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What is this design?

The Mandelbrot Set

The Mandelbrot Set, named after mathematician, Benoit Mandelbrot, is the collection of complex numbers that, when raised to a specified power, added to themselves, and then graphed on the complex number plane, remain within two units of the origin (0, 0). In math-ese: the set of all complex numbers z for which sequence defined by the  iteration z(0) = z,   z(n+1) = [z(n)][z(n)] + z,   n=0,1,2, ... remains bounded.

The complex number 0.3 –1.2i, for instance, is graphed like the ordered pair (0.3, -1.2) is graphed on the Cartesian real number plane. [In the complex plane, the vertical axis is the i-axis.] The number is squared and added to itself like this: (0.3 – 1.2i)2 + (0.3 – 1.2i). After one of these calculations, or iterations, becomes (0.9 – 0.36i +1.44i2) + (0.3 – 1.2i). Because the imaginary number i2 is defined as equal to –1, this expression simplifies to (–0.54 – 0.72i) + (0.3 – 1.2i), which further simplifies to –0.24 – 0.9i. The second iteration would be (–0.24 – 0.9i)2 + (–0.24 – 0.9i), and so forth. Numbers that remain less than two units from the origin after the specified number of iterations are defined as members of the Set. It is easy to see that performing even a very small number of iterations for a very small number of points requires a computer.

Each of the millions of pixels in this highly magnified detail of the Set, has been iterated 1,024 times. Those in the Set have been colored black. Other points are colored according to the number of iterations necessary for them to reach a distance of more than two units from the origin.

Upon first discovering the Mandelbrot Set in the late 20th century, mathematicians were, and still are, astounded that such a fantastically complex and beautiful object could be generated from such a simple set of rules.