Tetration: Iterative Enjoyment

摘要

© 2022 The Mathematical Association of America.Summary: This paper explores the hyper-operation of tetration involving both real and complex numbers. We describe some of the history related to this topic, and present tetration as a sequence using repeated exponentiaion. The authors use the Lambert W function and Lagrange inversion to describe how this sequence converges over a certain real interval. We then extend tetration to complex numbers and present a graph of part of the set of points in the complex plane for which the tetration sequence appears to converge. This graph has an intriguing, fractal-like structure. Potential connections with undergraduate mathematics courses are also discussed.