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Swirl Fractal 3 by fractalposter

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This fractal is a zoom of the mandelbrot set. It has a lot of beautiful swirls.

“Mathematically the Mandelbrot set can be defined as the set of complex values of c for which the orbit of 0 under iteration of the complex quadratic polynomial z(n+1) = z(n)*Z(n) + c remains bounded.
That is, a complex number, c, is in the Mandelbrot set if, when starting with z0 = 0 and applying the iteration repeatedly, the absolute value of z(n) never exceeds a certain number.

For example, letting c = 1 gives the sequence 0, 1, 2, 5, 26,…, which tends to infinity. As this sequence is unbounded, 1 is not an element of the Mandelbrot set.
On the other hand, c = i (where i is defined as i² = -1) gives the sequence 0, i, (−1 + i), −i, (−1 + i), −i…, which is bounded and so i belongs to the Mandelbrot set.

When computed and graphed on the complex plane the Mandelbrot Set is seen to have an elaborate boundary which does not simplify at any given magnification. This qualifies the boundary as a fractal.

The Mandelbrot set has become popular outside mathematics both for its aesthetic appeal and for being a complicated structure arising from a simple definition, and is one of the most well-known examples of mathematical visualization.
Benoît Mandelbrot and others worked hard to communicate this area of mathematics to the public."

This fractal will look great on any wall, at home or at a office.

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