Game of Life running on Penrose tiles

There's a fantastic feature in the New York Times about "The Lasting Lessons of John Conway's Game of Life" — well worth reading on its own, since they solicited short reflections from big thinkers on why Conway's famous cellular-automata gewgaw remains so fascinating, decades after its invention. Me, I first got Life running via a BASIC version in an early-80s computer magazine (like this one, in Byte). It fried my noodle; I was accustomed to programs deterministically doing things you expected, but not deterministically doing things you didn't.

Apparently, as the Times reports, Conway grew to hate his invention, to the point of shouting "I hate Life!" when someone mentioned it.

But the most intriguing note in that piece, for me, was learning how the computer scientist Susan Stepney got Life running on Penrose tiles. Penrose tiles are nonrepeating, so working out the ruleset is a tricky affair.

In this paper, she and Nick Owens describe their algorithm, and show off how they did it. Here's an example of them figuring out the possible neighbors for individual tiles …

The original Game of Life has figures that become stable — they don't evolve any more because the position of their tiles prevents any new ones being born, or any from dying. (Conway called these "Still Lifes".) Stepney and Owens found a bunch of still lifes in Penrose tiling, too …

One of the fun parts of the original Life were stable oscillating patterns, ones that got stuck in an evolutionary loop, reproducing the same shape like an animated gif. They found some of these in Penrose too — including these ones, which given the jagged geometry of Penrose tiling, they delightfully called "bats" …

Here's what one of the bats looks like, in its fluctuations!

Another famous construct in Life was the "glider" — an oscillating set of tiles that moved diagonally each time it looped around, so it flies off eternally into Lifespace. In 2012 some academics figured out how to make a glider in Penrose Life; there's video at in this New Scientist story. There's more stuff if you poke around online a bit — here's another scholarly paper on Penrose Life, and some video of Penrose Life on Youtube.

Super cool stuff.