The holes hiding between points

Connect the dots and watch a hole appear, survive and disappear.

Start with a point cloud and increase the distance at which nearby points connect. Components join, triangles fill in, and a loop can appear for a while before it disappears.

The actual point-cloud loop and its persistence barcode — 01 A ring at the selected connection distance. Pink edges mark a surviving cycle; the barcode shows the range of distances over which it persists.

What to look for

The pink edges show a surviving cycle. The barcode keeps track of how long it lasts as the distance changes. Five point clouds are checked using both matrix reduction and independent rank calculations.

Under the hood

An independently reusable mathematical engine and interactive browser experiment.

Exact finite data, explanatory notes and credited primary literature.

Five point clouds, five barcodes. Two independent calculations check which holes survive as the connection distance changes.