Embodied Approximation of the Density Classification Problem via   Morphological Adaptation
  The Majority (or Density Classification) Problem in Cellular Automata (CA) aims to converge a string of cells to a final homogeneous state which reflects the majority of states present in the initial configuration. The problem is challenging in CA as individual cells only possess information about their own and local neighbour states. The problem is an exercise in the propagation and processing of information within a distributed computational medium. We explore whether the Majority Problem can be approximated in a similarly simple distributed computing substrate - a multi-agent model of slime mould. An initial pattern of discrete voting choices is represented by spatial arrangement of the agent population, temporarily held in-place by an attractant stimulus. When this stimulus is removed the model adapts its shape and size, moving to form a minimal distance connecting line. The final position of this line is shown, in simple examples, to successfully represent the majority vote decision, and also accurately reflects the size of the majority. We note properties, limitations and potential improvements to the approach before returning full-circle by re-encoding this morphological adaptation approach in a simple (and more space efficient) 1D CA model. 
Jeff Jones
cs.ET