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ON A GENERALIZED FATOU–JULIA THEOREM IN MULTICOMPLEX SPACES.
- Source :
-
Fractals . Sep2009, Vol. 17 Issue 3, p241-255. 15p. 8 Color Photographs. - Publication Year :
- 2009
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *FRACTALS
*DIMENSION theory (Topology)
*SYMMETRY
*STATICS
*MECHANICS (Physics)
Subjects
Details
- Language :
- English
- ISSN :
- 0218348X
- Volume :
- 17
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Fractals
- Publication Type :
- Academic Journal
- Accession number :
- 43792843