Tessellation Symmetry:
Resizing / Inflation / Dilation
in Circle Limits, Spiraling, Concentric Rings, & so on

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We've already covered the types of symmetry that all tessellation experts agree upon: Translation, Reflection, Glide-Reflection, and Rotation. These are called "isometric", which is a fancy way of saying that the tiles don't change size.

But, what about patterns like "circle limits" that use gradually smaller and smaller tiles as they expand outward, and their opposites, the spirals and concentric circles that use larger and larger tiles as the patterns expand outward?

Many math experts say these are not tessellations. They say that the tiles must all be the same size, and the tessellations must entirely fill a plane.

It's true, these types of patterns might have trouble filling in the centermost point. However, the spirals and circles virtually finish the centerpoint. Such a pattern can so nearly fill the center as barely matters, in the way that a single atom is so small that it barely matters. As Spock of the original Star Trek TV series said, "A difference that makes no difference is no difference."

M. C. Escher did many spiral and circle-limit patterns. He even tried to make "square limit" patterns.