论文信息 - A GENERALIZED MANDELBROT SET FOR BICOMPLEX NUMBERS

A GENERALIZED MANDELBROT SET FOR BICOMPLEX NUMBERS

We use a commutative generalization of complex numbers called bicomplex numbers to introduce bicomplex dynamics. In particular, we give a generalization of the Mandelbrot set and of the "filled-Julia" sets in dimensions three and four. Also, we establish that our version of the Mandelbrot set with quadratic polynomial in bicomplex numbers of the form w2 + c is identically the set of points where the associated generalized "filled-Julia" set is connected. Moreover, we prove that our generalized Mandelbrot set of dimension four is connected.

Dominic Rochon | D. Rochon

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