Am 26.09.2016 um 11:52 schrieb omniverse:

> Had me thinking it might be one of those Penrose patterns before I realized
> those were said to be the last three. Of course I don't know what any of these
> are really, besides interesting!

The Penrose tilings are a family of curious tilings discovered by Sir
Roger Penrose in the 1970's.

The Penrose tilings have special properties that make them interesting
from both an aesthetic and mathematical point of view:

To the artist, the Penrose tilings have the rare property of exhibiting
pentagonal symmetry while at first glance appearing to be repetitive
(spoiler alert: they aren't; that would be impossible).

To the mathematician, the Penrose tilings have the rare property of
being /regular/ (meaning they follow a fixed set of construction rules
rather than randomly filling the plane with the tiles available) but at
the same time /aperiodic/ (meaning that they don't repeat -- no matter
what distance and direction you translate them, there are always tiles
that don't match up).

The three tilings are actually closely related; you could transform any
one of them into the other merely by applying a few simple substitution
rules.

There are other regular aperiodic tilings, but the Penrose tilings are
arguably the most aesthetic ones.

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