Noise

Random

Hash Functions

PCG Hash

uint pcg_hash(uint input)
{
    uint state = input * 747796405u + 2891336453u;
    uint word = ((state >> ((state >> 28u) + 4u)) ^ state) * 277803737u;
    return (word >> 22u) ^ word;
}

Noise

Value Noise

Perlin Noise

Simplex Noise

A simple way to generate terrain is to layer different noise functions together. This is a technique called Fractal Brownian Motion (FBM) popularized by Inigo Quilez. I also like the interactive explanation by Patricio Gonzalez Vivo in his The Book of Shaders.

/**
 * Generates Fractal Brownian Motion noise by layering multiple octaves of simplex noise
 * @param {number} x - X coordinate to sample
 * @param {number} y - Y coordinate to sample
 * @param {number} scale - Base frequency scale. Higher values = more zoomed out noise
 * @param {number} octaves - Number of noise layers to combine
 * @param {number} persistance - How quickly amplitude decreases per octave (0-1)
 * @param {number} lacunarity - How quickly frequency increases per octave (typically 2)
 * @returns {number} Combined noise value between 0 and 1
 */
function noiseFBM(x, y, scale = 1.0, octaves = 4, persistance = 0.5, lacunarity = 2.0) {
    let amplitude = 1.0
    let frequency = scale
    let height = 0.0
    let maxAmplitude = 0.0
    for (let i = 0; i < octaves; i++) {
        height += simplex2(x * frequency, y * frequency) * amplitude
        maxAmplitude += amplitude

        amplitude *= persistance
        frequency *= lacunarity
    }
    return height / maxAmplitude
}

https://www.reedbeta.com/blog/hash-functions-for-gpu-rendering/

Resources

https://www.youtube.com/watch?v=DxUY42r_6Cg

https://www.reedbeta.com/blog/hash-functions-for-gpu-rendering/

https://thebookofshaders.com/10/