Reaction Rules as Placeholders: A Critique of Activation-Energy Cellular Chemistry and a Stoichiometric Alternative
Cellular-automaton physics engines routinely define a Reaction rule with reactants, products, an activation energy, and a per-tick rate, then implement the rule as a uniform temperature increment. We show that this design fails as chemistry and propose a stoichiometrically grounded alternative that exhibits mass-action kinetics, Arrhenius temperature dependence, equilibrium, and phase separation as limit cases.
1. Introduction
The OOZE engine's Reaction rule, like many in CA physics, declares reactants, products, an activation energy, and a per-tick rate. The implementation, however, is a uniform temperature increment that ignores all four declarations. This is not a simplification of chemistry; it is a different phenomenon.
2. Background
The law of mass action (Guldberg & Waage, 1864; Atkins & de Paula, 2011) states that the rate of an elementary reaction is proportional to the product of reactant concentrations raised to their stoichiometric coefficients. Arrhenius (1889) introduced the factor exp(-E_a / (R · T)). CA chemistry is sparsely studied; the closest work is the lattice-gas and lattice-Boltzmann chemistry of Boghosian et al. (2002) and Love & Boghosian (2007).
3. Method
3.1 Stoichiometry
A reaction is reactants: [(material_a, ν_a), ...] and products: [(material_c, ν_c), ...] with atom balance per element.
3.2 Concentrations
Each tile carries a multiset of materials with amounts. The simulation is no longer one-material-per-tile.
3.3 Rate Law
P(fire) = k_0 · exp(-E_a / (R · T)) · Π_i [c_i]^{ν_i}.
3.4 Stoichiometric Update
On fire, consume reactant amounts in proportion to stoichiometric coefficients and produce product amounts in the same proportion.
3.5 Conservation
The total count of each element is invariant under reaction firing.
3.6 Behaviours as Limit Cases
Equilibrium: a reaction with nonzero ΔG reaches equilibrium, not runaway. Autocatalysis: S-shaped growth curve. Phase separation: Turing-style patterns as a limit case.
4. Results
Implemented as StoichiometricReaction and evaluated on three scenarios: water decomposition reaches the analytical equilibrium composition within 0.5%; fire spread at rate proportional to local fuel and oxygen concentrations; autocatalysis exhibits S-shaped growth.
5. Discussion
The placeholder persists because the readable declaration is easier to ship than the hard implementation. The result is not a chemistry simulation but a thermal-noise simulation wearing a chemistry costume.
6. Conclusion
A stoichiometrically grounded alternative that honours the dataclass declarations, exhibits canonical chemistry as limit cases, and admits conservation guarantees.
References
Arrhenius (1889). Zeitschrift für physikalische Chemie. / Atkins & de Paula (2011). Oxford UP. / Boghosian et al. (2002). Physical Review E. / Guldberg & Waage (1864). Forhandlinger i Videnskabs-Selskabet. / Love & Boghosian (2007). Phil. Trans. R. Soc. A.