OBSERVATION CHAMBER / MVP
Topology Flood
Edit a point cloud, compute H0/H1 persistence, and sweep epsilon to watch components merge and one-dimensional intervals appear and disappear.
01 / EDIT THE POINT CLOUD
Points and the current Rips complex
03 / READ THE FLOOD LEVEL
Topology at epsilon
- Points
- 4 / 60
- Components / beta0
- -
- beta1
- -
- H1 intervals
- -
- MST max error
- -
- Runtime
- -
Rips rule: an edge enters when d <= epsilon. A simplex enters only when every edge among its vertices is present. An interval is active when birth <= epsilon < death.
This Ripser build does not return representative cycles, so the apparatus does not invent a hole location.
Intervals, coordinates, MST check, and build details
Ripser 1.2.1 runs in a Web Worker. H0 finite deaths are checked independently against Euclidean minimum-spanning-tree edge lengths.
Finite 60-point browser model for H0/H1 only. This is not a formal topology proof, general-purpose TDA system, or engineering analysis.
Observation report
SYSTEM NOTE
The Vietoris-Rips complex VR_epsilon(X) contains an edge when ||x_i - x_j||_2 <= epsilon and a simplex when every pairwise edge is present. Betti numbers beta_0 and beta_1 count connected components and one-dimensional holes. A persistence interval is active when birth <= epsilon < death, and finite H0 deaths are checked against Euclidean minimum-spanning-tree edge lengths.
OBSERVATION GUIDE
Touchpoints for Observation
Observe points connect into components, loops appear and disappear, and those changes become H0/H1 persistence intervals.
- Add, move, or delete points, Compute persistence, then sweep epsilon while the Rips edges, simplices, Betti numbers, barcode, and diagram move together.
- At most 60 finite points are sent to Ripser 1.2.1 in a Worker.
- The interval convention is half-open: birth <= epsilon < death.
- No representative cycle is returned, so the display does not invent a location or outline for a hole.
This is a finite Euclidean point-cloud model limited to H0 and H1. It is not a formal topological proof, a general-purpose TDA system, or engineering analysis.
Runs inside the browser with no upload and no registration.
OBSERVATION POLICY
This lab runs in your browser. No image, pointer trace, or input is uploaded by this prototype.
Route
This chamber belongs to Structures & Symmetries.
STRUCTURE Back to Structures & Symmetries Route.