Emergence of a self-sustaining network of reactions in a flow reactor. (A) The squares show critical thresholds for subcritical (empty squares) or supracritical (coloured squares) growth of the reaction network as a function of the firing disc (maximum length of molecular species in the food set) and the probability P that a species catalyses a specific reaction. The darkness of a square reflects the proportion of 100 runs in which the network exceeded one of the following conditions: > 2 × 107 reactions or > 105 molecular species (note that in any finite system the reaction network cannot be explored infinitely due to mass constraints). (B) The crucial parameter P was decomposed into its two elementary probabilities: P' (the probability that a species can be catalytic) and P'' (the per reaction probability that this catalyst catalyses a reaction). When P' decreases P'' must be considerably higher for reaction networks to keep growing, but there is a threshold above which catalytic networks grow supracritically. (C) Weak inhibition does not prevent formation of large catalytic reaction networks. For values of P that do produce catalytic network growth, strong non-competitive inhibition is introduced by choosing with probability K that a species removes another species from the reactor completely if at least one molecule of the inhibiting species exists (this is clearly a worst-case assumption). Left: supracritical growth without inhibition. Middle: weak inhibition results in alternating fast and slow growth phases. Right: strong inhibition makes the network subcritical.