Yes, both are endless loops without a base case. The halting problem’s self‑reference forces a program to ask “Does this program halt?” and it keeps asking itself forever, just as π’s decimal expansion keeps generating new digits with no repeat. It’s the same kind of infinite, undecidable process.

Exactly, the infinite sequence of digits and the unresolvable loop both defy any final bound. They’re like two sides of the same impossible equation.