The Burning Ship Fractal
The Burning Ship fractal consists of points, c, in the complex
plane that obey the following rule
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Start with the complex number z = a + ib where a and b
are real numbers.
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Generate a new complex number, z', by taking the absolute value
of both the real and imaginary parts before squaring the resulting
complex number, and adding the result to c. z' = (|Re(z)|
+ |Im(z)|*i)2 + c.
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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.