Structural Cellular Hash Chemistry

Hash Chemistry, a minimalistic artificial chemistry model of open-ended evolution, has recently been extended to non-spatial and cellular versions. The non-spatial version successfully demonstrated continuous adaptation and unbounded growth of complexity (size) of self-replicating entities, but it did not simulate multiscale ecological interactions among the entities. On the contrary, the cellular version explicitly represented multiscale spatial ecological interactions among evolving patterns, yet it failed to show meaningful adaptive evolution or complexity growth. It remains an open question whether it is possible to create a similar minimalistic evolutionary system that can exhibit all of those desired properties at once, within a computationally efficient framework. Here we propose an improved version of Cellular Hash Chemistry, called 'Structural Cellular Hash Chemistry' (SCHC). In SCHC, individual identities of evolving patterns are explicitly represented and processed as the connected components of the nearest neighbor graph of active (non-empty) cells. The neighborhood connections are established by connecting active cells with other active cells in their Moore neighborhoods in a 2D cellular grid. Evolutionary dynamics in SCHC are simulated via pairwise competitions of two randomly selected patterns, following the approach used in the non-spatial Hash Chemistry. SCHC's computational cost was significantly less than the original and non-spatial versions. Numerical simulations showed that these model modifications achieved spontaneous movement, self-replication and unbounded growth of complexity (size) of spatial evolving patterns, which were clearly visible in space in a highly intuitive manner. Detailed analysis of simulation results showed that there were spatial ecological interactions among self-replicating patterns and their diversity was also substantially promoted in SCHC, neither of which was present in the non-spatial version.