{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T15:52:25Z","timestamp":1760889145127},"reference-count":16,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2016,1]]},"abstract":"<jats:p> The quadratic iteration is mapped within a nondistributive imaginary scator algebra in [Formula: see text] dimensions. The Mandelbrot set is identically reproduced at two perpendicular planes where only the scalar and one of the hypercomplex scator director components are present. However, the bound three-dimensional S set projections change dramatically even for very small departures from zero of the second hypercomplex plane. The S set exhibits a rich fractal-like boundary in three dimensions. Periodic points with period [Formula: see text], are shown to be necessarily surrounded by points that produce a divergent magnitude after [Formula: see text] iterations. The scator set comprises square nilpotent elements that ineluctably belong to the bound set. Points that are square nilpotent on the [Formula: see text]th iteration, have preperiod 1 and period [Formula: see text]. Two-dimensional plots are presented to show some of the main features of the set. A three-dimensional rendering reveals the highly complex structure of its boundary. <\/jats:p>","DOI":"10.1142\/s0218127416300020","type":"journal-article","created":{"date-parts":[[2016,2,19]],"date-time":"2016-02-19T06:18:57Z","timestamp":1455862737000},"page":"1630002","source":"Crossref","is-referenced-by-count":5,"title":["Imaginary Scators Bound Set Under the Iterated Quadratic Mapping in 1 + 2 Dimensional Parameter Space"],"prefix":"10.1142","volume":"26","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. 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