The Mandelbrot Set is defined as follows. Define f:
f[{a,b}]:= {a*a - b*b + c2, 2*a*b + c2}
where a, b, c1, c2 are real numbers, and c1 and c2 are constant.
For each point {c1,c2} in the plane, compute the iteration of f. That is, f[f[f[...f[{0,0}]...]]]. If this infinite iteration creates a resulting point further and further from the the point {0,0}, then the number {c1,c2} is defined to be not in the set. Otherwise it is in the set.
The above can be expressed in complex numbers. Using complex numbers, the function f is: f[z]:= z^2+C.
Here's a plot of the mandelbrot set:
Full Size image: Mandelset_hires.png
See wikipedia: Mandelbrot Set↗
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© 2006 by Xah Lee. (excluding mirrored pages or images.)