Holographic Automata for Ambient Immersive A. I. via Reservoir Computing

We prove the existence of a semilinear representation of Cellular Automata (CA) with the introduction of multiple convolution kernels. Examples of the technique are presented for rules akin to the "edge-of-chaos" including the Turing universal rule 110 for further utilization in the area of reservoir computing. We also examine the significance of their dual representation on a frequency or wavelength domain as a superposition of plane waves for distributed computing applications including a new proposal for a "Hologrid" that could be realized with present Wi-Fi/Li-Fi technologies. Keywords: Cellular Automata, Distributed Computing, Holographic Representations Introduction Distributed computing has a long history running the full half of the previous century and its development went hand in hand with the rise of connectionist paradigm out of the study of both natural and artificial neural networks [1]. Perhaps one of the first application of holographic principles in general computation are to be found in the entirely original method of tearing by Kron [2], later termed "Diakoptics", which was invented for the efficient solution of large electrical networks by decomposition.