Is It A Tessellation Or Not?
Two Cat Circle
Defining tessellation through examples
This is a beautiful piece of symmetry art by Dr. David, the original webmaster of www.Tessellations.org.
...But, is it a tessellation?
Put your mouse cursor over the green box below to see Webmaster Sethness's opinion.
Is This a Tessellation?
Why not? Well, it's not the big hole in the center.
Sure, the center is a large unexplained, unused gap.
We could forgive it, though, because we can imagine that
the rings of cats could get smaller and smaller, eventually filling up the center.
We don't have to see that; it's enough that we can imagine it's possible.
(Incidentally, That's how calculus works, too: we imagine smaller and smaller
approximations filling a space, until we can guess the outcome if those
approximations are infinitely small and thereby the gaps become negligible.)
So, what's the problem? It's the overlapping. Look at the orange tails.
This is what it looks like as a true tessellation of grey ordinary cats and orange Manx cats.
Unless the gray cat bodies are headless and the gray heads are really just lonely pumpkins,
those orange tails overlap every gray cat's neck.
The "tiles" in a tessellation shouldn't overlap.
If David had used Manx cats
instead of those cats with orange tails,
this would be a tessellation because Manx cats usually don't have tails.