Dan, do you mean one square of each size (per fundamental domain)? Because if you can have any number, the answer is "all positive integers". Start with a single square, and subdivide it as needed. On Mon, May 29, 2017 at 4:36 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Which suggests the question: For which N do there exist periodic tessellations of the plane using tiles that are squares of N distinct sizes?
(Or else N distinct symmetry classes.)
—Dan
On May 29, 2017, at 1:12 PM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Nicely spotted --- thanks! WFL
On 5/29/17, Stuart Anderson <stuart.errol.anderson@gmail.com> wrote: Wikipedia has a good article on these tilings;
Wikipedia.org/wiki/Pythagorean_tiling There are 4 names given: Pythagorean tiling Two squares tessellation Hopscotch pattern Pinwheel pattern (not to be confused with pinwheel tiling)
The only other thing about these tilings I am aware of that is not mentioned in the article is that these tilings can tile a torus. See Geoffrey Morley's article www.squaring.net/sq/st/st.html
To make the tiles really dance ... Danny Caligari; https://www.google.com.au/amp/s/lamington.wordpress.com/ 2013/01/13/kenyons-squarespirals/amp/
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