{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,14]],"date-time":"2024-09-14T09:05:38Z","timestamp":1726304738603},"reference-count":6,"publisher":"World Scientific Pub Co Pte Lt","issue":"09","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2003,9]]},"abstract":"<jats:p> 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. <\/jats:p><jats:p> 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.\" <\/jats:p>","DOI":"10.1142\/s0218127403008041","type":"journal-article","created":{"date-parts":[[2003,10,16]],"date-time":"2003-10-16T10:47:26Z","timestamp":1066301246000},"page":"2377-2491","source":"Crossref","is-referenced-by-count":33,"title":["A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science Part II: Universal Neuron"],"prefix":"10.1142","volume":"13","author":[{"given":"Leon O.","family":"Chua","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering and  Computer Sciences, University of California at Berkeley, Berkeley, CA, 94720, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Valery I.","family":"Sbitnev","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and  Computer Sciences, University of California at Berkeley, Berkeley, CA, 94720, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sook","family":"Yoon","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and  Computer Sciences, University of California at Berkeley, Berkeley, CA, 94720, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1142\/3801"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127402006333"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127401002250"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127402005157"},{"key":"rf6","volume-title":"DNA: The Secret of Life","author":"Watson J.","year":"2003"},{"key":"rf7","volume-title":"A New Kind of Sciences","author":"Wolfram S.","year":"2002"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127403008041","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:14:33Z","timestamp":1565136873000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127403008041"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,9]]},"references-count":6,"journal-issue":{"issue":"09","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2003,9]]}},"alternative-id":["10.1142\/S0218127403008041"],"URL":"https:\/\/doi.org\/10.1142\/s0218127403008041","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,9]]}}}