Persistent Homology Explorer

This tool allows users to explore persistent homology for several toy datasets in two dimensions. Users can select from different datasets with the dropdown, while simultaneously adjusting parameters like radius and number of points. The persistence diagrams show how topological features (connected components and loops) appear and disappear as the radius increases.

Note that by default the Vietoris–Rips persistence diagram is shown. Users can click on the labels in the bottom left under "Toggle Layers" to toggle them on and off in the persistence diagrams.

The calculations are approximated using a fast algorithm that is not exact for all datasets and may show spurious topological features along the diagonal of the persistence diagram, especially for larger numbers of points. The tool is meant for educational and illustrative purposes rather than precise computation.