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Saturday, August 06, 2016

Random but with Geometric Order

A mathematical, but but not very technical article, but the implications are not easily thought about. The non-order called randomness has a remarkable number of practical applications.  Such as crytology, for example or creating 'natural'  imagery. It turns out that if you build geometric structures based on randomness, they turn out to exist in classes.  Is that itself a kind of order?  Visually striking example images.

In Wired:   Mathematics are building new models of geometric randomness. by Kevin Hartnett

" ... these random shapes can be categorized into various classes, that these classes have distinct properties of their own, and that some kinds of random objects have surprisingly clear connections with other kinds of random objects. Their work forms the beginning of a unified theory of geometric randomness.

“You take the most natural objects—trees, paths, surfaces—and you show they’re all related to each other,” Sheffield said. “And once you have these relationships, you can prove all sorts of new theorems you couldn’t prove before.” ... " 

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