/sci/ - Science & Math

I found another interesting series of nested functions
[eqn]
\begin{align}
f_1(x, y) &= \exp(x - \exp(y)) \\
f_{n + 1}(x, y) &= \begin{cases}
f_n(x, x + \exp(y)) &n \text{ even} \\
f_n(x, x - \exp(y)) &n \text{ odd}
\end{cases}
\end{align}
[/eqn] and the related series
[eqn]g_n(x) = f_n(x, x)[/eqn] so that e.g. [math]g_5[/math] looks like
[eqn]e^{x-e^{x+e^{x-e^{x+e^{x-e^x}}}}}[/eqn] Here is a plot of [math]g_1[/math] through [math]g_{24}[/math] where the color goes from blue to red as [math]n[/math] increases.

Also anyone recognize [math]\lambda \exp(x - \lambda \exp(x))[/math] as the PDF of some named distribution?