For the sequence
\begin{equation}
a_{k+1}=\begin{cases}
a_k/2 & \text{if } a_k \equiv 0 \pmod 2, \\
3a_k+1 & \text{if } a_k \equiv 1 \pmod 2.
\end{cases}
\end{equation}
The Collatz conjecture is:
\begin{equation}
\forall\,a_0\in\mathbb{N}+1=\{1,2,3,\dots\}\\\,\exists\,k\ \text{such that}\ a_k=1
\end{equation}
I saw this video and thought of Collatz because the number of triangles in 2d Sierpinski is \(3n+1\) per iteration and the squares alignment makes me think of the division by 2.
I also think I remember \(1.58\) as the limit of a convergence rate for number of digits or something along those lines. Regardless, the analogy stuck better than most things I compare to this problem, so here's an orthographic visualization.
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