Path: utzoo!attcan!utgpu!jarvis.csri.toronto.edu!mailrus!csd4.csd.uwm.edu!bionet!agate!shelby!portia!hanauma!rick From: rick@hanauma (Richard Ottolini) Newsgroups: comp.graphics Subject: Re: fractals Message-ID: <4712@portia.Stanford.EDU> Date: 22 Aug 89 16:03:40 GMT Sender: USENET News System Reply-To: rick@hanauma (Richard Ottolini) Organization: Stanford University, Dept. of Geophysics Lines: 15 Fractals as a mathematical descriptor and fractals as a mathematical transform are separate although related concepts. A fractal as a description will have range of scales where it is valid. A transform consists of a set of basis functions, in this case fractals, that if properly chosen can represent any dataset to any degree of resolution. If the basis function resembles the data is representing, then the transform will be parsimonous, that is, a smaller desription wil be needed. A smaller description is useful for compaction. An analogy is Ptolemy and Fourier. Ptolemy used circles within circles to represent celestial motions. Because celestial motions were approximately circular, this was a parsimonous description, until one desired very accurate descriptions. Fourier discovered that a properly chosen set of circular functions can represent ANY dataset. When the dataset is monochromatic, then Fourier's description will be rather compact.