Procedural textures are generated from mathematical functions rather than captured from photographs or painted by hand. They are resolution-independent (you can evaluate them at any resolution), inherently seamless (when using tileable noise), and infinitely variable (changing a seed produces an entirely new result). Every texture generator on Texturize uses procedural techniques under the hood.
Noise Functions: The Foundation
Most procedural textures start with a noise function — a mathematical function that produces pseudo-random but smooth, continuous values across a coordinate space. Unlike random number generators that produce uncorrelated white noise, texture noise functions produce values that vary smoothly, creating organic-looking gradients and blobs.
Value Noise
The simplest approach. Random values are assigned to integer grid points, and intermediate values are interpolated (typically with cubic or quintic interpolation). Value noise is fast but tends to produce visible grid-aligned artifacts because the extremes always occur on grid points. It works well for simple clouds or as a base for more complex effects.
Perlin Noise
Ken Perlin’s gradient noise (1983, improved in 2002) assigns random gradient vectors to grid points and computes dot products with the distance to the evaluation point. The result has zero values at grid points (not extremes), which eliminates the grid-aligned artifact problem. Perlin noise is the industry standard for organic textures — clouds, terrain, marble veins, water caustics.
Simplex Noise
Also developed by Ken Perlin (2001), simplex noise uses a triangular (simplex) grid instead of a rectangular one. This reduces the number of gradient evaluations from 4 (2D) or 8 (3D) to 3 (2D) or 4 (3D), making it faster for higher dimensions. Simplex noise also has fewer directional artifacts than classic Perlin noise. Modern implementations like OpenSimplex2 avoid the original patent concerns.
Fractional Brownian Motion (FBM)
A single octave of noise produces smooth, blobby shapes. Real-world surfaces have detail at multiple scales: a mountain has a broad shape, medium ridges, and fine cracks. FBM layers multiple octaves of noise at increasing frequency and decreasing amplitude to simulate this multi-scale detail.
The typical formula: fbm(p) = noise(p) + 0.5 × noise(2p) + 0.25 × noise(4p) + ... Each octave doubles the frequency (lacunarity = 2.0) and halves the amplitude (gain = 0.5). The number of octaves controls the level of fine detail — 4 to 8 octaves is common. More octaves add computation cost but diminish in visual impact beyond 8.
Domain Warping
Domain warping feeds the output of one noise function into the coordinates of another: f(p) = fbm(p + fbm(p)). This distorts the noise field, creating organic, flowing shapes that look like swirling marble, lava flows, or weathered wood grain. Chaining multiple levels of warping produces increasingly complex and unpredictable patterns.
Our Marble Generator uses domain warping to create realistic vein patterns. The Lava Generator chains warping with color remapping to simulate molten flow.
Other Procedural Primitives
Voronoi / Worley Noise
Worley noise (also called cellular noise) generates patterns based on distance to randomly scattered seed points. The F1 function (distance to nearest point) creates cell-like patterns: cracked mud, scales, cobblestones. The F2−F1 function produces vein-like networks. Try the Voronoi Generator to experiment with these patterns.
Wave and Stripe Functions
Sine and cosine functions create regular stripes. Combined with noise for displacement, they produce wood grain (concentric rings distorted by noise), fabric weaves, and wave patterns. The Wood Generator uses displaced sinusoidal rings to model growth patterns.
Making Procedural Noise Seamless
The standard technique evaluates 2D noise on the surface of a higher-dimensional torus. For 2D seamless textures, you map (x, y) to four coordinates on a 4D torus: (cos(2πx/w), sin(2πx/w), cos(2πy/h), sin(2πy/h)) and evaluate 4D noise. This guarantees perfect wrapping with no blending artifacts. This is computationally heavier than non-tileable noise but produces mathematically perfect seams.
How Texturize Uses Procedural Generation
Every generator in the Texturize library is built on seeded Perlin noise, FBM, domain warping, Voronoi, or mathematical pattern functions. The seed-based approach means every configuration is reproducible — share the same parameters and seed, and you get the exact same texture every time. All noise evaluation uses tileable variants so every output is guaranteed seamless.