{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,20]],"date-time":"2024-07-20T01:31:40Z","timestamp":1721439100881},"reference-count":14,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2014,6]]},"abstract":"<jats:p> The quadratic iteration is mapped using a nondistributive real scator algebra in three dimensions. The bound set S has a rich fractal-like boundary. Periodic points on the scalar axis are necessarily surrounded by off axis divergent magnitude points. There is a one-to-one correspondence of this set with the bifurcation diagram of the logistic map. The three-dimensional S set exhibits self-similar 3D copies of the elementary fractal along the negative scalar axis. These 3D copies correspond to the windows amid the chaotic behavior of the logistic map. Nonetheless, the two-dimensional projection becomes identical to the nonfractal quadratic iteration produced with hyperbolic numbers. Two- and three-dimensional renderings are presented to explore some of the features of this set. <\/jats:p>","DOI":"10.1142\/s0218127414300171","type":"journal-article","created":{"date-parts":[[2014,6,24]],"date-time":"2014-06-24T06:12:32Z","timestamp":1403590352000},"page":"1430017","source":"Crossref","is-referenced-by-count":2,"title":["An Intrinsically Three-Dimensional Fractal"],"prefix":"10.1142","volume":"24","author":[{"given":"M.","family":"Fern\u00e1ndez-Guasti","sequence":"first","affiliation":[{"name":"Lab. de \u00d3ptica Cu\u00e1ntica, Depto. de F\u00edsica, Universidad A. Metropolitana \u2013 Iztapalapa, 09340 M\u00e9xico D.F., Ap. postal. 55-534, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2014,6,23]]},"reference":[{"key":"rf1","volume-title":"Chaos: An Introduction to Dynamical Systems","author":"Alligood K. T.","year":"2000"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01228279"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1533\/9780857099594"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-1984-15240-6"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1002\/9780470987643"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1080\/10236190410001731443"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/s00006-013-0386-4"},{"key":"rf10","volume-title":"Quadratic Mappings and Clifford Algebras","author":"Helmstetter J.","year":"2008"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-3650-4"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/j.cag.2005.03.011"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1119\/1.17465"},{"key":"rf14","first-page":"135","volume":"6","author":"Pavlov D. G.","journal-title":"Hypercompl. Numb. Geom. Phys."},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7643-9893-4"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1119\/1.16288"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127414300171","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T17:16:26Z","timestamp":1565198186000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127414300171"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,6]]},"references-count":14,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2014,6,23]]},"published-print":{"date-parts":[[2014,6]]}},"alternative-id":["10.1142\/S0218127414300171"],"URL":"https:\/\/doi.org\/10.1142\/s0218127414300171","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,6]]}}}