Tessellation Symmetry, Page 6 of 6:
What about Inflation (Resizing)?
Circle Limits, Spiraling, Concentric Rings, & so on
Escher paints a resizing spiral tessellation
We've already covered the three types of symmetry that all tessellation experts agree upon: Translation, Reflection, and Rotation (Sliding, Flipping, and Turning).
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?
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.
M. C. Escher did many spiral and circle-limit patterns. He even tried to make "square limit" patterns.
 A Circle Limit Tessellation by M. C. Escher 
Another Circle Limit Tessellation by M. C. Escher 
An unusual resizing Tessellation by M. C. Escher 
Another unusual resizing tessellation-- this one by Mr. Hop David
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"Fish Vignette" (1956): This tessellation of concentric rings, done by Escher in 1956, uses rotational symmetry (turning) and inflation (resizing).
All M.C. Escher works © Cordon Art BV - Baarn - the Netherlands.
A spiral tessellation of dogs by Mr. Hop David of Arizona.
Like the Escher picture above it, this one uses both rotation and resizing.
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