Placeholder Substructures III: A Bit-String-Driven ''Recipe Theory'' for Infinite-Dimensional Zero-Divisor Spaces
| dc.creator | de Marrais, Robert P. C. | |
| dc.date | 2007-04-02 | |
| dc.date | 2007-11-22 | |
| dc.date.accessioned | 2026-07-07T08:44:07Z | |
| dc.date.available | 2026-07-07T08:44:07Z | |
| dc.description | Zero-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.description | 32 pp., 1 fig. Third of 3-part "theorem/proof" exposition of 78-slide Powerpoint from NKS 2006, available at http://wolframscience.com/conference/2006/presentations/materials/demarrais.ppt V2: small fixes, 2 new notes. V3: Added small number of corrections (pp. 8, 15-16), one long remark (pp. 21-22), RE: 2nd type of box-kite flow pattern | |
| dc.identifier | https://arxiv.org/abs/0704.0112 | |
| dc.identifier | http://arxiv.org/abs/0704.0112 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142549 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 17D99 (Primary), 68Q80 (Secondary) | |
| dc.title | Placeholder Substructures III: A Bit-String-Driven ''Recipe Theory'' for Infinite-Dimensional Zero-Divisor Spaces | |
| dc.type | text |