32leaves.net

The beauty of maths

A2 phase plot

It’s not that I really could interpret this picture or tell you where exactly the patterns are comming from. But what’s highly interessting is the way they evolved. A couple of weeks ago I started playing arround again with cellular automata. While playing arround I started generating numbers where each number represents a unique population (as the population is a matrix over {0,1}, the matrix can be percepted as a binary stream). The picture above shows 500,000 generations (yes half a million) plotted in a logarithmically scaled phase plot. There for sure was total surprise when suddenly those patterns emerged.

Another neat picture is the “heatmap” showing how often a cell has been alive in respect of the total amount of generations.
heatmap

Again we see some neat patterns emerging. But why am I posting this, you might ask. Because I do think those pictures show (at least to some level) the inner beauty of math and its surrounding fields. That some “randomly” choosen system creates such patterns and shows strong symptoms of order is something I think is really amazing.

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