*From*: Mukund Sivaraman <muks banu com>*To*: Katie Harrison <harrison9340 googlemail com>*Cc*: gimp-developer-list gnome org*Subject*: Re: [Gimp-developer] Request for equations for Fractal Trace and QBist*Date*: Fri, 31 Aug 2012 17:08:29 +0530

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

**Follow-Ups**:**Re: [Gimp-developer] Request for equations for Fractal Trace and QBist***From:*Mukund Sivaraman

**References**:**[Gimp-developer] Request for equations for Fractal Trace and QBist***From:*Katie Harrison

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