Mandelbrot Kata

This a little programming exercise using the fractal domain, in particular the Mandelbrot Set.

Detailed explanations about the Mandelbrot Set can be found here: https://en.wikipedia.org/wiki/Mandelbrot_set

The goals of the kata are:

• Understand a little bit the mathematical concepts behind fractals.
• Apply Test-First Programming approach.
• Improve OO programming skills.

In order to finish the kata you have to draw two versions of the Mandelbrot fractal:

• ASCII graph: see file mandelbrot-160x160.txt
• Image (background white and mandelbrot set in black): see file mandelbrot-160x160.png

Math

Basically, there is a mathematical formula for complex number:

f(x) = z² + c

where z and c are complex number.

The Mandelbrot set is the set of complex numbers c for which the function does not diverge when iterated from z=0. Than means, given a c complex number, if you apply the formula to that number n times using the previous result as the new z number, that c belongs to Mandelbrot Set if the sequence does not diverge.

You can represent those complex number in a graph where x-axis is the real part of the complex number and y-axis is the imaginary part.

Drawing the fractal

You have to draw the portion of the graph between -2 and 2 real and imaginary parts. Mandelbrot Set is inside those limits.

Branches

There is a branch for each language with the scaffolding code.

• php
• javascript
• python

And different solutions in different branches like:

• php-solution1

Installation and running tests

See scaffolding branch README for the language.

Acknowledgments

• This kata was inspired by: https://github.com/edyoung/gnofract4d