The Fractal Boundary of the Power Tower Function

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Title: The Fractal Boundary of the Power Tower Function
Authors: Lynch, Peter
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Date: 23-Aug-2017
Online since: 2020-01-17T16:34:57Z
Abstract: We consider the function called the power tower function, defined by iterated exponentiation (or tetration) of the complex variable z. For real values x, it converges on the interval exp(−e)<x <exp(1/e). The function may be expressed as the inverse of the function x=y1/y, allowing an extension of the domain to 0< x <exp(1/e). It may also be expressed in terms of the Lambert W-function, enabling an analytical continuation to the complex plane.The boundary of the region of the complex plane for which the power tower converges to a finite value is fractal in nature. We show this by repeatedly zooming to higher magnifications, illustrating the deliciously intricate nature of the boundary.
Type of material: Conference Publication
Publisher: Associacao Ludus
Copyright (published version): 2017 Associacao Ludus
Keywords: Tetration functionLambert W-functionFractal mathematics
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Language: en
Status of Item: Not peer reviewed
Is part of: Nuno Silva, J. Recreational Mathematics Colloquium V: Proceedings of the Recreational Mathematics Colloquium V
Conference Details: Recreational Mathematics Colloqium V, Lisbon, Portugal, 28-31 January 2017
ISBN: 978-989-99506-2-7
Appears in Collections:Mathematics and Statistics Research Collection

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