"Cellular Automata + GMDH = Emergent Programming: A New Methodology for Hardware Intelligence"
The application of Cellular Automata with respect to machine learning algorithms is an area of active research   . This paper combines the Group Method of Data Handling  with Continuous Cellular Automata  (Figure 1.) resulting in a new Emergent Programming (EmP) algorithm  that is capable of machine learning while having many paths leading to an efficient and effective hardware implementation. The proposed Emergent Programming methodology employs a self-organizing hierarchical inductive learning algorithm and can be considered an instance in the space of Complex Adaptive Functional Networks (CAFN). In particular the 3-dimensional cellular learning model is based on a diffusion metaphor (Artificial Physics – Physicomimetics)  that allows the EmP/CAFN to dynamically adapt to new information while forgetting old information. The Emergent Programs presented in this paper are competitive with traditional GMDH results (Figure 2.) while being based on concepts (von Neumann Neighborhoods) that can be theoretically implemented in hardware using traditional or quantum computing .  Y. Bar-Yam. Dynamics of Complex Systems. Westview Press, Boulder, CO, 1997.  H. de Garis. CAM-BRAIN: The evolutionary engineering of a billion neuron artificial brain by 2001 which grows/evolves at electronic speeds inside a cellular automata machine (CAM). In E. Sanchez and M. Tomassini, editors, Towards Evolvable Hardware; The Evolutionary Engineering Approach, pages 76–98, Berlin, 1996. Springer.  R. P. Feynman. Feynman Lectures on Computation. Westview Press, Boulder, CO, 1996.  T. Gram, S. Bornholdt, M. Gro, M. Mitchell, and T. Pellizzari. Non-Standard Computation: Molecular Computation - Cellular Automata - Evolutionary Algorithms - Quantum Computers. John Wiley & Sons.  J. H. Holland. Emergence, From Chaos to Order. Adison- Wesley, 1998.  A. G. Ivakhnenko, V. V. Konovalenko, Y. M. Tulupchuk, and I. K. Tymchenko. The group method of data handling - a rival of the method of stochastic approximation. Soviet Automatic Control, 13:43–55, 1968.  M. Sipper. Evolution of Parallel Cellular Machines: The Cellular Programming Approach. Springer-Verlag, Heidelberg, 1997.  W. Spears and D. Gordon. Using artificial physics to control agents, 1999.