Braverman & Yampolsky have shown that there exist noncomputable Julia sets, i.e., there exist $c \in \mathbb{C}$ such that the Julia set of $f(z) = c + z^2$ is not computable. "A set is computable, if, roughly speaking, its image can be generated by a computer with an arbitrary precision."

Braverman, Mark, and Michael Yampolsky. "Non-computable Julia sets." Journal of the American Mathematical Society (2006): 551-578. (PDF download.)

My questions are:

Q. Is an explicit such $c$ known? A computable $c$?

It seems likely these questions are answered, perhaps in the cited paper. If anyone is familiar enough with this line of work to answer, I'd appreciate it.