The Fractal Boundary of the Power Tower Function
|Title:||The Fractal Boundary of the Power Tower Function||Authors:||Lynch, Peter||Permanent link:||http://hdl.handle.net/10197/11256||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 function; Lambert W-function; Fractal mathematics||Other versions:||http://ludicum.org/ev/rm/17||Language:||en||Status of Item:||Not peer reviewed||Is part of:||Nuno Silva, J. Recreational Mathematics Colloquium V: Proceedings of the Recreational Mathematics Colloquium V||Conference Details:||Recreational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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