In an attempt to expand my horizon toward the exploration of interactions among of agents, including humans and robots, one of the valuable leads I encountered was this investigation of the configuration space for interactions at the molecular levels in computational models of living systems.

The authors modeled simplified living systems consisting of different types of molecules: autocatalyst, membrane, food, and water. Autocatalysts consume food and produce additional autocatalysts; they also assist in the creation of membrane molecules from food. Water is largely inactive and is conserved. By observing the molecular concentrations, interactions can be analyzed and interesting behaviors can be investigated in more detail. This high-dimensional coupled, nonlinear dynamic system is described through a set of differential equations.

The specific simulations were done on a 40 x 40 square toroidal lattice, with a total of 8,000 differential equations, implemented in MATLAB. The system was initialized with a small circle of autocatalyst surrounded by a thin membrane ring in an environment with food dissolved in water. This initial configuration leads to a stable configuration after about 16,000 time steps, persisting for about 100,000 steps.

The introduction of perturbations (such as a small tear in the membrane) exhibits properties that can be characterized as robustness (configurations remain stable) and plasticity (emergence of different stable configurations) despite perturbations. A very small tear can be self-repaired by the system, whereas a slightly larger one leads to the terminal, uniform state (breakdown and death of the system).

It will be a challenge to apply the methods and techniques discussed in the paper to my analysis of interaction spaces for agents, but it looks like a promising path toward identifying viable interaction sequences, possible basins of attraction in the configuration space, and the influence of perturbations on interaction sequences.