kolen-j@neuron.cis.ohio-state.edu (john kolen) (07/07/90)
Very quick question: Is the standard algorithm for computing fractal dimension from a set of data points similar to the "Box Counting" theorem in Barnsely's _Fractals Everywhere_? That is, for increasing values of n, determine the number of boxes of size 1/(2^n) to cover the set of points and plot this value with 1/(2^n) on a log-log graph. The slope of the plotted points (if it exists) being the resulting dimension. Thanks John Kolen ----------------------------------------------------------------------------- John Kolen (kolen-j@cis.ohio-state.edu)|computer science - n. A field of study Laboratory for AI Research |somewhere between numerology and The Ohio State Univeristy |astrology, lacking the formalism of the Columbus, Ohio 43210 (USA) |former and the popularity of the latter -- John Kolen (kolen-j@cis.ohio-state.edu)|computer science - n. A field of study Laboratory for AI Research |somewhere between numerology and The Ohio State Univeristy |astrology, lacking the formalism of the Columbus, Ohio 43210 (USA) |former and the popularity of the latter
ktc@aplcen.apl.jhu.edu (Kim Constantikes) (07/09/90)
The boxcounting dimension (and algorithm) is an approximation to the rigorous Hausdorff dimension, which is usually accepted as the "Fractal dimension". There are a multitude of other dimensions as well, such as information dimension, simularity dimension, cluster dimension, etc. These dimensions usually, but not always, agree. Note that boxcounting is a particularly poor choice for estimation of the dimension of experimental data. For a rigorous treatment of these subjects, see Falconer, "The Geometry of Fractal Sets". See Feder, "Fractals", for a good introduction, or the AMS collection on fractals for a more rigorous but succinct treatment. My own experience is that estimation of the Hurst exponent via range scaling analysis is the best first approach.