So the leading digit graph looks pretty much the same between 10 iterations and 10,000. The double leading digit graph doesn’t. Is that a resolution issue or indicative of some deeper, underlying property?

Let’s do a million iterations, for 1,000,001 values of x.

The double leading digit graph looks fairly similar to the n=10,001 graph.

But there’s a catch.

The 11423 (a) iteration yielded x = 0.5 due to truncation error.

The next time that happens is n=44063. (b)

It happens again at 79519. (c)

(c-a)/(b-a) =|= 2

Inception noises.