Back in 1975 (punch-cards days), I wrote a program in Algol 60 draw the Penrose Tiling, and every 10 or fifteen years since then I have re-written it in whatever language I was current with. Penrose’s recent Nobel prize prompted me to have another go, so this time it is Grasshopper’s turn!

Grasshopper does not support recursion, so I had to generate the pattern’s recursive layers by repetition of components. For artistic purposes, this is fine, and gives better control of exactly how the pattern is to unfold.

Back in 1975, I broke the pattern down into Pentagons, Lozenges, Stars and Wedges, so each of these gets a cluster, and each is then built with a combination of the others at the next level down. Maybe there are better ways to do it, but that is how it was. There are eleven different connections from one level to the next. String theory may be involved?

Star1.gh (497.7 KB)

The version of the pattern that actually got published at the time omitted bits of the pattern, which shows the rules of the recursion rather nicely. Adding some culling of components, we get:

Snowflake1.gh (570.0 KB)

Best wishes, and Season’s Greetings!

Bob Mackay