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A Generalized Mandelbrot Set of Polynomials of Type 𝐸𝑑 for Bicomplex Numbers

  • Ahmad Zireh
Published/Copyright: March 10, 2010
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Georgian Mathematical Journal
From the journal Volume 15 Issue 1

Abstract

We use a commutative generalization of complex numbers called bicomplex numbers to introduce the bicomplex dynamics of polynomials of type 𝐸𝑑, 𝑓𝑐(𝑀) = 𝑀(𝑀 + 𝑐)𝑑. Rochon [Fractals 8: 355–368, 2000] proved that the Mandelbrot set of quadratic polynomials in bicomplex numbers of the form 𝑀2 + 𝑐 is connected. We prove that our generalized Mandelbrot set of polynomials of type 𝐸𝑑, 𝑓𝑐(𝑀) = 𝑀(𝑀 + 𝑐)𝑑, is connected.

Received: 2006-12-04
Published Online: 2010-03-10
Published in Print: 2008-March

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