Learn how to create basic fractal patterns using iterative mathematical functions.
- Understand iterative algorithms in shaders
- Learn to create self-similar patterns
- Practice using loops and mathematical transformations
Fractals are patterns that repeat at different scales:
- Self-similarity at multiple zoom levels
- Created through iterative processes
- Mathematical beauty in simple rules
Basic fractal algorithm:
`glsl
vec2 z = uv;
for (int i = 0; i < iterations; i++) {
z = transform(z);
if (length(z) > threshold) break;
}
`
- Mandelbrot: z = z*z + c
- Julia sets: z = z*z + constant
- Simple geometric transformations
Create a simple fractal pattern using iterative coordinate transformations.
1. Start with centered UV coordinates: uv - 0.5
2. Use a loop to apply transformations repeatedly
3. Track when values exceed a threshold
4. Color based on iteration count
5. Experiment with different transformation functions
You should see an intricate fractal pattern with repeating structures at different scales.