G-Force – Energy and Time

Mandelbrot approximations in G-Force

A few years back, when I was doing FlowFields for G-Force based on chaos theory and fractals, I did some Julia set ones but concluded that the Mandelbrot set was impossible. However, I recently realized that Nth-order approximations to Mandelbrot were doable for any finite N. Last night I got 1st through 6th order ones working, and they look quite a bit different from what I expected.

My initial expectation was that the Nth-order approximation would fit inside the Nth nested bounding curve. This image from Peitgen et al., *Chaos and Fractals: New Frontiers of Science*. Therefore, I expected that the approximations might also be nested.

Here’s a slightly different view of the “lemniscates” from mathworld.wolfram.com. Note that although these were nominally computed from the exact same formula, they are not identical to the ones in the previous picture.

For a baseline, here’s an image of my Julia Seahorse FlowField. Julia sets are doable because the “motion” of each pixel is defined by a global constant (the complex number C that “indexes” that set). If you know X, Y, and C, you know everything you need to know. But for the Mandelbrot set, pixel motion needs X, Y, and the coordinates of where that pixel originally started. Every pixel needs to know its ancestral home. There’s no way to code that in G-Force, so I concluded that Mandelbrot cannot be done.

Here’s the 1st-order approximation. It clearly has a fractal boundary. It seems to have both up-down and left-right mirror symmetry, which matches wolfram.com‘s first bounding curve, but not Peitgen’s. The formula is srcZ = Z^2 + Z. Each pixel takes one correct step, but then forgets where it came from, so each subsequent step is “wrong”.

The 2nd-order approximation begins to look vaguely like the final set. The formula is srcZ = (Z^2 + Z)^2 + Z, which represents two steps before the pixels forget. (The white lines are the waveshape used to “excite” the FlowField, and should be ignored.)

Here’s the 3rd-order approximation, srcZ = ((Z^2 + Z)^2 + Z)^2 + Z. Surprisingly, this appears to no longer be a connected set, since there is a substantial gap between the left bulb and the main body.

Digital Dome G-Force

Last night, I found out that the Otterbox Digital Dome at FCMOD has a commercial license for G-Force (and Whitecap and Aeon), and they’ve already worked out the technical details for mapping those onto their 4K x 4K pixel spherical screen. That means I can just bring my config set on a USB stick and VJ using their SW and computer. Any EDM folks interested in rocking the dome? I am so stoked …

Play It Forward

I’ll be doing live image synthesis at the Play It Forward charity benefit. So stoked to be working with The Acidophiles and other local electronica artists again!

Miranda

Had a delightful photo shoot with the lovely Miranda S. to make sprite images for G-Force, then made the sprites and used them.

This is Carol’s and MollyB’s favorite.

This is one of my own FlowFields, based on a Julia set.

Another one of my own FlowFields (called “Smoke And Mirrors”).

When two Mirandas are not enough. This one reminds me of Rilke’s “ranks of angels” from the first Duino Elegy. “Wer, wenn ich schriee, hörte mich denn aus der Engel Ordnungen?” (“Who, when I cry out, hears me among the ranks of angels?”)