Thursday, December 31, 2009

Running out of oughts

We've made it to the end of another year; time to fill the air with showers of confetti and sparks. The blue moon is already up there, quietly taking care of itself.

Blue New

It's amazing to think that's it's going to be 2010 tomorrow. When I was a kid, the idea of a year with a 2 at the beginning of it seemed impossibly far away, some kind of fantastic science-fictional future. Now that we've had ten of them, the future has become the present, and an awful lot of it is disappointingly ordinary. But then I have to remind myself that I can type things that appear on a magical glowing screen, and push a button, and then people on the other side of the world can see them more or less instantly. And if I want to, I can carry around a thing smaller than my hand, that lets me access the world's largest and most random reference library. That's pretty awesome.

Monday, December 28, 2009

Turn the crank

This is a small offshoot of a project I'm working on: a distraction which turned out to be quite nice on its own.

untitled [mecha-noir]

Friday, December 25, 2009

Silent night

It's been a beautiful clear day, not really cold enough to be icy, but with that perfect winter clarity of light. I love how quiet and deserted the city is on holidays: empty streets, empty parking lots, strange but restful stillness in every direction.

untitled [winterurban]

Merry Christmas to the internet, and to the internet a good night.

Saturday, December 19, 2009

Happily, the snow is on the other coast

Oof, I seem to have abandoned fractals lately in favor of typesetting, furniture-moving, and hibernation. This is always my least-productive time of year. I'll be awfully happy once we get past the solstice and the light starts to increase again.

Here is a picture made during some weather that seemed especially dark and inexorable.

Event Horizon

Friday, December 11, 2009


Finally, with some help from my able assistant (who knows how to talk to the terminal window) I've gotten the process working, and put a large zoomable fractal online. If this one seems to work out all right, and doesn't give my web host trouble, I'll do some more.

Rusting Dragon

This was one of my contest entries. I like the metallic texture that becomes visible when the picture is magnified, and I also like the sort of hunched, brooding quality of the thing. It reminds me both of the shipping cranes down in the industrial end of town, and of my cat, when she's tensely coiled and watching pigeons. Motionless, but with the sense that it might do something if you turned your back and didn't watch it too closely. Or that it's only standing still because it's been there for an enormously long time, in all sorts of weather, and all its gears and pulleys have corroded and fused themselves into immobility.

Here we are again

Home again, to all my favorite domestic conveniences. Here is a picture in honor of our beloved Coffee Engine (although strictly speaking, it refers equally well to tea, chocolate, or even cola).

Dark Stimulant

I'm completely torn between Pittsburgh and Seattle lately. Pittsburgh is where I grew up; it has wonderful decaying-industrial architecture, rents seem ridiculously low, and many of my favorite people live there. Seattle, on the other hand, has a huge amount of delicious local food, a lovely temperate climate (only it's cold lately!), and plants that don't make me sneeze & itch for ten months out of the year. Now that I'm done with school, it's my big chance to decide where I want to end up establishing myself, and I can't decide where I want to be. Somewhere else entirely, perhaps.

Friday, December 4, 2009


All is madness and chaos. I'm slinging a couple of quick pictures onto the internet before I leave town. Man, I mostly can't stand holidays in their usual overwhelming & commercial form, but that doesn't stop me making pictures of them.

Evergreen Holiday
Aluminum Holiday

Fortunately, this upcoming trip isn't actually for the holiday. So I'll be able to get home and go back into hiding before the full onslaught hits.

Friday, November 27, 2009

Great works of art and the miserable books about them

Oh man, this horrible book. I keep wishing I could somehow just sum it up in a couple of pithy, brief paragraphs, but so far it hasn't worked. And the more energy I spend thinking about it, the less I bother to make pictures, so that it threatens to cut off my productivity altogether. (Although it has also gotten me away from the computer for a bit, so maybe that's not so bad.)

Wednesday, November 18, 2009

No bulbs, just flat

Wow, I've finally finished reading Great Works of Art and What Makes Them Great. By the end it was more like skimming than reading, and even more like picking through a sticky heap of chicken entrails in hopes of reading someone's fortune. An unpleasant bunch of prose, especially when taken in large continuous doses. I definitely have one more installment to write about the book, but I'm taking a break from it for now.

There seems to be all sorts of excitement lately about the Mandelbulb formula. Lots of interesting pictures to look at. I tried one of the formulas myself, but my computer is way too old and slow for me to do any reasonable exploring. The eighth-power bulb pictures did make me curious about what an eighth-power regular old-fashioned Mandelbrot would be like, and since I've never done much messing with higher-power Mandelbrots I thought I'd have a look.

They're less immediately satisfying to zoom into the the standard power-two image. They're so dense with little seven-lobed minibrots that there's practically no room for them to develop the intricate patterns that you usually see. But by zooming fairly deeply, some interesting forms do appear.

untitled [mandel^8]

Thursday, November 12, 2009

Anarchy reigns in the world of art today*

After four semesters of art history classes, one of the biggest questions I had was "Wait a minute, what exactly was such a big deal about Modernism anyway?" We had looked at a fair number of the better-known Impressionist paintings, and proceeded from there through Matisse and Mondrian and Picasso and the usual famous names, and it all seemed like just a bunch of familiar, slightly dull stuff. More dates to memorize. The teacher was telling us that it was really earth-shaking and revolutionary, but since I'd been seeing these paintings reproduced on a million coffee mugs and tote bags and umbrellas my whole life, that didn't make any sense to me at all.

(Good heavens, the ludicrous verbosity of the book I've been reading seems to have rubbed off a bit. Let me see if I can put this behind a cut.)

Tuesday, November 10, 2009


I've finally had a chance to take a better look at the contest, and I find that I'm left feeling a little bit let down or disappointed. Not with any individual image, necessarily (although as several people have pointed out, a couple of them aren't even really fractal), but that this year's selections seem to be heavily weighted toward texture-fields and minimalism.

"So, which one was your favorite?"

"Oh, I liked that one that was textured all over, mostly orange and white, with just a little blue."

"Yeah, that was my favorite too. We'd better make sure it gets printed."

The thing is, out of twenty-five winners, do there really need to be three that fit this description?

With the more minimal ones, I mostly just wonder what advantage there is in printing them very large, since there's not particularly any new detail to be revealed. Graphically, they will no doubt be quite effective, but they seem to ignore the specific potential of fractals to be full of interesting surprises when magnified.

It's all gotten me started thinking about the strengths and weaknesses of fractals as a medium, and why I like them, which seems to be maybe different than why other people like them, and what the implications are for my own future work and the fractal-art world in general. It's too much for me to process! And it's all mixed up with a book I'm reading lately, written in the early 1920s and intended to explain why Modernism was (a) degenerate & evil and (b) doomed to be quickly forgotten. There seem to be some possible historical parallels, but I suspect it's going to take me some time to sort them out.

Still, it does reinforce my idea that it would be really good if there were more fractal events than just this occasional big contest. I'm beginning to wonder if I might be able to organize some kind of small-scale thing. It's an intimidating thought.

Saturday, November 7, 2009

Less grit, more dissolve

One more, the same flavor.

untitled [glowing phoenix]

And the contest results have been posted, so there's a big pile of new pictures to look at. Hooray!

I really do wish there were more fractal events. Not huge major contests, necessarily, but some kind of regular checking-in kind of thing. I'm not sure what format I would want it to have; the main thing is that I like when there are a whole bunch of new pictures to look at all at once, and I would be glad if it happened more often. Every so often I go look at the fractal section at DeviantArt, but it's not sorted out very well, and I get tired of wading through all the anime sketches on scanned notebook paper. And I hate the site's graphic design, so I don't go there very often in any case.

Thursday, November 5, 2009

Hard gritty rainbows

I think a large part of the fascination with these grainy inside fractals is how difficult I find them. The Mandelbrot set, by now, is quite familiar: I've explored it very thoroughly, and learned a lot about how its patterns fit into each other. I know it well enough that I can fairly reliably navigate to any kind of pattern I decide to look for. With coloring methods, too, many of them have become familiar enough to be very precisely controlled, which is what allows me to make those literal, illustrative images that I still can't decide whether I like or not.

But these Nova insides are unknown territory, strange and foggy, and (at least so far) nearly impossible to get a grip on. Patterns stack up on top of each other, sliding in and out of focus as the maxiter changes. It's clear that they're following some kind of deeply-structured logic, but so far I haven't been able to understand it well enough to predict what it might do in any given spot.

So working with them is hard. And it turns out that I've been somehow craving something hard, something frustrating, something impossible to understand quickly. Maybe it's because I'm free of school. School was horrible in a whole bunch of ways, but it did at least give me a fair amount of hard stuff to bash at.

I have conversations with the Professor sometimes, usually around exam time, when his students are complaining bitterly that things are too hard. And I sympathize, except that when I'm only doing easy things, it's as though I can feel my brain cells shriveling up. Doing something hard helps keep me in shape, so that I don't turn into a sad dull boring person, full of complaints about how hard everything is.

With these two images, I'm trying to see if some of my comfortable, familiar techniques (like the three-layer spectra) can be used on any of these infuriating sandy fractals.

Dragon & Phoenix Soup

Chain Reaction

Sunday, November 1, 2009

Infinite exoskeletons

This is really a better Halloween image than yesterday's. It's all full of centipedes and crawly wriggly things.


I'm still wandering around the extra-relaxed, exponentially-smoothed insides; this one's a PhoenixDoubleNova. They're so incredibly full of detail that framing an image becomes very difficult. There's stuff everywhere, and in a lot of areas the density is fairly uniform, so there's nothing to act as a focal point. Not very many coloring methods work well on the insides of sets, either, so there aren't too many options for getting variety in the layers. It becomes more a matter of changing the gradient density and the maximum iterations, and then just a lot of exploring to find good places.

I seem to remember reading once that astronauts wanting to take pictures from space ran into similar difficulties. When you're in orbit around the earth, it doesn't matter which direction you point a camera, because there's always something spectacular. Foreground, background, everywhere, all around. Sometimes working with fractals feels that way too.

Saturday, October 31, 2009

All Hallows' Eve

Bonfire Sparks

Another Double Nova inside image. This one is mostly Pseudo Lyapunov instead of Exponential Smoothing.

Following Columbus in a rowboat

Aha! I think maybe I am starting to get the hang of this a bit.


And all I had to do was take a small wrench to the Exponential Smoothing. It's always pleasing when that works.

Sunday, October 25, 2009


I've been working on uploading fractals from 2002 to my gallery, and finding many that are full of rainbows. That must have been when I first started experimenting with my three-layer technique. I remember being all interested in atmospheric optics around that time, so probably that was what inspired me to try making pictures with that kind of look.

And it also reminded me that I've been meaning to write a page about how to put spectra into fractals, and now I have. I hope somebody out there may find it useful.

Here's a new fractal that I made while I was messing with some of the tutorial images.

Glass Rings

Wednesday, October 21, 2009

Quantum effects

Today I came across an interesting page about aliasing artifacts, and it got me thinking about artifact patterns as applied to fractal art. Where does this op-art, moiré effect come from? Well, it's all because of quantum, you see. Writers of popular fiction like to use quantum as a sort of shorthand for stuff that's way too scientific and complicated for us to explain or you to understand, but it's actually quite simple when you remember that quantum has to do with quantity. A quantum is a small discrete unit of something. In physics, the something is physical matter or maybe energy, and the weirdness associated with the word comes from the fairly weird behavior of tiny discrete particles (or maybe waves) of energy (or maybe matter). Really, it's probably too scientific and complicated for me to explain.

But in thinking about on-screen digital images, the quantum is the perfectly familiar and understandable pixel, the small discrete dots of light that make up the picture. And the weirdness comes from the inability of computers to display any details smaller than will fit into one pixel. If the image has some black and white stripes that get smaller than one pixel wide, the computer will use various methods to guess whether any given pixel (which really contains part of a black stripe and part of a white stripe) should be all-black or all-white. This means that the patterns are completely scale-dependent: if you add more pixels, more detail will fit; the computer's guesses change, and the pattern changes also. Maybe it resolves into lots of parallel fine lines, or nested concentric circles. Whatever happens, the original effect is altered or lost.

The (im)practical result of all this is that if you've made some interesting image full of aliasing artifacts, you can't print it at any size larger than a postage stamp. Or can you? I started wondering how it might be possible.

First I made this picture:

Quantum 400x400

Then I rendered it as a 1600x1600 Photoshop document in layers, leaving out the one with the aliased pattern. The pattern layer I exported as a separate file, 400x400 pixels, which I then re-sized without resampling, so as not to let it get all blurred. I dropped that into the appropriate place in the layered document, did a bit of tweaking and tidying, and got this:

Quantum 1600x1600

That seemed to work well, so I tried it again at 2400x2400, big enough to print an 8" square at 300dpi.

Quantum, printed

There doesn't seem to be any particular reason that the technique wouldn't work at even bigger sizes, although with any large file you do eventually run into the limits of your computer's memory. And there's the difficulty of merge modes. Ultra Fractal has some merges available that Photoshop doesn't, so some effects can't be duplicated precisely. For some kinds of images, it would be easier to render a single layer and simply scale it up. The large pixelation would lend itself well to some interesting non-computer interpretations, too: I can imagine amazing woodcuts, or intricate careful drawings on graph paper, or brilliant neo-pointillist gouaches. The thing I like about today's experiments, though, is that it combines the blocky old-school computerized look with the infinite fractal detail available. The gradients around the disc are smooth, the line of wavy blobs has its proper intricate edge, and there's some subtle texture in the inside region that shows up on the print.

Tuesday, October 20, 2009

Old Favorites

The new fractal gallery is up and running, in a small way. If everything is working right, it won't look too enormously different than the old version, but the navigation and inner workings are substantially changed. Right now, what's in it are pictures from the first year and a half (or so) that I was making fractals. I have one or two small things to smooth out still, and then I'll be adding more pictures. So far I'm very pleased about how it's working; it's very easy to add new stuff. (And the stylesheets don't render properly in Internet Explorer 6! Of course! Bah phooey. No one should be using IE6 anymore anyway. This means you, Mom.)

It's been a little strange, going through all my archives of ancient fractals. I'm a little taken aback by the simplicity of color, the frequent clumsiness, the obvious lack of knowledge about the program. But at the same time, they have a kind of raw direct energy that seems good. And in some cases, I've been interested to see the beginnings of ideas that I now have spent many years developing in all sorts of directions. It's a sort of cross between archaeology and navel-gazing, and probably of no interest to anyone but myself.

This picture was made after I'd been using Ultra Fractal for less than a month, I think.

Chebyshev Avocado

Before UF, I'd spent a couple of months messing with Fractint, and the sharp-edged areas of bold color give the UF image a similar style.

So now I just have another eight years' worth of parameters to sort through, and decide what else to include. And a small amount of code still to tweak. I will probably need to make more tea.

Sunday, October 18, 2009

How to shuffle the pictures

And then there's my poor neglected website, which I've been feeling guilty about since before I started my senior year at Cornish. All summer I've been telling myself I need to add some new stuff to it, and I keep putting it off and not doing it.

Eventually I realized that I'm not updating it because it's a complete drag to update: I have to gather together some small collection of maybe-related images, arrange them in some suitable order, write a new HTML page (or at least dump them into the template), update links, etc. I practically always post things on this weblog instead, because it's much simpler and requires less thought.

I started thinking, "What I need is a gallery that works more like the rest of the internet. It can be more interactive, more content-driven, it can have an interface that's more responsive to the user." And then I said "Ew, you're thinking like a horrible graphic-designer marketing wonk. Stop that."

What it really needs to be is fun to play with. If it's fun to play with, I'll play with it, and so will my prospective audience. I can scrape off the clinging shreds of my graphic-design training, stop thinking like a damned artist, and just make internet time-waster toys instead.

So I've been turning my fractal gallery into a thing you can play with. It's nearly done. Tonight it had a brief round of beta-testing I sent the test-link to my mom and she said it was wonderful. So it will probably go officially live pretty soon.


Wednesday, October 14, 2009

Flame on

Following the example of a couple of people on the UF mailing list, I wanted to try using an Apophysis-generated flame as an imported image. Flames, being of course fractal, tuck themselves rather neatly into the overall composition, and function more or less as texture. It seems like a good way to add a certain depth and complexity of color without piling up an unwieldy number of layers or adding a lot of slow-rendering distortion algorithms to the basic trap.

Gosh, this means I'm going to have to open up Apophysis again, and try to remember which bits I'd worked out how to use, and make some stuff to use as components. That would solve one of my ongoing difficulties with flame fractals, actually, which is that I'm never able to decide how they should be cropped, or how much of the edges should be visible. As a finished image, a flame often looks a little isolated and weird when the entire form is surrounded by an area of solid color. But zooming them is problematic, and I'm always sad to lose the overall shape of the thing; they have a kind of satisfying completeness when you can see how all the parts fit together into a coherent entity. As a plugged-in image trap, that wholeness would be an advantage.

untitled [flame trap test]

The flame I used in this one was almost perfectly circular, so it's not actually all that useful a test. But I didn't have one with a more irregular shape handy, because all my existing renders are too carefully cropped and zoomed. That'll teach me to try and frame things artistically.

Tuesday, October 13, 2009

How much is too much?

My misgivings about the potential uses of the image importer are sorting themselves into two basic categories, thusly:

1. It's too easy.
2. It's too hard.

Unhelpful, that. The easiness is simply that once you learn the basic technique, there's nothing at all to stop you from dropping any image, or dozen images, into any fractal. This results in both a sort of whee, fun! effect, and the usual vague disquiet common to fractal art, the part that says this is way too easy and fun; I'm just sitting here pushing buttons, it can't possibly count as anything serious.

The hard part, though, is that you have to be careful about which pictures you use. They need to be fairly high resolution, even for a smallish screen-sized render, because the distortions introduced by the orbit trapping tend to magnify certain bits enormously, and the resulting pixelation can be quite noticeable. Once you have your high-resolution image, it has to be very carefully cleaned up in Photoshop (or equivalent) to get the alpha channel tidy. Even if the pixelation isn't a problem in the main part of the imported image, the edges can start looking ragged very quickly.

So in addition to needing some substantial background in using Ultra Fractal, you also need a reasonable familiarity with some graphics editor. And this is even before getting into questions of the aesthetic merit of the resulting conglomerations. Fractals are inherently complex things, and adding photographs to them is a whole new and different kind of complexity. A photograph of a single-colored object is never a single color; it has highlights and shadows and reflected colors from the surrounding environment, it has variations introduced by the lighting and noise from the film grain or CCD. It's made up of hundreds or even thousands of variations on the general palette, in shadings that may or may not be smooth. By comparison with photographs, I've been finding it kind of amazing to realize just how smooth and orderly fractals really are. In trying to combine the two, keeping the look and feel of the whole image consistent becomes more difficult because the intrinsic textures are so dissimilar.

I worry that the easy factors combined with the hard factors will produce an end result of many pictures made with little attention to the technical details. Heh, and having typed that, I realize that it's a perfectly good description of all fractal art, and indeed most digital art in general. Easy to do, not necessarily easy to do justice to. I should probably stop worrying about it, and just keep experimenting. Because, hey, whee fun!

I can follow up yesterday's introductory noisemaker with a full orchestral performance on the

Illuminated Musical Contraption

It may be worth pointing out that I have actually kept this one quite controlled. The color palette is restricted to a blue-orange-yellow split complement, and the overall composition is structured around a couple of major vertical arcs. However, in spite of my attempts at restraint, the effect is more or less completely ZOWIE BLAMMO, and the thing looks it should play a selection of Raymond Scott's greatest hits.

Monday, October 12, 2009



* The Wonderful Fractalodeon *
in full life-like color

The Like of Which has Never Previously Been Displayed.


Baffles even the most learned
Men of Science.

Actually it seems to have put the Professor to sleep. Probably I should give the ballyhoo a rest, too. I am indebted to Wikipedia for the use of their French horn.

Sunday, October 11, 2009

A light bulb

Today I tried using the image import feature, for the first time since my couple of brief experiments when UF5 first came out. I'm still substantially intimidated by it, mainly because it adds such a large new dimension of possibilities to an already overwhelming number of choices. How in the world can I ever manage to decide what pictures I need infinitely many of?

I've gotten used to the idea of fractals being, for the most part, purely abstract. They don't necessarily need to mean anything, they just need to be arranged in pleasing compositions of color and shape. The thing about importing images is that it instantly changes the picture from abstract and non-threatening to concrete, specific, nailed-down and potentially fraught with meaning. Suddenly I have to think about concept, which I am exceedingly wary of. It's the sort of thing required by art school, and beloved of the kinds of artists I really dislike. I don't want my stuff to turn into Political!Art! all full of sleek graphical representations of talking-heads-of-state or Hitler's brain on drugs or what have you.

Except that I've also spent a fair amount of time in the last several months making fractals that are definitely illustrations, and approach something like recognizable. Sometimes I even have a concept in mind, much as I might hate to admit it.

So I figured it was time to drag out some of my favorite recurring motifs, the ones I'm comfortable with, and put them into fractals to see what they do. I started with this light bulb.

A Light Bulb

A Julia set introduced some nice distortions, making the shape more globe-like. But it's still quite recognizable, and not terribly interesting except that it makes kind of a good dark/light pattern.

Julia Bulbs

I had another fractal window open, with a different picture I'd been working on, an Ikenaga Roots-Mandel. So I tried pasting the image trap into one of the layers, and ended up with something like a steam-powered carpet slipper.

Brass Slippers

This one seems cheerfully bizarre enough that I'd like to pursue it further, and maybe add some layers with more images: say, a tuba or something. It would be fun to see if I could make some really ridiculous fractal contraptions. Or, y'know, talking-heads-of-state.

Wednesday, October 7, 2009

It's all done with mirrors

...whose end, both at the first and now, was, and is, to hold, as 'twere, the mirror up to nature...
—William Shakespeare, Hamlet, Act III scene ii

. . . . . . . . . . . . .

The Universe—some information to help you live in it.
1 AREA: Infinite.
6 ART: None.
The function of art is to hold the mirror up to nature, and there simply isn't a mirror big enough—see point one.
—Douglas Adams, The Restaurant at the End of the Universe

Holding a Mirror Up

I still don't really know what the point of art is, or if it has a point, or if in fact there's any such thing at all. I also suspect that the above image owes something to the work of Olafur Eliasson, in addition to the quoted authors.

Friday, October 2, 2009

Strong primary colors

Train of thought, only loosely connected:

Stripes -> Circus -> Calder's Circus -> Alexander Calder. It occurs to me that Calder's mobiles are about physics and gravity in the same way that fractals are about math. The underlying science or algorithm is a lot of what makes the effect of the thing work, but the resulting piece of art goes much deeper than a simple set of equations.

I remember looking up Calder in one of my art history textbooks, and being completely annoyed that he had been left out. Since then, it has been a small secret ambition of mine to get just famous enough that some future student is offended that I've been left out of their history book. I figure the chances are pretty slim, but it's good to have goals.

Small Universe (after Calder)

Wednesday, September 30, 2009

I'm not dancing here tonight

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

Carnival Lights

Tuesday, September 29, 2009

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.

Monday, September 28, 2009

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]

Sunday, September 20, 2009

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.


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.

Thursday, September 17, 2009

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?

Monday, September 14, 2009

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.


(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.)

Saturday, September 12, 2009

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.

Friday, September 11, 2009

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.

Wednesday, September 9, 2009


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.


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.

Sunday, September 6, 2009

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]

Thursday, September 3, 2009

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]

Tuesday, September 1, 2009

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.

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.

Monday, August 31, 2009

Out of character, out of time, out of cheese error

Wow, I can't believe it's the end of August already. That means I've survived NaArMaMo! I did manage to make something nearly every day, and I posted something every day, even if the thing I posted wasn't necessarily the thing I made. I will therefore confer upon myself the Award of Reasonable Successfulness.

As a final end-of-August outburst, I'm posting another limerick and its accompanying fractal. I have to say, the picture really never worked quite right until I added the neon stars.

When out on the town acting girly,
Fair Julia sometimes grows surly,
And I strongly suppose
The chief cause of her woe's
That her beaux always bail out too early.

Party Girl

On the principle that all art is to a certain extent self-portraiture, I begin to worry a bit about my character, morals, habits, and color sense. Maybe I'm just feeling over-exuberant because I'm done with my enforced month of art.

Now I think I'm probably going to give myself a short break from art-making. But I'm actually quite happy to have had a reason to get back into the habit of writing regularly; I don't think I've been such a dedicated blogger in years. I should try to keep it up, if I can.

Sunday, August 30, 2009

Go faster!

I've done some further investigation of yesterday's excruciatingly slow fractal, and discovered that in setting it to render larger, it had indeed gone into arbitrary precision, which accounts for some of the slowness. I also figured out that I could switch to the associated Julia set and get an almost identical effect without having to zoom so deeply. So I've got a different version rendering now, and it says it has a mere three hours to go. Hooray!

Some tinkering with a nearby Mandelbrot region, and some nice quick simple orbit trap coloring, has given me an idea for a possible label design. I'm not sure about the color. It seems somewhat too dark.

Saturday, August 29, 2009

Somewhat less than one pixel per second

I remember when I got my first computer, and I downloaded Fractint and would sit and watch as it rendered images, one slow line at a time. And I remember my early days of using Ultra Fractal, when new coloring methods would be written, some of them were ridiculously complicated and would render one slow line at a time.

Over the years, technology has advanced, processors have gotten faster, and I can open up some of those old parameters and have them appear in a few quick seconds. But somehow, I always still seem to end up staring at my monitor, transfixed, as an image appears one slow pixel at a time. Sometimes it's because I'm doing deep zooms, that get into arbitrary precision. Sometimes it's lots of layers. Sometimes it's ever-more elaborate coloring methods.

This tiny snippet is probably the slowest combination of things I've tried so far. It's a Mandelbrot zoom, with Extended Precision, fairly close to the boundary (so needing lots of iterations to avoid blank gaps), and with my own parametric coloring in a particularly slow configuration. At 400 x 400 pixels, this took four hours to render. I wanted to do a test of whether it would look like I expected, so as to be used in a larger, several-layered image. Unrendered, it dissolves into a mass of crunchy pixels.

So now I'm wondering, is it worth doing the somewhat larger render of the image that this is a component of? It looks like the guilloche-pattern effect is working the way it's supposed to. If I go by my on-screen working version, the colors and layers are okay. Render time estimate is somewhere between 850 and 900 hours. That's more than a month, assuming it doesn't slow down a lot when it gets near the minibrot in the middle.

Well, I've started it. It can mutter away in the background while I'm thinking of other things.

Friday, August 28, 2009

Hey, where did the texture go?

I suppose I have to give NaArMaMo some credit for kicking me in directions that are somewhat different than usual. I'm not necessarily convinced they're good directions, but it's interesting to see what falls out of my brain after I'm way past being out of ideas. This one is basically the result of me pushing the 'pretty' button* over and over and over until something happened.

untitled [hex-star-chain]

There's something about it that reminds me vaguely of anime. It's partly the color, I think, and partly that some of the shapes look like puffy cartoon clouds.

. . . . . . . . . . .

* This only comes with the super-secret hax0red version of the program, of course.

Thursday, August 27, 2009

I don't know if I mean disco or Dante's

There's not much excuse for this one, but I made it today and so up it goes. Isn't August over yet? I don't know how people survive the novel-writing thing in November.

Julia Inferno

Wednesday, August 26, 2009

In which art-making grinds to a halt

Portfolio still needs work.
Label still needs work.
Help file for coloring method still needs work.
Spent all day in semi-comatose state. Art is basically not happening today.

However, the UF mailing list has unexpectedly broken out in fractal humor, which is exactly like you'd expect: it's funny only to an infinitesimally small segment of the population, and arguably not even funny to them. It gives me an excuse, though, to post limericks. So here is one.
A volatile fractal geometer
Saw an insect, and hurled a small bomb at her:
"The chaotic effect
Of that butterfly wrecked
My picnic, and broke my barometer!"

And an old fractal, by way of illustration. This one's from early 2003.


Tuesday, August 25, 2009

Too much like last time

Current problem: I want to make a label for my binder-portfolio-thing, so that I will have something to put in the complicated window. Six years ago, I made such a label, and I'm finding that the process of making a new one has me all horribly tied in knots. I wasn't expecting that. I thought most of the old bad stuff had been adequately dealt with, but evidently it hasn't.

So I've been all stuck, and finally decided to see if I still had the parameters for the old label. They should have gotten the full napalm treatment, but no, they're still moldering away in some of my archives. And now that I've rendered them again, they look a little flat. A little dull. Some of that, I remember, was fixed by a suitable application of typography, but the colors are more monochrome than I might like.

At least that solves the problem of wondering whether I should just re-use the thing as it is. It would definitely need some tweaking. And I think maybe I will scrap my more recent attempts, because they look too similar, and try to figure out some different approach entirely.

Monday, August 24, 2009

Petroleum by-products

Arrgh, I'm up to my elbows in a project that has reminded me of all the reasons why I don't like bookbinding very much. This thing (if I ever get it finished) is in some senses nothing more than an oversized, glorified, three-ring binder. But I'm covering it in iridescent bookcloth, and giving it a small business-card-sized window on the front, which is incredibly slow and fiddly to construct.

According to my plan, if it all works out right, this will become a portfolio for the transportation and display of fractal prints. Hooray. But at the moment, I'm hating the stupid thing.

In between changing my exacto blade and picking glue off my fingers, I'm continuing to tinker with the hypocycloids. This particular experiment ended up looking somehow toxic and ominous. Because of that, and because it's fairly closely related to my recent money-ish image, I'm calling it

Big Oil

Sunday, August 23, 2009

More self-promotion

I'm back to working on a couple of real-world projects, so I don't have a new fractal to post. Instead, here is a link to a page that may or may not become the new splash page on my website.

morgan bell
digital & analog artist

Even if I don't use it for that, I'm happy to have made the silly thing. It makes me laugh. Also, it makes me wonder if it might be fun to use the a and the E to design a logo.

Saturday, August 22, 2009

Time to build the Identity Crisis Booth

Today I read two articles on the New York Times website, one a complaint about some art being unsuitable for children, the other a description of a work of (performance?) art in which coffee was given away. Between the two articles, I've been reminded of a whole bunch of things in the current state of the art world that make me unhappy enough to deny that I am an artist at all. Really, I wish there was some better word to describe what it it I am, and what it is I do, because "art" doesn't seem to have anything much to do with it.

First, there is the kind of art that is supposed to be shocking. It isn't, anymore, but people keep making the stuff and insisting that it challenges people. As far as I can tell, the only challenge involved is trying to find something to say about it other than "Bah, another one about bodily fluids." If there is still any shock value to be had, it's limited to unsuspecting parents suddenly realizing that their afternoon's outing with the kids is going to involve a lot more explanation (and teachable moments—ugh, what a horrible phrase) than they had planned.

The difficulty with this over-saturation in shock art is that eventually it reaches a stage where if you're making something that isn't pornographic, or woven out of your dead grandfather's armpit hair, or saturated in your own menstrual blood, no one is willing to admit that it might be art. It will be dismissed as mere decoration, pretty-making, inconsequential, something to hang over the couch. It isn't art; it doesn't count. I really hate that particular aspect, mainly because it means it's hard for me to be taken seriously (hey, my stuff's often pretty!), but also because it's incredibly narrow and limited. It means there's not much out there that I want to look at, or be curious about, or be inspired by.

The coffee thing is much simpler to explain, I think. If people can't tell whether a thing is supposed to be art or not, and if when they're told it is art, they only become more confused, that work of art has failed. Yeah, there are artists out there who will say that the point of their art is to produce bafflement and to make people question their entire view of the world, and their place in it, and art's relation to them, and blah blah blah. As far as I can tell, that kind of art mainly produces irritation rather than insight, and as such, is completely full of shit.

Maybe I should write a manifesto.

Anyway, the image I'm posting today is only tangentially related to all this. Mainly it was an exercise in applying some of yesterday's shapes to an actual fractal. Arguably, it's also related to my recent letterpress License to Print Money.

Economic Debacle or Hardly Currency

Friday, August 21, 2009

Technical interlude

I accidentally made a useful discovery about this parametric-curves coloring method I've been working on. It's nearly done, and I've been working on writing a help file, but of course mostly I just spend time playing with it.

Originally, it made dotted shapes, like these.

Then just recently, I had some help, and got it to do joined lines, as well.

It turns out, if you type the wrong thing in certain parameters, it can also do things like this.

Click on the pictures for bigger versions, especially the last batch—they look really cool when you can see all the fine lines.

And then all these can be mapped onto fractals, exactly like any other orbit trap. Those last complicated ones become fairly slow to calculate, but no worse than some of the other coloring methods out there. I have a number of potential-images-in-progress using some of this stuff. They're fiddly to work with, because their geometry is extremely non-fractal, and so it's easy to end up with a kind of awful jarring mismatch of styles. But I think I'm starting to find ways of integrating them into compositions with reasonably good effect.