AS/A2 Pure 5 Pure 6

P4 Topic 3: Complex numbers
The Mandelbrot set
Move c to a fixed location. Move a to 0, and then click the Step button to advance through the iterations. If c is inside the colored area, and a starts at 0, then a will never escape to infinity. If you move c, then be sure to move a back to 0 before continuing. Yopu might find it helpful to have either of the Plot or Line options checked.

Summary The Mandelbrot set, shown in blue, is a part of the Argand diagram that arises from an iterative process. Start by choosing a complex number, c The complex number z0 = 0 A sequence of complex numbers zn is found by the iterative process: zn = zn-12 + c After each step, check the size, or modulus, of zn Repeat this process. If |zn| remains less than 2, then the original point c is in the Mandelbrot set. This fractal is named after Benoit Mandelbrot who discovered it in 1976 and is largely responsible for the present interest in fractal geometry. He showed how fractals can occur in many different places in both mathematics and elsewhere in nature. He was born in Poland in 1924 into a family with a very academic tradition. His father, however, made his living buying and selling clothes while his mother was a doctor. As a young boy, Mandelbrot was introduced to mathematics by his two uncles. For more about Mandelbrot go to this Mandelbrot biography. For more on the Mandelbrot set read Chaos by James Gleick, or The Armchair Universe by A.K.Dewdney. The Plane Graphic Calculator java applet