This is mainly an illustration of the sequence ${\displaystyle S}$ =  A327041, the bitwise ORs of the binary exponents of the non-negative integers.

The 8×256 matrix above shows the integers 0...255.
The 3×128 matrix below shows the sequence ${\displaystyle S}$.   Each of its columns corresponds to two columns of the matrix above.

The black dots in the matrix above are a scatterplot of ${\displaystyle S}$.
A dot can be on a light or a dark field. The first dot is split between both.
Columns where the dot is on a light/dark field are pink/blue. The respective integers (here 0...255) shall called female/male.

Let ${\displaystyle F}$ =  A246537 and ${\displaystyle M}$ =  A246418.
${\displaystyle F(n)}$ is the number of females and ${\displaystyle M(n)}$ is the number of males among the first ${\displaystyle 2^{2^{n}}}$ non-negative integers.

• ${\displaystyle F(3)=97}$ and ${\displaystyle M(3)=159}$.
  There are 128 dots. On the right all 64 are on dark. On the left 15 are completely and the first one is half on dark. So 79.5 dots are on dark, which is the expected half of 159.

• ${\displaystyle F(2)=3}$ and ${\displaystyle M(2)=13}$.   Among the first 8 dots there are 1.5 on light and 6.5 on dark background.

• ${\displaystyle F(1)=1}$ and ${\displaystyle M(1)=3}$.   Among the first 2 dots there are 0.5 on light and 1.5 on dark background.