Penrose tilings

Nearly everyone has seen a tessellation- a periodic, repeating pattern- in their lives. Even a floor with square tiles of the same size is an example of a tessellation, as it is a pattern which repeats in a consistent manner and consists of equal shapes.

However, some patterns can be aperiodic.

Take a look at this pattern:

An example of Penrose tiling

The above image may seem like a tessellation- it appears to be a repeating pattern of thick and thin parallelograms. However, if you look closely, it is not periodic at all. Up close, it looks more like this:

This is clearly irregular, as it is not a consistent pattern of parallelograms.

These are Penrose tilings! They are used in tiling in real life, such as this portion of land in Helsinki: