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 Facts:

• Fractals are geometric figures where each part resembles the whole (self-similarity)
• They're often created by iterating a function - repeating a process over and over
• Fractals are found in nature (think snowflakes and broccoli) and in math!

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.

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• Fractal Type: Switch between different fractal algorithms