srandom: Bipolar Random Generation

Balanced Distribution Functions for Symmetric Patterns

Signed random functions generate values in the range $[-1, 1]$ instead of the typical $[0, 1]$. This balanced distribution creates more natural symmetric patterns and eliminates the bias toward positive values common in standard random functions.

Mathematical Foundation

The transformation from standard random to signed random applies the linear mapping:

$$\text{srandom}(x) = 2 \cdot \text{random}(x) - 1$$

This shifts the $[0, 1]$ range to $[-1, 1]$ while preserving the uniform distribution properties. For vector outputs, the same transformation applies component-wise.

Special vector functions use enhanced mixing coefficients:

$$\text{srandom2}(p) = 2 \cdot \text{fract}(16k \cdot \text{fract}(p_x \cdot p_y \cdot (p_x + p_y))) - 1$$

Where $k = (0.3183099, 0.3678794)$ provides improved spatial distribution.

Function Variants

Function	Input	Output	Purpose
srandom	float	float	Signed 1D random
srandomVec2	vec2	float	2D to signed scalar
srandomVec3	vec3	float	3D to signed scalar
srandom2Vec2	vec2	vec2	Enhanced 2D vector
srandom3Vec3	vec3	vec3	Enhanced 3D vector
srandom3Vec3Tiled	vec3, float	vec3	Tileable 3D vector

Implementation

ライブエディター

const fragment = () => {
      const p = uv.mul(6)
      const flow = srandom2Vec2(p.floor())
      const gradient = dot(p.fract().sub(0.5), flow)
      const intensity = gradient.mul(2).clamp(-1, 1)
      return vec4(intensity.step(0), intensity.abs(), intensity.mul(-1).step(0), 1)
}

ライブエディター

const fragment = () => {
      const coord = vec3(uv.mul(4).floor(), 0)
      const direction = srandom3Vec3(coord)
      const strength = direction.length()
      const color = direction.mul(0.5).add(0.5).mul(strength)
      return vec4(color, 1)
}