Iterative Penrose, 28th of April 2012.

iteration 0

In >> the previous post I promised to show how I made the Penrose tiling. Without too much writing, the process is shown in the images below and above. It all starts from the initial shape (above) which is iteratively subdivided to obtain new shapes (triangle subdivision).

iteration 1

To get a Penrose tiling one needs to specify the rules governing the transformation of one triangle into two new ones. Those rules are different for the red and light triangle in the image above.

iteration 2

Of course, in the rules for the triangle subdivision, a characteristic scale appears: the golden ratio.

iteration 3
iteration 4
iteration 5
iteration 6
iteration 7
iteration 8

A starting shape for the iterative subdivision needs not be a decagon, as shown in the image below.

decagon, Penrose

One can also start from some other starting, initial shape (below).

polygon, Penrose
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Last updated on 28th of April 2012.