The Fractal Boundary of the Power Tower Function

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dc.contributor.authorLynch, Peter- Associacao Ludusen_US
dc.descriptionRecreational Mathematics Colloqium V, Lisbon, Portugal, 28-31 January 2017en_US
dc.description.abstractWe 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.en_US
dc.publisherAssociacao Ludusen_US
dc.relation.ispartofNuno Silva, J. Recreational Mathematics Colloquium V: Proceedings of the Recreational Mathematics Colloquium Ven_US
dc.subjectTetration functionen_US
dc.subjectLambert W-functionen_US
dc.subjectFractal mathematicsen_US
dc.titleThe Fractal Boundary of the Power Tower Functionen_US
dc.typeConference Publicationen_US
dc.statusNot peer revieweden_US
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