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The best fractal renderer and editor for Mac is Fractal Architect 3D (available from Mac App Store - https://itunes.apple.com/us/app/fractal-architect-3d/id722452540?mt=12). I have been working as a beta tester of the app and I can say it's the most intuitive fractal app on any platform and certainly one of the most powerful. It's fractal flames done the Mac way!

I have made a series of youtube tutorials that you can watch to check FA3D out.

Overview: youtu.be/hqndE_MJiPg

In depth - Variants editor: youtu.be/yAn23_4MYFc

In depth - random variations settings: youtu.be/wqZ9TDV3Ubg

In depth - working with colors: youtu.be/hwNMav04Cvg

These guys talk a big game about Chaotica being slow (here http://www.fractalarchitect.net/blog/2013/12/rendering-on-the-new-mac-pro/), I wonder if they will ever consider backing up their claims with actual numbers  ;D

I have not tested the compared speed myself, but I don't think that is so interesting. When it comes down to it Fractal Architect is much more user friendly and intuitive and, from what I have seen of it much more powerful. For me it's the fractals that are important, not how many seconds I have to wait. I haven't tested GPU rendering myself since my Mac doesn't support it.

Well, that's funny, because Chaotica isn't the one overselling performance at the expense of image quality! Show me just one high quality image produced with FA, and we have a discussion...

You can take a look at this one. it's 4000x3000 px. I posted three fractals in this set on Google+ today.

https://plus.google.com/u/0/photos?pid=5965706557657110498&oid=113210195985045745953

Resized, recompressed images are not really putting your best foot forward...

I am very keen to do a proper comparison: post a PNG image and the flam3 params, and any rendering information you might want to add. I'll post back a PNG image, with the same.

Are you interested in doing a fair comparison? I'm not about to go through that work just to fuel an argument. I'm sure both Chaotica and Fractal Architect 3D can render high quality fractals. But what's interesting is how inspiring and intuitive it is to work with the apps. I use several different fractal apps myself and I have found that they all have their strong and weak points. In my eye the most inspiring app is Fractal Architect 3D.

I realise the burden isn't yours to bear, but they are the ones essentially calling a Duel, saying "Users of Chaotica will be crying", and then showing up with no pistol and only strong language.

I've asked my star beta tester (which I guess you are for FA), and an expert in Apophysis, to post here about doing a simple comparison. A commercial product making such strong claims should be able to stand up to the most basic scrutiny / fact checking, no?

I believe that blog post was about the new Mac pro and the fact that FA3D use GPU rendering. Not much to make a fuzz about in my eyes. I'll redirect you to Steven Brodhead, who is the programmer of Fractal Architect. I think you guys should be better off being inspired by each other than battle over words.

Well, as user, i would like to see some actual numbers and examples (unfortunately there are no proper examples on the website) before buying a software.

There are examples of fractals. What examples and numbers do you miss? I'm sure it can be arranged.

Hey Lelle.

First, full disclosure: I'm an avid beta tester for Chaotica, but I guess that just puts me and you on the same footing bias-wise.

Second, apologies in advance for what will probably turn out to be a wall of text. I'm a thorough person by nature and I think in paragraphs, not quips. :P

I think part of the issue here is that everyone talks about "high quality" images without ever explaining what exactly they mean by that. To me, high quality means smoothness of anti-aliasing (no jaggies), while retaining an overall sharpness that lets details and textures be seen. These two concerns can be surprisingly difficult to balance! After that, I value an absence of grain, although this of course is partially determined by rendering time and not quite as program-dependent as the aa... but, since grain is occasionally unavoidable or even desirable, we should lastly take into account that some programs just seem to have much more attractive and "natural looking" grain.

With that in mind, the google plus image you've linked does not particularly impress me, sorry to say. The extent of the visible jaggies almost reminds me of a photo that has been oversharpened in photoshop or something like that. The grain in the background, aside from being very prevalent and unsmooth to begin with, just looks... very harsh. I have similar issues with the example images on the fractalarchitect website.

To this I would contrast...

• ...the smoothness of the thin lines and bright edges in works like these: Example 1 (http://fc08.deviantart.net/fs70/f/2013/030/f/0/tripolar_by_zy0rg-d5t9tqh.png) Example 2 (http://fc08.deviantart.net/fs71/f/2013/139/8/9/book_of_moths_by_fardareismai-d65ufwe.png) Example 3 (http://fc06.deviantart.net/fs71/f/2013/199/1/3/the_eyes_of_asclepius_by_fardareismai-d6e10op.png)
• ...the clarity of detail in these: Example 4 (http://fc04.deviantart.net/fs71/f/2013/297/b/7/tech_miracle_by_tatasz-d6rmkpc.png) Example 5 (http://fc00.deviantart.net/fs71/f/2012/342/b/8/coven_in_circles_by_fardareismai-d5neca6.png)
• ...the soft, subtle "photographic" look of the grain in this: Example 6 (http://fc07.deviantart.net/fs71/f/2013/345/f/a/fissure_of_chaos_by_chaosfissure-d6xme9v.jpg)

But, for a more one-to-one comparison we really should use the same params. I think these http://pastebin.com/gEjDxUS4 would be good; they are fairly simple, no plugins needed, etc. But if you want we can also compare with any flam3-compatible params you have.

---

It's not that I think the intuitiveness of the interface is unimportant, but to me, if I can't use that interface to generate a nicely sharp and anti-aliased image, then... the user-friendly UI is almost wasted. I realize this is a personal opinion, and especially if someone is a new user they might not be so fussed about jaggies and grain and whatnot, but my point is that a solid rendering core and high quality image processing is more substantial and fundamental to a fractal renderer than a flashy, "inspiring" interface, especially for a longtime or serious user. It seems to me that newer users are often easily impressed when they can quickly churn out colorful wispy designs, but after years of making fractal art and looking at literally thousands of renders, I am quite inured to hyperbolic claims about "blowing anything else out of the water" which are then followed by the kind of aliased, julian-based, semi-randomly-generated mandalas that I've already seen hundreds of times before.

Far said everything ^^

You know, not just saying the software you test is way better than everything else, but showing concrete examples: renders and more renders, same params all programs =)

I agree with you Far that quality is very important. I have not tested the unlimited version of Chaotica so I can't easily compare the rendering quality between the two. But I don't agree that quality is overshadowing user interface in importance. They are both important to me. If I turn your example around I can just as easily say that the best rendering quality in the world would not be as interesting if the interface did not lend itself to inspiring creative work and discovery.

It's important here to make clear that I'm not coming into fractal making from a mathematic interest side but from an interest in the produced art. When I say that Fractal Architect blows everything else out of the water I'm not talking about astounding rendering quality, I'm talking about astounding user experience. And when it comes to user experience and shear inspiration value, I maintain that Fractal Architect is the best out there. But as I said earlier in this post, every fractal program has its weak and strong points, and there are reasons to use several of them together many times.

As for the quality of the renders, the example I provided was not straight out of FA but post processed in Aperture. I might have overdone the sharpening on that one to suit the medium. I'll be glad to do a comparison render of the file you suggested. If Chaotica turns up the best quality I think we will take that as a reason to make Fractal Architect better, but I will still maintain that the user experience of FA is better. To understand my view of fractal images you can look at this gallery with images I've made with Fractal Architect: https://plus.google.com/u/0/photos/113210195985045745953/albums/5845848728961026337

We all go about making art in different ways, so it's only natural that we will be drawn to different tools to make that art. I think it's important to be inspired by each other to find new ways and revalue old ideas and habits.

Just quoting,  :beer:


Also, FA blog claims that:

We arent talking about user experience, we are talking about speed and image quality, so please dont.

Very bold statements here :-) I had a quick view of one of the videos and must say that I liked the interface from what I saw so far.
But statements like "blowing anything else out of the water" and cites like "Users of ... and JWildfire will be crying" are just distracting me. JWildfire has a very strong and mature user community, I never saw them crying :-) Of course, a GPU renderer can be very fast. But as some people already stated, quality counts first if it comes to fractal art.

So I'm also very interested to see any hard facts :-) The images I saw so far, seem only to be random fractals. Not bad at all, also JWildfire makes heavy use of random fractals, but usually those are no good ressource for comparing rendering results.

Andreas
 

The unlimited (Studio) licence is not required to compare moderate resolution (1.23 megapixel) images, however if you would like to do a comparison I would be happy to provide you with a Chaotica HD licence (up to 4 megapixels). The new 1.5 beta with (basic) motion-blurred animation support, much faster rendering and many user interface improvements is just dying for some testing! :)

Please let me know by email or PM if you're interested. I'll be making a blog post about this soon, too!

I don't think the resolution limit in the free version should get in the way of assessing things like anti-aliasing. But, probably even better are the several hundred finished artworks at http://chaoticafractals.deviantart.com, which should be more than sufficient to give anybody a good idea of what the rendering looks like.


Well... I briefly alluded to this in the last paragraph of my previous post, but I guess I should state more clearly that I don't personally find FA's interface to be all that inspiring. For now I'm only going off of your videos, but it seems to rely far too much on randomization tools. I know that this is very subjective, but pressing "roll dice" and then picking a generated thumbnail out of a group kind of sounds like the opposite of creative work to me. :-\ This isn't to say that randomization is "wrong" or that it shouldn't be in the program; obviously randomization tools can be useful. I just think it's a stretch to call a heavily randomization-based fractal making process "inspiring."

As for "user experience"... man, I understand that parts of chaotica's UI are heavily in development, I'm not really trying to dispute that at all. XD But I think the size and quality of the chaoticafractals gallery is a good sign that the work-in-progress interface isn't holding artists back that much.


Me too, actually. That's actually why I value the render quality so much, because of the effect it has on the "produced art." If I were in this only for the math then I could probably overlook the ugly aliasing, but as an artist, I cannot.

I could probably respond to a lot more stuff, but I will just cut to the main purpose of this comment: my sample render! ;D

(https://dl.dropboxusercontent.com/u/3935350/comparisonrender.png)

I only made one change to the params I linked earlier, which was to lower the Gamma Threshold to 0 (I would have done that before I made the pastebin, but just forgot). Anyway, hopefully you can change that from within Fractal Architect, or if not, just change gamma_threshold="0.02" to gamma_threshold="0.0" in the xml before you import. Last but not least, I just kept the 800x800 size that it was at but I can definitely render a much bigger version if you would like to compare that too.

With Apophysis and JWildfire both free, and with JWildfire giving regular updates, I'm afraid Fractal Architect 3D does not stand a chance and will not even be looked at for $49.95. What I've seen from the program does not justify the price difference.....I'd like to be wrong, but don't think so

Hi Guys,
I am Steve Brodhead Sr. the author of Fractal Architect and Flam4CUDA for Mac.
My son, Steven Brodhead Jr., who is not involved in Fractal Architect development, is the author of Flam4CUDA for Windows which he wrote in 2007.
I am thankful to have such a gifted son to able to become one of the pioneers of CUDA development without any help
(Flam4CUDA for Windows had been one of the first 10 CUDA programs that Nvidia featured on their website way back then.)

In 2008 and 2009, Flam4CUDA for Windows was benchmarked at 100 to 200X faster than flam3, but of course this performance improvement
was totally dependent on the FLOPS capability of the GPUs used and the FLOPS capability of the CPU used for flam3.

What made the speed differential? Its all in the Chaos game algorithm and its total dependence on fast floating point operations and transcendental functions.
If you parallelize the algorithm and do a good renderer implementation, the rendering speed can scream. Performance of the core flame fractal algorithm
scales directly to the power of the GPUs used. And contrary to some claims, the renderer results are exactly the same as on a CPU.

For the EXACT same reason, virtually no one plays 3D games using a CPU software renderer if they have a fast GPU (or GPUs) available.

CPUs and GPUs are different devices with different strengths and weaknesses. But this has been very well documented elsewhere. You might go to anandtech.com and check out their many articles on GPUs, CPUs, CUDA, OpenCL, and of course his most recent review of the new Mac Pro.

I will post much more later today along with the render results.

Well, i understand the chaos game part - lots of mathy people in this thread lol - and all I want are examples and more examples =D
Or maybe a trial version so we can just check it out by ourselves  :beer:

Hi Steve (Sr.), good to see you joining the discussion, hopefully soon with results!

One caveat: please don't selectively reply to my emails - it was nice discussing Chaotica details, but I do ask that you take down the misinformation on your product comparison page, or at least not refer to Chaotica by name with all those inaccuracies. I've taken the time to write you a detailed email with everything that's wrong on the list, and only ask that you stop representing my product on your page however you like. I'm posting this here since you seem to have time to make posts on Fractal Forums now, but I made that request some days ago...

[edit: Thank you, and sorry for mentioning it here unnecessarily I guess.]

"We arent talking about user experience, we are talking about speed and image quality, so please don't."


I have been talking about user experience all along. If you don't want to talk about it it's fine with me, but I will continue to talk about the user experience. I can see that rendering quality and speed is an important issue for the developing team behind Chaotica. It's important to us too, but it's not the only important thing. Let me tell you a bit of the idea behind Fractal Architect 3D.

The core idea behind FA is very customizable randomness. Chaotica and all other fractal apps can make fractals from scratch and edit them with a systems of triangles, or affine transforms as the Chaotica team prefer to call it. So can FA, so there's no difference there. Most fractal app can also make random fractals. But this is where Fractal Architect really differs from the rest. The amount of control over the randomization process goes very deep in FA.

• You can pick your transforms and set a max weight.
• You can set the limits for the transform parameters (from -2000 to 2000 or -0.0005 to 0.0005 or whatever)
• You can set the transforms you want to link (including type, weight, parameters and number)
• You can set final Xforms
• You can set the symmetry
• you can set random Xaos
• You can set the 3D camera parameters

You can also save all of those as a favorit combination, name them, categorize them, rate them, export and import them.

When you find something interesting you can put them in the stash and choose which ones to develop later. When you find something you want to edit you can run it through the variants editor. here you can randomize

• transform weights
• variants weights
• parameters
• Final Xform
• Xaos
• Symmetry
• Brightness and gamma settings
• Camera parameters
• Color gradient
• Color rotation
• Background color
• Color speed
• Triangle movement, rotation and sizes
• Mix ins of extra variations per transforms

All this can be set to very precise amounts. This is no ordinary randomization, it's a very powerful sketching tool. Like a painter sketch his painting with caracole before doing it in oil, the randomization in Fractal Architect lets the user sketch his fractal, before doing the deep editing in the Triangle Editor.

This is the strong point of FA that we are as proud of as the Chaotica team of their rendering quality. If you want to compare the rendering quality wouldn't it be fair to compare the fractal editing and user experience too?

Sorry but:
1. You didnt explain you were talking about experience until people asked to prove it.
2. Experience is very personal thing, as Far mentioned.
3. Speed and quality measures are objective. So we go for objective.

Also, in your comparisons, you only focus on whatever is good for you. Which is biased, and, as a statistician, i can tell you: bias is bad =)
Like not mentioning you were talking ONLY about user experience until we asked for renders. Or forgetting to add AA to the software comparison (basically just listed all the features FA has and didnt mention whatever it doesnt have  :beer:)

About user experience. As it was mentioned many times, its a very personal thing. For instance, your description was quite a major turn down for me =(
I usually fractal having an idea about what each element does. So, first of all, rather than controlled randoming, i prefer controlled experimentation. Because its faster (if you want, for example, to randomize the position of a transform, you can just move it around in the editor) and allows me to change the rules any moment. Plus i can just observe the fractal changing as i move the transform and can choose a perfect position for it. To random something like this I would need to hit randomize button over 9999 times.
Second, I do a few math based stuff, which is entirely not random. Even more, you need to do lots of math to rotate, scale and position everything correctly, and any randomization would insta ruin it. Of course i'm not any close to this guy, take a look at the fine work: http://zy0rg.deviantart.com/art/Octopus-363366336 (http://zy0rg.deviantart.com/art/Octopus-363366336)
Finally, "sketching" sounds like doing lots of work and then ahve to type in all the numbers anyway =D
So see, i just don`t want to make random fractals =) And when i do, i make them in a non random way =)

Also, last but not least, and sorry for caps: TRIANGLES!
Its not that we prefer calling them affine transforms. That thingy you call "triangles" has many uses in mathematics, and also has a name for it. Which is used by people minimally familiar with the underlying math: http://en.wikipedia.org/wiki/Affine_transformation (http://en.wikipedia.org/wiki/Affine_transformation)
Why not triangles?
1. Well, they do have a name after all. It looks kinda like if someone decided to use a word "rectangle" when talking about a computer, for example.
2. It is misleading. One of the most common mistakes new users make is actually thinking that transforms have a trangular shape. Now try creating a Sierpinsky carpet with "triangles". If you call them transformations, it will be way easier to understand and make.

These are the categories that were taken down from my web site. I will post only Fractal Architect's stats here.

I hereby publicly challenge the Chaotica developer to reveal his feature list comparison.

Price                                                                                      $50 FA 3D,    FA Sampler - Free, No Trial period - useable forever
Product Version                                                                       3.1.0
Platforms                                                                                Mac
GPU Rendering Available                                                          Yes
GPU Brands supported                                                             ATI, Nvidia, Intel Iris (HD 4000 & HD 5000)
Render Size License Limit                                                         FA 3D - None,   FA Sampler - 1.23 Megapixels
Render Device Limit                                                                 FA 3D - GPU or CPU,  FA Sampler - CPU
# of Variation types included                                                     FA 3D - 330     FA Sampler - 45
3D Fractals                                                                              FA 3D - Yes      FA Sampler - No
Sub-Flame Support                                                                   No
LayerZ Support                                                                         No
Vector Objects as Flames                                                           No
Custom Variation Architecture                                                    FA 3D - Variation Sets      FA Sampler - only 45 popular variations from Flam3
Max # of Variations Max per Variation Set                                   128 (typically you hit the limit on the next line first)
Max # of Variations and Variation Parameters Per Variation Set     216
# of Variation Sets Viewable and Editable at the Same time          Unlimited  (FA Sampler only its 1)
Pause/Resume Renders - Saveable Render State                          Yes
Progressive Rendering                                                                Yes
Photoshop-Like Color Curves                                                       No
Random Generator                                                                     Yes, See randomization controls below
Random With Control                                                                  Yes
Random Final Transforms and Linked Transforms Available             Yes
Random Favorites (Memorized Settings that are Exportable/Importable)     Yes
Stash                                                                                         FA 3D - Yes,    FA Sampler - No
Variant Editor                                                                              FA 3D - Yes,    FA Sampler - No
Variant Editor Categories                                                             15   See posting below for list of categories
Editor Fractal Image Quality                                                         High - its render quality is a user changeable setting
Editor Fractal Image Size                                                              Small to Large - it can be detached and resized as you like
Triangle Editor                                                                             Yes
Color Gradient Editor                                                                    Yes
Quicklook  (open temporary larger view of a fractal - resize however you want)          Yes
Keyframes                                                                                  FA 3D - Yes,    FA Sampler - No
Create PDF Folio of Keyframes                                                      FA 3D - Yes,    FA Sampler - No
Finder Thumbnails (Finder is the equivalent of Windows Explorer)    Yes
Use PDF Folio or Video for Finder quicklook                                    FA 3D - Yes,    FA Sampler - No
Make Video Animations                                                                FA 3D - Yes with full Motion Blur if desired,    FA Sampler - No
Loop/Morph Video Animation                                                        FA 3D - Yes,    FA Sampler - No
Make Video Animations by Animation Parameters in Triangle Editor  FA 3D - Yes,    FA Sampler - No
Render To File                                                                              Yes
Render to Image File Sequence                                                      FA 3D - Yes,    FA Sampler - No
Convert Image File Sequence to Video                                            FA 3D - Yes,    FA Sampler - No
Splice Videos                                                                                FA 3D - Yes,    FA Sampler - No

Hi Steve,

I'll take that challenge! But before I do, please let me see if I have the current situation straight:

FA claims so far:

• Blows everything else out the water - Thoroughly refuted by 3 parties, unaddressed.
• Faster rendering - Still no evidence, appeal to GPU hype/authority.
• High quality rendering - Still no evidence.
• Push-button randomisation is more "inspiring" than deliberate design - Unaddressed.

It's apparently now time to bear even more burden of proof, even though I'm not the one making empty claims...


Of all the Chaotica features I could list, there is one that I really think FA should answer first:

• Can make decent quality images

By Far's carefully explained image quality criteria, we're still waiting on any evidence at all. I'm not letting this one go- just show one decent quality image that came straight out of FA, params included. I don't believe it's possible, especially if you've just followed the same tired old flam3 rendering recipe from the 90s.

If you think image quality is just the "quality" setting in flam3, as your feature list seems to suggest, then the discussion is best left to the many artists who choose Chaotica over other programs - it's simply because it's the only one that doesn't make ugly renders, and not having ugly renders turns out to be quite important for artists.

It gets even worse when you consider that Chaotica, Apophysis and JWildfire all use double precision rendering, which is very important for chaotic fractal iterations - does FA do this, or do you again sacrifice image quality for speed?

As far as I'm concerned, if a piece of commercial art software is incapable of making decent quality images on its own, it's not really art software is it? Even Apophysis makes far higher quality images, and I've seen better results from JWildfire too; their price is hard to beat, and their performance with CPU rendering (such as Lelle uses exclusively) is far better than FA's by your own measurements.


This inexcusable fact ought to practically end the discussion, though I guess I'll have try looking beyond this fundamental flaw (besides the other bold claims left unaddressed) before finishing some kind of laundry list of features and buttons in the interface, which seems to be what you've delivered and are expecting from me...

Hi Thomas  [possibly private email address removed by moderator]    (lycium) since you have threatened to sue me in this email:

Hi,

I don't expect a reply to the very long mail, but I do ask that you take the misinformation on your comparison page down, otherwise I'll have to look into legal action.

Thanks,


Thomas


I have decided to pursue this discussion at a later date of my choice, when I am able to give this whole discussion proper attention.

I asked you about a week ago simply to remove completely false information from your comparison page, very specifically. I think that's totally fair to ask, just like you might ask me to take incorrect information about your product down from mine if I did that. Instead you edited the table to correct one error, and then left it until posting here today.

While we're posting each other's correspondence, I really am perplexed by this-


If you are so concerned about JWildfire and don't regard FA as a competitor to Chaotica, then why exactly are you guys here throwing all the punches, and then declining to give the hyperbolic claims any substance?

So uh... meanwhile... I've been holding off posting again until Lelle put up the comparison render he mentioned yesterday. Is that still happening? :hmh:

Though, if I'm being honest I have to say I find it a little bit premature to be issuing public challenges when multiple people have asked, starting at post number four, to see an example of FA's best image quality and so far the only response has been a grainy and aliased image... which then turned out to be postprocessed anyway. :-\

Gentlemen.

Maybe you have issued a call to arms before you even know what you are warring over?


It seems to me that this debate should not be public. The awareness of public visibility sometimes does strange things to our reason and our common sense. I think it is not too late to take a step back, to take a deep breath, and get a bit of a distance between your anger and your better self.

Punch a bag if that helps. Call up an old friend and vent if that helps. Run five miles if that helps.

Then consider, both of you, if maybe this whole conversation should start over. Perhaps even with two apologies? Certainly with less publicity.

Thank you for stating that more diplomatically than I could ever have done!

I was debating locking or moving this thread to a hidden section as it was obviously deteriorating to bickering.

I shall remind all involved that in advertising law it is perfectly fine to say "I am The Best!" or "This program beats every other program out there!"  but it is considered slander to say my program is better than {name of some competing specific program}.

So if we could please limit these statements to either specific statistic comparisons or just broad general statements, things would be much less heated.

Thanks.  O0

I think it is generally accepted that advertising consists of lies and disinformation for the biggest part. Objective comparisons based on exchangeable flame seeds is great, but it does indeed overlook the user experience. Which for many artists is a big thing, if you ask me. Problem with GUI's, layout, styles and artists in general is the subjectivity. This is their main tool, like lies are a big tool of advertisers. For me the phrase "done the Mac way" is a big turnoff. For others it will be the hook.

The Big Battle (that's how wars start out, right?) between FA and Chaotica seems to be:

1. User experience
2. Image quality

The first case just ask for lots of user reviews, with all the bias and subjectivity that comes with it. This will easily turn out to be a mud-throwing contest, but it should not. The second ask for objective comparisons out output, based on equal input. Then close-up and diff's, where the subjectivity creeps in again. That OK, as long as we are aware. Keep the game light, don't start the next techwar.

By the way, I love to judge the pics! Bring them on ...  :fiery:

Viewers, we need to make sure your browser is color managed first before you proceed.
This link: http://photographylife.com/is-your-browser-color-managed (http://photographylife.com/is-your-browser-color-managed) will tell you if it is or not.

If its not color managed, this article will tell you which browsers you can use: http://petapixel.com/2012/06/25/is-your-browser-color-managed/ (http://petapixel.com/2012/06/25/is-your-browser-color-managed/)
(Might be out-of-date. I read somewhere that last fall, Chrome had finally become color managed.)

Far, the image you posted did not have a color profile to it, so I used the Mac ColorSync Utility to tag one copy of the image as sRGB and one as AdobeRGB.
Here are the two tagged images:

Far's Chaotica Image tagged with sRGB color profile
(https://dl.dropboxusercontent.com/u/7233470/comparisonrender_sRGBtagged.png)

Far's Chaotica Image tagged with AdobeRGB color profile
(https://dl.dropboxusercontent.com/u/7233470/comparisonrender_AdobeRGBtagged.png)

Viewers, if these two images look the same your browser is definitely NOT color managed and will not show the correct image colors.

The AdobeRGB color profile has a wider color gamut, so the fractal will show more color saturation.
The actual pixels in the file are not changed (no color matching done). The only difference between the files is the attached color profile.
The browser uses the file's attached color profile to know how to interpret the color values in the image.

Flam4CUDA for Mac (I am its author) and all Fractal Architect versions are color managed and ask for the color profile to attach to the
image files it produces. I personally prefer AdobeRGB over sRGB for the richer colors.

All these images produced by Fractal Architect in this post were rendered on this Mac laptop:
Retina Mid 2012  15" Macbook Pro  (laptop) with a Nvidia GeForce GT 650M and i7 CPU with 8 Gb of memory.
The native display resolution of this particular Mac is 2880 x 1800 pixels (its Apple's 15" Retina display).

Fractal Architect 3d version 3.1.2 was used to produce these images.
The current release available today (January 10, 2014) on the Mac App Store is version 3.1.1.
The next post will have commentary on the changes made for version 3.1.2.

Fractal Architect 3D image rendered with this GPU and color profile sRGB.   Render quality 5000. Super Sampling Width: 0.35 pixels Adaptive Gamma: OFF
(http://fractalarchitect.net/Competition/CompetitionFractalGPU_sRGB.png)

Fractal Architect 3D image rendered with this GPU and color profile AdobeRGB.   Render quality 5000. Super Sampling Width: 0.35 pixels Adaptive Gamma: OFF
(http://fractalarchitect.net/Competition/CompetitionFractalGPU_AdobeRGB.png)

Fractal Architect 3D image rendered with Intel i7 CPU and color profile sRGB.   Render quality 5000. Super Sampling Width: 0.35 pixels Adaptive Gamma: OFF
(http://fractalarchitect.net/Competition/CompetitionFractalCPU_sRGB.png)

Fractal Architect 3D has a new render setting called Adaptive Gamma (discussed in next post).

Fractal Architect 3D image rendered with this GPU and color profile sRGB.   Render quality 5000. Super Sampling Width: 0.35 pixels Adaptive Gamma: ON
(http://fractalarchitect.net/Competition/CompetitionFractalAdaptiveGammaGPU_sRGB.png)

There are a number of topics I will discuss.

First: apologies for slow image downloads. Dropbox's upload server seems to be down. https://forums.dropbox.com/topic.php?id=110208
The web server I use is a dog compared to Dropbox. I will change the links to Dropbox when its back up.

Second:

I will only mention one thing about the images: The coloration of portions of the central orange orb.

Fractal Architect 3D corrects for clipping of the RGB color channels for each pixel when the Fractal Histogram is converted to an RGB image.
Scott Draves, the inventor of Flame Fractals, wrote this excellent article on the effect of clipped RGB colors: https://code.google.com/p/flam3/wiki/HighlightPower (https://code.google.com/p/flam3/wiki/HighlightPower)


I suspect that the Chaotica renderer used a small Highlight Power setting for this fractal rendering. (This is a hunch, but let me show you why.)

Fractal Architect has a built in Histogram viewer that shows the state of the histogram and contains a lot of useful image. It gives the overall Histogram statistics and allows you to inspect each pixel in the histogram (the red X). It also shows the place in the histogram with the most hits (the blue X).

Its a monochromatic image with black pixels having zero hits and white having the highest hits.

(http://fractalarchitect.net/Competition/Histogram.png)

Note the biggest color discrepancy between Chaotica and FA in the color orb is at points in the histogram having very high number of hits.
For example, the pixel at the red X had 202,880 hits compared to the mean hits per pixel of 3025 hits per pixel.

More to follow...

Adaptive Gamma

If you study the mathematic logic used by all flame fractals renderers today, there are in fact two erroneous assumptions in the math formula
used to convert a specific pixel's histogram value to the final pixel's RGBA color value.

Those incorrect assumptions are:

1)  100% of the points in the renderer point pool are retained by the fractal and hit the histogram.
2)  Every point in the point pool is 100% fused.

For example, for the competition fractal the retained fraction is only 30% - not 100%. (See Histogram stats shown in histogram view)
That means that the calculated gamma value used to convert the histogram to the RGBA color value is incorrect.

The main effect of this error on the image is that the output image will be dimmer than it should be and color saturation be lower.
You can manually compensate for this error by just tweaking the Gamma value of course.

Fractal Architect 3D has a new optional Adaptive Gamma on/off setting. If turned on, FA will correct the gamma value for the retained point fraction and fused
fraction. The last image in the images post above was produced with Adaptive Gamma turned on.
Note the improved tonal range, brightness, and color saturation.

Of course, you could fiddle with the Gamma setting too to achieve the same affect. Adaptive Gamma just gets you a lot closer to the ideal image without you having to play with the Gamma value.


Anti-Aliasing

Fractal Architect (all versions), Flam4CUDA for both Mac and PC uses a Gaussian Dither algorithm to achieve anti-aliasing.
Its only setting is called Super Sample Width whose units are in pixels. A good default value is 0.35 pixel.

That was the setting used in the FA images shown above.

Fractal Architect does not support Flam3 Super Sampling where you render the image to twice the size of the desired image size and have the renderer produce an image that is 1/2 the internal rendered size.

You can still do this manually in Fractal Architect by rendering to twice the desired size and by using a Photo or Image editor to reduce the final image to the desired size.



Open Source Fractal Architect OpenCL Rendering Engine

The Fractal Architect 3D OpenCL rendering engine kernels are Open Source and are licensed under GPLv3 just like Apophysis.
The kernel templates and the entire variation library source code is included in the Application bundle downloaded from the Mac App Store.
The actual OpenCL kernel source code used to build each variation set are found in the app's Application Support directory.

Being open source, it can be used by any open source flame fractal project as an alternate renderer. (Though it may take a bit of work to do.)
Other open source projects can embed the source code into their own projects and customize it as they wish.
My only request is that they call this alternate renderer the Fractal Architect Rendering Engine in their documentation and About window.
This is just a personal request - its not mandatory.

Being licensed under GPLv3, the license is Irrevocable which means I can't change my mind in the future. It is yours forever.

Later this year, I plan to create an Open Source project for a demonstration basic reference renderer that will run on
Windows, Mac, and Linux. It will be able to read Apophysis, Flam3, JWildfire, and Chaotica fractal files. It will render images to any size.
Since it will be based on the Fractal Architect OpenCL Rendering Engine, it will run on any OpenCL compliant GPU and CPU.
It will be the exact same rendering engine that the Fractal Architect 3D app uses.

Being a small working renderer, I hope the simple reference implementation will encourage other open source projects to adopt the rendering engine.

Andreas, you have created some exciting new ways to combine and layer fractals in JWildfire. I would like to work with you, if you wish, to get the FA alternate renderer fully capable of supporting your new innovations. I would love to see JWildfire crank out fractals on good hardware.

Viewers please look at the awesome images Andreas' innovations make possible: https://plus.google.com/communities/118391398023168606746


Fractal Architect 3D version 3.1.1

This render competition turned out to be a great assist to the FA rendering engine by exposing previously unknown render bugs.

We found 2 serious rendering issues in version 3.1.0, which is the must recent update on the Mac App Store:

1) There was a rendering artifact surrounding the central orange orb when rendering on the Nvidia GT 650M GPU.
    My son correctly diagnosed the problem as a Full Warp vs Half Warp granularity issue that allowed a race condition in the point pool.
    Fixed!! Thank you Steven.

2) The CPU renderer did not show the rendering artifact. Instead, the problem for CPU rendering only occurred when
 a fractal had both a Final Xform and one or more transparent  normal Xforms,  the transparent Xforms would be visible in the rendered image.
 (The GPU render did not have this problem.)
   Fixed!

The effect of these renderer changes on the ATI GPU families and Intel HD Iris GPUs has not been tested yet.
I will get this tested and released later this week. Of course, Apple has to take its testing & review whack at the app too before you can get
it from the Mac App Store. So in 10 days or so, you will have the renderer fixes in the upcoming update.



.

Pencil Thin Lines Anti-Aliased

To achieve thin - thin lines that are anti-aliased, its easy.
Render to 1600 x 1600. Reduce the image size to 800 x 800. Here I used Acorn with Lanczos scaling. No other changes made with Acorn.

Fractal Architect 3D image rendered with GPU and color profile AdobeRGB.  Render quality 5000.
2x Supersampling     Super Sampling Width: 0.35 pixels Adaptive Gamma: ON
(https://dl.dropboxusercontent.com/u/7233470/CompetitionFractalAG2XLanczos.png)

Find the Tiles Contest

When rendering on an old 2009 GPU with 256 Mb of GPU memory, you might find that you only have 60 Mb of video ram available.
(The 2012 Macbook Pro I have been using has 1024 Mb of GPU memory by the way.)

Time to tile !!

OK some people say tiles are bad and make for poor images.
I intend to disprove that and you will help me.

This 1600x1600 image has more than 1 tile.

Send an email to me by going to http://fractalarchitect.net (http://fractalarchitect.net) and click on the Contact Me link at the bottom of the page.
In the email tell me how many render tiles were used to create this image.

The first 15 people that can tell me the correct number of tiles in this image will get a Mac App Store Promo code that will let you download
Fractal Architect 3D for free!

The contest closes on January 21, 2014 or after 15 people tell me the correct number of tiles - which ever occurs first.
The correct number of tiles and a histogram showing the number of entries for each tile count will be posted afterward.

Have fun!

(https://dl.dropboxusercontent.com/u/7233470/CompetitionFractalAG2XTiled.png)

In your example you attached an Adobe RGB profile to an existing image without any profile (thus assumed to be sRGB in browsers). This will make the image look different, but on most platforms it will just increase the contrast and clip the color values when converting to sRGB. A typical monitor is pretty close to the sRGB gamut.

Instead, test if you can see any difference between this sRGB PNG (made from a screenshot):
http://blog.hvidtfeldts.net/media/sRGB-gimp-with-profile.png

And your Adobe RGB tagged image:
https://dl.dropboxusercontent.com/u/7233470/comparisonrender_AdobeRGBtagged.png

The situation may be different for prints on wider gamut monitors and printers, but even there is some discussion whether it is worth it: http://www.kenrockwell.com/tech/adobe-rgb.htm

Hi, I'm responding here, because I don't know what messaging-platform you use otherwise (and your site currently seems to be down), feel free to contact me per personal message or e-mail to discuss this further.

Regarding the discussion: very interesting, but I think too many topics inside of one thread. I would suggest to create a new category "Fractal Architect" and create one thread per topic.

Best regards,
Andreas

Hi. 

Many people dislike and distrust posts in a forum requesting people send an email.  It's a common tactic of spammers and other shady characters to harvest email addresses.

I suggest everybody just post their replies here rather than use an email.

And to prove I practice what I preach, my guess is - 206!

No ...  wait.

That's my age.

I'd guess 4 tiles, as the image is not big enough to justify any more.

Will this software run on OSX 10.5?

I refuse to upgrade past that as most of my favorite programs don't work on 10.6 or higher.

It doesn't really matter as my macbook is down anyhow and I'm too broke to get it fixed, but if I ever do get the money, I'll fix the one I have before getting a new one  O0


The site being down is another great reason to just post here!

I noticed a lot of crowding of the recent posts page from this thread too - I think I may merge a bunch of double and triple posts by the same person consecutively.  Does anybody else think this program deserves it's own sub-forum?  It may not have the staying power to justify that, but it is generating a lot of discussion!

I'm trying to post some images, but I can't fit them within the allowed attachment size. I've rendered them to png. What do you prefer, change to a compressed format or lowering the size? Or maybe better to put them on another site and just link to them?

Put them on another site and just link to them.  Or embed them with the [img] tag.

Many people don't click outside links to see the images, but embedding works fine.

Attachments are not intended for images except for illustrating minor points.  They are mostly for parameter files and other non image content.

256 tiles  ;D (I don't have a Mac so feel free to give my prize to whoever wants it  :dink:)

Hi Steven, thanks for those lengthy writeups, very informative.

I have a quick question. I don't have a mac, so I've been playing with flam4cuda on Windows, gotten from here:

http://sourceforge.net/p/flam4/code/HEAD/tree/

I wanted to know if that code is the most up to date, and if it's what's used in FA? It renders images to file, but always seems to crash. Either way, I've been examining the code and would be interested in contacting you further on it. What is the best place to reach you for that? Thanks.

as a quick oppinion, the rendered image seems very blurry, which isn't good since one would want the lines to be sharp and contrasting with the blurry blobs. Wonder if you could render it with sharper AA.

No need to guess; I turned off highlight power entirely for my render. Being unsure what highlight power options FA had, I decided to go with the most basic/"raw" option of just not using it.

But I'm honestly not that concerned about exact color-matching; it is understood that different renderers will probably handle tonemapping slightly differently. And anyway, in practice, most chaotica users use the curves to drastically alter the colors of the render anyway, so a slight saturation difference between FA and Chaotica's renders is basically a non-issue to me.


This, however, is a much bigger deal. Having to render larger and downsample in a separate image processing problem just to get adequate clarity and fineness of details? No, this is something a fractal renderer should definitely be able to do out of the box!


Uh, actually, apophysis has accounted for this for as long as I can remember (I've been using the program for nearly ten years). I don't think it is implemented quite the same as your adaptive gamma, but the end result is that there is no loss of brightness when, e.g, zooming a fractal in:

(https://dl.dropboxusercontent.com/u/3935350/apo%20zoomed%20out.png) (https://dl.dropboxusercontent.com/u/3935350/apo%20zoomed%20in.png)

The zoom was the only thing changed between these renders; I did not have to manually edit the brightness or gamma.

I'm not sure what you mean when you say "Every point in the point pool is 100% fused." My understanding of this term is that the "fuse" consists of some initial iterations that are not displayed. So, either an iteration is part of this fuse and is discarded, or it is not part of the fuse, and it is displayed. It is a binary off/on thing; it wouldn't make sense to say an iteration was "20% fused" or whatever.

So, what I think you're getting at is that other renderers don't account for the discarded iterations when they are determining brightness, but I could be wrong because the phrasing was very unclear to me.

Also, I am skeptical that your "points retained" measurement is accurate. Chaotica also measures this (it calls it "efficiency") but it is giving a value of about 72%! It is possible there are some differences in, say, how many iterations are being discarded due to being in the fuse, but I would be surprised if the effect on the efficiency was THAT drastic. I would have to do some more investigation to come to a firm conclusion on what exactly is going on here... However, I will say that having designed the parameters in question, I think that 30% efficiency is probably low, considering how sparse the samples outside the frame are and the sheer density of hits on those thin, bright lines.

Re: tiled renders, I think a better question is how big the render has to be before tiling is a necessity. To get a rough idea of the values involved, I did a quick test and found that chaotica could go up to approximately 5000x5000 pixels (with a little bit of supersampling) or 6700x6700 pixels (with supersampling turned off entirely) while staying under a GB of RAM. Now, I am unsure how closely these values would translate over to rendering on a GPU... but it is a nice starting point to gauge where exactly the "tile threshold" is in the first place. I've rendered a lot of print-res images and never needed to use tiles; of course, I wasn't dealing with the memory restrictions of a GPU but I also didn't have much of an issue with the speed of the print renders either. So, to me, while tiles can be handy in some situations, more often they are just more trouble than they are worth.

Another potential factor, for truly huge renders, is: when does the speed penalty of needing to render multiple tiles due to limited GPU memory outweigh the speed increase from using the GPU? I don't even have an estimate for how big you'd have to render before using all your available memory to render one big tile on a CPU would be just as fast as rendering many tiles in sequence on a GPU but it is certainly interesting to think about!

---



Anyway, this has been a long post going over many topics. When it comes to the original issue of image quality in renders, the crux of this post is that I do not think a fractal renderer should rely on outside programs (even if it is "just" a resize) to achieve clarity of detail and avoid blurriness. :-\ I already have to do this when I use Ultra Fractal... I'm glad I don't have to do it for IFS too. Unfortunately, while the renders you posted are the best FA renders I've seen so far, I still find the slight blurriness of the aa and reliance on postwork for thin lines to be a barrier to truly stellar image quality. I also was not particularly fond of the look of the grain in the "thin" regions (like the orange spots just to the inside of the curve in the bottom right hand corner) although admittedly that is both subjective and subtle.

(http://Flam4CUDA for Windows)

I love Pharmagician's (on deviant art.com) term for many open source projects:  AbandonedWare

Flam4CUDA for Windows and Flam4Cuda for Mac are officially: AbandonedWare

No one is maintaining or enhancing those projects at the moment. You can look at the project page on SourceForge
and see that it has been a long time since either me or my son have worked on those projects. If you would like to work on that project I would be happy to
get you in contact with my son as he is the project administrator. Please send me a personal email with your contact info and I will pass it in turn to my son.

Flam4CUDA for Windows was written when CUDA version 1 and 2 were the current versions. Now its at version 6. There has been a LOT of changes of the CUDA runtime API which is most likely why Flam4CUDA for Windows crashes on a version 6 runtime. I vaguely remember having to make changes in
Fractal Architect 2 when either CUDA 4 or CUDA 5 was released (due to CUDA runtime API changes).
If you think you do want to work on the project, I would be happy to tell you what I had to change by looking back in my project's source code history.

(http://Xaos Support on these older GPU accelerated Renderers)
Flam4CUDA (both platforms), Fractal Architect 2 OpenCL (older version of FA) renderers do not support Xaos.
Xaos is a table of conditional probability weights to be applied each iteration of the algorithm. Google for Apophysis and Xaos for many articles on the topic.

Fractal Architect version 3 and 3D do support Xaos. (The free version of Fractal Architect is a version 3 product but does not offer 3D fractal variation support.)

To get Xaos support, you must modify the CUDA kernels to support a different point pool design. My son and I call this "single point pool vs multiple point pools".

Thanks for the info Steve, I appreciate it.

Tataz,
the issue you are talking about boils down to how all digital representations of mathematically continuous values (often loosely called "analog" values)
introduce a small amount of error that engineers and designers try very hard to make "invisible".

Mathematically, on this particular fractal, the thin line curves in fact have "zero" width and are similar to the Dirac Delta function used in theoretical physics, engineering, and mathematics. To see, this zoom in by 2x and re-render again. Do this multiple times. The width of the line will always be 1 single pixel wide regardless of how far you have zoomed into the picture.

The pixel layout of the histogram determines which pixels intersect the lines and which do not. Those pixels will be assigned a "hit" and will contribute to the final histogram used to create the fractal image.

Anti-aliasing is a processing step to eliminate the jagged appearance of a continuous curve on a finite resolution display. (if the resolution of your display is high enough - you can't see the jaggies at all at normal viewing distances. That's why Apple makes such a big deal about their "Retina" displays)

Anti-aliasing can be done at the histogram construction step or later when converting the histogram values to the final image (or both).

One very important side-effect of the core Chaos IFS algorithm that Scott Draves invented, is that you dont "know" where those lines are inside the render. You can only "infer" their position by the hits collected on the histogram. This is a very well researched field under the term "Statistical Sampling". At the level of a single pixel, there is significant aliasing error created by digitizing a continuous input function. But at normal viewing distances with a large enough grid resolution, this statistical sampling error vanishes to an invisibly slight noise - otherwise this would be a useless technology to create images with.

Anti-aliasing takes the individual pixel values and effectively "smears" the jagged line of pixels by smearing the luminosity of neighboring pixels across each other so the human eye sees a smoother curve. The side effect of this is that the line's apparent width increases.

The Fractal Architect renderer adds dithering noise to the image to reduce the appearance of aliasing. This totally counter-intuitive step
works quite well and is the "key" secret ingredient used by audio engineers to improve the the final mastering quality of audio CD's, DVD's, etc.
They add very low levels of almost inaudible random noise to a recording which actually makes the recording sound more like an analog recording.

So the width of curve 1 pixel wide will be increased to most likely 2 pixels approximately. If the renderer "knew" where the lines were it could reduce the anti-aliasing width increase to a small fractional increase over the original 1 pixel wide line.

There is a very important fundamental theorem called the Nyquist Sampling Theorem, which enters into play here too.

So how do renderers produce anti-aliased lines that are 1 pixel wide? They use super-sampling where by the image is rendered larger than required and anti-aliased at that higher resolution. Then you simply use image size reduction to get the final required image size. With 2X Supersampling, the 2 pixel wide anti-aliased lines are reduced to 1 pixel wide.

The problem with Supersampling is that it is very computationally expensive e.g. for 2X Supersampling, the render would take 4X as long to render.
Because of that performance penalty most exhibition renders don't use it, unless they want to display 1 pixel wide anti-aliased lines.

Supersampling has been around a long time. Its a Flam3 rendering parameter and that renderer dates back a decade or more to its origins.

Its easy to do supersampling with Fractal Architect too if you wish. (See post above)

Dude, you have got to stop explaining things that are common knowledge as if you are the only one here that knows about them. It comes across really condescending.

Tatasz is currently pursuing a Master's Degree in statistics; when you tell her things like "This is a very well researched field under the term 'Statistical Sampling'" and "There is a very important fundamental theorem called the Nyquist Sampling Theorem" it just makes you look like a buffoon. How would you feel if I came up to you and went, "Now, this is the mouse, you can use it to click icons and control the computer..."? I don't expect you to know the full details of anybody's background but you can reasonably assume that the people in this thread are plenty tech-literate and math-literate already. You don't have to explain basic things. If we are unclear on something you are talking about, we'll just ask.

So basically tata knows full well why your lines are a bit fuzzy; what she's saying is essentially what I said: the lack of oversampling and need to do it in an outside program is a problem.

Hiya!

Well, I am a statistician and studied lots of math, and i know well what AA is, and also about some possible implementations.
Your render is excessively blurry. Also, i've seen a few comments from your beta tester stating that the images he shared were postworked to sharpen them. This leads me to conclude that its a generic characteristic.
While some blur is not always bad, at some situations, we artists may want a sharp, very sharp, render.

I feel semi-obliged to jump in here with a "me too" and mention that Glare Technologies' main software product is not Chaotica but Indigo Renderer (http://www.indigorenderer.com/), which is all about physics and statistics. Chaotica is the relaxing easy stuff to do after a day's work on real monte carlo methods :tongue1:

So yes it might be a bit premature to be pointing the audience ("viewers!") at wikipedia  ;D

Edit: Also, even after all this talk and explanation, the folks at Orbit Trap took the opportunity to completely miss the point in a mini-review (http://orbittrap.ca/?p=5274) of Chaotica!  :beer:

Far - some replies:

Percent retained:  Calculate the total number of iterations across all pixels. Call this TOTAL. Sum up the hits on the histogram. Call this HITS.
Percent retained = HITS / TOTAL

I have no idea what the Chaotica efficiency value indicates.

FA tracks the iteration history of every single point in the point pools. A point is not recorded on the histogram unless its iteration count is greater than the Fuse threshold. If due to the formula calculations, a point value becomes either Infinite (INF) or NAN, it is discarded and replaced with another random point, whose iteration count is reset to zero. That new point will not be recorded on the histogram until its iteration count exceeds the Fuse threshold.

I have also experimented with not replacing the points, and you end up with a much "thinner" histogram. The approach in current renderer seems to work better than the pure discard approach.

Fuse artifacts look like a fuzzy square pillow centered on your fractal.

Fuse % is the percent of all points in the point pool whose iteration count < Fuse threshold at the completion of the render.

I don't think I am the first person doing this stuff inside the core render kernels.
This is not Rocket Science. (Odd joke expression - since I am an ex-Rocket Scientist)

Tiling ====
Flam4CUDA for Windows was developed on a gaming PC with multiple top-of-the-line graphic cards (back in 2007/2008).

Porting it to the Mac in 2009 revealed:
1) It needed to be scaleable down to work as well with thumbnail sized images as well as it worked with large images.
2) It needed to work well with with the modest Nvidia laptop GPUs on the 2009 Macbook Pro and their 256 Mb of Vram.
    (Of which > 100mb would have been filled by the Operating system's textures after a fresh reboot.)
3) It needed to not hog the CPU processor, so you could surf the web while doing a big render, etc.

For item 2, the answer was tiling. The point I made in the contest post, was that tiling is for all practical purposes: invisible.
See for yourself! If they are so bad, then tell how many tiles you see and where they are !!!
So far no one has given the correct answer.

Would someone care to comment on how many tiles were used to render the Avatar movie to the Imax 5k resolution ??? (I don't know the answer.)

There are two minor features which are in FA that are mostly for the developer's benefit and not the fractal artist.
1) You can force it to tile even when there is plenty of memory available. (You could use this to prevent FA from grabbing Vram needed by other programs.)
2) You have a Histogram viewer - which was built so I could see the histogram. It's useful for determining when to stop a render, when all areas in the fractal
     have adequate hits to eliminate noise in low density regions.

When is Tiling necessary =====

    // Note: formula for amount of memory is: 3 Mb  +  (36 * area / 1048576) Mb
    // or  max area is: (X - 3)*1048576/36 with X in Mb units
    //
    // so for 35 Mb total, the max area is: 932,068 pixels squared or about 1000x932 pixels
    // so for 45 Mb total, the max area is: 1,223,338 or about 1280x956  pixels
    // so for 90 Mb total, the max area is: 2,534,059 or about 2560x956 pixels
    // 1440x900 => 47.49 Mb, 1366x768 = 38.02 Mb, 1920x1280 = 86.375 Mb

So for 5000x5000, we need 858.3 Mb of Vram to render the image without needing to tile it.
My 2012 Macbook Pro has 1024 Mb of Vram.

The Mac Pro I have on order has 6144 Mb of Vram on each GPU.  It will be able to render an image
13,373 x 13373 without tiling.

In 2014, 2 Gb of Vram on a desktop GPU is commonplace.

It looks like our data structures used in the renderer are approximately the same size based on the numbers in your post.

Tiling Performance Cost ====
Lets say you have a 5000 x 5000 final image size. An 8 pixel overlap is needed to split this into two tiles. This will require two separate renders
of 2508X5000.
This is the same as a single render of 5016x5000. So the performance penalty is 0.32% which is totally negligible.

For larger images, the performance penalty percentage decreases exponentially.

Tataz,
I am sorry. I had no idea what your education background or course of study was.

I was trying to summarize Statistical Sampling basics (and not very well I guess) for someone that has had absolutely no exposure
to Statistics. Its hard to do in a few paragraphs.

My own educational background is:
BS Chemical Engineering LSU - Magna Cum Laude - Top of Chemical Engineering class
Almost MS Electrical Engineering U of Texas Austin (I was transferred to a city far, far away by my employer and could not complete the degree in absentia.)
MBA concentration in Finance from University of Chicago. Graduated top 7%.
University of Chicago is widely recognized as the top university in the world for both Economics and Finance and has been for many decades.
See: http://www.uchicago.edu/about/accolades/22/

I received a good education. I am not a statistician. I am sure you know way more than I do about that field of study.
Its used heavily in the fields of Economics and Finance as I am sure you are well aware.

There are many people smarter than myself. I don't know and can't know everything.
My son knows way more about rendering and computer graphics algorithm than I do. He is smarter than I am for sure.

And I do wish you luck in the profession of your choice. Its an exciting world out there and there is so much to learn.
Learning is a life long process and won't stop after you leave graduate school.

Who knows? Maybe you will be authoring the next big Statistics textbooks!

I concede that Supersampling needs to be supported in Fractal Architect, even though it is easy to do it yourself outside the product.
I will add Highlight power as a render parameter, just like Flam3. It is effectively set to a value of 1 right now.

As often happens, I awoke after a nap with fresh insights on AA (anti-aliasing). Combining an edge detection step with the anti-aliasing
might be a better way and may make costly supersampling unnecessary (maybe).
A quick Google search reveals I am not the only person who has thought of this. So in the coming weeks I will be experimenting with different anti-aliasing algorithms and lets just see what pops out!

Other experiments:
1) See affect on performance from using Chaotica's approach to making any variation type usable as a pre or post variation.
2) Provide an alternate kernel for fractal rendering where Xaos is not used. This should provide a good performance increase.
3) Revisit density estimation and see if this can be improved.
4) Drop the separate pre-fuse step and incorporate fusing it into the main render loop. This should help the problematic Intel OpenCL compiler handle
 bigger variation sets. Where the OpenCL compiles for the Intel CPU take a fraction of a second, compiles for the Intel Iris GPUs take over 2 minutes.
(What's going on Intel/Apple ??) I suspect the compiler is inlining the big IterateLoop with all the variation formulas in it.
5) Figure out how to do some of the recent JWidlfire innovations on this renderer.

Apple released the bug fixes for Fractal Architect 3D as version 3.1.1 today.

The revised render performances for this version is posted here:  http://www.fractalforums.com/index.php?topic=18257.0
These render performance represent Apple laptop render speeds - not what a high end desktop can do.

Conclusion:
Just like for video gaming, it pays to get the best discrete GPU from either Nvidia or AMD.
In 2013, the Intel Iris integrated (HD 5000) GPUs are substantially slower for flame fractal rendering than a good discrete GPU from Nvidia or AMD.

Both the AMD and Nvidia GPUs beat the render times of their paired Intel i7 quad core CPUs by a factor of 3.6X (or 260%) - a whopping performance advantage.

These were measured on stock Macbook Pro's from 2011 and 2012.

There were 7 tiles in the contest image. No one reported the correct number of tiles.

If you can't find the tiles in a rendered image, there can't be a quality issue from tiling.

The software allows you to restrict the amount of memory used to render an image, thus forcing tiling to occur.
It is a feature that is a handy tiling testing tool, but not really very useful for users - unless you want to run some other program
that needs a good amount of GPU video RAM.