Lawrence D'Oliveiro wrote: > In message <slrnh33j2b.4bu.pe...@box8.pjb.com.au>, Peter Billam wrote: > >> Are there any modules, packages, whatever, that will >> measure the fractal dimensions of a dataset, e.g. a time-series ? > > I don't think any countable set, even a countably-infinite set, can have a > fractal dimension. It's got to be uncountably infinite, and therefore > uncomputable.
Incorrect. Koch's snowflake, for example, has a fractal dimension of log 4/log 3 ≈ 1.26, a finite area of 8/5 times that of the initial triangle, and a perimeter given by lim n->inf (4/3)**n. Although the perimeter is infinite, it is countably infinite and computable. Strictly speaking, there's not one definition of "fractal dimension", there are a number of them. One of the more useful is the "Hausdorf dimension", which relates to the idea of how your measurement of the size of a thing increases as you decrease the size of your yard-stick. The Hausdorf dimension can be statistically estimated for finite objects, e.g. the fractal dimension of the coast of Great Britain is approximately 1.25 while that of Norway is 1.52; cauliflower has a fractal dimension of 2.33 and crumpled balls of paper of 2.5; the surface of the human brain and lungs have fractal dimensions of 2.79 and 2.97. -- Steven -- http://mail.python.org/mailman/listinfo/python-list