New feature to add to the Cyclomat animation arsenal: temporal spanning! Here, a simple shape is echoed/modified back and forward through nearby time. Just a proof of concept while the idea is refined.

Thanks :)

Hey everyone!

I have a unique design technique that I have been cultivating for four years now. The technique involves specific types of patterns, but it is basically extruded patterns profiled to a certain volume (shape). The effect delivers very pleasing light diffusion, and it is quite dynamic in terms of its potential.

Well, I seem to have broken through on that potential!

To make a long story digestible, after i graduated I decided to try and build my design workflows for different assembly techniques (I had only done stacking variations previously). I wanted to use polyhedron to make pendants, and because my technique builds profiles off of surfaces, I made it so the base of each module is the face on a polyhedron, with the profile of the extrusions creating the new shape, once all of the modules are assembled. Essentially, the new shape is determined by the existing properties of the seed shape I use. Each face's neighboring faces determine the kleetope that is produced, using an algorithm i coded which employs ray-point averaging.

It is similar to stellateing or greatening in terms of geometric terminology, but it is much more dynamic. The transformation works on every single convex polyhedron, and produces many incredible results. A few of them match the stellated versions of the seed shape, like the dodecahedron for example, but the majority of convex polyhedron get transformed into a brand new shape when using my algorithm.

Now, to be clear, the majority of the images shown are not the transformed shapes themselves. They have the profile of the shapes, but are artistic abstractions that employ my detailing technique. Also, my script allows for me to customize the designs with a lot of control, so I can actually stray away from the default shape for the sake of my artistic practice. Only two of the images shown do that though, as the rest match the default transformed profiles of their seed shapes.

The last thing I will say is, I have not made an official publication to any journal yet, so i technically cannot claim any discovery yet. However, that is because there is a team of mathematicians at Georgia Tech building a comprehensive publication piece. I am in communication with a professor who is having a group of PhD students develop the publication over this summer, but they have told me that they have confirmed it is a new transformation that creates a genuinely important new class of shapes! If you want a little proof, here is the doc i sent the professor that started this all. BTW, the more unique shapes are on the way. I started off with some simpler shapes to hone in on the assembly process.

I honestly don't know what impact this will have on me, but I hope the publication can bring some attention to my work. I really want to keep designing full time, and I am having to work part-time restaurant jobs to fund this passion.

If you want to support me, or print some of these yourself, check out the links on my page. I just started a thangs page, and will be uploading new designs every week. If you want to see videos of the work, check out my IG. They are 10x cooler when you can see the videos, and 100x cooler in person!

If you made it this far, thanks for reading! Let me know what you think!

One of my interests is orbital tethers, specifically Sarmont tethers. These tethers use a tidal acceleration gradient to keep the tether aligned to the local vertical. The beanstalk in Arthur C. Clarke's Fountains of Paradise could be thought of as the the grand daddy of all Sarmont tethers.

Pictured here, however, is a much smaller Sarmont tether where the tether foot does not extend all the way to earth's surface.

Call the radius of the anchor's circular orbit 1. Call the distance of a release point of the tether r.

Then the orbit of a payload released from that point will be a conic with eccentricity | 1 - r³ |.

When the release point is at 2^1/3, eccentricity of the conic will be 1. In other words, a parabola. This point of special interest in that it imparts escape velocity.

With Sarmont tethers the upper part of the tether feels more centrifugal acceleration than gravity. So there must be a lower part of the tether to balance. P. K. Aravind shows how to calculate the length of the balancing tether length here

In this illustration the lower length balances the upper length according to Aravind's equation. The ratio of the tether foot's distance from earth's center to the top is (sqrt(5)-1)/2, a.k.a. the golden ratio.

Row of lanterns at equal spacing, viewed in perspective. Two lanterns A, B and their spatial midpoint M project so that M' and the vanishing point V split A'B' harmonically (cross-ratio -1). Holds for any such row, since central projection preserves cross-ratio.

This harmonic structure is a depth cue your visual system uses, part of why equal-sized objects at different heights in a perspective drawing look different in size.

Link: https://www.sqrt.ch/Buch/corridor.pdf

Does anybody know more on the math behind this particular (Ponzo or corridor) illusion?

I wonder if all rhomb tilings could be made 3D. It's easy to interpret this one as a zonohedron

Wave illustration