# 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.

A NetLogo model by Rik Blok.

Explore the Mandelbrot Set and these related fractals:

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) = z2 + c (same as Multibrot with d=2)
• Multibrot: f(z,c) = zd + c
• Mandelbar: f(z,c) = Conj(z)d + c
• Burning ship: f(z,c) = (|Re(z)| + i |Im(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.

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:

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• by Rik Blok