A fractal is a never-ending pattern that repeats at different scales—zoom in, and you'll keep seeing similar shapes. They're often generated by simple mathematical rules but produce infinitely complex, self-similar structures.
| Fractal Type | Formula / Rule | Key Traits |
|---|---|---|
| Mandelbrot Set | zn+1 = zn² + c | The iconic "bug-shaped" fractal. Maps which complex numbers c produce bounded orbits. |
| Power 3 (Cubic) | zn+1 = zn³ + c | Cubic version of Mandelbrot. More lobes, rotational symmetry, and wild spirals. |
| Julia Set | zn+1 = zn² + c (c is fixed) | Each point in the Mandelbrot set spawns a unique Julia set. |
| Tricorn | zn+1 = conjugate(zn)² + c | Uses complex conjugate. Mirror-symmetric, three-lobed "tricorn" shape. |
| Burning Ship | zn+1 = (|Re(zn)| + i|Im(zn)|)² + c | Absolute values create sharp, flame-like structures rising from the plane. |