External Angles and Hubbard Trees

Heinz-Otto Peitgen and Peter H. Richter
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Heinz-Otto Peitgen: Universität Bremen, Fachbereich Mathematik
Peter H. Richter: Universität Bremen, Fachbereich Physik

Chapter 5 in The Beauty of Fractals, 1986, pp 63-92 from Springer

Abstract: Abstract It is well known that analytic functions f:ℂ→ℂ are a powerful tool for solving problems of two-dimensional electrostatics. The Cauchy-Riemann differential equations imply that Ref and Imf are both solutions to Laplace’s equation ∇2F= 0, and that the two families of curves Ref= const and Imf= const intersect each other orthogonally. Therefore, if u=Ref say, describes the surface of a charged conductor, the lines Ref= const are equipotential lines and Imf= const the corresponding field lines.

Date: 1986
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DOI: 10.1007/978-3-642-61717-1_5

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