My name is Daniel Geisler, welcome to my web site dedicated to promoting research into the question of what lies beyond exponentiation. Tetration is defined as iterated exponentiation but while exponentiation is essential to a large body of mathematics, little is known about tetration due to its chaotic properties. The standard notation for tetration is 1a=a, 2a=aa, 3a=aaa, and so on. Mathematicians have been researching tetration since at least the time of Euler but it is only at the end of the twentieth century that the combination of advances in dynamical systems and access to powerful computers is making real progress possible. It is my hope that this site will have something of interest for everyone from high school students to mathematicians researching tetration. I particularly recommend taking a look at the section on fractals and maybe even getting a copy of Fractint and exploring tetration on your own.
Tetration sites with peer reviewed information
Check out Ioannis Galidakis' web site for his recent papers including On Extending hyper4 and Knuth's Up-arrow Notation to the Reals
Galidakis, Ioannis and Eric W. Weisstein,
Power Tower , From MathWorld--A Wolfram Web Resource
Nice website on background information relevant to tetration, with new content
constantly being added.
MacDonnell, J. F.
Some Critical Points of the Hyperpower Function,
International Journal of Mathematical Education, 1989, Vol. 20, #2, p.297
Informally peer reviewed
sci.math.research Number of good discussions on tetration research.
Tetration Forum Lively site on tetration research.
Other tetration sites
Andrew Robbins' Tetration web site.
Robbins has proposed a way to extend tetration to the real numbers.
Dmitrii Kouznetsov's Tetration and superlog web site.
Kouznetsov has also proposed a way of extending tetration.
Wikipedia: Tetration Worth checking out.