Tag: math

Patterns in shells, cellular automata, knitting and music

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.

A post shared by Greg Linch (@greglinch) on

“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!

Advancing math and science: Benoit Mandelbroit, fractals and identifying new patterns

An absolutely fascinating episode of NOVA on fractals! Along with my general interest in science and — more recently — math, material like this always makes me think of how we can apply lessons from others fields to journalism. For example, Nate Silver and his statistical models becoming more prominent this election cycle.

Below are some quoted highlights from the show — re-ordered for better flow in this context.

Narrator:

For generations, scientists believed that the wildness of nature could not be defined by mathematics. But fractal geometry is leading to a whole new understanding, revealing an underlying order governed by simple mathematical rules.

Keith Devlin, whom you might recognize as NPR’s “math guy:”

The key to fractal geometry, and the thing that evaded anyone until, really, Mandelbrot sort of said, “This is the way to look at things, is that if you look on the surface, you see complexity, and it looks very non-mathematical.” What Mandelbrot said was that… “think not of what you see, but what it took to produce what you see.”

Devlin:

So this domain of growing, living systems, which I, along with most other mathematicians, had always regarded as pretty well off-limits for mathematics, and certainly off-limits for geometry, suddenly was center stage. It was Mandelbrot’s book that convinced us that this wasn’t just artwork; this was new science in the making. This was a completely new way of looking at the world in which we live that allowed us, not just to look at it, not just to measure it, but to do mathematics and, thereby, understand it in a deeper way than we had before.

On design

Narrator:

If we could understand more about how the eye takes in information, we could do a better job of designing the things that we really need to see.

Bonus: 

Look out for one my favorite scientists — Geoffrey West! (Why? In short, read A Physicist Turns the City Into an Equation. I’m slightly obsessed with new ways of quantifying things, such as impact.)

If you can’t see the embed above, watch on You Tube.