  We present a general procedure to generate infinitely many BBP and BBP-like
formulas for the simplest transcendental numbers. This provides some insight
and a better understanding into their nature. In particular, we can derive the
main known BBP formulas for $\pi$. We can understand why many of these formulas
are rearrangements of each other. We also understand better where some null BBP
formulas representing $0$ come from. We also explain what is the observed
relation between some BBP formulas for $\log 2$ and $\pi$, that are obtained by
taking real and imaginary parts of a general complex BBP formula. Our methods
are elementary, but motivated by transalgebraic considerations, and offer a new
way to obtain and to search many new BBP formulas and, conjecturally, to better
understand transalgebraic relations between transcendental constants.
