Homology playground

Boundary diffusion demo

Select simplices (click to cycle 0 → +1 → −1) and repeatedly apply the boundary operator plus its transpose. We animate how the chain diffuses between dimensions — edges push into vertices and triangles, then flow back out across the mesh.

Current mode

Edge chain

Energy (L₁ weight): 0.00

Legend

  • Positive (blue) — oriented with the current flow.
  • Negative (amber) — pushing opposite to the flow.
  • Opacity encodes magnitude; click shapes to reseed the excitation.

Navigation

Back to Qatar network demo

ABCDE

Vertices

  • A0
  • B0
  • C0
  • D0
  • E0

Edges

  • AB0
  • BC0
  • AC0
  • CD0
  • AD0
  • DE0
  • AE0

Triangles

  • △ABC0
  • △ACD0
  • △ADE0