The Mandelbrot set consists of points, c, in the complex plane that obey the following rule

Start with the complex number, z = 0 + i0.

Generate a new complex number, z', by multiplying z by itself and adding the result to c. z' = z2 + c.

Repeat steps 1 and 2. If the complex number z goes toward infinity, then the starting point, c, is not a member of the Mandelbrot set. All numbers that remain bounded are members of the set.

It can be shown that if the magnitude of z is greater than 2 , then z will approach infinity. The code assumes that the number c is in the set if |z|>2 after 256 iterations. In order to show how rapidly a number fails the test, we color the pixel corresponding to the number of iterations.

Author : Francisco Esquembre and Wolfgang Christian.

Text and original idea from the Open Source Physics project manual

Date : July 2003

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