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The Fractal Boundary of the Power Tower Function
Author(s)
Date Issued
2017-08-23
Date Available
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
Web versions
Language
English
Status of Item
Not peer reviewed
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
This item is made available under a Creative Commons License
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