Conceptual Representations: What do they have to say about the Density Classification Task by Cellular Automata?

In this paper, Aitana, a Developmental Cognitive Artifact developed byMarques (2006), is used to produce “conceptual” representations of the best known Cellular Automata (CA) rules that perform the Density Classification Task (DCT) (see e.g. Packard, 1984, 1988; Mitchell et al., 1993). The resulting redescriptions are then analysed from the viewpoint of their similarity, in terms of their cell state-update functions. We show that these new conceptual representations can reveal knowledge about these rules that is not accessible on the implicit level (CA in their look-up table form). We also show how the resulting abstractions can be considered suitable for the formation of “Conceptual Spaces”, wherein rules that perform similar computations are positioned in close proximity.