InfinityMathArt

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?

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.

Inspired by a similar work from @xponentialdesign

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?