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On The Mandelbrot Set For I**2 = ±1 And Imaginary Higgs Fields, Jonathan Blackledge

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We consider the consequence of breaking with a fundamental result in complex analysisby lettingi2=±1wherei=√−1is the basic unit of all imaginary numbers. An analysis of theMandelbrot set for this case shows that a demarcation between a Fractal and a Euclidean object ispossible based oni2=−1andi2= +1, respectively. Further, we consider the transient behaviourassociated with the two cases to produce a range of non-standard sets in which a Fractal geometricstructure is transformed into a Euclidean object. In the case of the Mandelbrot set, the Euclideanobject is a square whose properties are investigate. Coupled with the associated Julia sets and othercomplex plane mappings, this …