thomson@cs.utah.edu (Rich Thomson) (04/04/91)
In article <1991Apr4.163135.25063@leland.Stanford.EDU> rick@hanauma.Stanford.EDU (Richard Ottolini) writes: >I notice there are some geological phenemena that are scale-invariant in 3-D >and over time. Is this a fractal with dimension at least 3? Probably more like it is a fractal with dimension between 2 and 3, imbedded in 3-space. For instance, the standard middle-thirds Cantor set has dimension ln(2)/ln(3), which is somewhere between 0 and 1. The standard Cantor set is imbedded in the real-line. This is not to say that there aren't fractals with dimension higher than 3, but they are imbedded in some space R^n, n > 3. -- Rich Rich Thomson thomson@cs.utah.edu {bellcore,hplabs,uunet}!utah-cs!thomson ``Read my MIPs -- no new VAXes!!'' --George Bush after sniffing freon
rick@hanauma.Stanford.EDU (Richard Ottolini) (04/05/91)
I notice there are some geological phenemena that are scale-invariant in 3-D and over time. Is this a fractal with dimension at least 3?
stam@dgp.toronto.edu (Jos Stam) (04/05/91)
Richard Ottolini writes: >I notice there are some geological phenemena that are scale-invariant in 3-D >and over time. Is this a fractal with dimension at least 3? Why not? Fractals exist in all dimensions. Now, find its fractal dimension... Has anyone tried to generate such fractals? As the phenomenon is 4 dimensional this could generate interesting animations: "fractal animations" :) Of course there are limitations: most of the current synthesis techniques are already too expensive for 3D phenomena. But, with a couple of Crays... cheers, Jos
musgrave-forest@cs.yale.edu (F. Ken Musgrave) (04/09/91)
In article <1991Apr4.163135.25063@leland.Stanford.EDU> rick@hanauma.Stanford.EDU (Richard Ottolini) writes: > >I notice there are some geological phenemena that are scale-invariant in 3-D >and over time. Is this a fractal with dimension at least 3? I depends upon the geological fractal you're talking about. Mountains may be seen as 2.x dimensional, and clouds as zerosets of 3.x dimensional fractals (as the coastline is the zeroset of a mountain). So you may already invoke a fractal dimension greater than 3 in a geological structure, even without taking time into acount. I'm trying to imagine a phenomenon with the same statistical beavior in time as in space... Can you be more specific? Ken -- "But what do we do about moose and squirrel?" -Boris Badanov F. Kenton ("Ken") Musgrave musgrave@yale.edu (203) 432-4016 Yale U Depts of Math and CS Box 2155 Yale Station New Haven, CT 06520