# Mandelbrot Set

Explore the Mandelbrot set and some related fractals. (I know… this isn't a population model. But it's too much fun to leave out :) )

# Demonstration

This movie was made by turning on the **record-png** switch and the **zoom-every** button, and setting the **jump-size** to 1%. The sequence of PNG images were stitched together with Windows Live Movie Maker.

# More information

## The Mandelbrot Set

A NetLogo model by Rik Blok.

http://www.zoology.ubc.ca/~rikblok/wiki/doku.php?id=science:popmod:mandelbrot_set:start

Explore the Mandelbrot Set and these related fractals:

## Mappings

Each fractal is defined by a function in the complex plane. Starting with an initial value z=0, each point c in the plane is repeatedly iterated through the map, z → f(z,c). The mapping function is characterized by an exponent, d (**d-multibrot-exp** slider in the simulation), as follows:

- Mandelbrot: f(z,c) = z
^{2}+ c (same as Multibrot with d=2) - Multibrot: f(z,c) = z
^{d}+ c - Mandelbar: f(z,c) = Conj(z)
^{d}+ c

A point c is excluded from the set if the value z diverges after repeated iteration. In the simulation, excluded points are painted a color indicating how many iterations were required to decide they have diverged. Black points indicate undecided candidates that may belong to the set.

## Other implementations and examples

This implementation of the Mandelbrot set is neither fast nor beautiful -- it's just a proof of concept and a demonstration of how to code in NetLogo. If you're interested in the Mandelbrot set or similar fractals, check out these excellent pages:

- Last Lights On - video of Mandelbrot zoom to 10
^{228}