Anti-Aliasing Fractals

Hello,

over the last years I have spent quite a bit of time thinking about how to render my fractals in the best possible way. I'm quite sensitive to image quality, at least I think so, since I'm often the only one to complain about it in the first place.

Just recently I found a great way for getting phenomenal results that doesn't include any costly software, it uses the completely free tool imagemagick.

Here's a comparison of a part of a FullHD image:

1. Ultra Fractal's Working Window (using Anti Aliasing) (0.44 s)
2. Ultra Fractal Rendering, AA Normal (3.92 s)
3. Ultra Fractal Rendering, AA Non-Adaptive (Threshold 0.1, Depth 4, 3x3) (22 minutes 41.75 seconds!!)
4. Ultra Fractal Rendering at 16k, AA Normal (3 minutes 8 seconds), then downscaled to FullHD (4.4 s)
5. (not shown!) like 4 but without AA on the high-res render, cuts down render time from 3 minutes to about 45 seconds, basically no visible difference!

The downscaling command is:

convert "$infile" -colorspace RGB -resize 1920 -unsharp 0x0.75+0.75+0.008 -colorspace sRGB ../out/"${infile%.png}_2k.png"

Personally, I like the extremely clear look on the rightmost image (number 4) the most. There is some perceptible difference between 2 and 3, but considering that the render time jumped from 4 seconds to about 1362 seconds, which is more than 300 times longer, the result is somewhat underwhelming.

This isn't a complaint or anything, just sharing my findings so maybe someone will find them useful. I'm willing to give some pointers with imagemagick as it's mostly a command line tool and some might not be used to that kind of thing.

Phillip

I've used other free image programs that do resizing, including two that I've stuck with, Irfanview and FastStone. I haven't tried imagmagick. It would be interesting and perhaps useful to compare the results from different programs. If you want to share your upr, I could experiment, or if not, try one of my fractals.

Here's the complete thing, it's not a public formula. Feel free to test it on your side. And of course, anyone, feel free to use the formula for whatever if you like it.

It would be interesting to compare the results!

Copy4OfFractal3 {
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}

Testgelände.ufm:testing_example_new {
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}

Sorry for the double post, but I did some more work on this to establish a baseline for comparison. Since I spent several hours in the past weeks testing this stuff, I though people might as well benefit from my obsessive testing, it would be a shame if it went to waste. I might repeat this series with an image that has some thin lines in addition to pixelated areas.

The following code is for a 200x400 pixel section of the previous fractal I use for the comparisons below. The following fractal was used, rendered at 200x400 pixels:

AA_testing {
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}

Testgelände.ufm:sinh_MB_BS_cycling {
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}

Feel free to use this for your own tests.

Below is a rather comprehensive comparison of different render methods:
NOTE: THE FORUM SQUISHES THE IMAGE INTO THE PAGE COLUMN, MAKING THEM SOMEWHAT SMALLER. OPEN THEM IN A SEPARATE TAB TO SEE THE THEM AT 100% SIZE
UF AA Presets:
None, Qucik, Normal, Non-Adaptive

UF AA Custom with Threshold 0.1, Subdivisions 4 (2x2)
Depth of 1, 2, 3, 4

UF AA Custom with Threshold 0.1, Subdivisions 9 (3x3)
Depth of 1, 2, 3, 4

The supersampling section includes more images than are necessary because I wanted to see at which point supersampling stops benefitting from UFs native normal AA:

Supersampling, base image Rendered with AA Off
2x2, 3x3, 4x4, 5x5

6x6, 7x7, 8x8, 12x12

Supersampling, base image rendered with AA Normal
2x2, 3x3, 4x4, 5x5

6x6, 7x7, 8x8, 12x12

Render times for the different methods in seconds:

The render times in this chart range from 0.04 s (A01) to 129.72 s (C04). Activating normal AA increases the render time by a factor of about 9. Not too surprising as it's a very pixelated image and adaptive AA will have to work on a large part of the image, this is further illustrated by non-adaptive AA taking only 20% longer than normal AA.

The custom AA is extremely dependent on the chosen depth and as shown in the images above, higher depth settings do little to improve the quality while inflating the render time beyond any reasonable quality/time ratio. Note that the 129 second render was a 200x400 pixel fractal on a Ryzen 9 3900X!

Manual super-sampling from a non-anti-aliased fractal (i.e. rendering a larger version and then using imagemagic to downscale the image) yields great results starting at around 5x5 SS, beyond that there are little to no visible differences between the images. For most purposes 4x4 will be sufficient. When combining UF's normal AA with manual SS, even 2x2 SS seems to do great, using higher SS together with UF's normal AA doesn't improve the image quality in any way that I could see.

Normal and non-adaptive AA do a similar job in this particular instance, but non-adaptive might pull ahead with thin lines on smooth background (see manual). Custom AA with 4 subdivisions doesn't seem to be worth it for final high quality renders, at 9 subdivisions results are good with a depth of 2, anything higher takes unreasonably long while doing essentially nothing for image quality.

However, due to the missing sharpening done when downscaling with Imagemagick, the colors in high-detail areas look a lot more washed out with all of UF's built in methods. Some people might like the smoother look, for those, the normal AA or custom using 0.1/2/9 will do just fine. It seems that for a rather pixelated fractal, it takes about 12 - 20 times the time of the raw non-anti-aliased fractal's render time to achieve what I would consider a pristine render.

In my opinion, the sweet spot for best image quality in UF alon is either A03 or C02. When willing to use ImageMagick, it is either D03 for most applications and users, or D04 for very picky users. Their render times are as follows:

A03: 0.35 s for users who are OK with the smooth look)
C02: 2.37 s for users who want more detail but not use any 3rd party software
D03: 0.52 s sweet spot for most renders
D04: 0.74 s sweet spot for ultra HQ renders

//edit: As expected, thin lines, especially where they're dense, are even trickier to render. Here's the test fractal:

AA_testing2 {
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}

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;
; Mandelbrot Set.
;
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ifb.ucl:Cuchulain {
;Caracas, Venezuela
;Jan 09 2003
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gnd.ucl:gnd-disk-perlin-noise {
; According to "Disk Plasma" colouring method
; Mark Townsend, June 1st, 2000
; Based on an idea from Earl Hinrich
;
; "Perlin Noise"
; Colouring method by Mark Townsend, Nov 17th, 2000
; Based on original code by Ken Perlin,
; with ideas from Damien M. Jones.
; Slope method according to Damien M. Jones's work.
;
; Gilles Nadeau, April 28th, 2008
;
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}

Again from left to right:
UF built in:
None, normal, non-adaptive, custom (0.1, 2, 9)

Supersampling from UF high-res render, AA off
3x3, 4x4, 6x6, 8x8

Supersampling from UF high-res render, AA normal
2x2, 3x3, 4x4, 12x12 (!)

So it seems that for this image, extreme supersampling is required. The only render I would consider flawless is the bottom left (AA normal, 12x12 supersampling) which is complete overkill for most purposes. But it's the only one where the thin lines aren't translated into moirée or at least some kind of noise.

Thanks for the detailed comparisons! It's on my to-do list to improve the anti-aliasing algorithm for the render to disk feature -- I agree that it can make the image fuzzier than it needs to be. Theoretically it should be better than just upsampling when rendering and downsizing later, but at the moment, it often isn't and that is not what you want.

I also did some testing on Philip's original fractal. A useful experiment is to open a fractal at the size of rendered images. Use pixel as the formula and image from standard.ucl as the coloring. Use two layers with two different renders and Difference as the merge mode.

I found that depth 2 and depth 3 gave the same image, i.e. the result was all black. Depth 4 was not better.

Some have suggested rendering with double or triple the original linear dimensions and normal anti-aliasing, then downsizing. I tried this, downsizing with FastStone image viewer (Lanczos2 filter); it gave slightly better results than the original. The downsized double, triple, and quadruple versions were apparently identical.

I often find that post-processing with slightly increased contrast and/or slight sharpening is better and quicker than custom anti-aliasing. It of course depends on the particular fractal. This seems to be source of the improvement noticed when Philip used imagemagick.

Yes, I'm pretty sure it's the sharpening that is doing the most heavy lifting when it comes to the ultimate improvement in image quality compared to UF's built-in functions. I recently implemented a jitter transform to see if it helps with moiré. It helps a bit but it's tricky to get it right.

Is there a way to access the size of a pixel, i.e. the distance to the pixels nearby, during either transform or fractal calculations? This would greatly help to automatically determine the jitter amount.

Hello again,

I found an older post on this forum that let me access pixel dimensions. Using that I modified a very simple jitter transform that I wrote to try and get rid of heavy moiré in some fractals. High bailout gaussian integer is a prime example for this. The structures that are caused by the very dense and regularly spaced dots can cause moiré effects that span hundreds of pixels, no amount of anti-aliasing will ever get rid of those. Here's an example of a raw render using UF's normal AA:

Here's a comparison using jitter:

I also tested supersampling:
A: Raw UF render, normal AA: native, 4xSS, 16xSS, 64xSS

B: UF render with jitter, normal AA: native, 4xSS, 16xSS, 64xSS

So you see that jitter can help with moiré, but it still adds quite a bit of noise that needs to be dealt with. The good thing is that it doesn't change the render time, so there is no additional cost when going from A to B. I will upload the jitter transform to the public formulas ASAP.

Phillip

That's a good idea, and it could be a built-in rendering option.

Glad you like it! If you're interested, there's a Discord server of fractal artists (not UF only) and there are some people who are really good with graphic programming. They could probably come up with much better version of what I posted here, and they're generally really helpful.

Here's an invite link: https://discord.gg/fSb4gq8e

Just a suggestion, feel free to join or not. Other fractal software devs are hanging out there too, and they're usually not tortured with questions/complains/suggestions.

Most talk is about the art/math/methods, so it's very interesting for someone who's into fractal art. And of course, this is an invitation to anyone else who might read this, too. We always like to see new artists or even just people interested in fractal art.