Tuesday, November 2, 2010

Autumn leaves as globular clusters?

As I looked at the red leaves falling around a maple tree in my yard, I was reminded of an appendix in Pickover's Chaos in Wonderland called "Build Your Own Globular Cluster".  I dug it out and found the equation
p = 1/(1+r²)^n
where p is the density of stars in the cluster, r is the radius, and n is a so-called polytrophic index, "typically 2.5<n<3.2".  The index also provided a program for plotting globular clusters, but I found it difficult to understand, so I went about creating my own from the equation.  I used the inverse function r(p), and let p be a random number between 0 and 1.  The result looked very similar to the pattern of leaves I saw on the ground, but I still wonder if this was the right equation to us, or if a normal distribution would be more appropriate.

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