Iterated Function
Systems
Larry Riddle
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Sierpinski n-gons

By changing the initial polygon and scale factor, it is possible to generate other types of fractals. The idea is to start with a regular n-sided polygon, then scale the polygon by a factor r so that n copies of the scaled polygon exactly fit inside the original polygon. The Sierpinski pentagon is such an example with n = 5 and r = 0.381966. The figure below shows the first iteration for a hexagon and the limit set.

The scale factor r for an n-gon is

where denotes the greatest integer less than or equal to n/4. The only affine transformations needed for the iterated function system is scaling by r and translations. The translations can be taken to be

for k = 1 to n, where w is the radius of the initial polygon, that is, the distance from the center of the polygon to each vertex. Click here for the details.

Home Sierpinski Gasket Sierpinski Carpet Sierpinski Pentagon Heighway Dragon
McWorter Pentigree Pentadentrite Koch Curve Koch Snowflake Levy Dragon