Occasionally, I take some time to explore equations in other dimensions. Fractals fall into this class, as do these equations which trace out to become these twisty, sinuous, and gauzy images.
These images are created purely with mathematics. They are a sort of a graph or visualization of a penternion (five-dimensional shape) plotted in three-dimensions and projected onto the two-dimensional image. So what we see is just a three-dimensional slice of a shape of shape from a hyperspace.
The method is an Iterated Function System — a feedback loop, where coordinates are fed through an equation, and the new coordinates are drawn to the image before being fed back through the equation. A single image requires billions of these computations and iterations. A separate and parallel function colors the images.
The algorithms are in the same class as those used in Scott Draves’s Electric Sheep software. I think the equations I use are different —
I search the penternion space by adjusting variables of an equation, looking for beautiful slices of the space. As I adjust the variables in tiny increments, I expose a nearby slice and the shape begins to animate as I move through the space. It’s similar to viewing the slices of a CAT-scan. Working with systems like this is similar to working with Mandelbrot fractals and other complex algorithmic systems — you don’t create the shapes, you discover them, the way a miner finds precious gems. Once you find them, you can “polish” them, but you have to take them as they come, features, flaws, and all.
The software has been sitting on the shelf for a number of years, but I’ve recently dusted it off to see if I can explore the spaces some more. I’m working on some animated sequences, that I hope to post here, as well has create larger-resolution animations for exhibition.
I developed the software and created equations several years ago for my friend Richard Baily, who animated various sequences for feature films, which include:
The Core,
Solaris
A Wrinkle in Time
Superman Returns
He also produced some animated loops that have been making the rounds in the ambient video and music visualization market.