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Some beautiful and interesting reading about Penrose tiling and Islamic tile work can be found at this site:
http://www.saudiaramcoworld.com/issue/200905/the.tiles.of.infinity.htm
Penrose Tiling
2007, Mosaic made of cut colored paper, 24" x 36"
Dedicated to Josie who gave me the colored paper and challenged me to do something with it, to Jonas who got me interested in Penrose tilings, and to Adam who displays it in his office
A Williams' Baby Blanket design
This design is inspired by the work I did as a principal scientist in biostatistics. One of my roles was to provide randomization schemes for clinical trials of new drugs or treatments.
The blanket shows the six possible squares in a 4-treatment, Williams design. This is used in randomization of subjects to sequences of treatments where each subject will receive all treatments but according to a randomly chosen order of treatments.
In each Williams square, each treatment follows another treatment only once. This design is used where there is a possibility that a subject could have carryover effects from the previous treatment.
I thought it would make a good baby blanket :)
For my first grandson, I designed a sweater featuring a Sierpinski Carpet pattern. I love fractal designs, and this one, although complicated to stitch, was a lot of fun to make.
In 2023, a non-repeating pattern with a single polygon (an "einstein tile") was discovered by David Smith. The first non-repeating pattern, the Penrose Tiling, used two polygons (see my first image).
I decided it would make a cool baby blanket.
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