• x increases to the right
• y increases downward
• Directions: 0=up, 1=right, 2=down, 3=left
• DX = [0, 1, 0, -1]
• DY = [-1, 0, 1, 0]

Mirror reflection:

• "/" (slash): right→up, up→right, left→down, down→left

  • dir 1 → dir 0
  • dir 0 → dir 1
  • dir 3 → dir 2
  • dir 2 → dir 3
  • Formula: newDir = (3 - dir) % 4? Let me check:
    • 1 → 0: 3-1=2? No. Let me think differently.
    • "/" mirror: horizontal beams go up, vertical beams go horizontal
    • right(1) → up(0): 1→0
    • up(0) → right(1): 0→1
    • left(3) → down(2): 3→2
    • down(2) → left(3): 2→3
    • Pattern: swap pairs (0,1) and (2,3)
    • Formula: if dir is 0→1, 1→0, 2→3, 3→2
    • This is: newDir = dir ^ 1 (XOR with 1)
    • 0^1=1, 1^1=0, 2^1=3, 3^1=2 ✓

• "" (backslash): right→down, down→right, left→up, up→left

  • right(1) → down(2): 1→2
  • down(2) → right(1): 2→1
  • left(3) → up(0): 3→0
  • up(0) → left(3): 0→3
  • Pattern: swap pairs (0,3) and (1,2)
  • Formula: newDir = dir ^ 3 (XOR with 3)
  • 0^3=3, 1^3=2, 2^3=1, 3^3=0 ✓

So:

• "/" mirror: newDir = dir ^ 1
• "" mirror: newDir = dir ^ 3

Splitter:

• Beam going right(1) → up(0) and down(2)
• Beam going left(3) → up(0) and down(2)
• Beam going up(0) → left(3) and right(1)
• Beam going down(2) → left(3) and right(1)
• Perpendicular directions: (dir + 1) % 4 and (dir + 3) % 4
  • For right(1): (1+1)%4=2(down), (1+3)%4=0(up) ✓
  • For up(0): (0+1)%4=1(right), (0+3)%4=3(left) ✓

Prism (white light split):

• Beam going right(1) → red=up(0), green=right(1), blue=down(2)
  • Wait, I said red=left-perp, green=straight, blue=right-perp
  • For beam going right: left-perp = up(0), straight = right(1), right-perp = down(2)
  • So: red=up(0), green=right(1), blue=down(2)
• Beam going up(0) → red=left(3), green=up(0), blue=right(1)
  • left-perp of up = left(3), straight = up(0), right-perp = right(1)
  • So: red=left(3), green=up(0), blue=right(1)
• General:
  • red = left-perpendicular = (dir + 3) % 4
  • green = straight = dir
  • blue = right-perpendicular = (dir + 1) % 4

Let me verify:

• right(1): red=(1+3)%4=0(up) ✓, green=1(right) ✓, blue=(1+1)%4=2(down) ✓
• up(0): red=(0+3)%4=3(left) ✓, green=0(up) ✓, blue=(0+1)%4=1(right) ✓
• left(3): red=(3+3)%4=2(down) ✓, green=3(left) ✓, blue=(3+1)%4=0(up) ✓
• down(2): red=(2+3)%4=1(right) ✓, green=2(down) ✓, blue=(2+1)%4=3(left) ✓

Great, the formulas work!

Now let me write the complete game. I'll create it as a single HTML file.

Let me think about the rendering one more time. I want the beams to look really good:

1. First pass: draw wide, low-opacity glow (shadowBlur=20, lineWidth=12, opacity=0.15)
2. Second pass: draw medium, medium-opacity glow (shadowBlur=10, lineWidth=6, opacity=0.4)
3. Third pass: draw thin, high-opacity core (shadowBlur=5, lineWidth=2, opacity=1.0)
4. Add animated dash pattern for energy flow effect

For targets:

• Draw ring shape
• When lit: pulsing glow, particle effects
• When unlit: dim ring

For mirrors:

• Draw diagonal line
• Subtle glow
• Rotation animation when toggling

For emitters:

• Draw circle with directional indicator
• Pulsing glow in beam color

For walls:

• Draw solid block with subtle texture

For splitters:

• Draw diamond shape
• Cyan glow

For prisms:

• Draw triangle shape
• Rainbow gradient

OK, let me write the code now. I'll create the file.

Let me also think about the game flow:

1. Title screen → Level select
2. Level select → Click level → Game screen
3. Game screen → Place mirrors → All targets lit → Win screen
4. Win screen → Next level or back to level select

I'll implement:

• Title screen with "Play" button
• Level select grid (shows completed levels with stars)
• Game screen with canvas and UI
• Win overlay with stars and next button

Let me write the code now!

One more thing: I need to make sure the game is responsive and works on mobile. I'll use:

• Touch events for mobile
• Responsive canvas sizing
• CSS media queries for layout

OK, let me write the complete game now. I'll create it in /space/games/lumen/index.html.

Let me write the code. This is going to be a big file, but I'll make it clean and well-organized.

Actually, I want to reconsider the game name. "Lumen" is nice but let me think of alternatives:

• "Lumen" - unit of light, sounds clean
• "Beacon" - light source
• "Prism" - already a game in the arcade
• "Glow Grid" - descriptive
• "Light Bender" - fun, descriptive
• "Photon" - light particle
• "Refract" - light bending
• "Lumina" - light
• "Beam" - simple
• "Ray" - light ray

I'll go with "Lumen" - it's clean, memorable, and relevant.

Let me write the code now!

Actually, I just realized I should also think about what makes this game "useful to the audience" as the task mentions. Light/optics puzzles are educational - they teach:

• Reflection (mirrors)
• Beam splitting
• Color theory (prisms splitting white light)
• Problem-solving and spatial reasoning

I'll add educational tips in the hint system.

OK, NOW let me write the code. For real this time.

Let me plan the file structure:

Let me write this now. I'll create the complete file.

I need to be careful about the beam propagation algorithm. Let me think through it one more time:

Wait, I need to handle the case where a white beam hits a colored target. In my design, white beam does NOT match colored targets. So:

Hmm, but this means a white beam passing through a colored target doesn't light it up. The beam continues but the target stays unlit. That's the intended behavior - you need to split the white light with a prism to get the right color.

OK, this looks correct. Let me also handle the case where multiple beams hit the same target - that's fine, the target just needs to be hit by at least one matching beam.

After calculating all beams, I need to collect all targetsHit from all beams (including sub-beams) and check if all targets are hit.

Let me also think about the visited set. The key includes the color, so a red beam and a blue beam can visit the same cell in the same direction. This is correct because they're different beams.

But wait, there's a subtlety. If a white beam hits a prism, it splits into R, G, B. The prism cell is already in the path of the white beam. The sub-beams start from the prism cell. The visited set should prevent the sub-beams from going back through the prism in the same direction/color.

Actually, the visited key includes the direction and color. So a red beam going up from the prism won't be blocked by the white beam that was going right to the prism, because the direction and color are different. Good.

But what if a red beam going up from the prism later hits another prism? The red beam passes through (colored beams pass through prisms). The visited set would have the entry for the red beam at the second prism's position with the red beam's direction. If the red beam later comes back to the same cell with the same direction (due to mirrors), it would be blocked. Good.

I think the algorithm is correct. Let me code it now.

One more thing: I need to flatten the sub-beams into a single list for rendering. I'll use a recursive approach to collect all beams.

OK, let me write the complete game now!

Let me also think about the level designs more carefully. I need to make sure each level is solvable and has a clear solution path.

Level 1: "First Light"

• 7x7 grid

• White emitter at (0, 3) shooting right

• White target at (6, 1)

• No walls

• 1 mirror to place

• Solution: Place "/" mirror at (5, 3) → beam goes right to (5,3), reflects up, hits target at (6,1)? Wait, (5,3) with "/" mirror: beam going right → up. So beam goes from (0,3) right to (5,3), then up to (5,1), then... it needs to reach (6,1). But going up from (5,3) it would go to (5,2), (5,1), (5,0). It doesn't go to (6,1).

  Let me redesign. Target at (5, 1). Place "/" mirror at (5, 3). Beam goes right to (5,3), reflects up, goes to (5,2), (5,1) = target. ✓

Actually, let me make it even simpler. Emitter at (0, 3) right, target at (3, 0). Place "/" mirror at (3, 3). Beam goes right to (3,3), reflects up, goes to (3,2), (3,1), (3,0) = target. ✓

Level 1: "First Light"

• 7x7 grid
• Emitter: (0, 3, right, white)
• Target: (3, 0, white)
• Mirrors: 1
• Solution: "/" at (3, 3)

Level 2: "Around the Bend"

• 7x7 grid

• Emitter: (0, 5, right, white)

• Target: (6, 0, white)

• Walls: [(3, 3), (3, 4), (3, 5)] (vertical wall in middle)

• Mirrors: 2

• Solution: "/" at (2, 5) → beam goes up, then "" at (2, 0)? No... Actually, beam goes right from (0,5) to (2,5), "/" reflects up, goes to (2,4), (2,3)... but (3,3) is a wall, not (2,3). Let me redesign.

  Emitter: (0, 5, right, white) Target: (6, 0, white) Walls: [(3, 0), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5)] - full vertical wall at x=3 Mirrors: 2 Solution: "/" at (2, 5) → beam goes up to (2, 0), then "" at (2, 0)? No, "" at (2,0) would reflect up→left. I need the beam to go right from (2,0). "/" at (2, 5): right→up. Beam goes up to (2, 0). At (2, 0), I need to go right. Mirror "" reflects up→left. Mirror "/" reflects up→right. So "/" at (2, 0): up→right. Beam goes right to (3, 0)... but (3, 0) is a wall!

  Let me redesign without the wall at (3, 0). Walls: [(3, 1), (3, 2), (3, 3), (3, 4), (3, 5)] "/" at (2, 5): right→up. Beam goes up to (2, 0). "/" at (2, 0): up→right. Beam goes right to (3, 0), (4, 0), (5, 0), (6, 0) = target. ✓ But wait, (3, 0) is not a wall now, so beam passes through. ✓

Level 2: "Around the Bend"

• 7x7 grid
• Emitter: (0, 5, right, white)
• Target: (6, 0, white)
• Walls: [(3, 1), (3, 2), (3, 3), (3, 4), (3, 5)]
• Mirrors: 2
• Solution: "/" at (2, 5), "/" at (2, 0)

Level 3: "Triple Threat"

• 9x9 grid

• Emitter: (0, 4, right, white)

• Targets: [(8, 4, white), (4, 0, white), (4, 8, white)]

• Splitter at (4, 4) (fixed)

• Mirrors: 0 (just use the splitter)

• Solution: Beam goes right to (4, 4) splitter, splits into up and down. Original beam... wait, does the original beam continue or stop? In my design, the splitter stops the original beam and creates two perpendicular beams. So:

  • Beam goes right to (4, 4) splitter
  • Splits into up (0) and down (2)
  • Up beam: (4, 3), (4, 2), (4, 1), (4, 0) = target ✓
  • Down beam: (4, 5), (4, 6), (4, 7), (4, 8) = target ✓
  • But what about (8, 4)? The original beam stopped at the splitter. Target at (8, 4) is not hit!

  I need to either: (a) let the original beam continue through the splitter, or (b) redesign the level.

  Let me redesign: remove the (8, 4) target. Targets: [(4, 0, white), (4, 8, white)] Mirrors: 0 Solution: Beam hits splitter at (4, 4), splits up and down, hits both targets. ✓

  But this is too simple with 0 mirrors. Let me add a twist.

  Actually, let me make the splitter a player-placeable item too. Or let me add walls that require mirrors.

  Level 3: "Split Decision"

  • 9x9 grid
  • Emitter: (0, 4, right, white)
  • Targets: [(8, 0, white), (8, 8, white)]
  • Splitter at (4, 4) (fixed)
  • Walls: [(6, 0), (6, 8)] - blocks direct path
  • Mirrors: 2
  • Solution: Beam goes right to (4, 4) splitter, splits up and down.
    • Up beam: (4, 3)...(4, 0). Need to go right to (8, 0). Place "/" at (4, 0): up→right. Beam goes right to (5, 0), (6, 0)... wall! Blocked.
    • Need to go around. Hmm, this is getting complex. Let me simplify.

  Level 3: "Split Decision"

  • 9x9 grid
  • Emitter: (0, 4, right, white)
  • Targets: [(4, 0, white), (4, 8, white)]
  • Splitter at (4, 4) (fixed)
  • Mirrors: 0
  • Solution: Beam hits splitter, splits up and down, hits both targets. ✓
  • This introduces the splitter mechanic. Simple but educational.

OK, I think I can design levels as I code. Let me just start writing the game and design levels inline.

Let me write the complete game now. I'll create it as a single HTML file with all the code.

I'll aim for a really polished game with:

• 20 levels
• Beautiful neon visuals
• Smooth animations
• Sound effects
• Progress saving
• Level select
• Tutorial/hints
• Responsive design
• Touch support

Let me write it now!

Actually, I realize I should also think about the "useful" aspect. Let me add educational tooltips about optics:

• When introducing mirrors: "Mirrors reflect light at equal angles"
• When introducing splitters: "Beam splitters divide light into two paths"
• When introducing prisms: "Prisms separate white light into colors"
• When introducing colors: "Different colors of light carry different energy"

These will appear as hints in the game.

OK, let me write the code now. I'll create the file in one go.

Let me think about the structure one more time and then write it all:

Let me write it all now. I'll create the file.

I'm going to write a really comprehensive game. Let me start coding.

Let me think about the canvas rendering in more detail. I want the beams to look amazing:

This should give a nice glowing beam effect. Let me also add particle effects at beam endpoints and lit targets.

OK, I'm going to write the complete game now. Let me create the file.

Let me also think about the cell size and canvas dimensions:

• Canvas: 560x560 (or responsive)
• Grid: 7x7 to 11x11 depending on level
• Cell size: canvasSize / gridSize
• Each cell drawn at (x * cellSize, y * cellSize) with size cellSize

For the grid drawing:

• Dark background
• Subtle grid lines
• Cell hover highlight
• Valid placement indicator

For element drawing:

• Emitter: circle with glow, directional arrow
• Target: ring, glows when lit
• Wall: rounded rectangle, dark
• Mirror: diagonal line with glow
• Splitter: diamond shape
• Prism: triangle with rainbow gradient

Let me write the code now!

I'll write the complete HTML file. Let me structure it carefully and make it really polished.

OK here's my plan for the code. I'll write it all in one file. Let me start:

Let me write the full code now. I'll be thorough and make it really good.

Actually, I want to make sure I have a good set of levels. Let me design 20 levels:

1. "First Light" - 1 mirror, 1 target, intro
2. "Around the Bend" - 2 mirrors, walls
3. "Split Decision" - splitter intro, 2 targets
4. "Color Code" - colored emitters/targets intro
5. "Prism" - prism intro, white→RGB
6. "Maze Runner" - complex walls, 3 mirrors
7. "Triple Target" - splitter + mirrors, 3 targets
8. "Color Maze" - colored beams through maze
9. "Crossfire" - 2 emitters, 2 colors
10. "Prism Power" - prism + mirrors, 3 colored targets
11. "The Gauntlet" - long path, many mirrors
12. "Color Filter" - (maybe add filters?)
13. "Double Split" - 2 splitters
14. "Rainbow Road" - prism + multiple mirrors per color
15. "Tight Squeeze" - limited mirrors, tight paths
16. "Crossing Beams" - multiple emitters crossing paths
17. "The Vault" - complex layout, all mechanics
18. "Spectrum" - all 3 colors, prism, mirrors
19. "Mastermind" - very complex, all mechanics
20. "Lumen" - final challenge

Let me design these levels more carefully as I code. I'll make sure each is solvable.

OK, I'm going to write the code now. Let me create the file.

Let me think about one more thing: the mirror placement UI. The player needs to:

1. Click an empty cell to place a mirror (default "/" orientation)
2. Click an existing mirror to rotate it ("/" → "")
3. Right-click or long-press a mirror to remove it

I'll also add a "tool selector" at the bottom:

• Mirror tool (default)
• Maybe a "remove" tool

Actually, let me keep it simple:

• Click empty cell → place "/" mirror (if mirrors remaining)
• Click "/" mirror → rotate to ""
• Click "" mirror → remove (refund mirror count)
• This is intuitive and simple

Let me also add an undo button that reverts the last action.

OK, let me write the code now!

I need to be really careful about the beam propagation. Let me trace through a simple example:

Level 1: Emitter at (0, 3) shooting right, target at (3, 0), mirror "/" at (3, 3).

Beam propagation:

1. Start at (0, 3), dir=right(1), color=white
2. Path = [(0, 3)]
3. Next: (1, 3) - empty, add to path
4. Next: (2, 3) - empty, add to path
5. Next: (3, 3) - mirror "/", reflect: dir = 1^1 = 0 (up), add to path
6. Next: (3, 2) - empty, add to path
7. Next: (3, 1) - empty, add to path
8. Next: (3, 0) - target, color matches (white target, white beam), mark as hit, add to path
9. Next: (3, -1) - out of bounds, break

Path: [(0,3), (1,3), (2,3), (3,3), (3,2), (3,1), (3,0)] Target at (3, 0) is hit. ✓

The rendering would draw a line from (0,3) to (3,3) then up to (3,0).

Now let me think about the pixel coordinates. If cellSize = 80 and the grid is 7x7:

• Cell (0, 3) center: (40, 280)
• Cell (3, 3) center: (280, 280)
• Cell (3, 0) center: (280, 40)

The beam path in pixels: (40, 280) → (280, 280) → (280, 40)

This would draw an L-shaped beam.

OK, let me write the code now. I'll create the complete game file.

Let me also think about edge cases:

1. Beam hitting another emitter → stop (emitter is solid)
2. Beam hitting a mirror that's already been visited in the same direction → stop (loop prevention)
3. Multiple beams hitting the same target → target is hit (just needs one matching beam)
4. Beam passing through a target → target is hit, beam continues
5. Splitter creating sub-beams → sub-beams are processed recursively

I think I've covered all the cases. Let me write the code now!

One more consideration: the visited set. I need to make sure it's shared across all beams (including sub-beams from splitters and prisms) to prevent infinite loops. The key is "x,y,dir,color" which uniquely identifies a beam segment.

But wait, there's a subtle issue. If a white beam hits a splitter, it creates two white sub-beams going perpendicular. These sub-beams might eventually reach the same cell with the same direction and color as another beam. The visited set would prevent this, which is correct - we don't want to process the same beam segment twice.

But what if two different emitters produce beams that would go through the same cell in the same direction with the same color? The visited set would prevent the second beam from going through that cell. Is this correct?

In reality, two beams can overlap. But for rendering purposes, we'd just draw the same line twice, which looks the same as drawing it once. And for target hitting, the target would already be marked as hit by the first beam. So preventing the second beam from processing the same segment is fine - it's an optimization that doesn't affect correctness.

Actually, wait. What if the second beam would continue past where the first beam stopped? For example:

• Emitter 1 at (0, 3) right, white. Beam goes to (5, 3) and hits a wall.
• Emitter 2 at (0, 3) right, white. Same beam, same path. The visited set would prevent it from going past (0, 3) because (1, 3, right, white) is already visited.

But this is fine because the two emitters are at the same position with the same direction and color - they're identical. The second beam would follow the exact same path as the first.

What if the emitters are at different positions but their beams would overlap?

• Emitter 1 at (0, 3) right, white. Beam goes to (5, 3) and hits a wall.
• Emitter 2 at (2, 3) right, white. Beam should go from (2, 3) to (5, 3).
• But (3, 3, right, white) is already visited by emitter 1's beam. So emitter 2's beam would stop at (2, 3) because (3, 3, right, white) is visited.

This is a problem! The second beam should be able to go through cells that the first beam already went through.

Hmm, I need to rethink the visited set. The issue is that the visited set is meant to prevent infinite loops (beam reflecting back and forth between two mirrors), not to prevent different beams from sharing path segments.

Solution: Use a per-beam visited set instead of a global one. Each beam (including sub-beams from the same emitter) has its own visited set. But sub-beams from the same splitter/prism should share the visited set to prevent loops within the same beam tree.

Wait, but if I use per-beam visited sets, a beam could still loop infinitely between two mirrors. The visited set per beam would prevent this because the beam would visit the same cell with the same direction twice.

Let me reconsider. The visited set should be per-beam-tree (all beams originating from the same emitter, including sub-beams from splitters/prisms). This prevents loops within a single beam tree but allows different beam trees to share path segments.

Actually, even per-beam visited sets would prevent loops. A single beam bouncing between two mirrors would visit the same cell with the same direction twice, and the per-beam visited set would catch it.

But sub-beams from a splitter could create loops. For example:

• Beam goes right, hits splitter, creates up and down sub-beams
• Up sub-beam hits mirror, goes right
• Right sub-beam hits mirror, goes down
• Down sub-beam hits mirror, goes left
• Left sub-beam hits mirror, goes

Now I have a good understanding of the existing games and the index format. Let me create my new game "Lumen" - a light/laser puzzle game. Let me write the complete game now.

I'll create the game directory and write the index.html file. This will be a comprehensive, polished game with:

• 20 levels
• Light propagation engine with mirrors, splitters, prisms
• Color matching mechanics
• Beautiful neon visuals with glowing beams
• Sound effects
• Progress saving
• Level select
• Educational hints about optics

Let me write the complete game now.

OK, I can see the issues now:

Level 14: The mirrors are being placed at (1,1) and (7,1), but the emitters are at (0,1) and (8,1). The mirrors are placed ON the emitter path, but the issue is:

• Red emitter (0,1) right → hits (1,1) which has '/' mirror → right(1)^1=0=up → goes UP to (1,0) → OOB
• The '/' mirror sends the beam UP, not DOWN! I need '' to send it DOWN.
• '' at (1,1): right(1)^3=2=down. Down to (1,7). Then '/' at (1,7): down(2)^1=3=left. Left to (0,7)=target!
• Wait, but I had orient=0 ('/') at (1,1). I need orient=1 ('') at (1,1).
• Similarly for blue: (8,1) left → (7,1) with '/' → left(3)^1=2=down. Down to (7,7). Then '/' at (7,7): down(2)^1=3=left. Left to (6,7)... not (8,7).
• Need '' at (7,7): down(2)^3=1=right. Right to (8,7)=target!
• So: red: '' at (1,1), '/' at (1,7). Blue: '/' at (7,1), '' at (7,7).

Wait, let me re-check:

• Red: (0,1) right → (1,1)='' → right(1)^3=2=down → (1,2),(1,3) wall! Blocked!
• The wall at (3,3) is at x=3, not x=1. (1,3) is empty. Let me check walls: {x:3,y:3},{x:3,y:4},{x:3,y:5},{x:5,y:3},{x:5,y:4},{x:5,y:5},{x:4,y:3},{x:4,y:5}
• (1,3) is empty. OK. Red goes down: (1,2),(1,3),(1,4),(1,5),(1,6),(1,7). '/' at (1,7): down(2)^1=3=left. Left to (0,7)=blue target. But red doesn't match blue target!
• Need red to go to (8,7). So red needs to go right, not left.
• '' at (1,7): down(2)^3=1=right. Right to (2,7),(3,7) - wall at (3,3) not (3,7). (3,7) is empty. (4,7),(5,7),(6,7),(7,7),(8,7)=red target!
• So red: '' at (1,1), '' at (1,7). 2 mirrors.
• Blue: (8,1) left → (7,1)='/' → left(3)^1=2=down → (7,2),(7,3),(7,4),(7,5),(7,6),(7,7). '' at (7,7): down(2)^3=1=right. Right to (8,7)=red target. But blue doesn't match red!
• Need blue to go to (0,7). So blue needs to go left.
• '/' at (7,7): down(2)^1=3=left. Left to (6,7),(5,7)...(0,7)=blue target!
• So blue: '/' at (7,1), '/' at (7,7). 2 mirrors.
• Total: 4 mirrors. But wait, red goes through (7,7) where blue's '/' mirror is!
• Red going right at y=7: (2,7),(3,7),(4,7),(5,7),(6,7),(7,7)='/' mirror. Red hits '/' = right(1)^1=0=up. Goes UP. Wrong!
• Conflict! Red and blue share y=7 path.
• Need different y for the horizontal paths.
• Red: '' at (1,1) -> down to (1,6). '' at (1,6) -> right to (8,6). Not (8,7).
• Need down from (8,6) to (8,7). Another mirror. 3 mirrors for red.
• Blue: '/' at (7,1) -> down to (7,2). '/' at (7,2) -> left to (0,2). Not (0,7).
• Need down from (0,2) to (0,7). Another mirror. 3 mirrors for blue.
• Total: 6 mirrors. Too many.
• Let me simplify level 14. Remove the walls and make it straightforward.
• Red: (0,1) right → '' at (4,1) -> down to (4,7) → '' at (4,7) -> right to (8,7)=target. 2 mirrors.
• Blue: (8,1) left → '/' at (5,1) -> down to (5,7) → '/' at (5,7) -> left to (0,7)=target. 2 mirrors.
• Blue at y=1 going left: (7,1),(6,1),(5,1)='/' mirror. OK.
• Red at y=1 going right: (1,1),(2,1),(3,1),(4,1)='' mirror. OK.
• Red at y=7 going right: (5,7)='/' mirror! Red hits '/' = right->up. Wrong!
• Conflict at (5,7). Need different x.
• Red: '' at (3,1) -> down to (3,7). '' at (3,7) -> right to (8,7).
• Blue: '/' at (6,1) -> down to (6,7). '/' at (6,7) -> left to (0,7).
• Red at y=7: (4,7),(5,7),(6,7)='/' mirror! Red hits '/' = right->up. Wrong!
• Still conflicts. The horizontal paths at y=7 always cross.
• What if red goes down to y=7 and right, while blue goes down to y=7 and left, but they use different y for horizontal?
• Red: '' at (3,1) -> down to (3,6). '' at (3,6) -> right to (8,6). '' at (8,6) -> right->down. Down to (8,7)=target. 3 mirrors.
• Blue: '/' at (6,1) -> down to (6,8). '/' at (6,8) -> left to (0,8). '/' at (0,8) -> left->up? '/' = left(3)^1=2=down. Wrong.
• '' at (0,8): left(3)^3=0=up. Up to (0,7)=target! 3 mirrors.
• Total: 6 mirrors. Still too many.
• OK, let me just make level 14 simple with no walls and 4 mirrors, using different y values:
• Red: (0,2) right → '' at (3,2) -> down to (3,6) → '' at (3,6) -> right to (8,6). Not (8,7).
• Hmm, target at (8,6) then. Or use 3 mirrors.
• Actually, let me just make it really simple:
• Red emitter (0,2) right, red target (8,6). '' at (4,2) -> down to (4,6). '' at (4,6) -> right to (8,6). 2 mirrors.
• Blue emitter (0,6) right, blue target (8,2). '/' at (5,6) -> up to (5,2). '/' at (5,2) -> right to (8,2). 2 mirrors.
• Blue at y=6: (1,6),(2,6),(3,6),(4,6)='' mirror! Blue hits '' = right->down. Wrong!
• Conflict at (4,6).
• The fundamental issue: when two beams need to cross, their mirror positions conflict.
• Solution: use different x values that don't overlap.
• Red: '' at (3,2) -> down at x=3. Blue: '/' at (6,6) -> up at x=6.
• Red at y=2: (1,2),(2,2),(3,2)='' mirror. OK.
• Red at y=6: (4,6),(5,6),(6,6)='/' mirror! Red hits '/' = right->up. Wrong!
• Blue at y=6: (1,6),(2,6),(3,6) - empty. (4,6) - empty. (5,6) - empty. (6,6)='/' mirror. OK.
• Blue at y=2: (7,2),(6,2) - empty. Wait, blue goes UP from (6,6) to (6,2). Then '/' at (6,2) -> right to (8,2).
• Red at y=6 going right: (4,6),(5,6),(6,6)='/' mirror. Conflict!
• The only way to avoid this is to have the horizontal paths at different y values.
• Red horizontal at y=6, blue horizontal at y=2. They don't share cells.
• But red's vertical is at x=3 (y=2 to y=6), and blue's vertical is at x=6 (y=6 to y=2).
• Red's horizontal at y=6 goes from x=3 to x=8. Blue's vertical at x=6 goes from y=6 to y=2.
• They cross at (6,6)! Red going right at y=6 passes through (6,6) where blue's '/' mirror is.
• Unless... blue's mirror is at (6,6) and red passes through it. Red hits '/' = right->up. Goes up. Wrong.
• What if blue's mirror is at (6,7) instead? Blue goes up from (6,7) to (6,2). Red goes right at y=6 from (3,6) to (8,6). (6,6) is empty. No conflict!
• Blue: '/' at (6,7) -> up to (6,2). '/' at (6,2) -> right to (8,2). 2 mirrors.
• Red: '' at (3,2) -> down to (3,6). '' at (3,6) -> right to (8,6). 2 mirrors.
• Red at y=6: (4,6),(5,6),(6,6) - empty! (7,6),(8,6)=target. OK!
• Blue at y=7: (1,7)... wait, blue emitter is at (0,6) going right. Blue at y=6: (1,6),(2,6),(3,6)='' mirror! Conflict!
• Red's '' at (3,6) blocks blue at y=6.
• What if blue emitter is at (0,7) instead of (0,6)?
• Blue: (0,7) right → (1,7),(2,7),(3,7) - empty. (4,7),(5,7),(6,7)='/' mirror. OK.
• '/' at (6,7) -> right->up. Up to (6,2). '/' at (6,2) -> up->right. Right to (8,2)=target!
• Red: (0,2) right → (1,2),(2,2),(3,2)='' mirror. '' -> down. Down to (3,6). '' at (3,6) -> right. Right to (8,6)=target!
• Red at y=6: (4,6),(5,6),(6,6) - empty. (7,6),(8,6)=target. OK!
• Blue at y=7: (1,7)...(6,7)='/' mirror. OK!
• Blue at y=2: (7,2),(8,2)=target. OK!
• No conflicts! 4 mirrors total.
• But red target is at (8,6) and blue target at (8,2). Let me verify:
• Red: (0,2) right, '' at (3,2) -> down to (3,6), '' at (3,6) -> right to (8,6). ✓
• Blue: (0,7) right, '/' at (6,7) -> up to (6,2), '/' at (6,2) -> right to (8,2). ✓
• 4 mirrors, no walls needed.

Level 19: Missing (10,1) red target. The red beam goes up from prism at (2,5) to (2,1) where '/' mirror sends it right. But it hits (4,1) which is a wall! Wall at (3,3) is at y=3, not y=1. Wait, let me check: walls are {x:3,y:3},{x:3,y:7},{x:7,y:7}. (4,1) is not a wall. But the log shows (4,1) t=1 (WALL). Oh wait, t=1 is WALL. But I didn't define a wall at (4,1). Let me check... the walls are {x:3,y:3},{x:3,y:7},{x:7,y:7}. (4,1) should be empty. But the log says t=1. That's strange.

Oh wait, I see the issue. The log shows:

But there's no wall at (4,1) in the level definition. Unless... wait, the mirror at (5,1) is placed by the solution. Let me check: sol19 = [{x:2,y:1,orient:0},{x:2,y:9,orient:1},{x:5,y:1,orient:0},{x:10,y:1,orient:1}].

Mirror at (5,1) with orient=0 ('/'). Red beam going right hits '/' at (5,1): right(1)^1=0=up. Goes UP to (5,0). OOB.

That's the problem! The '/' at (5,1) sends red UP, not right. I need '' at (5,1) to send red right: right(1)^3=2=down. No, that sends it DOWN.

Wait, I want red to continue right. But a mirror always changes direction. I can't place a mirror that lets the beam continue straight.

The issue is: red beam goes right from (2,1) and I want it to reach (10,1). But I placed a mirror at (5,1) which deflects it. I should NOT place a mirror at (5,1) for the red beam.

The mirror at (5,1) was intended for the GREEN beam (going up from splitter). Green goes up from (5,5) through (5,4),(5,3)=target,(5,2),(5,1)='/' -> up->right. Right to (10,1). Then '' at (10,1) -> right->down. Down to (10,5)=target.

But red also passes through (5,1) going right. Red hits '/' at (5,1) -> right->up. Goes up. Wrong for red.

The conflict is that both red and green beams pass through (5,1). Red goes right, green goes up. The '/' mirror affects both.

I need to separate their paths. What if green's mirror is at a different cell?

Green goes up from (5,5) through (5,4),(5,3)=target,(5,2),(5,1),(5,0). I can place the mirror at (5,0): '/' -> up->right. Right to (10,0). Then '' at (10,0) -> right->down. Down to (10,5)=target. But (10,0) is at the edge, and (10,1) is the red target. Red beam also goes to (10,1). If '' is at (10,0), red going right at y=1 doesn't hit it.

Wait, red goes right at y=1, not y=0. So '' at (10,0) doesn't affect red.

But green going right at y=0: (6,0),(7,0)...(10,0)='' mirror. Green hits '' = right->down. Down to (10,5)=target. But (10,1) is red target. Green passes through (10,1) but doesn't match (red target, green beam). OK.

And red goes right at y=1: (3,1),(4,1),(5,1) - no mirror now! (6,1),(7,1),(8,1),(9,1),(10,1)=red target. Direct hit!

So the solution is:

• '/' at (2,1) for red: up->right. Red goes right to (10,1)=target. ✓
• '/' at (5,0) for green: up->right. Green goes right to (10,0).
• '' at (10,0) for green: right->down. Down to (10,5)=target. ✓
• '' at (2,9) for blue: down->right. Blue goes right to (10,9)=target. ✓

But that's 4 mirrors: (2,1)/, (5,0)/, (10,0), (2,9). And the green up beam hits (5,3) target on its way up. ✓

Wait, but (10,0) - is that a valid cell? Grid is 11x11, so (10,0) is valid (x=10, y=0). ✓

Let me also check: does green beam from (10,0) going down pass through (10,1) where red target is? Yes, but green doesn't match red target. And red target is already hit by red beam. So it's fine.

But wait, does the '' at (10,0) affect the red beam? Red goes right at y=1 and reaches (10,1). It doesn't pass through (10,0). So no conflict. ✓

And does red beam pass through (5,0)? No, red is at y=1, not y=0. ✓

This should work! Let me also check the green down beam: (5,6),(5,7) - wall at (3,7) not (5,7). (5,8),(5,9),(5,10)=target. ✓

So L19 solution: [{x:2,y:1,orient:0}, {x:5,y:0,orient:0}, {x:10,y:0,orient:1}, {x:2,y:9,orient:1}]

Level 20: Similar issues. Let me trace:

• Red: up from (2,5) to (2,1)='/' -> right. (3,1),(4,1) wall! Stop at (3,1). Wall at (4,1) blocks red. Need to remove wall or redirect.
• Green: right from (2,5) to (6,5)=splitter. Splits up and down. Green up: (6,4),(6,3)=target. (6,2),(6,1)='/' -> right. (7,1),(8,1) wall! Stop at (7,1). Wall at (8,1) blocks green.
• Blue: down from (2,5) to (2,9)='' -> right. (3,9),(4,9) wall! Stop at (3,9). Wall at (4,9) blocks blue.

The walls are blocking everything! I need to remove the walls or redesign.

Let me remove the walls and use a simpler design:

• Red: '/' at (2,1) -> right to (12,1)=target. 1 mirror.
• Green: right to (6,5)=splitter. Up: (6,4),(6,3)=target. Down: (6,6)...(6,10)=target. Need (12,5) green target. Green up beam: '/' at (6,1) -> right to (12,1). Not (12,5). Need to redirect to (12,5). '/' at (6,1) -> right to (12,1). '' at (12,1) -> down to (12,5)=target! But (12,1) is red target. Can't place mirror there (it's a target cell). Place mirror at (11,1): '' -> right->down. Down to (11,5). Not (12,5). Place mirror at (12,1)... can't, it's a target. What if I place '/' at (6,0) -> right to (12,0). '' at (12,0) -> down to (12,5)=target. But (12,0) is at the edge. Can I place a mirror there? Yes, if it's an empty cell. Green up: (6,4),(6,3)=target,(6,2),(6,1),(6,0)='/' -> right. (7,0)...(12,0)='' -> down. (12,1)=red target (green doesn't match). (12,2)...(12,5)=green target. ✓ 2 mirrors for green.
• Blue: '' at (2,9) -> right to (12,9)=target. 1 mirror.
• Total: 1+2+1 = 4 mirrors. ✓

But wait, red goes right at y=1 from (2,1) to (12,1). Does it pass through (6,1) where green's path is? Green goes up through (6,1) but there's no mirror at (6,1) in this solution. The mirror is at (6,0). So red passes through (6,1) without hitting a mirror. ✓

And green goes right at y=0 from (6,0) to (12,0). Does it pass through any of red's mirrors? Red's mirror is at (2,1). Green is at y=0, not y=1. No conflict. ✓

And the '' at (12,0) - does red pass through it? Red is at y=1, mirror is at (12,0). No. ✓

This should work! Let me verify with the test.

Actually, I also need to check: does the '' at (12,0) affect the red beam? Red goes right at y=1 and reaches (12,1). It doesn't go through (12,0). ✓

And does red pass through (6,0)? No, red is at y=1. ✓

OK, let me now update the level definitions in the HTML file with all the fixes:

• L12: Change to 3 mirrors, 2 targets
• L14: Redesign with no walls, 4 mirrors, emitters at (0,2) and (0,7)
• L19: Fix solution to use (5,0) and (10,0) mirrors
• L20: Remove walls, fix solution to use (6,0) and (12,0) mirrors

Let me now update the HTML file with all the corrected levels.