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I've read Draves' paper on the Apophysis Flame algorithm and for the most part its well written, very understandable and complete.  One area he seems to have neglected, however, is the number of times he iterates for a given point.  The quality parameter dictates how many sample points are iterated on but in the algorithms for each individual point, the psuedo-code for the algorithm is simply

   iterate {
      ...
   }

with no indication of the number of iterations.  He says he skips the first 20 iterations but then how many more iterations are traversed is never discussed.  From experimenting with Apo I think it's probably a constant number but I'm not 100% positive and I have no idea what the number might be.

Anybody out there know anything about this?  I'm contemplating writing something that doesn't actually produce the flame but will show the set of points iterated off a starting point but I don't know how many iterations to show in order to accurately reproduce what Apo is doing.

Thanks!

Darrell Plank
jar_czar@msn.com

i usually don't restart the iteration until i've done enough iterating for the next image update. this works most of the time because ifs tend to be chaotic, the important property of which is being bounded; even if this is not the case, almost always there is a nonlinear function like sin which is going to "trap" the iteration in a reasonable area. when this is not the case, i ad hoc determine a maximum iteration depth and do some multiple of that number of iterations (restarting between each) before the next image update.

i don't know if this is what apophysis uses (i'm allergic to delphi), but it works well for me :) if you're looking for proof that it works ok, you can check my deviantart gallery (all works made using my programs).

let us know how you get on, and post some pictures :)

I believe Apophysis has a parameter that allows the user to control the number of iterations on a given fractal - if done properly the actual number of iterations performed should also be based on the fractal dimension of the object and the resolution/magnification of the image but basing it on the fractal dimension is tricky when using non-linear modifications as is usually the case with flame fractals.