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Title: Three Dimensional Mandelbrot Fractals
Author: Mithun Aiyswaryan
Institution: University Of Kiel
Description: The concept of the Mandelbrot set is a set in the complex plane. The algorithm for the Mandelbrot set goes as follows: Make a complex number z equal to 0 + 0i. Choose a point on the complex plane and make a complex number c equal to its coordinates. Make z = z2 + c and iterate this infinitely. If the number did not go to infinity, then c belongs to the set and can be coloured black. Otherwise, you can colour c depending on how quickly it went to infinity (All the points the same colour require the same number of iterations to reveal that they are attracted to infinity). Repeat these steps for all points on the plane. The Mandelbrot set corresponds to the formula z = z2 + c. The formula z = z2 + c produces the most famous Mandelbrot set, but other formulae produce different Mandelbrot sets. For it to be classed as a Mandelbrot set c must be the variable and z must start at the point (0,0). One of the remarkable features of the Mandelbrot set is that if you choose a point c and magnify it you will find the Julia set corresponding to that formula and that value of c. This has been proved for many values of c but at present it is conjectured that inside the Mandelbrot set are all the possible Julia sets each sitting upon their own value of c.
Keywords: Mandelbrot, Julia, Sets,Fractals, Mithun, Kiel
File Name: mandels.m
File Size: 2 KB
File Version: 1.0
Matlab Version: 6.0 (R12)
Date: 2003-08-09
Downloads: 4353
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