Title: Is the Mandelbrot-Set actually a multifractal? Post by: Chillheimer on June 07, 2016, 05:10:54 PM During my research for another encyclopedia article about marine animals & fractals I stumbled upon this obituary for Benoit Mandelbrot in the "journal of plancton research" (to be surprised again where we can find fractals!)
http://plankt.oxfordjournals.org/content/early/2011/03/05/plankt.fbr008.full anyways, in it there is this paragraph: Quote The first fractal paper published in the Journal of Plankton Research, entitled “Intermittency in the plankton: a multifractal analysis of zooplankton biomass variability” (Pascual et al., 1995), went well beyond the concept of fractal itself. Multifractals can indeed be considered as a generalization of fractal geometry initially introduced to describe the relationship between a given quantity and the scale at which it is measured. While fractal geometry describes the structure of a given pattern with the help of only one parameter (the fractal dimension DF), multifractals characterize its detailed variability by an infinite number of sets, each with its own fractal dimensions. isn't the same true for the mandelbrot set, being a 'multifractal map' of all julia sets? Title: Re: Is the Mandelbrot-Set actually a multifractal? Post by: Max Sinister on June 08, 2016, 10:36:15 PM I wouldn't be surprised, but I would have to read the article carefully.
BTW, marine animals? Like fractal shapes of shells and sea snails? Title: Re: Is the Mandelbrot-Set actually a multifractal? Post by: Chillheimer on June 08, 2016, 11:56:09 PM yes, but not just:
http://fractalogy.org/marine-animals/ still very unfinished, but all important source papers are linked at the bottom. besides the 'standard examples' of shells I find especially the plancton part and the diatoms intriguing Title: Re: Is the Mandelbrot-Set actually a multifractal? Post by: Max Sinister on June 09, 2016, 10:29:25 PM I liked the feather stars. |