# Is there a mathematical term, practical application, or area of math that covers a function raised to itself?

Some abstract examples would be: $f(x)^{f(x)}$ or $f(x)^{f(x)^{f(x)...}}$ Actual equations I've attempted to look at can be viewed here on desmos.com There seems to be a pattern of common convergence, and a relation to the functions raised to a constant power, but in my searches I have yet to find any meaning or usage.

• Wikipedia calls it tetration–and it lists other coined terms. $f(x)^{f(x)^{f(x)\cdots}}$ can be written compactly as $^nf(x)$. – Antonio DJC Feb 23 '17 at 4:55

$f(x) = \sin(x) \quad \rightarrow \quad f(x)^{f(x)}$