A pentaflake, or sierpinski pentagon, is formed by successive flakes of six regular pentagons.[3] Each flake is formed by placing a pentagon in each corner and one in the center. Its Hausdorff dimension is equal to \textstyle{\frac {\log(6)} {\log(1+\varphi)}} ≈ 1.8617, where \textstyle{\varphi = \frac{1+\sqrt 5}{2}} (golden ratio). The \textstyle{\frac {\log(6)} {\log(1+\varphi)}} is obtained because each iteration has 6 pentagons that are scaled by \textstyle{\frac {1} {1+\varphi}}. The boundary of a pentaflake is the Koch curve of 72 degrees. There is also a variation of the pentaflake that has no central pentagon. Its Hausdorff dimension equals \textstyle{\frac {\log(5)} {\log(1+\varphi)}} ≈ 1.6723. This variation still contains infinitely many Koch curves, but they are somewhat more visible.
Set the iteration. Press space. NOTE: This is not an exact pentaflake, but a close representation made up of pentigrees.
