TDA Playground

Explore freely with the full TDA pipeline and experiment with datasets.

TDA Playground

Explore the full TDA pipeline: generate a point cloud, build the Vietoris-Rips complex, and visualize persistent homology with barcodes. Try different shapes to build intuition for how topology appears in the persistence output.

Vietoris-Rips Complex

Adjust ε to see how the complex evolves. Watch the Betti numbers change as components merge and loops form.

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Vertices
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Edges
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Triangles
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β₀ (components)
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β₁ (loops)

The Vietoris-Rips complex connects points within distance ε and fills in all cliques. Watch how topological features (components, loops) appear and disappear as ε increases.

Persistence Barcode

The barcode summarizes the birth and death of all features across the filtration. Long bars are significant; short bars are noise.

Hover over a bar to see details. Long bars indicate significant topological features; short bars are typically noise.

Congratulations!

You've completed the TDA learning module. You now understand:

  • How to build simplicial complexes from point clouds
  • The Vietoris-Rips construction and filtrations
  • Homology groups and Betti numbers
  • Persistent homology and the matrix reduction algorithm
  • Barcodes and persistence diagrams
  • Real-world applications in science and engineering

To go deeper, explore libraries like GUDHI, Ripser, and giotto-tda for production-ready TDA implementations.