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FRACTALS WITH HYPERBOLIC SCATORS IN 1 + 2 DIMENSIONS

M. FERNÁNDEZ-GUASTI

Lab. de Óptica Cuántica, Depto. de Física, Universidad A. Metropolitana Iztapalapa, 09340 México Ap. Postal. 55-534 D.F., Mexico

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https://doi.org/10.1142/S0218348X15500048Cited by:0 (Source: Crossref)

Abstract

A nondistributive scator algebra in 1 + 2 dimensions is used to map the quadratic iteration. The hyperbolic numbers square bound set reveals a rich structure when taken into the three-dimensional (3D) hyperbolic scator space. Self-similar small copies of the larger set are obtained along the real axis. These self-similar sets are located at the same positions and have equivalent relative sizes as the small M-set copies found between the Myrberg-Feigenbaum (MF) point and -2 in the complex Mandelbrot set. Furthermore, these small copies are self similar 3D copies of the larger 3D bound set. The real roots of the respective polynomials exhibit basins of attraction in a 3D space. Slices of the 3D confined scator set, labeled (s;x,y), are shown at different planes to give an approximate idea of the 3D objects highly complicated boundary.

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