Fractal Brownian Motion (FBM)

Create complex patterns with self-similarity by layering multiple noise octaves (usually Perlin or Simplex noise) with varying frequencies and amplitudes, often used to generate natural phenomena like mountains, clouds, and water surfaces.

Overview

• Generate procedural noise and map it to color.

Learning Objectives

• Understand the basic principle of Fractal Brownian Motion: achieved by iteratively layering noise.
• Learn how to implement the FBM algorithm in GLSL, including controlling octaves, persistence, and lacunarity.
• Master how to use FBM to generate natural-looking textures like terrain and clouds.
• Be able to adjust FBM parameters to achieve different styles of noise effects.

Prerequisites

• noise-functions
• looping-constructs

Inputs

• vec2 u_resolution — Canvas size in pixels.
• float u_time — Time in seconds.

Key Concepts

• Noise is built from random values on a grid plus smooth interpolation.

vec2 i = floor(p);
vec2 f = fract(p);
vec2 u = f*f*(3.0-2.0*f);
float n = mix(mix(a,b,u.x), mix(c,d,u.x), u.y);

• Map noise to color with mix or thresholds.

vec3 color = mix(colorA, colorB, n);

How To Implement (Step-by-step)

• Scale UV to control frequency (e.g. p = vUv * 6.0).
• Compute base noise (hash/valueNoise).
• Optionally sum octaves (FBM) for detail.
• Map noise to grayscale or color.

Self-check

• Does it compile without errors?
• Does the output match the goal?
• Are key values kept in [0,1]?

Common Mistakes

• Clamp t into [0,1] when needed.
• Don’t use raw pixels without normalization.
• Make sure edge0 < edge1 for smoothstep().
• Change frequency by scaling before fract().