Placeholder Substructures I: The Road from NKS to Scale-Free Networks Is Paved with Zero-Divisors

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dc.creatorde Marrais, Robert P. C.
dc.date2007-03-26
dc.date2007-11-22
dc.date.accessioned2026-07-07T08:44:20Z
dc.date.available2026-07-07T08:44:20Z
dc.descriptionZero-divisors (ZDs) derived by Cayley-Dickson Process (CDP) from N-dimensional hypercomplex numbers (N a power of 2, at least 4) can represent singularities and, as N approaches infinite, fractals -- and thereby,scale-free networks. Any integer greater than 8 and not a power of 2 generates a meta-fractal or "Sky" when it is interpreted as the "strut constant" (S) of an ensemble of octahedral vertex figures called "Box-Kites" (the fundamental building blocks of ZDs). Remarkably simple bit-manipulation rules or "recipes" provide tools for transforming one fractal genus into others within the context of Wolfram's Class 4 complexity.
dc.descriptionComments: 20 pp., 2 fig. First of 3-part "theorem/proof" exposition of 78-slide Powerpoint from Wolfram Science's NKS 2006, available at http://wolframscience.com/conference/2006/presentations/materials/demarrais.ppt [v2: small fixes][v3: remarks added(p. 17) RE: 2nd kind of box-kite flow pattern, and future work focusing on it.]
dc.identifierhttps://arxiv.org/abs/math/0703745
dc.identifierhttp://arxiv.org/abs/math/0703745
dc.identifierComplex Systems, 17 (2007) 125-142
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/142621
dc.subjectRings and Algebras
dc.subject17D99 (Primary), 68Q80 (Secondary)
dc.titlePlaceholder Substructures I: The Road from NKS to Scale-Free Networks Is Paved with Zero-Divisors
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