InfinityMathArt

I love pictures and mathematics. @infinitymathart on IG/TikTok

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Improbable movement.

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Simulating 100,000 stars and 3 black holes subject only to their mutual gravity makes a beautiful and chaotic ballet. Here the star trails are color-coded according with their speed.

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Concave and convex.

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Weigted Voronoi Stippling Experiment No. 2: walking cat. This was a bit tricky make loop perfectly but I eventually figured out that one solution is to let the whole animation run for a while and hopefully the trajectories of the moving stipples will stabilize. It seems to work. What do you think?

Cat model: Attribution: sketchfab.com, burgeonistsolutions, Creative Commons Attribution-NonCommercial

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Einstein, Tesla, Voronoi: a Weighted Voronoi Stippling Morphing experiment.

This animation explores the fluid transformation between two images using a custom implementation of Weighted Voronoi Stippling, driven by exactly 10,000 points.

The Technique: Voronoi Stippling is a generative art technique that places points (sites) on a canvas, with each point claiming the region of pixels closest to it. By making the points denser and larger in brighter areas of a source image, a detailed stippled portrait emerges. The “weighted” aspect means the point distribution is directly influenced by the image’s brightness map.

Achieving a Perfect Loop: The core challenge of this project was to create a seamless, looping morph between two distinct images (Einstein and Tesla). A simple crossfade between two independently generated stippled images results in a chaotic, jumbled mess as points have no inherent correspondence.

The solution was a hybrid pre-computation strategy:

State A: A set of 10,000 points is fully relaxed to form the image of Einstein. The Morph: Starting with this initial configuration, the points are not reset. Instead, the underlying brightness map is slowly interpolated from Einstein’s to Tesla’s over a series of steps. With each small change in the map, the points run a few iterations of Lloyd’s relaxation, gently nudging them towards their final positions. State B: The final result of the morph is a new set of points that forms the image of Tesla. Critically, because it was morphed from State A, it maintains a perfect, one-to-one correspondence with the original points.

This ensures that during the final animation, every single point travels the shortest and most elegant path, creating a hypnotic and organic flow that loops flawlessly.

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White noise.

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Relativity.

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I wasn't very happy with my previous attempt because the colors were way off of what I had intended. As a twist, the spiral now is elliptical while preserving almost constant speed movement. I used a technique similar to @necessary-disorder's replacement technique to obtain a perfect looping gif. To achieve constant speed movement along Euler's spiral involves parametrizing it by arc-length. This, in turn, involves solving for t when computing s=s(t), for s the arc length and t the angular position. Fortunately, for t > 1, s(t) is approaches t^2 very quickly, hence t is well approximated by sqrt(s). In the case of the elliptical spiral, this approximation is still very good if the eccentricity is kept low. In other words, a lot of cool mathematics was used to generate this image. Any thoughts?

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Unda Quadrata.

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Riding the wave.

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Color rotations.

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Inspired by a similar work from @xponentialdesign

The circles alternate from partially empty to partially full, controlled by a periodic function of time in [0, 1]. Each circle receives an offset that is a normalized distance from the center of the grid.

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Inpired on a work by @xponentialdesign.

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Inpired on Luminous Revolving Doors Grid by @xponentialdesign.

This was a bit tricky for me. I wanted the disks to spin all in the same direction while keeping the perfect loop. So I took a periodic function f(t) representing the speed of rotation for t on [0, 1], then defined F(t) as the a constant alpha times integral of f(s) for s from 0 to t (using the Trapezoidal rule). Next I computed alpha so that F(1)-F(0) (the area under the curve) would become an integer. During the animation, as the time t ranges from 0 to 1, I simply multiply F(t) by 2*pi to get the angular position. I summed 2*pi*t to this to get a base rotation. The disks on the n x n grid received an offset value of (i+j)/n and I add this offset, say, F(t + o), to obtain the traveling wave. So in the end the angular position of the (I,j) disk on the grid is 2*pi*(t + F(t + offset(i,j))). Anyone has a simpler idea that works?

Source code here.

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