Fractal Brownian Motion (FBM)
📝 Exercise Goal
💡 💡 Tutorial Content
Learn how to implement fractal Brownian motion (fBm) to create complex natural textures.
Learning Objectives
- Understand the mathematical principles of fractal Brownian motion
- Learn how to layer multiple noise octaves
- Master advanced techniques for creating natural textures
Key Concepts
Fractal Brownian Motion (fBm)
fBm is created by layering multiple noise functions with different frequencies and amplitudes:
- Each octave has twice the frequency of the previous
- Each octave has half the amplitude of the previous
- Produces self-similar fractal characteristics
Octave Layering
`glsl
float fbm(vec2 p) {
float value = 0.0;
float amplitude = 0.5;
float frequency = 1.0;
for (int i = 0; i < octaves; i++) {
value += amplitude * noise(p * frequency);
amplitude *= 0.5;
frequency *= 2.0;
}
return value;
}
`
Parameter Control
- Octaves: Number of detail layers
- Persistence: Amplitude decay rate
- Lacunarity: Frequency growth rate
Exercise
Implement a fractal Brownian motion function to create natural textures like clouds or terrain.
Hints
1. Start with a basic noise function
2. Implement the octave layering loop
3. Try different octave counts (4-8 octaves)
4. Adjust persistence and lacunarity parameters
5. Use the result to control color or height
Expected Result
You should see complex natural textures with multiple levels of detail, resembling clouds, mountains, or other natural phenomena.