Penrose Tiling

Penrose TilingHi Folks:

This image shows our most recent Hug Zone chalk art drawing. The idea was independently created by the mathematician Roger Penrose. It’s a form of aperiodic tiling, and the idea has been around for millenia. For more on that, see here:

Our chalk art pattern is basically the story of two diamonds (rhombi):

Since a circle is 360°, for this pattern we divide 360 by 5 and that gives us an angle of 72°. If we mirror that angle and join the two together, we create a diamond (rhombus). By rotating 5 diamonds by 72° each, we create what looks something like a pentagon (5 sides) but is actually a decahedron (10 sides). To create the second diamond we use the outside angle from the decahedron.

There are any number of ways to combine these two diamond shapes, but for our chalk art we started with (a simplified version of) the decahedron shape and added two secondary diamonds to each point of the existing diamonds.

From there we just continued to build out the pattern. It looks much more complicated than it is, but it is pretty. A more complex version of the same two diamonds used in a different pattern can be seen here: Roger Penrose at Texas A&M University.

Okay, that’s it for now. Remember to hug the ones you love, today!


P.S. Unfortunately this pattern only lasted a few days before the rains wiped it out, but such is the nature of chalk art. We’ll take all of the healthy rain we can get!!


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