The Mandelbrot Set:
$Z \mapsto Z² + C$ (or more precisely) $Z_{i+1} = Z_i ^2 + C$
Where $Z$ and $C$ are complex numbers.
Can this well-established equation be rearranged to determine things that would otherwise take a large or infinite number of iterations or tests with different values of $C$?
Such as the smallest bounding box that would contain all values for $C$, where $Z$ bails out in a given iteration.