PERLIN NOISE — PROCEDURAL TERRAIN GENERATOR

TERRAIN PARAMETERS

Perlin Noise: smooth, gradient-based noise with coherent structure across scales.

Fractal Brownian Motion (fBm): sum of Perlin noise at multiple octaves, each with halved amplitude (persistence) and doubled frequency (lacunarity).

Result: H(x,y) = Σ_{k=0}^{N-1} persistence^k · noise(lacunarity^k · x, lacunarity^k · y)

The Hurst exponent H controls roughness. Mountains, clouds, rivers, planets — all via fBm.