Looking phenomenal, nicely done

Thank you

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“It turns out that an eerie type of chaos can lurk just behind a façade of order – and yet, deep inside the chaos lurks an even eerier type of order.” Douglas Hofstadter

looks good! i'm pleased that you didn't use that nasty hacked-gaussian filter for this released image

maybe you're getting tired of my suggesting it, but try a proper reconstruction filter like the tent filter i described, and you'll be amazed how much better it looks than even this result... the box filter tends to blur the image too much, while also letting extraneous high frequency informtion leak through; the tent filter does a lot better in both cases, and is still really easy to implement.

I need to review what you said about the tent filter. I think at the time it didn’t make much sense because I was still averaging exit values instead of colors.

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“It turns out that an eerie type of chaos can lurk just behind a façade of order – and yet, deep inside the chaos lurks an even eerier type of order.” Douglas Hofstadter

the tent filter is, again, just (1-|x|)(1-|y|), where x and y are in [-1,+1] around the sample location at (0,0). obviously your pixel's sample location isn't always at (0,0), it's at (x,y), so then you just define x' and y' to be relative to the sample location (x,y) instead of (0,0).

As it goes right now I think I may be doing this already.

I have a test point, whose [real, complex] value is usually much less than one. However, I treat the area around the sample point as a unit area. The test areas do not overlap, but do touch. They are also stratified, and I average the sum of the color components by the number of stratifications.

Now looking at your description I have one question, am I supposed to do something with this product? (1-|x|)(1-|y|)

I am assuming that the (x,y) values are relative to a unit square centered at (0,0).

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“It turns out that an eerie type of chaos can lurk just behind a façade of order – and yet, deep inside the chaos lurks an even eerier type of order.” Douglas Hofstadter

that's your weight, your "bias" as you formerly called it. so let's say you want to work out the colour for pixel (10, 4); you first offset by 0.5 to get to the centre of that pixel's "area", then sample a full pixel to the left and right, above and below of (10.5, 4.5) - that is from (9.5,3.5) to (11.5, 5.5) - weighting each sample you take inside this region by (1-|x-10.5|) * (1-|y-4.5|). now i'm not 100% sure that the tent filter as given is normalised, and i really don't feel like doing a double integral to confirm it, so you might like to check that with a high quality monte carlo integration - if it gives like 1.00001 then you can be reasonably sure it's normalised.

btw, i suspect you weren't doing the offsetting by 0.5 previously, which explains the slight offset in the comparison images you posted in your scraps.
btw2, how deep a zoom is this image?
btw3, could i please get the equation for the palette you used in this image?

LOL, lots of btw! I'll do my best to try and find out the info for you.

As for some of the posts in my scraps, God only knows what bugs I had in the code.

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“It turns out that an eerie type of chaos can lurk just behind a façade of order – and yet, deep inside the chaos lurks an even eerier type of order.” Douglas Hofstadter

Zoom is 4096 or 1/4096 as used inside the program.
Iterations 475

The color equations are normalized so the max iterations is 2PI and the return values range between 0~255.

r = sin(15x) +1
g = sin(15x + .5PI) +1
b = sin(15x + PI) + 1

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“It turns out that an eerie type of chaos can lurk just behind a façade of order – and yet, deep inside the chaos lurks an even eerier type of order.” Douglas Hofstadter