Fixed Point of $x_{n+1}=i^{x_n}$ [duplicate]

complex-numbers tetration power-towers

We had this question quite recently, as I recall. But I cannot now find it. Anyway, here we see $a_n$ for $n$ from $1$ to $50$. They are converging, right?

enter image description here

The limit is: $$ \frac{2i}{\pi}W\left(\frac{-i\pi}{2}\right) \approx .4382829366+.3605924718 i $$ Of course $W$ is the Lambert W function.

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