Re: Looking for an explanation of Barnsley's 'colour stealing' method




On 21 May 2007 20:51:05 -0700, catenary@xxxxxxxxxxxxxxx wrote:

Hi,

I've been reading Michael Barnsley's book 'Superfractals', but to be
honest some of the more mathematical parts are going a little over my
head. I'm particularly interested in a method he calls 'colour
stealing', in which the colors used to display an IFS are taken from
another image. Unfortunately I can't quite follow his explanation of
what's going on - though I feel that it can't *really* be all that
complicated. Is it just that there's a 'background' IFS driven by the
same random numbers as the 'foreground' IFS, which picks up the color
of the point where it stops?

Is anyone aware of (or willing to post?) a more basic explanation of
this technique? A fragment of (pseudo)code would be particularly
helpful.

Trying the read the mathematical shorthand, I conclude that in color
stealing, two IFS algorithms are started simultaneously. These are
not necessarily the same. The path followed by one is used to locate
a sensing point within a pre-existing image which is used as a color
source. The color of that point is used to color an image being
painted by the other IFS.

I hope this is essentially the method. Any corrections or improvements
to my simplistic guess would be welcome.

Here is an audio description which claims to be low math.
http://www.fields.utoronto.ca/audio/05-06/dynamics_day/kunze/
Unfortunately, the talk is all audio without the slides. It becomes
clear, given what I listened to, that it is essential to understand
fractal tops to completely grasp color stealing. At this point, I
don't.

Barnseley has a site which offers explainations of colour stealing.
http://www.superfractals.com/colour_stealing/colour_stealing.htm
In the pop-up article, he seems to skip past fractal tops.

My simplified description is based on the article:
http://wwwmaths.anu.edu.au/~barnsley/pdfs/fractal_tops.pdf which has
a heavy math explaination of color stealing. (I don't recommend it for
the explaination, but several of the illustrations show the
technique's results nicely.)

As the illustrations in the second citation show, the result is a very
natural (nature-like) coloration of the fractal image.

Like you, I would welcome snippets of code or pseudocode which would
serve to eliminate ambiguity and bypass the opacity of the formal
expressions used in these cited "explainations"

John
.