Welcome to the infinite jungle gym full of mathematical oddities! I watched "Donald in Mathmagic Land" a bunch growing up and loved the scenes where it visualized abstract geometry concepts. So for a while now I've been chewing on different ways to bring my nostalgia to life in a new way.

I recently stumbled across the PrayMitive plugin for After Effects and instantly knew it was what I've been waiting for. It utilizes the ray marching technique which is really interesting since the geometry is implicit, meaning the shapes are defined by rules/equations, and so you can achieve things which are otherwise difficult in typical 3D animation. I'm obsessed with animated booleans since there's so much to explore with this technique, especially since each primitive can be deformed with a bend, twist, wave, or ripple modifiers. Also the plugin includes some built-in rim light options that uses a Normals map to colorize the shader in uniquely beautiful ways. It was sometimes interesting to invert the boolean cutout and do an intersection type boolean instead of the subtraction type boolean. So I jammed with PrayMitive and created 32 different core scenes. And then I created some variations on each of those core scenes, ending up with 164 total scenes. At some point I realized that I wanted to have the camera orbit around the abstract shape, but I didn't want to be constrained by the vanilla AE camera. So I bought the HandyCam AE plugin which I have been eyeing for a while now and it simplified what I wanted to do. I love that it takes inspiration from the camera-and-aim rig from Maya.

I was thrilled to see that PrayMitive allowed me to render out the Normals pass directly. I've long thought that the Normals pass results in strangely wonderful colors and have always wanted to utilize these visuals directly. From there I also rendered out the base Beauty pass. With all of those scenes rendered out as frame sequences, I got curious and experimented with different ways to apply a rainbow vibe onto each of the abstract shapes. So I applied the Colorama FX onto the Normals frame sequence which was exactly what I was hoping for. For the Colorama FX I set the "Modify: Hue" so as to retain the shadows, set the "Cycle Reportions: 4" to have more rainbows repeated in Normals range, and then animated the phase shift so that the rainbow moved across the surface. Kinda a weird use of Normals but why not? I rendered all of these scenes as solo video clips for any VJs that want to jam with them directly.

With all of the abstract shapes completed, now it was time to bring everything together and make the shapes float around in various ways. This ended up being more tedious than I had anticipated and had to spin my wheels a bit before anything stuck. Some scenes use a curve as a motion path. Or have all of the shapes doing their own motions and yet parented to a null to get more complex motion happening. Or just some basic keyframing. I also wanted to experiment with the Furikake AE plugin but I ran out of time, perhaps a future experiment to return to. I did some slitscan experiments which was quite satisfying on these abstract shapes. Although I've learned that doing slitscan processing on UHD footage is much too heavy to process. So instead I scaled down the render to HD resolution, rendered out the slitscan processing, and then used Topaz Video AI to uprez back up to UHD resolution. Not an ideal workflow and slow to render out but the results are amazingly bizarre. As much as I wanted to render out everything including an alpha channel, the file sizes were enormous. But then I realized that all of the shapes were very evenly lit and contained no black shadows, which meant that if I made the background black and rendered out to MP4, then VJs could simply apply the Auto Mask FX in Resolume and have the alpha channel generated on the fly.

Now on to part 2! With a bunch of abstract shapes completed for the foreground, I wanted to create a complex background that felt vast and mathematical. Then I remembered a clever technique that was engineered by Duncan Brinsmead (principal scientist at Autodesk’s R&D) which I stumbled across while working at the Charles Hayden Planetarium. Basically you can create the illusion of an infinite lattice structure by relying on one-way mirrors. This is possible with 3D animation since each successive light bounce can achieve true 100% reflection and so I'm only limited by how many reflection bounces the render engine allows for. So I lined up a series of one-way mirrors and made a long corridor so that I could seemingly fly through this infinite lattice, but in reality I could only fly through a small part of the mirror tunnel. Then I used a fluid container to make the illusion of atmospheric distance, which is important since utterly perfect reflections end up with simply too much visual complexity in the final render. Since the fluid is extremely transparent (just 4%) it appears to be foggy in the distance, but it's just the fluid density becoming more dense with each successive reflection. From there I animated the camera within the mirror corridor, but so that the video clip could perfectly loop I had to make the beginning/ending camera positions be located within the exact middle of the end caps of the mirror tunnel. From there I did some scene variations and experimented with adding deformers so that the mirror corridor was distorted in wild ways. Although this made doing a perfect loop a bit of a nightmare but it's close enough. I wanted to rebuild the scene using Redshift (GPU rendering) but didn't see why I should since it already looked great and just needed to use the good ole Mental Ray render engine. I had kinda dreaded working with the Mental Ray engine again (CPU rendering) but to my surprise it was faster than I had remembered and the render times were comparable in this context. If you're curious to learn more about this mirror hall technique, check out my old blog post or Duncan's livestream.

I explored two different core Maya scenes, which was a cube lattice and dodecahedron lattice. What's fascinating about a dodecahedron is that it's actually physically impossible to arrange it into a lattice and so it cannot be perfectly tessellated. If you try to line up all of the edges to other dodecahedrons then you'll end up with gaps or overlaps. But due to the mirror illusion, it seems like a dodecahedron can be tessellated. Mathematical magic! Occasionally you might see where the scaffolding doesn't meet up and that's just an artifact of this process. I find this a odd aspect of humanity, in that we're often so dazzled with the complexity that we're unable to parse what's actually happening. I tried to do some facing angle tweaks to the color so that the hue would change with each bounce but looked super messy.

After rendering out the lattice scenes from Maya, I imported the frame sequences into After Effects and did some various experiments in adding rainbow colors into the scenes. I did this by first making a topmost solid layer and set it to use the Hue blend mode. From there I used the Gradient Map FX to create a color mapping space and then Colorama FX to get the rainbows happening. I made some different variations of the Gradient Map FX so that the rainbows would be applied in alternate ways onto the Maya renders. For the "RainbowNoise" scenes I added some Turbulent Displace FX after the Colorama FX so that I could make it feel more organic. Overall this technique feels like a hacky way to colorize a video clip, but it looks great and so who cares. When jamming in Resolume, I'd recommend throwing the Hue Rotate FX onto these clips for some trippy looks.

A while back I read the book "Everything and More: A Compact History of Infinity" by David Foster Wallace and it introduced me to the Riemann hypothesis. It's visuals like these that I see in my mind's eye when I think about such mathematical wonders and all of the amazing concepts that have been discovered, hence my love of mathematics. Care for some musica universalis?

Released February 2026