Why the points connect
Points drift across the background of this website while edges and faint triangles repeatedly form between them. The graphic is more than decoration. It reflects a mathematical idea that connects to my research and to the character of the website itself: individual data points gradually become a structure.
The animation is based on a Vietoris–Rips complex. Start with a set of points and choose a distance threshold. Two points are connected whenever their distance is below that threshold. If three points are connected pairwise, the triangle between them is filled in. In this way, a point cloud gives rise to a simplicial complex.
As the threshold changes, connections appear and disappear. The same data can therefore be viewed at different scales, which is one of the central ideas of topological data analysis. The animation makes this process visible: the points move slowly while the threshold periodically expands and contracts. New local patterns keep emerging without giving the image a fixed centre.
This perspective has shaped my research since my doctoral thesis on the representation theory of persistence modules. My later work on Hodge Laplacians and statistics on simplicial complexes moved towards applications in biology and medicine. The background motif visualises this path: abstract mathematical structures brought to life—and into the life sciences—through real-world data.
The implementation first renders a static SVG, so the motif is visible immediately and still works without JavaScript. A canvas animation then takes over. If reduced motion is enabled, the graphic remains static.
The result brings together two sides of my work: understanding mathematical structures and translating them into working software.