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.