Tuesday, February 2, 2010

Mandelbrot Fractal - Part 1

I'm going to describe the Mandelbrot fractal, the most beautiful fractal that I know. I assume you have experience with complex numbers (addition, multiplication...).


First of all, what is the Mandelbrot fractal? It's a set of points. To draw the fractal, you must plot every point that is in the Mandelbrot set. The Mandelbrot set is defined using this formula :
z = z2 + c
|z| > 2

where z and c are complex numbers and c is the point you are testing, such as : c.real = x, c.imag = y.

If the condition is true, the point is in the set. If it isn't true, you must iterate using the first formula. If, after a maximium number of iterations, the condition is still false, then the point isn't in the set.

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