snoise: Simplex Noise Generation

High-Quality Procedural Pattern Synthesis

Simplex noise represents an advancement over Perlin noise, offering improved computational efficiency and reduced directional artifacts. These functions generate organic, natural-looking patterns through gradient-based interpolation across simplex grids.

Mathematical Basis

Simplex noise operates on a triangular (2D) or tetrahedral (3D/4D) grid structure rather than the square grid of classical Perlin noise. The algorithm:

1. Grid Skewing: Transform coordinates to simplex space using skewing factor $F_n = \frac{\sqrt{n+1}-1}{n}$
2. Vertex Identification: Determine simplex vertices containing the sample point
3. Gradient Calculation: Compute gradient vectors at each vertex
4. Falloff Application: Apply distance-based falloff with kernel function $(0.5 - r^2)^4$
5. Contribution Summation: Sum weighted contributions from all vertices

For 2D simplex noise, the transformation uses: $s = (x + y) \cdot F_2 \text{ where } F_2 = \frac{\sqrt{3}-1}{2}$

Function Variants

Function	Input	Output	Purpose
snoiseVec2	vec2	float	2D scalar noise field
snoiseVec3	vec3	float	3D scalar noise field
snoiseVec4	vec4	float	4D scalar noise field
snoise2	vec2	vec2	2D vector noise field
snoise3Vec3	vec3	vec3	3D vector noise field
snoise3Vec4	vec4	vec3	Time-varying 3D vector field

Implementation

ライブエディター

const fragment = () => {
      const p = uv.mul(8)
      const n1 = snoiseVec2(p)
      const n2 = snoiseVec2(p.add(vec2(100, 100)))
      const distortion = vec2(n1, n2).mul(0.1)
      const final = snoiseVec2(p.add(distortion)).mul(0.5).add(0.5)
      return vec4(vec3(final), 1)
}

ライブエディター

const fragment = () => {
      const p = vec3(uv.mul(5), iTime.mul(0.3))
      const noise3d = snoise3Vec3(p)
      const turbulence = noise3d.dot(noise3d).sqrt()
      const layers = snoiseVec3(p.mul(2)).mul(0.5).add(
              snoiseVec3(p.mul(4)).mul(0.25).add(
                      snoiseVec3(p.mul(8)).mul(0.125)
              )
      )
      return vec4(turbulence, layers.mul(0.5).add(0.5), noise3d.x.mul(0.5).add(0.5), 1)
}