Cellular Automata (CAs) have potential as powerful parallel computational systems, which has lead to the use of CAs as reservoirs in reservoir computing. However, why certain Cellular Automaton (CA) rules, sizes and input encodings are better or worse at a given task is not well understood. We present a method that enables identification and visualization of the specific information content, flow and transformations within the space-time diagram of CA. We interpret each spatio-temporal location in CA’s space-time diagram as a function of its input and call this novel notion the CA’s Canonical Computations (CCs). This allows us to analyze the available information from the space-time diagrams as partitions of the input set. The method also reveals how input-encoder-rule interactions transform the information flow by changing features like spatial and temporal location stability as well as the specific information produced. This general approach for analysing CA is discussed for the engineering of reservoir computing systems.

The complexity of cellular automata is traditionally measured by their computational capacity. However, it is difficult to choose a challenging set of computational tasks suitable for the parallel nature of such systems. We study the ability of automata to emulate one another, and we use this notion to define such a set of naturally emerging tasks. We present the results for elementary cellular automata, although the core ideas can be extended to other computational systems. We compute a graph showing which elementary cellular automata can be emulated by which and show that certain chaotic automata are the only ones that cannot emulate any automata non-trivially. Finally, we use the emulation notion to suggest a novel definition of chaos that we believe is suitable for discrete computational systems. We believe our work can help design parallel computational systems that are Turing-complete and also computationally efficient.

In order to develop systems capable of modeling artificial life, we need to identify, which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time dynamical systems. The method distinguishes between different asymptotic behaviors of a system's average computation time before entering a loop. When applied to elementary cellular automata, we obtain classification results, which correlate very well with Wolfram's manual classification. Further, we use it to classify 2D cellular automata to show that our technique can easily be applied to more complex models of computation. We believe this classification method can help to develop systems, in which complex structures emerge.