ON A GENERALIZED FATOU–JULIA THEOREM IN MULTICOMPLEX SPACES
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In this article we introduce the hypercomplex 3D fractals generated from Multicomplex Dynamics. We generalize the well known Mandelbrot and filled-in Julia sets for the multicomplex numbers (i.e. bicomplex, tricomplex, etc.). In particular, we give a multicomplex version of the so-called Fatou-Julia theorem. More precisely, we present a complete topological characterization in ℝ2n of the multicomplex filled-in Julia set for a quadratic polynomial in multicomplex numbers of the form w2 + c. We also point out the symmetries between the principal 3D slices of the generalized Mandelbrot set for tricomplex numbers.
2012 ◽
Vol 34
(1)
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pp. 171-184
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2017 ◽
Vol 39
(9)
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pp. 2481-2506
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2005 ◽
Vol 15
(09)
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pp. 3039-3050
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2008 ◽
Vol 22
(04)
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pp. 243-262
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1994 ◽
Vol 14
(4)
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pp. 787-805
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