It was suggested that I explain terms in future, I apologise but since I was pointed here by a fellow fractal artist who is also a Mathematician by profession I assumed all members of the list would be familiar with more general fractal terminology - which with the level of math generally discussed on the list is just about the only terminology that I'm up to speed on :) IFS == Iterated Function System as used in the famous "Barnsley Fern" which uses 4 affine transforms but general IFS can use any type of transform essentially provided the overall result is (mostly) contractive (if using the chaos-game or contractive deterministic rendering methods) - reference: http://classes.yale.edu/fractals/ RIFS = Recurrent IFS, not sure of the definition bit I found it used in a number of places several years ago and the fractal types/algorithms involved matched changes I had made myself to enhance standard IFS. LRIFS - Language Restricted IFS - by far the most interesting and general form, with sufficiently sophisticated algorithms can produce equivalent results to general L-Systems (again see the Yale link) When an IFS is rendered every final point basically has a genetic code formed by the path through the tree of transforms used to get to that point (or *from* that point when rendering using the escape-time method) in the case of convergent rendering the *last* transform used gives the transform domain that the point belongs to, in the case of divergent, escape-time rendering then the first transform gives the transform domain for the point concerned. Kaleidoscopic IFS is produced using the standard escape-time method (as in "normal" Mandelbrot or Julia fractals) to render IFS fractals by deciding which transform to use on each iteration based on the position of the entry point - in this way for standard non-overlapping IFS (i.e. where the domains for no two different transforms intersect) the result can exactly match the standard IFS method (using a full tree) e.g. the Menger Sponge etc. When used with overlapping areas the results often produce kaleidoscopic effects especially when the transforms are varied to produce animations. On 5 Jun 2011, at 15:51, David Makin wrote:
Nevermind, I realised the answer is quite obviously "yes" (provided that the full attractor is finite).
On 5 Jun 2011, at 13:24, David Makin wrote:
Hi,
I have a fractal related question that's inspired by the recent escape-time KIFS fractals (Kaleidoscopic IFS).
KIFS can be used to produce any regular symmetrical IFS that does not involve overlap of the first level transform domains (please forgive my possibly inaccurate terminology but I hope you get what I mean) such as the Menger Sponge or Sierpinski Tetrahedron but not IFS that have overlapping first level transform domains.
My question is: Is it correct that *any* IFS fractal system (affine or not) (or indeed RIFS or LRIFS) can be written as a standard escape-time system using positional conditionals if said conditionals identify which of the first level transform domains the current (input) point belongs to *and* the first level transform domains do not overlap ? (Of course the situation for RIFS and LRIFS would be more complex requiring knowledge of which transforms are active at that depth in the IFS tree etc.)
bye Dave _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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