Now the user is asking me to build an Asteroids game using canvas. I first need to analyze the user's specific requirements: it should be a single-player game where the player controls a spaceship to shoot asteroids. The spaceship should be able to thrust, rotate, fire, wrap around the screen edges, and the asteroids should be able to split into smaller pieces. The game should also have a scoring system and a lives display.

First, I need to consider the overall structure of the game. The page layout should have a full-screen canvas as the game area, with a control panel overlaid on top to display the score, high score, and lives. There should also be start and game over screens.

In terms of game mechanics, the physics system is crucial. The spaceship should have thrust and inertia, so I need to implement a simple physics engine with acceleration and friction. When rotating, the direction of thrust should change accordingly. Bullet firing should have a cooldown timer.

Regarding the game AI, asteroids don't need complex AI; they just need to move in a straight line. But I need to design the asteroid generation logic and the splitting mechanism. Large asteroids should split into two medium ones when hit, and medium ones into two small ones.

For the visual style, the user requested procedural vector graphics without external resources. I can use simple geometric shapes: triangles for the spaceship, polygons for asteroids, and small dots for the stars in the background. I can add some glow effects to give the game a retro vector game feel.

The interaction logic needs to handle keyboard input: arrow keys for rotation, the up arrow for thrust, and the spacebar for shooting. I also need to consider mobile adaptation by adding touch controls.

The game flow includes: start screen -> gameplay -> game over -> restart. The scoring system awards points based on the asteroid size, and lives decrease when colliding with an asteroid.

Technically, I need to create a Particle class for the explosion effects, an Asteroid class for the asteroids, and a Ship class for the player. The main game loop will handle updates and rendering.

I also thought about adding sound effects, but since external resources aren't allowed, I might have to skip that for now. I could add some simple particle effects to enhance the sense of explosion.

Now I feel I've considered the main aspects of the game and can start writing the code.

I've created a complete Asteroids game with all the requested features. The game includes:

**Gameplay Features:**
- Vector-based ship with thrust (up arrow) and rotation (left/right arrows)
- Shooting mechanics with spacebar
- Screen wrapping for all objects
- Asteroids that split into smaller pieces when hit (3 sizes: large → medium → small)
- Score system (20/50/100 points based on asteroid size)
- Lives system with visual indicators
- Progressive difficulty (more asteroids per level)
- Invulnerability period after respawn

**Visual Features:**
- Procedural vector graphics for ship, asteroids, and bullets
- Particle effects for explosions and thrusters
- Glowing neon aesthetic with cyan/orange colors
- Animated starfield background
- Smooth animations and screen transitions

**Controls:**
- Desktop: Arrow keys for movement, Space to shoot
- Mobile: Touch controls for left/right rotation, thrust, and fire

**UI Elements:**
- Real-time score and high score display
- Lives shown as ship icons
- Start screen with instructions
- Game over screen with final score
- Persistent high score storage

The game is fully self-contained in a single HTML file with no external dependencies, ready to run in any modern browser.