Algorithms

Physics-based fluid dynamics simulations implementing Navier-Stokes equations, smoothed particle hydrodynamics (SPH), and real-time water rendering. Features wave propagation, viscosity modeling, and interactive fluid behavior visualizations.

Deep dive into Terraria’s world generation mechanics. Analyzes biome placement algorithms, cave system generation, ore distribution patterns, structure spawning logic, and the mathematical foundations behind procedural 2D sandbox worlds.

Mathematical exploration of Minecraft’s world generation algorithms. Implements LCG random number generation, multi-octave Perlin noise terrain, structure placement theory, Ender Dragon pathfinding AI, and stronghold ring distribution analysis with publication-quality visualizations.