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true 3D Julia setWhite ElephantEntry point
White Elephant
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Posted by: floppyHat April 09, 2016, 12:42:38 AM

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quaz0r
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April 12, 2016, 12:38:58 AM
you got the smooth coloring to work, cool.   smiley   for that other stuff you mentioned you should start a thread somewhere else asking about that and one of the resident math geniuses will probably know the answers.  certainly not me though   cheesy
floppyHat
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April 11, 2016, 11:12:49 PM
Many thanks again for that link Mr. Fractal Fertilizer!   I have just implemented the log(log) interpolation and it seems to have largely obviated serious banding, at least for the small bit of the standard power 2 M-set I have so far tested it on.   I did have to up my bailout value from 2 to 32 to stop the "smooth iteration count" going negative.

And I'm wondering what the equivalent would be for convergent functions like Newton formulae, Moebius transforms etc.   My bailout condition for these is checking if the difference between the last two magnitudes is less than a small value, i.e. if

abs(final magnitude - penultimate magnitude) < 0.000000001.

I suppose it would be reasonable to use a log(log) formula on the space between zero and 0.000000001.   I shall try this! smiley  But would love to hear how others approach it...
quaz0r
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April 11, 2016, 12:59:47 PM
well generally people use different logic for what to do with inside points
floppyHat
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April 11, 2016, 12:51:54 PM
The case of final magnitude < bailout is not covered, though.   This is the case where you hit max. Iterations and z is still in the set.   Using the log log method runs into the issue that the final magnitude varies from zero to bailout, and log(0) is minus infinity.   So hoiw do people generally deal with this?
floppyHat
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April 11, 2016, 11:20:56 AM
Thanks @Quazor, a quick scan of that thread and I realise that's probably what I need to do. I'm doing a linear interpolation, not even log, let alone log log!  Hopefully implementing this will cure my banding.   I'll let ye know...
quaz0r
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April 10, 2016, 12:43:35 AM
http://www.fractalforums.com/programming/please-explain-smooth-coloring/

how does this compare to your implementation?  note there is a typo in the formula on some of the posts that i point out in the last post
floppyHat
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April 09, 2016, 04:48:56 PM
@hapf I'm pretty sure it was 256 its. Might have been 512.   But sometimes the lush effects get lost at higher iteration counts...

@quaz0r No, I wish I didn't have it!   I get a "real iterations" value by seeing how far an escaping point has escaped outside the escape radius, or if it hasn't escaped then how far inside it is.   This gives me a fractional part to add to my iteration count.   Then I use these numbers to interpolate between colours using the JavaFX method
Code:
Color.interpolate()
.   The banding seems to come from this, so perhaps I need to do the interpolation differently.   Currently, though, I'm too busy exploring convergent functions!
hapf
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April 09, 2016, 10:28:54 AM
Enough iterations? Colours are very nice.
quaz0r
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April 09, 2016, 01:44:10 AM
is the banding between level sets intentional here?  i seem to recall my images looking like this before i figured out my smoothing formula was wrong

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