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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!

Danny King
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    To me, "universality" refers to something unrelated (http://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. – bradhd Apr 06 '13 at 18:33
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    Read this: http://www.ams.org/journals/bull/2003-40-01/S0273-0979-02-00970-9/S0273-0979-02-00970-9.pdf – Potato Apr 06 '13 at 18:35
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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 06 '13 at 18:46
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    Here's another good write-up. Take a look at the references for more information. http://terrytao.wordpress.com/2010/09/14/a-second-draft-of-a-non-technical-article-on-universality/ – Potato Apr 06 '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 06 '13 at 18:51
  • Here's a MOOC that looks related that a friend shared with me on Facebook http://www.complexityexplorer.org/online-courses/1/intro_video – Danny King Apr 06 '13 at 19:42
  • @DannyKing Your question is probably appropriate for the nearly-in-beta-SE http://area51.stackexchange.com/proposals/64216/mathematics-learning-studying-and-education.

    Check out the proposal and commit to it if you're interested. Then we can get it off the ground and get the site in beta!

     – Xoque55 Mar 03 '14 at 04:56

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