Penrose Tiles


So Penrose came up with a tiling system where the same pattern never repeats but every picture i see has loads of repeating patterns. Am i missing something or am i just stupid?


the Penrose pattern is not exactly repetitive. There are small variations. Not that those patterns still have a very large 5-fold symmetry.

Prior to those patterns, mathematicians thought a 5-fold symmetry was generally impossible to do filling all the area fully. It still is impossible if you restrict yourself to exact repetitions. but once you lift that strict repetition, there are 5-fold patterns such that of Penrose.

This was nothing less than a revolution which changed so much our view of what symmetries really are.

It’s not that it *never* repeats, it’s that it doesn’t repeat infinitely. With most tilings, like squares or triangles, you just take the same shape and repeat it in a row forever. With Penrose tiling, you might find a shape repeated somewhere else in the pattern, but if you look for a whole row of repeated shapes stretching out forever, you won’t find it.