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 Krishnakumar December 2, 1998 03:24

Fractal grids

Do you think that you can reduce computational time or have any other advantages by using fractal grids. The computational time is of the order of N^n ( N= no. of points; n=dimension) I presume. This means having a fractal grid for three-d might save time.

 jay December 2, 1998 18:59

Re: Fractal grids

Can you define a "fractal grid" ?

 Krishnakumar December 3, 1998 12:40

Re: Fractal grids

A fractal is an object of fractational dimension. A fractal grid is something like the julia set or cantor set or the seirpenski triangle or the mandelbrot set. Since they have a dimension which is a fraction, a fractal grid might be better off for computational time.

 jay December 4, 1998 14:50

Re: Fractal grids

Correct me if I'm wrong but that doesn't seem to define fractal *grid* yet.

Fractal dimensions are used to describe objects which display the quality of "self-similarity," i.e objects where microscopic portions when zoomed-in, look more-or-less like the macroscopic/global geometry. These are also objects for which the classical euclidean concept of dimension does not apply (for which reason the concept of fractal was in fact invented.) All the sets mentioned, julia, cantor, mandelbrot are examples of fractals, i.e. mathematically generated examples of geometries that defy the euclidean concept of dimension, and therefore require the concept of fractals to measure their "dimension." So, coming back to the original question: How would you define a fractal *grid* ? We have to first be able to define it before we are able to generate and use it! So far we have only defined/described fractals, not fractal *grids* !

 Krishnakumar December 8, 1998 13:04

Re: Fractal grids

A fractal grid is one of these fractal sets generated up to a finite number of iteratons. So strictly speaking it is not a fractal. But these kind of grids may have some advantages( like cokmputatonal time). I was asking whther they will be of some advantage over the existing methods of grid generation. I don`t know much fractal dynamics so I don`t have any idea how to go about generating "fractal" grids. But do you think there is any difference in fractal and algebraic grids. They do look similar from the mathematical point of view.

 I. Dotsikas December 11, 1998 12:29

Re: Fractal grids

I have some difficulties in understanding what you mean. We want to generate a computational grid ( from a two or three dimensional shape). This grid is supposed to have two or three dimensions. How can you achive to reduce the dimensionality from two to 1.xy while keeping the two dimensional, euclidean, information? Don't forget that the 'dimension'-definition varies from the eucledian geometry and that you might have to transform your equations. What do you really mean with fractal grid ? In the self similar turbulence you could ??? try it. Go ahead try to write your code. In your case I would rather try something else. Good luck!!

 R.krishnakumar December 12, 1998 07:01

Re: Fractal grids

Actually.. I just wanted to check out if a fractal grid can exist and if it does, does it have some advantages. I did see any great diff between (the so-called) fractal grids and the present ones. Infct .. I didn`t even know what it is. I thought some of you guys out might see something in this. I guess the idea is really futile. If any of you guys do see some way of having fractal dimensional grids .. please do take the troubl to inform about it.

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