Sierpinski Square Step Pyramid
3,977 views · Published 21 September 2011 · 0:39 · Indexed 11 October 2026
Channel: Paul Nathan · 2011 · Education
The Sierpinski fractal square based pyramid constructed with a cuboid seed (rather than a pyramid) up to level 7. The progression through the levels is also shown. This fractal was generated using the IFS (iterated function system) approach. In this approach, a base feature is recursively copied and transformed. In the present case there are 5 transformations per iteration involving only isotropic scaling and transformation (no rotation or shear). The 4D transformation matrices are given at the start of the video. This particular fractal has, in the limit of infinite recursion (fractals are limit objects), zero volume and infinite surface area. The purpose of this video was to demonstrate that the limit object is independent of the specific geometry of the base feature. Initially the object looks nothing like a pyramid, but even after 7 iterations the result begins to resemble the perfectly self-similar object obtained by having a pyramid as the base feature. Now, go make one out of LEGO!! For level 7 you will need 5^7 = 78,125 cube bricks (although longer bricks could be substituted in some places).
