running the simple draw_koch(function with different depths makes it easy to see the way in which each side of triangle can be dissected into further triangle like shape this can be repeated to multiple depths giving more detailed structured in which the same shape is repeated again and again mandelbrot set probably one of the most famous fractal images is based on the mandelbrot set the mandelbrot set is the set of complex numbers for which the function does not diverge when iterated from for which the sequence of functions (func( )func(func( )etc remains bounded by an absolute value the definition of the mandelbrot set and its name is down to the french mathematician adrien douadywho named it as tribute to the mathematician benoit mandelbrot mandelbrot set images may be created by sampling the complex numbers and testingfor each sample point cwhether the sequence func( )func(func( )etc ranges to infinity (in practice this means that test is made to see if it leaves some predetermined bounded neighbourhood of after predetermined number of iterationstreating the real and imaginary parts of as image coordinates on the complex planepixels may then be coloured according to how soon the sequence crosses an arbitrarily chosen thresholdwith special color (usually blackused for the values of for which the sequence has not crossed the threshold