psrdnoise: Periodic Rotating Simplex-Like Dimensional Noise

Advanced Periodic Noise with Gradient Rotation Control

The psrdnoise function generates Perlin-like noise patterns with enhanced control over periodicity and gradient rotation. Unlike standard noise functions, it provides seamless tiling capabilities and gradient rotation parameters for sophisticated texture generation.

The mathematical foundation follows simplex-like grid transformations with explicit control over periodic boundaries:

$$\text{psrdnoise}(x, p, \alpha) = \sum_{i} w_i^4 \cdot g_i \cdot d_i$$

where $w_i$ represents corner weights, $g_i$ are rotated gradient vectors by angle $\alpha$, and $d_i$ are distance vectors from simplex corners.

Basic Usage Patterns

Live Editor

const fragment = () => {
      const p = position.xy.mul(iTime)
      const n = psrdnoise(p)
      return vec4(vec3(n), 1)
}

Mathematical Properties

Property	Description	Implementation
Period Control	Seamless tiling boundaries	vec2(px, py) period parameters
Gradient Rotation	Dynamic gradient direction	alpha rotation angle parameter
Dimensional Support	2D and 3D implementations	psrdnoise2D, psrdnoise3D
Derivative Access	Surface normal computation	Built-in gradient calculation

Function Variants

The implementation provides multiple overloads for different use cases:

Function	Input	Output	Purpose
psrdnoise(x)	vec2	float	Basic 2D noise
psrdnoisePeriod(x, p)	vec2, vec2	float	Periodic 2D noise
psrdnoiseAlpha(x, p, α)	vec2, vec2, float	float	Rotated 2D noise
psrdnoise3(x)	vec3	float	Basic 3D noise
psrdnoise3Alpha(x, p, α)	vec3, vec3, float	float	Rotated 3D noise

Advanced Pattern Generation

The combination of periodicity and rotation enables complex pattern synthesis:

$$P(x,t) = \sum_{k=1}^{N} A_k \cdot \text{psrdnoise}(f_k x, p_k, \alpha_k t + \phi_k)$$

This layered approach creates intricate textures with controllable animation characteristics and seamless boundaries for tileable patterns.