The attractor structure of logarithmic iterations in the complex plane
Pascal Wallisch
TL;DR
This paper investigates the behavior of iterative logarithmic functions in the complex plane, revealing that they converge to specific attractor points whose structure varies with the base used.
Contribution
It introduces a novel empirical approach to analyze the attractor structures of logarithmic iterations in the complex plane, highlighting the dependence on the base.
Findings
Iterative logarithmic functions converge to attractor points in the complex plane.
Different logarithmic bases lead to different attractor points.
The geometric structure of these attractors is characterized.
Abstract
We use the methods of empirical mathematics to show that iterative logarithmic operations will result in an attractor point on the complex plane. Moreover, we demonstrate that different bases converge onto different attractors. Finally, we elicit the geometric structure of these attractors.
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Taxonomy
TopicsIterative Methods for Nonlinear Equations