Fractal Flames search algorithm?

[Softology]

I have been getting back into rendering fractal flames.

The one thing I need advice with is how to determine if a random set of parameters is going to make a "nice looking" fractal or not.

At this stage I select random values for the probabilities and coefficient values and then do the following tests;

1. As the points are iterated I consider the test parameters bad if the values between the last and current point are too small (less than an epsilon value).  This helps weed out the images that have an instant single point attractor.

2. If the points grow in size too large from the origin then I assume the the attractor is always expanding and heading off to infinity in all directions so this is also a bad result.

3. If any of the points become NAN or INF or -INF then the parameters didn't work, so this also flags the skip this set of parameters flag.

4. During the test itrerations (I currently use 10000 iterations to allow them to settle down) I also count the unique pixels hit.  You can get a series of points that are not attracted to a single point but maybe 10 or so points.  This results in a flame with only 10 active pixels so the result is boring.

But even with these checks I do still get less than ideal results when testing random parameters.  Any more mathematical way to tell if the parameters are going to result in a better looking fractal image?

I tried the same log/log code as in the 3D strange attractors as shown here http://technocosm.org/chaos/attr-part2.html but that didn't seem to work with flames.  I am looking for a similar magic formula that applies to flame fractals.

Any ideas or tips?

I am getting some good results lately, but really want to save the user having to click a random button more times than necessary to get an aesthetically pleasing image.

Thanks,
Jason.







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