random: Deterministic Pseudo-Random Generation

High-Quality Hash Functions for Procedural Randomness

Pseudo-random generators create deterministic yet unpredictable values from input coordinates. These functions transform spatial coordinates into seemingly random distributions through mathematical hash operations, enabling reproducible stochastic patterns.

Mathematical Foundation

The implementation uses polynomial hash functions with large prime multipliers to achieve uniform distribution:

$$\text{random}(x) = \text{fract}(\sin(x \cdot c) \cdot s)$$

Where $c$ represents coordinate mixing coefficients and $s$ is a large scaling factor (43758.5453) that amplifies small differences in the sine function.

For multi-dimensional inputs, dot products combine coordinates:

$$\text{random}(\vec{p}) = \text{fract}(\sin(\vec{p} \cdot \vec{c}) \cdot s)$$

Function Variants

Function	Input	Output	Purpose
random	float	float	1D scalar random
randomVec2	vec2	float	2D position to scalar
randomVec3	vec3	float	3D position to scalar
randomVec4	vec4	float	4D position to scalar
random2Float	float	vec2	1D to 2D vector random
random3Vec2	vec2	vec3	2D to 3D vector random
random4Vec3	vec3	vec4	3D to 4D vector random

Implementation

Live Editor

const fragment = () => {
      const p = uv.mul(20).floor()
      const r = randomVec2(p)
      const cellColor = random3Vec2(p).mul(0.5).add(0.5)
      const noise = r.step(0.7)
      return vec4(cellColor.mul(noise), 1)
}

Live Editor

const fragment = () => {
      const scale = 8
      const coord = uv.mul(scale).floor()
      const rnd = random4Vec2(coord)
      const pattern = rnd.x.mul(rnd.y).mul(rnd.z).step(0.3)
      const hue = randomVec2(coord.add(vec2(100)))
      const color = vec3(pattern.mul(hue))
      return vec4(color, pattern)
}