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A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science Part II:: Universal Neuron.
- Source :
-
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering . Sep2003, Vol. 13 Issue 9, p2377. 115p. - Publication Year :
- 2003
-
Abstract
- Wolfram's celebrated three-input Cellular Automata is further developed and extended from the perspective of neural networks. A single explicit formula involving two nested absolute-value functions and eight adjustable parameters called synaptic weights, is presented. Such a neuron is proved to be universal by specifying the synaptic weights of all 256 local rules. Applying the nonlinear dynamics concepts developed from Part I of this multipart series of papers, we present the rational for partitioning the entire set of 256 local rules into 16 distinct gene families, each composed of 16 gene siblings. Such a partitioning allows us to explain, if not predict, the pattern features generated from each local rule. Finally, these 16 gene families of Cellular Automata rules are encoded onto a new compact and insightful representation called the "double-helix torus." [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02181274
- Volume :
- 13
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- International Journal of Bifurcation & Chaos in Applied Sciences & Engineering
- Publication Type :
- Academic Journal
- Accession number :
- 11110315
- Full Text :
- https://doi.org/10.1142/S0218127403008041