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

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.

Mysteries



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

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.