The Mandelbrot Set is a set of points which forming a fractal
pattern named after Benoît Mandelbrot, who is its discoverer and who has made extensive studies of this set of points and fractals. The Mandelbrot
Set is a set of points on the complex plane, whose definition is based on the simple iterative equation
z_{n}_{+1} =
z_{n}^{2} + c
where c is a complex number. The Mandelbrot set is defined a the set of all c’s
such that when substituted into the above iterative equation, the absolute value
of z will be bounded after applying the above recursive equation repeatedly
using any initial value for z.
Although the Mandelbrot Set arises from a simple equation, when
computed and plotted, the Mandelbrot Set forms a fractal complicated structure.
Its shape and structure come with aesthetic appeal and many interesting
properties under various scaling or magnifications.
Various fractal images may be formed from the magnifications of
Mandelbrot Set. Below are different parts of the
Mandelbrot set under various magnifications:
