@nprofile1q... it looks like others have submitted issues and PRs suggesting to use other irrational numbers too.
I think that all kind of flavors are possible if one uses the Spigot algorithm, since it allows to efficiently find any binary substring inside of the binary representation of any transcendental number, as long as it can be expanded into an infinite series.
(p.s. not sure if it applies to algebraic irrational numbers too though, i.e. if the algorithm still works fine with e.g. √2).