Game Development: 2D, 3D, 4D, 5D and 4K–8K+

1. The game loop, time and state

Every game, in any number of dimensions and at any resolution, is a loop that reads input, advances a simulation by a measured slice of time, and draws the result. This lesson builds that loop properly: delta time, a fixed timestep with an accumulator, interpolation, and a frame budget you can spend on purpose.

2. 2D worlds: sprites, tile maps, collisions and the camera

Two-dimensional games are not simplified 3D. They are a different set of trade-offs: hand-drawn art, pixel-exact control, grids and cheap collisions. This lesson covers screen coordinates, sprites, tile maps, box collisions that cannot be tunnelled, cameras and parallax, and how to keep pixel art sharp on any screen.

1. 3D worlds: vectors, matrices and projection

A third dimension adds one axis and one new problem: showing a 3D world on a flat screen. The mathematics is small, with vectors, the dot and cross products and 4 × 4 matrices, and getting a point onto the screen is a chain of coordinate spaces, from model to world to view to screen. This lesson builds both by hand and ends with a spinning cube drawn from nothing but numbers.

2. Building in 3D: light, physics, performance and engines

Almost nobody ships a game by writing their own renderer. This lesson covers what an engine gives you: scenes and transforms, meshes, materials and light, physics that stays stable, and the levers that keep a scene inside its frame budget. It ends with a practical way to choose between Godot, Unity, Unreal and the web libraries.

1. The fourth dimension of space

A fourth spatial dimension is not mystical: it is a fourth number in every point. This lesson builds a tesseract from a rule you already know, rotates it in six planes, shows two ways a flat screen can see it (projection and slicing), and explains how real games such as Miegakure, 4D Toys and 4D Golf make a four-dimensional world playable.

2. The fourth dimension of time and sensation

Time is the fourth dimension every game already has. This lesson turns it into something you can design with: deterministic simulations that can be replayed and rewound, time as a coordinate in noise that makes seamless animation loops, and the engineering of 4D experiences, where seats, wind, mist and rumble are timed on a cue sheet with safety limits.

3. Five dimensions and beyond

After the fourth dimension, "dimension" simply means "independent axis of state". This lesson uses 5D Chess with Multiverse Time Travel to show timelines as an axis, builds an immutable multiverse data structure, generalises rotation, projection and search to any number of dimensions, and meets the curse of dimensionality, the reason high dimensions behave nothing like three.

1. Ultra-high resolution: 4K, 8K and beyond

Resolution is the other kind of dimension in this course, and it multiplies the cost of every pixel you shade. This lesson puts numbers on 4K, 5K, 8K and 16K: pixels, nanoseconds per pixel, frame-buffer memory, memory traffic, cable bandwidth and texture memory. It ends with the question that decides everything: how many of those pixels can a human eye actually use?

2. Scaling to every screen, and shipping

Players own screens from a 720p phone to an 8K television, and one build has to look right on all of them. This lesson covers measuring performance honestly, dynamic resolution, upscaling, foveated rendering, quality tiers, and the practicalities of shipping a game from Ghana: download size, metered data, heat, testing on real devices and accessibility. It ends with the course project.