A spin network is a graph whose nodes are quanta of 3D space and whose edges are quanta of area threading through them. Each edge carries a half-integer spin label j from an SU(2) representation; the eigenvalue of the area operator on a surface pierced once by that edge is discrete, not continuous:
 = 8πγ ℓP² √(j(j+1)) (γ ≈ 0.2375, Immirzi parameter)
A node where several edges meet is a quantum of volume — the volume operator's eigenvalue grows with the spins of the edges incident on it. Evolving the network in time sweeps out a 2-complex called a spin foam: a history of nodes splitting into edges and edges into faces. The faded stacked copies above the network are exactly that — a discretized, causal history of the same graph, replacing a smooth spacetime with a fundamentally granular one at the Planck scale.
- New node spin — the j assigned to the next node you add (colors and size scale with j).
- Add node — places a new quantum of space at a free position in the graph.
- Add edge — enter connect mode, then click two nodes to link them with a quantized-area edge (its j is set from the two endpoints).
- Evolution speed — how fast new spin-foam time-slices are stacked above the network; 0 pauses the foam.