Re: [Gimp-developer] Request for equations for Fractal Trace and QBist

[Mukund Sivaraman <muks banu com>]

Hi Katie

On Thu, Aug 30, 2012 at 10:44:21PM +0100, Katie Harrison wrote:
> Hi, I love using the Fractal Trace and QBist filters, but I wish I could
> apply similar effects to SVG images, so I'd like to (attempt to) write
> Inkscape extensions that do something similar. My problem is that I'm just
> a python developer who can't read c code, so I was wondering if the math
> equations used by these filters are written down somewhere, or if there is
> someone on this list who knows what they are?

For Fractal trace, the method is simple. If you are not familiar with
the Mandelbrot set, first make yourself familiar with it so that you
can write a program to draw it.

http://en.wikipedia.org/wiki/Mandelbrot_set

I see that you are not familiar with C, but here is a small
simplistic program to draw it that you may still be able to follow:

https://banu.com/blog/27/rest-in-peace-mandelbrot/

Once you have understood it, here's how the Fractal trace works. For
every point in the target image (mapped to the set, and in set
co-ordinates) say z = c = (x,y), Fractal trace puts the point through
the equation:

z = z^2 + c

On every iteration, z is a new point in the set. Typically this point
hops around and around the original (x,y).  [The XaoS program has a
nice animated illustration of this in its help section.]

After many iterations, either the point stays close to (x,y), or
'escapes' and jumps far away from (x,y).  You should be able to
determine if you should stop iterating based on the distance of the
current value of 'z' from (x,y), or after 'N' iterations if the point
has not ventured far (and likely won't).  [This is the same type of
escape checking that you'd do when drawing the Mandelbrot set.]

Once you decide to stop iterating, the color of pixel (in image
co-ordinates) corresponding to resulting value of 'z' (in set
co-ordinates) is set as the color of pixel in the target image (in
image co-ordinates) corresponding to the (x,y) point (in
set-coordinates).

This class of operation is called a 'map', as the color of the point
maps to that of another.  Usually some sort of sampling is also
performed around (x,y) (in the domain of the map) to get rid of
aliasing.

That is all. If you have understood how the Mandelbrot set is generated
and are able to write a program to generate it, then doing the Fractal
trace should be straightforward after that.


Kind regards,

Mukund