Using #SageMath instead of #Maxima was more productive (the syntax is much nicer, though I think #Sage may use Maxima under the hood).

Managed to derive the symbolic Jacobian of the #Mandelbulb iteration (#Juliabulb variant, where the `+C` is a constant), and substituted in some numerical values to get the condition number at various points.

The even-power bulbs have singularities at the poles (near x = y = 0) with the condition number increasing without bounds, and the odd-power bulbs also have singularities, e.g. power 3 bulb near $(x = 0, y = t cos(pi/6), z = t sin(pi/6))$.

This can probably be deduced from the Jacobian determinant which I think works out as:
$$ (n r^n)^3 cos(n \phi) log(r/cos(\phi)) / 3$$
When it is 0, problems...