Hi Axel, Carl and all others,
This has been an interesting experiment. I was trying to produce these Julia fractals, since 8-10 years ago, when I was still on usenetand was using Maple V rel 4, but it was a pita.
Now at school, they wanted to see them as part of my PhD thesis, so I started switching between versions.
With V they did complete on small grids (100x100) in about 10-20 minutes, so V was essentially useless. I had to have several samples and took too long to generate animations.
My school then updated to Maple 9 and there the results were similar on smallish grids, just a tad faster, in the order of 5-8 minutes.
Now the school also wanted me to evaluate between versions, so by pure accident I tried it on 13 and it worked, so I was able for the first time to see what these Julias look like, even under animation.
They also had 18, so I tried them there and hence the discrepancy.
Looks like Carl found the culprit? That is amazing! I thought that maybe 18 did not take advantage of java property or something to that extent. Oh well.
Please feel free to experiment with the code. I know of no other program which can produce these with additional attractors included, except Xaos, but neither it nor other programs which accept custom functions have a way to calculate the limits (either the main feature, or the secondary attractors outside the Shell-Thron region), so the Fatou basins are always black.
For best results, choose c values close to the Shell-Thron boundary, shown on the upper part of the code.
Many thanks to all who looked at this. Can't wait to try Carl's solution!
PS: the code is aptly optimized through the years. Even the use of globals is the best solution in this case. I experimented with using only locals, takes too long on Maple 13. For example, lim and lambda need to be global so they can be ready for each iteration. If I changed to a local calculation, it still drags, even on 13.
PS2: My old web page was scrapped by the Brain virus. I lost everything, but parts of it were saved at the www.archive.org. If anyone wants to take a look, send me an email and I will reply on how to access it.
Thanks again everyone!