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# The Mandelbrot set is a set of points in a complex plane, c, of the orbit, which is how the function operates under the iteration of zn+1 = zn2 + c around 0.

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• Essay length: 603 words
• Submitted: 20/04/2012
University Degree Mathematics

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Mandelbrot Set

The Mandelbrot set is a set of points in a complex plane, 'c', of the orbit, which is how the function operates under the iteration of zn+1 = zn2 + c around 0. A value of 'c' is included the Mandelbrot set if the orbit of 0 undergoing the iteration of zn+1 = zn2 + c, and the value s does not tend to infinity. In other words if the orbit of 0 tends to infinity, then that the 'c' value is not in the set.

To see this properly let 'c' be any complex number and then let zn be 0 in the iteration of zn+1 = zn2 + c, you will notice that you will get c back from the resulting answer; 02 + c. This can repeated by letting c be x for the next iteration in the original equation, and this will yield c2 + c. You can continue repeating putting the previous answer in for x into the equation and the result will be (c2 + c) 2 + c. Doing this continuously will create a list of complex numbers and if these complex numbers are increasing in size and

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