I'm not dancing here tonight

Also I've been listening to a fair amount of Tom Waits lately.

Carnival Lights

Accordion and calliope

Still thinking about the intersection of archaic and modern, wondering how the mathematical regularity of computed pattern relates to earlier forms of art and artifact. While I was out of town this past weekend, I spent some time in a store full of interesting antique furniture and salvaged things. They had a couple of small toy theater sets, for puppets or maybe marionettes, made of crumbling cardboard and decorated in the style of Italian opera: beautiful Commedia dell'Arte designs.

I love those kinds of things, all crammed full of more florid unnecessary ornamentation than the entire twentieth century ever produced. And it's that quality that appeals to me about fractals, too. If I were a better (and more patient) draftsman, I would make drawings or paintings in that style, but fractals are the medium I'm good at, and in which I have enough experience and practice to make my ideas manifest.

So this one is about old theater, and also some kinds of current theater. It's about brilliant silk and layers of lace and bright paint and striped socks. It's about making the surroundings at least as worthy of attention as the spectacle they enclose. And it's also about the resources I have right now, in the year 2009, that allow me to put together an image using precise calculation, so that every piece is exactly where it belongs. The composition is one of the two that I think of as being most typically fractal: the "One Big Spiral" motif. (The other one is of course the minibrot, which is arguably as classic a theme as the still life with flowers.)

The Old and the New



Perhaps I can think of fractals as being similar to an instrument, such as an accordion. Even if most of the general public thinks of an accordion only in terms of Lawrence Welk oompah, it can also be used for anything from tango to zydeco to Michael Jackson parody. And fractals, likewise, are capable of a much wider range than they're usually given credit for.

Something old, something new

I've just come home after a weekend trip to go to my cousin's wedding. It was quite good, as these things go, and besides the usual festivities it was a chance to see one of my favorite uncles. This particular uncle is one of the coolest people I know (although it's true that I'm a really introverted geeky person, and therefore my ideas about 'cool' are probably suspect). He lives in a house of some historical significance, which he keeps in immaculate condition. He collects Japanese prints and other art. He spends some of his time building and restoring things like harpsichords and antique clocks.

My uncle thinks fractals are incredibly stupid.

I am somewhat distressed by this, but it's understandable. He's lived in Silicon Valley since he was at Stanford in (I think) the mid-'70s. He was therefore perfectly placed to be right in the middle of the grooviest, most psychedelic, overwhelming onslaught of fractals that ever happened anywhere. He's a guy who really understands about beautifully-crafted things that have been made by skilled human hands, and is quite rightly suspicious about crude bright show-offy art spit out of a computer.

So I find myself wondering, would it be at all possible to interest someone like my uncle in the kinds of pictures I've been making? Or is it simply foolish of me to even consider it? For that matter, I'm still struggling to reconcile my own fondness for archaic mechanical technologies (like letterpress printing) with my continuing interest in all this pixelated mathematics.

It has given me some new, possibly difficult things to think about. Who is my audience, really? What might they like, besides fractals?

Here's a spiral with Spirograph patterns. It's either festively pensive, or pensively festive, and it suits my present mood.

untitled [traditional spirograph julia]

Little & fiddly as eXtreme sport

I've spent the last couple of days looking at the incredibly detailed images made by Dan Wills, and trying (with only minimal success) to make some similar ones of my own. I haven't really done much exploring of the inside areas of fractals before now, and I'm finding them both fascinating and frustrating.

So far, I've had the best luck with the PhoenixDoubleNova formula. When the inside is colored with exponential smoothing, it makes a mass of gritty particles, in which can be distinguished vague mandelbrot-ish shapes and other color zoning. Adjusting the maximum iterations seems to change how much shape is visible through the speckly stuff. Trying to zoom in on interesting shapes is a little like blundering around in a sandstorm.

Like so.



Which would be no fun at all, except that when the fractal is rendered and anti-aliased, an amazing amount of tiny detail appears. Any fractal has an infinite amount of detail, of course, because that's what makes it a fractal. But with these nova-style inside images, the mind-bending infinitude is really there, present in a way that I find very compelling.

Even after anti-aliasing, enough texture remains that the pictures seem a little like grainy photographs—they don't have that perfectly-clean smoothness that many computer-generated things have. And every one of those little specks of color-shift is another infinite stack of interlocking spirals, all in perfect array.

Skywatching



This is a kind of thing I'd love to see printed big (BIG! Four or five or ten feet across kind of big), because its visual effect would change drastically when it was viewed at various distances. From far away, you'd get the overall effect of the colors and shapes in the composition, from medium-far it would be textured and complex, and from right up close your entire field of view would be full of tiny repeating shapes that reflected the larger whole. A perfect illustration of what fractals are all about.

Remember the time you said you'd give me a dollar?

Okay, this one is definitely a Bennie. Although you'd have to zoom in a bit to see the minibrot in the middle.



In theory, this series should be worth an infinite amount of money, right?

Unnatural uses for plane tilings

Oh, say. I've just realized that Samuel Monnier's wallpaper tiling plug-in can be used as a trap shape. This means there are an overwhelming number of texturing things I need to try doing. Here's a simple honeycomb background, as a first quick test.

Hive



(How did I manage to not figure out about doing this months ago? There are places I definitely could have used it. Time to re-work some old parameters, probably.)

Timelines and epicycles

Today's image is (a) directly stolen from the Spirograph instruction book I used to have, back in the day; (b) a companion piece to this one; (c) ludicrously slow to render.

A Modern Universe (for the City of the Future)



The pure-white background is disconcerting for me to look at. I rarely make anything so undiluted. But I wanted it to reflect the clean white sleek look of Modern design. All it needs is a bit of really geometric sans-serif type, a single word maybe, placed so as to provide the maximum amount of dynamic balance.

I very much want to make a big print of this one. The pattern-doubling repetitions around the minibrots are amazingly intricate, and would probably be worth examining more closely.

Still playing

This seems likely to turn into an actual series of related images, all sepia-toned and vignetted to indicate historic something-or-other. Or at least with suggestions of paper underlying the patterns.

Scribblings of My Misspent Youth



I've been thinking for some time about the question of whether or not fractals are really abstract. They're obviously not the same thing as a picture of, say, a person, or a still-life with fruit, but they're not just arbitrarily-placed colors and forms. Strictly speaking, I suppose a fractal is a graph of numerical data, a perfectly accurate picture of information. It's abstract the way a weather map or a stock chart is abstract—and arguably none of these things are abstract at all, being representations of real things. (Are pure numbers real? That's a still more difficult question, to which I suspect the answer is mu.)

But with the addition of the Spirograph patterns, I'm illustrating something more concrete: one of the more important influences of my childhood. And so the series of hypotrochoid fractals takes on all sorts of connotations. It's about nostalgia, and trying to recapture the good bits of one's own life. It's about how children learn the world, and find that complexity is hidden even in the things given to them as trivial toys. And it's about the tendency of adults to consistently, patronizingly, underestimate the intelligence of anyone under five feet tall.

Playing

Last night, quite late, I finally took a few deep breaths and gave myself a quick pep talk, and uploaded my first Ultra Fractal coloring method to the official database. It even has a handy help file or reference guide.

Probably, for someone who's a programmer, writing a coloring algorithm isn't too much of a big deal. But I'm definitely not a programmer, and so this feels like an accomplishment to me. It works, and it does exactly what I want it to do, and it didn't exist until I made it. Somehow that's more satisfying than any of the art I've made in the last five years. (I'm not sure how much that's also to do with the important fact that it wasn't for school.)

I've been messing with versions of this coloring method for years, off and on, and so to a certain extent I've been using it all this time, but when I was working on the help file I realized that I had never really tried making anything that referred specifically back to the Spirograph that had inspired it. So for a couple of days now I've been making pictures that make me feel like I'm a kid with a bunch of plastic gears and multicolored ballpoint pens. It makes me laugh to realize how little my aesthetic approach has changed since I was about seven years old. But at the same time, it all fits in beautifully with the things I was doing at the end of my last year of school: art inspired by games and toys, which had in turn been inspired by math. Tangrams. Sculptures with superballs. Vending machines full of word permutations (which the Professor assures me is a branch of mathematics called "combinatorics").

It is weirdly satisfying to be able to recreate the particular Spirograph that I always used to think of as "the hard one," and not worry about whether the pen was going to slip just as I finished drawing the next-to-last loop.

Nostalgia



On the other hand, I really liked my collection of different-colored pens. I wonder if my mom still has my old Spirograph stashed in her attic somewhere.

Alternating or direct currency

As a matter of fact, it probably is all about the Pentiums. Although I haven't been keeping track; there's probably some much better/cooler/geekier kind of processor available by now. Bah, and I can't even say this is a Benoit and call it a Bennie, because it's actually a Julia. Oh well.

Now that this is rendered, I'm wondering if it needs some kind of a border.

untitled [illegal tender]

Early scientific psychedelia is the best kind

I've just discovered the animations of one John Whitney, who built an amazing analog computer and used it to make moving geometric patterns. When digital computers started to become available, he used those as well.

Of the movies I've seen so far, I think Permutations is my favorite. It looks like it's made of hypocycloids, which is exactly what I've been tinkering with myself, all summer, so it has a pleasing familiarity. I'm making a mental note that I need to start learning how to make animations. And also a quick sketch, because those are more easily remembered than mental notes.

untitled [after John Whitney]

Dull statistical analysis!

This is my antidote to too much art-making: I wasted half a day writing down data about the 2007 Fractal Art Contest, and did a little bit of number-crunching.

The first thing I found was that it's nearly impossible to accurately figure out which fractal-generating program has been used to make which image. There are certain kinds of effects that seem typical of Ultra Fractal, and Xenodream is pretty recognizable because it makes 3-D things (but then what about POV-Ray and other raytracers?), and flames might be Apophysis or they might be any one of half-a-dozen other options. It's entirely possible that there are people out there who are writing their own custom code, which isn't available to the public at all. No information at all is provided with the entry images, so if bias is going to be introduced on the basis of which program was used, the judges are all going to have to be clairvoyant so they can know which pictures to be biased in favor of.

So my statistics are highly speculative, and are based purely on guesswork and my own familiarity with the programs in question.

Out of 344 total entries, I found anywhere from 175 to 244 that looked like they could have been made with Ultra Fractal. Apophysis and other flames accounted for 51 images. 8 pictures looked like Xenodream, leaving 41 unidentifiable. There were a handful that could have been made in Fractint, and a few that had coloring I associate with the Tiera-Zon/Sterlingware/Flarium family of programs. Several appeared to have been made or significantly altered in some other graphics program, like Photoshop.

Total Entries
Ultra Fractal 71%
Apophysis 15%
Xenodream 2%
Other 12%

There were 15 winning entries, of which (again, guessing) 10 were Ultra Fractal, 3 were Apophysis, and 2 were Xenodream.

Winners
Ultra Fractal 67%
Apophysis 20%
Xenodream 13%

Possible conclusions:

1. There is no way to be sure of which program was used, short of contacting all the entrants individually and pestering them for information.
2. Winning spots are being stolen from users of less-popular fractal generators because of bias in favor of Apo and XD!!!1!
3. All the images are being made in UF, because it's flexible enough to imitate all competing programs.
4. Actually, the numbers look pretty normal, and there's no reason to suspect major bias or conspiracy or anything like that.

Free bonus conclusion:
Possibly, the people who have paid money for their fractal generators are more motivated to learn how to use them to make pleasing and effective images, such as might win contests. The more casual user, who downloads a free program and doesn't use it as often, has less experience and therefore is less likely to make a really impressive image. Better tools don't guarantee better results, but they do make some aspects of the process easier. I know for an absolute fact that I would have given up on fractal art years ago if I hadn't had access to UF's precise color controls.

Free bonus fruitcake conclusion:
If you think there's bias against non-UF images, you should see the bias against anything with mirror or kaleidoscopic symmetry. Seriously. It's crazy, man.