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)