Thursday, December 28, 2006

The Shoulders of Giants

Note: This began as a reply to Tina Oloyede's "Whose Picture Is It Anyway?" post. It got longer than a reply comment ought to be and perhaps wandered a bit afield, so I decided to make it its own post. And it's not directed at Tina specifically any more, except for a little bit at the end.

We stand upon the shoulders of giants.

When creating fractal art with a program like Ultra Fractal, there are many layers of giants on whose shoulders we stand. We use formulas, which are in many cases not just mathematical formulas, but algorithms, programs written by other hard-working people. These formulas run in Ultra Fractal, written by the hard-working Frederik Slijkerman. Ultra Fractal was written with Delphi, a commercial product, the labor of many people. Delphi runs on Windows, a gargantuan product written by hordes of Microsoft serfs (many of whom are bright and creative people). Windows runs on PCs with x86-compatible processors, the work of legions of chip designers for AMD or Intel (or others). These processors operate in motherboards that are the products of still more dedicated engineers.

You can carry the chain back as far as you like, and extend the principle to other fractal tools. The basic concept is the same: when you make a tool, and you share that tool with others, you don't own what they create with it (unless you've specifically indicated so in your license, which would be incredibly crass and is seldom done).

This is different from a derivative work. A derivative work is where you start with someone else's product and produce a similar type of product. For example, if I took someone else's tool and, rather than use the tool as intended to create something, I change the tool. That would be a derivative work and may infringe on a copyright. (It depends on the tool's license.)

Of course I don't think Tina was asking a legal question, and that's good, because I Am Not A Lawyer and This Is Not Legal Advice. Rather, I think Tina was asking a more complex question. I sometimes think in terms of "strong" and "weak" formulas and tools.

A "strong" tool is one whose effects are so powerful, so distinctive that, to those who are familiar with the tool, its use is indelibly etched into the work. In UF terms, this would be particularly obvious algorithms (Triangle Inequality Average, anything with fBm in it, etc.) At the next level it would include tools like Apophysis. Things so distinctive that it's hard to create with them without it looking similar to other things created with that tool.

"Weak" tools are just the opposite; they leave plenty of room for the artist's own style to show through, because their own specific traits are less blatant.

The interesting thing is that although I have named my tool categories based on their obviousness in the products of those tools, if you were to name them based on the tools' flexibility and capability the labels would be flipped. A "strong" tool in the obviousness sense is a "weak" tool in the flexibility sense. So really, "weak" tools can be much better, because you have so much more freedom. Of course, this does mean they take more time to learn.

Where it gets really tricky is where an artist's style is based on a strong tool. This is what we ask of artists: that they be creative. The more "strong" tools an artist uses, the more their style comes from their tools, rather than their choices in using those tools. Is the artist really expressing themselves? Or just pushing buttons until they get something pretty? Is it the artist, or the tool? (This is very much what Tina was getting at.)

We have this angst, as fractal artists. Some of us have had experiences where, once we describe what we do, people get in a huff and say, "well any chimp can do that!" I've personally been called out on this during a presentation I was giving on fractal art. So sometimes we are very insistent that fractal art is art. But there will always be people who think that, because we do it with a computer, we are not really being creative, and this is an idle pursuit. That we are dilettantes, dabblers, not really artists. This would not bother us if we didn't have a little sliver of doubt within us, or if we couldn't point to plenty of people for whom those labels apply (and who do not seem to be bothered by it like we are). Are we really artists? Will there be a fractal Renoir, or Picasso, or da Vinci? Will any of this be remembered in twenty years? Fifty? Two hundred?

This is our elephant in the room. We feel that sometimes our tools make things too easy. We want to be visually distinct from each other. But we all use the same tools. So we're afraid that an outsider will look at our work and think it is all the same. That we really didn't contribute much. And we're afraid that maybe they're right. Because most famous artists didn't make six hundred images in ten years. The fact that we can produce so much suggests that perhaps we didn't put as much of ourselves into it as we ought.

My suggested cure is not very complicated.

  1. Approach "strong" tools with caution. Use them judiciously. Overusing them is a crutch, an easy fix. If your style depends largely on tools someone else has created, broaden your reach. Try something new.
  2. Prefer more generalized tools, that leave you room to express your own style. If you develop your own style that is distinct from the "normal" things your tools do, you will know that it is you who is in charge, not your tool-maker. This has the added benefit of giving your more confidence in what you're doing.
  3. The best fractal artists are those who know enough about their tools to be able to imitate the styles of other artists. If they can do that, then you know that they are making choices about how their art looks because they can, not because it's all they know how to do. Practice doing this. It is a very educational, confidence-building, and skill-building exercise.
  4. Spend lots of time with each image. This is something I am still learning to do. Don't let an image out until it's really ready. Filter, filter, filter. Keep all that bad stuff; hard drive space is cheap and parameters are compact. Look at your old stuff from time to time to remind yourself how far you've come. Periodically rework an old image that you didn't feel was quite done. Over time your standards will go up and your "productivity" will go down. That's OK. Great art is seldom made in five minutes.

If fractal artists want fractal art to be taken seriously as art, then above all what we need to prove is that fractal art is the expression of artists, not the default representation of basic mathematics. So, master your tools and force them to express what you want.

Specific reply for Tina: the images shown clearly bear the traits of the tools used. And yet they also show your style. Tool-makers love to see their tools used; that's the point of sharing the tool in the first place. But the best, most satisfying thing for me as a tool-maker is always when someone uses the tool to do something new that I never thought of.


Blogger David Makin said...

Just thought I'd make a slightly contrary point about strong tools - leaving "toolmarks" is sometimes a good idea especially if overall the image is not defined by the tool used but echoes of its use are left for the observant. I'm not well versed in the history of Art but I believe leaving such toolmarks is not without precedant.
Also thinking about the colouring formulas available in Ultrafractal (for example) I don't know which tools I'd actually call "weak" !
In addition any can be made weak simply by adjusting the relative effects of the layers on the final product so there's no need to be afraid of using tools you perceive as "strong".

12/28/2006 9:54 PM

Blogger aartika said...

Damien - thank you for your eloquent thoughts and advice on this subject :-)

12/29/2006 10:08 AM

Anonymous Anonymous said...


To some degree, toolmarks are inevitable; after all, we are creating art with fractals, which themselves will impose their own marks on our works. I think what I'm getting at is more like when one or just a few repeated features seem to dominate an artist's style with little variation. For example, if I found a gallery of fifty Phoenix spirals all colored with TIA, I think I might be inclined to question the artist's creativity.

Certainly it's possible to use TIA in a weakened way. Actually, Janet once challenged me to use a Lake transform creatively. I wish I could remember where that image went. I don't think I was successful, but it was an interesting challenge. And I do have a very popular (exhibited) image from years ago done with TIA that doesn't look like TIA. That's one of the reasons I like it; it's something different from the normal. But if I'd made ten images with the same coloring, it would've been less interesting. (It's Banded Clouds in case you were wondering.)

Many of the "distinctive" coloring formulas in UF are "strong" precisely because they're distinctive. It's the generic ones that are so flexible that can be put to many uses. Experience helps you identify specific options used within the formulas, even. I'd love to have a generic formula assembly system where I could re-use parts, but that would require years of software development.


12/29/2006 12:27 PM

Anonymous Anonymous said...

The idea of appropriation has always been a fuzzy one. Where would Warhol be, where would Rauschenberg be, if not for appropriation? And let's not forget Pollock, who apparently tapped into these mysteries before Mandelbrot. It is the similacra at work with digital tools to reproduce what has already been reproduced, though as fractal manipulators, we seek to call forth things that the world has not seen before, and may or may not care about their generational reproduction. It is interesting that Baudrillard in The Conspiracy of Art looks at a singular time when he stumbles on a moment with nature, and sees [the chaotic world of the fractal as possibly] the one place where true art may reside today. It's just great to be building on such legacies, and, as you note, in addition to the software creators who frequently go unnoticed while making the tools available for those of us who desire or receive recognition.


12/29/2006 6:22 PM

Blogger David Makin said...

This comment has been removed by a blog administrator.

12/29/2006 9:24 PM

Blogger David Makin said...

I follow and I agree wholeheartedly with your point regarding an artist whose work appears "formulaic" - I think this is one of the stumbling blocks with trying to develop a style - it's easy to slip into a formulaic method and it's why I deliberately don't try to cultivate a style myself - any recognisable style in my work thus being completely subconscious.

"I'd love to have a generic formula assembly system where I could re-use parts, but that would require years of software development."

I'm hoping Frederik may get around to something like that, for now we can use layering to put different parts together.

I think I managed to use the lake transform most creatively (of my own works) in "Leap of Faith"

12/29/2006 9:30 PM

Anonymous Anonymous said...

The music world doesn't seem to frown on bands being "influenced" by those that came before, as long as it's not "too close". I finally heard the song that My Sweet Lord was reckoned to be a steal from and apart from the bridge, I wouldn't have said it was "too close". However, IIRC, "the judge did not agree and he told him so-oh-oh-oh".

@steve, the Rauschenberg and Baudrillard were new to me. Thx.

12/31/2006 1:21 PM

Blogger Keith said...

I think that it's important to look at your viewers. Most viewers who are outside of the fractal world will not know the difference between a weak or strong tool. That concept only applies to people who know how to build fractals. Is it important to impress them? Maybe a little, but it's more important to get the attention of outsiders.

For example, let's look at the images the you, Janet and Kerry provided for that article. One was an IFS Mandelbrot, both pretty strong considering that IFS has become the fractal poster child through Apophysis. There was a glyph, an fbm and an orbit trap - all fairly strong in my opinion. That article and the images that you provided made me proud to be a fractal artist. I don't think that the average reader reacted with a, "damn, there's another fbm image". I'm sure that they were impressed.

The Fractal Universe calendar is another example. It's full of strong stuff. My 2 cover images, years ago, were TIA. There is always someone on the inside of the community complaining about the quality of the images in the calendar, probably because of its "strongness", but yet the publisher continues to publish it. It sells.

The thing is, with a limited number of tools and a lot of people using them, everything eventually becomes strong.

IFS images made with Apophysis are the strongest of them all. I really am sick of all of the flames that are appearing on the community sites, but at the same time, Apophysis is doing a better job educating people about fractals than any tool ever has.

I don't think that the art of fractals has evolved to the point where we need to be concerned about something being over used or too recognizable. Most of the people who are concerned about creativity are on the inside. They're us and who cares what we think? We need to be focused on our viewers - our customers. I know, that contradicts the notion of building what makes you happy, but if you are happy with a randomly generated image that was made with a strong tool and your viewers are too, then everyone is happy. Right?

1/01/2007 1:51 PM

Anonymous Anonymous said...


I agree that anyone who has not seen enough of a tool to identify it as "strong" will not recognize it. That doesn't mean there are no strong tools. If you can look at a large number of images and still not decisively say "this image uses this particular tool X" then X is not a strong tool. It is versatile enough to adapt to each person's style. But arguing over this point is not productive.

What I really want to respond to is your statement, "it's more important to get the attention of outsiders." I want fractal art to be well-represented, by which I mean I want what people think of when they think of "fractal art" to be the good, high-quality stuff. Years ago, if anyone knew about fractals at all, they thought of psychedlic, rainbow-colored banded spiral shapes. Now, that is not so prevalent.

The article--and I assume you mean this article--contains several pictures. When I was asked for images, I chose several specifically designed to cover a lot of territory, rather than just a few. (I don't know how Kerry and Janet decided on their images. I didn't even know who else had been contacted.) The two images of mine used are Mandelbrot+fBm and Mandelbrot. Kerry's "Warm Glow" is a Buddhabrot, which is not an IFS at all. Janet's "Tapestri" is popcorn-based. I didn't see any glyph.

As for IFS becoming "the fractal poster child through Apophysis," I think that is just your perception based on the communities you frequent on the net. Apophysis images are extraordinarily difficult to produce as prints larger than 20" or so. I have tried twice, for two exhibitions, and the render times were absurd. This contributes to the lack of exhibited Apophysis images, which other than the net is what people will end up perceiving fractal art to be. (*Technical note: as long as the image fits in RAM, render time is basically linear with respect to number of pixels. Once you run out of memory, though, it is linear with respect to the number of pixels squared, so when you double the width and height, you increase render time not by 4x, but by 16x. Over the weekend I figured out what kind of machine I'd need to be able to render 8000x6000 flames in a more reasonable time frame, and it checked in at about $4K, not including the modification time needed to flam3 or Apophysis to make it work.)

The Fractal Universe calendar that you mention is an interesting case, but I would be careful about drawing conclusions based on it. Avalanche has been publishing this calendar for many years; I remember when Rollo Silver was the one artist in it. Since Avalanche foots the bill for printing the calendar, and eats those costs if the calendar doesn't sell, they are averse to risking that investment. They have a formula that they know works, so they stick to that formula year after year. The editors know which images Avalanche likes, and while they submit a good selection, Avalanche makes the final picks. And that is why, year after year, what you see in the Fractal Universe calendar is basically the same kind of thing: brightly-colored images with a high spiral content. I'm not saying this to put down anyone (neither editors nor artists) as they are providing what Avalanche wants, and Avalanche is selling to their target market. Shelf space for calendars is competitive, so it is not as if Avalanche can afford to produce ten different calendars and have them all do well; they choose what they think will be most profitable for them. This is not the same as choosing the best art, unless you equate "best" with "most profitable."

You said, "I really am sick of all of the flames that are appearing on the community sites, but at the same time, Apophysis is doing a better job educating people about fractals than any tool ever has." Well, I'm going to both agree and disagree. I agree that seeing so many postings of Apo random batch results is pretty sickening. It's great that people are having fun, and are sharing their enthusiasm with others. I get sick of it because so much of it is dreck. If it were all good stuff I might feel otherwise.

But I disagree that Apo has done a good job educating people about fractal art. Flame fractals predate Apophysis (Draves' flame implementation, QSflame, and KPT FraxFlame all spring to mind) so it is Apo's low barrier to entry that makes it popular. Anyone can download it and produce a random batch of a hundred flames; they pick one that looks good, and feel like they're getting somewhere. Other fractal tools aren't nearly as easy to come to terms with. This is a well-established pattern with software; tools with the fewest options are easiest to learn, but put a cap on what can be produced. Powerful tools are the hardest to learn but the possibilities are almost unbounded. Paul Carlson's Mind-Boggling Fractals, when it was available, also introduced a lot of people to fractals, but it was fairly restrictive in its choices. The difference is that MBF introduced concepts that apply to other fractal programs and types. Apophysis and flames are... flames. I think that flames, while interesting, are at the moment a bit of a dead end fractal-wise. So Apo introduces people to flames, not fractals, and making the transition out is not so easy.

You say, "I don't think that the art of fractals has evolved to the point where we need to be concerned about something being over used or too recognizable." Well, that is a matter of opinion. I would suggest that, instead, there is perhaps a trend that (in my opinion, worth whatever you suppose) should be avoided. Far easier to say now, "let's be careful of that," than to travel down that road for some distance and realize we are off-course. And you say, "if you are happy with a randomly generated image that was made with a strong tool and your viewers are too, then everyone is happy. Right?" I say, "it's not that simple." When you post something on the net, everyone can be your audience. When you exhibit, everyone (insiders or not) can see. We can either choose to be typecast (and, given enough exposure, people will start to see patterns, even if they don't know the names for them) or we can choose to show the breadth and diversity that fractal art can really offer.

Repetition or diversity. It's our choice.


1/02/2007 11:06 AM

Blogger Keith said...


After thinking this through a little more I have to say that I agree with you.

I keep wanting to compare fractals to photography. Everyone has a camera and thousands of random pictures are being snapped daily but photography still makes good art. The comparison doesn't work because photography is well established and fractal art is not.

My flop really flipped after I thought about the fine arts show at the fair that I was in last fall. I wasn't too impressed with the image that won first place. I wanted to say that the judges needed to be educated about fractal art so that they knew a good computer picture when they saw one. Then it hit me: One of my images was a TIA and the other had a Julia with a point trap. Maybe those judges weren't so uneducated after all. They might have seen my stuff before and thought that the computer did all of the work. It's hard to say what really happened.

We have talked about Rykk's popularity before. It's possible that he is popular because he followed your suggestions and showed real creativity.

About Apophysis and flames and fractals: I dare you to get on the apo list and say that flames are not fractals. ;-) Seriously, the trouble with apo is that it is free and easy, and its popularity is going to continue to increase. As this happens, "flame" = "fractal" more and more. I'm not sure why that matters but I am pretty sure that in the future the general public with think fractal when they see a flame.


1/03/2007 3:55 PM

Blogger Michael said...


I render a lot of large flames with apophysis. My usual render setting are 8100 x 5400 with 2X OS, quality 4000. Usually takes between 14 and 16 hours. I don't know what you consider a reasonable render time, but i saved over $2K. This size takes about 2669 MB to render in one slice, which i have no problem with. Unfortunately the jump up to 8000 x 6000 is too much. I have a feeling that if i upgrade to a 64 bit windows, and the rest of my memory becomes addressable, then it should work, but i'm yet to see. It could be an apophysis problem too.

I understand what you mean with flames not being fractals. So many flames are a disgrace to fractals - not because i don't find them pleasing to look at (for there must be room for beginners) - but because long time apophysis users gawk over them again and again. This is what leads to content flamers and ugly online fractal galleries. But flames are changing. And a few people are making impressive flame fractals.

1/04/2007 4:35 AM

Blogger Damien Jones said...


The images I was rendering had fairly high quality settings, else they wouldn't render properly--they were very diffuse images. I had render times in the two-week range. I've done UF fractals with longer render times but at least there I can split up the work between PCs automatically; with flames the algorithm simply doesn't lend itself to this, and because of the RAM consumption the computer is nowhere near as usable for other things during the render. (In the DOS days when I used FractInt to render very large images, I often had this problem; tying up the computer for days on end was not pleasant.)

As for flames not being fractals: I never said that. What did say sums up to two points: 1. learning how to use and create flame fractals does not translate easily to non-flame fractals because many of the concepts are different; 2. flame fractals are, at the moment, a dead-end. (Lack of arbitrary transformation formulas locking you into the pre-built transformations is a major blocking point; not being able to render high-resolution flames is another.)


1/05/2007 8:47 AM

Blogger David Makin said...

> not being able to render high-resolution flames is another

I don't suppose anyone has any ideas how to get #hits type colouring values when rendering IFS using the inverse (escape-time) method ?
If there was some way to do so then it should be possible to render flame type fractals with render times and memory use comparable to that of normal escape-time fractals.

1/05/2007 12:23 PM

Blogger Damien Jones said...


The problem with using the escape-time method is that your transforms overlap, and in any situation where that happens, you have to follow both paths. Of course as soon as you hit another overlap, you have to fork again, so pretty quickly you end up with a lot of forks. It may be doable, but it certainly wouldn't be straightforward.

The other issue is that this may not adapt well to the flame coloring algorithm, which isn't just based on the number of hits, but rather a drifting index into the gradient and accumulating RGB values. I'm not sure I want to try to think about a way to make that happen. (smile)

I did recently see an article about using a clever algorithm to accelerate Buddhabrot rendering by selecting samples from the main set that impact the pixels in the view window; it's funny because I saw it shortly after discussing real-time Buddhabrot rendering with demoscene programmers at ICM, and at the time they concluded it couldn't be done. This might be adaptable in some fashion to flame rendering, but probably only for zoomed flames (which take a lot more time to render than unzoomed flames).


1/05/2007 2:50 PM

Blogger David Makin said...


My beta "RIFS" formula includes an escape-time algorithm that does go down all paths (at least up to the point where a path is no longer on the fractal).
For example it renders Barnsley's fern around 3* slower than using the chaos game or deterministic methods which may not sound that great except that the time is still comparable to that for "normal" escape-time fractals and you can render it at any size without problems.

1/07/2007 6:35 AM

Blogger David Makin said...

For anyone who's wondering where the beta IFS formula for Ultrafractal is, you can get it here.

1/12/2007 6:44 AM


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