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I'm fascinated by what I think is called Universality in mathematics. What I mean by this is systems with simple rules displaying very complex behaviours in aggregate. Conway's game of life, Wolfram's A New Kind of Science (http://www.wolframscience.com/nksonline/toc.html) and this excellent article http://www.empiricalzeal.com/2013/03/01/the-universal-laws-behind-growth-patterns-or-what-tetris-can-teach-us-about-coffee-stains/#more-2837 are what I mean.

I am struggling to find resource to explore this topic further. Could anyone give me some pointers for where to learn more about this?

Searching on Google or for books on Universality doesn't seem to give me much.

  • Is this universality or something else? Are there terms I can search around?
  • Are there other related areas of mathematics I should look in to?
  • Can you suggest books, articles, videos, interest groups, etc?

Thanks!

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To me, "universality" refers to something unrelated (en.wikipedia.org/wiki/Universal_property). I'm not sure if this is exactly what you're looking for, but you may be interested in reading about chaos theory and dynamical systems in general. –  Brad Apr 6 '13 at 18:33
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You might want to look for books on dynamical systems, and also for material on central limit theorems in probability theory. –  Potato Apr 6 '13 at 18:46
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Here's another good write-up. Take a look at the references for more information. terrytao.wordpress.com/2010/09/14/… –  Potato Apr 6 '13 at 18:48
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I took a look at the Yunker paper referenced in the article you linked, and some more key words to look for might be Brownian motion and stochastic (partial) differential equations (this falls under the heading of probability theory). –  Potato Apr 6 '13 at 18:51

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