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On Fri, 28 May 1999 21:27:56 -0700, Ken <tyl### [at] pacbell net> wrote:
>
>
>Mandelbrot:
>
> Why will the mandelbrot pigment pattern not tile as other patterns
>will ? I could not find anything specific about it in the docs but
>it seems to behave similar to the way the planar, spherical, and
>box patterns behave i.e. in 1 unit square only non repeating patterns.
The M-set is calculated in the following way:
1. Take a point (X,Y).
2. Let a complex number C=(X, i*Y) where i is the imaginary unit
sqrt(-1).
3. Have another complex number Z=(0,i*0).
4. Perform the iteration Z=Z*Z+C .
5. Repeat 4. until a) Z*Z>=4 or b) you reach the maximum number of
iterations specified.
The color assigned to point (X,Y) is the number of iterations needed
so that Z*Z goes above 4 (it is assumed that in this case Z will
approach infinity very quickly). Therefore, any point lying at a
distance of more than 2 from the origin will lead to bailout on the
second iteration. That's why the Mandelbrot pattern is confined within
a circle of radius 2 centered at the origin, so it will not tile.
You can use a repeat warp, though.
---------
Peter Popov
ICQ: 15002700
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