 Tetration.org What Lies Beyond Exponentiation? # Overview  Tetration by Escape Tetration by Period

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 $^{1}a=a, ^{2}a=a^a, ^{3}a=a^{a^a},$ 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.

The big question in tetration research is how can tetration be extended to complex numbers. How do you compute numbers like $^{.5}2$, and $^{\pi i}e$ ? This web site will show how to compute these and other problems. See the Tetration page for a one page overview of extending tetration to the complex numbers.