I'm taking an introductory comp-sci course this semester, and my professor pulled up this graphic while explaining mergesort (the graphic shows blocks of size $2^{-n}$). For some reason, the vertical lines that appear in this photo look familiar to me, but I can't seem to find anything online or put my finger on it. Is there a name for a fractal that's generated in this manner?
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It bears a small resemblance to both the Cantor set and the Blancmange curve, mainly because those are both fractals that are depicted as heights above (or below) an interval that gets split in some way.
Looks like the position of the first nonzero bit when counting in binary.
An expression might be $v_2(n)$ where $v_m(n)$ is the largest power of $m$ that divides $n$.
This can be expressed in a few ways.
$m^{v_m(n)} | n$, $m^{v_m(n)+1} \not\mid n$.
Algorithmically,
$v_m(n)= \begin{cases} m | n &: 1+v_m(n/m)\\ \text{else}&: 0\\ \end{cases} $