setreplace

Wolfram models in Python — hypergraph substitution systems with the exact semantics of Wolfram's SetReplace, plus HypergraphPlot-style rendering, powered by a Rust engine. No Wolfram Language license, no graphviz, no native dependencies to install.

import setreplace as sr

# The rule from the Wolfram Physics Project announcement
system = sr.evolve("{{x, y}, {x, z}} -> {{x, z}, {x, w}, {y, w}, {z, w}}",
                   [[1, 2], [2, 3], [3, 4], [2, 4]], events=1500)
system.plot()        # ↑ renders inline in Jupyter

States are plain list[list[int]]; rules are the same strings the SetReplace docs use. Evolution is incremental and fully deterministic (seeded), and every token and event keeps its causal history:

rule = "{{v1, v2, v3}, {v2, v4, v5}} -> {{v5, v6, v1}, {v6, v4, v2}, {v4, v5, v3}}"
system = sr.evolve(rule, [[1, 2, 3], [2, 4, 5], [4, 6, 7]], events=10)

system                       # <HypergraphSystem: 10 events, 5 generations, 13 edges, MaxEvents>
system.final_state           # [[7, 2, 9], [7, 14, 6], ...]
system.evolve(max_events=100)
system.termination_reason    # "MaxEvents" | "FixedPoint" | "MaxGenerations" | ...
system.tokens()[0]           # Token(atoms=[1, 2, 3], creator_event=0, ...)
system.causal_graph_plot()   # layered causal graph, inline
system.plot().save("state.png")

sr.set_replace([[1, 2], [2, 3]], "{{a_, b_}, {b_, c_}} :> {{a, c}}")   # [[1, 3]]
pos = sr.layout(system.final_state)   # {atom: (x, y)} for matplotlib & friends

The engine is a verified port of SetReplace's C++ core: test vectors lifted from SetReplace's own suite, plus live cross-checks against SetReplace under wolframscript — final states, event traces, causal graphs, and every event ordering agree exactly. The renderer's palette and arrowhead geometry are transcribed from SetReplace's style sources, and large states lay out in seconds via a multilevel spring-electrical embedding.

Docs, gallery, and the Rust crates: github.com/kovasb/setreplace-py.

Independent reimplementation of SetReplace (MIT) by Max Piskunov and contributors; not affiliated with the SetReplace project, the Wolfram Physics Project, or Wolfram Research. MIT licensed.