The multiway graph shows all possible evolution histories of a string rewriting system. Each node is a state; each edge is a rule application. Branching means the system explores multiple futures simultaneously — this is the origin of quantum superposition in the Wolfram model.

Node brightness encodes path weight — the number of distinct paths from the initial state. These weights are the quantum amplitudes: brighter nodes have higher probability of being observed.

The causal graph tracks which rewriting events enable which others. If event A produces a state that event B needs, there’s a causal edge A → B. This partial order is the discrete analog of a Lorentzian spacetime manifold.

Causal invariance — when all branch orderings produce the same causal structure — is a key property. It’s the discrete equivalent of general covariance in general relativity.

The branchial graph connects states that share a common ancestor one step back. Its geometry is branchial space — which converges to projective Hilbert space with the Fubini-Study metric. Distance here measures how "quantum-different" two branches are.

Close branches interfere constructively (amplitudes add). Distant branches decohere — the observer can’t identify them, and they behave as separate classical worlds.

Branchial evolution animates the branchial graph step by step, showing how the branching structure grows and recombines over time. The distance histogram (right panel) tracks the distribution of pairwise branchial distances at each step.

Watch for clustering — it signals decoherence. When groups of states become branchially distant, the observer sees them as separate classical outcomes.

The spacetime view uses Wolfram-style hypergraph rewriting — rules that transform sets of relations (hyperedges). The resulting spatial hypergraph encodes emergent geometry: its large-scale structure approximates a smooth manifold whose dimension and curvature are measurable.

The foliation slider lets you slice through the causal structure, showing the spatial hypergraph at different "moments" — the discrete analog of choosing a spacelike hypersurface in GR.

The coarse-graining slider implements Jonathan Gorard’s observer model. The observer imposes completion rules on the multiway graph by identifying branches whose causal futures are isomorphic at a given resolution. This Knuth-Bendix completion is formally equivalent to wavefunction collapse.

At resolution 0 you see the full quantum state. As you increase coarse-graining, branches merge, causal invariance rises, and the system looks increasingly classical. Orange edges are completion edges — the observer’s identifications.

3D views (Spacetime): Click + drag to orbit, Ctrl + click + drag to pan, scroll to zoom.

Flat views (Multiway, Causal, Branchial): Click + drag to pan, Shift + drag to rotate, scroll to zoom.

Hover over any node to see its state and metadata. Click a node to highlight its causal history. Use the Scenes dropdown for curated configurations that demonstrate specific physics.