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Have you considered simply ignoring whether they are in the M-set or not?  Points which escape quickly will not have much effect on your histogram.  They fall out of the iteration loop quickly and contribute very little to increasing the hit count of any individual pixel.  A very simple solution to that is to simply not plot the first few iterations - a classic escape-time view of the M-set looks almost the same after 20 iterations as it does after 2000 iterations, so just ignore the first 20 iterations before you start updating the hit count on the individual pixels.

Points which are very close to the border and require hundreds of iterations will follow a path very similar to the points just barely over the border, and only the last few iterations will vary significantly.  Again, that's only a few iterations and those will have very little effect on increasing the hit count of any individual pixel.

I play around a fair bit with orbit path Buddhabrot-style fractals, and I always ignore whether the point being tested escapes or not.  I'm old school, so I still have enough fun with Fractint that I'm not ambitious enough to bother updating to anything more current - probably I will some day, but I'll treat that as a retirement project!  In Fractint, you don't have the option of ignoring the first iterations, so you usually get a regular grid resulting from the first iteration or two, but if the colour scheme is set so that the lowest hit counts are the faintest colours, then you hardly notice that.  Here's one of my favourite orbit path animations, ignoring whether the points fall in or out of any set.

<a href="http://vimeo.com/moogaloop.swf?clip_id=49084660&amp;amp;server=vimeo.com&amp;amp;fullscreen=1" target="_blank">http://vimeo.com/moogaloop.swf?clip_id=49084660&amp;amp;server=vimeo.com&amp;amp;fullscreen=1</a>

Ryan

What i dont like about the buddhas is the random distribution of starting positions
i think interestin patterns could be found by somehow generalized aproach to scan a grid at least to check out what very dense starting positions vary . . .

Ryan D, That sounds like a promising idea, I will try it out

Edit: Still using my code the way it was but only adding orbit traps if their iterations count is > 20:
- Low maximum iteration counts fail often (they don't pass the acceptable-orbit-trap test often)
- A lot less noise around the image, looks nicer when the glowing cloud around the Buddhabrot hugs tighter instead of being spread out in a circle. Also builds a nice looking Buddhabrot without noise much faster.
- The glowing cloud around the Buddhabrot is affected in the sense that it kind of looks like a Buddhabrot rendered at 20 maximum iterations. In the picture below there is some lightning-looking stuff (I actually like it) around the head that never appeared before without the > 20 test.

Normal result for red max iterations = 1,000,000; green max iterations = 10,000; blue max iterations = 100:


Result of doing the n > 20 test for red max iterations = 1,000,000; green max iterations = 10,000; blue max iterations = 100 (I did not wait very long by comparison to the other images for this to be produced, it is faster):


Normal result for all max iterations = 20 (for reference):

ker2x, I tried making a diagram in Photoshop to explain and realized a random range of (-0.5 to 0.5) does miss some points. Here is the diagram anyway:



- The small red squares are pixels that do not belong to the Mandelbrot Set
- The small green squares are pixels that do belong to the Mandelbrot Set
- The pink areas are the random deviation every red pixel has (only shown at the boundary of the Mandelbrot Set)
- The light green areas might be part of the Mandelbrot Set and I am missing those

I will change the code to use a random range of (-1.0 to 1.0) and then that will completely cover the boundary

I have no clue about the scheme involved, but about quasi-random (LDS) instead of pseudo?

matsoljare, that would be really cool but other than just taking a lot of screenshots I don't know of an easy way to use JavaScript to render a movie. It looks like some other people on this thread also have Buddhabrot renderers, maybe they would be more prepared.

By iteration count increasing did you mean:
- The maximum iteration count for one / all the color channels
- The minimum iteration count that was confusing me in the last few posts
- Something else?