Patterns in shells, cellular automata, knitting and music

May 6th, 2013 § 1 comment

Earlier tonight I read the following article (via an NYT piece about Nautilus mag):

Biologists Home in on Turing Patterns: Was Alan Turing right about the mechanism behind tiger stripes?

For the work that led to his 1952 paper, Turing wanted to understand the underlying mechanism that produces natural patterns. He proposed that patterns such as spots form as a result of the interactions between two chemicals that spread throughout a system much like gas atoms in a box do, with one crucial difference. Instead of diffusing evenly like a gas, the chemicals, which Turing called “morphogens,” diffuse at different rates. One serves as an activator to express a unique characteristic, like a tiger’s stripe, and the other acts as an inhibitor, kicking in periodically to shut down the activator’s expression.

And then watched an older video linked from it:

Mathematical Impressions: Shell Games

From the description:

One-dimensional, two-state cellular automata produce a list of bits at discrete time steps, whose output, depending on the parameters, may be trivial or very complex. Surprisingly, this simple mechanism can be Turing complete — that is, capable of calculating anything that any computer can calculate.

The knitting part reminded me of this photo I took of one of my mom’s crocheting pattern books:

"I can read patterns. It's kind of like programming," says @excdinglyrandom while crocheting next to me.

“I can read patterns. It’s kind of like programming,” says @excdinglyrandom while crocheting next to me.

I then went to Hart’s site, which included a link to his daughter’s YouTube page. I hadn’t watched one of Vi Hart‘s videos for a while, so I browsed and immediately clicked the one on Folding Space-Time:

And, of course, it reminded me of Crab Canon on a Möbius Strip:

All of this really just being another reminder that I need to continue reading Gödel, Escher, Bach!

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