Braverman & Yampolsky have shown that there exist noncomputable [Julia sets](https://en.wikipedia.org/wiki/Julia_set),
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](http://www.ams.org/journals/jams/2006-19-03/S0894-0347-05-00516-3/S0894-0347-05-00516-3.pdf).)
> 
> 
> 


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.




---


**Answered**.
The question is answered in the paper Igor identified, particularly in its
full version:



> 
> Braverman, Mark, and Michael Yampolsky.
>  "Computability of Julia sets." [arXiv link](http://arxiv.org/abs/math/0610340v2). 2007.
> 
> 
> 


They prove there exist computable $c \in \mathbb{C}$ such that the Julia set
of $c + z^2$ is not algorithmically computable, and provide an algorithm 
for computing such a $c$. Under the assumption of a complex dynamics conjecture
(due to Buff & Chéritat),
they obtain a polynomial-time algorithm for computing such a $c$,
i.e., $n$ bits of $c$ can be computed in time polynomial in $n$.


No *explicit* $c$ is known, as far as I can tell.
(Their algorithms would not be easy to implement.) 



Is an explicit $c$ known to lead to a noncomputable Julia set?
Constructing such polynomials is the topic of a [follow-up paper by Braverman and Yampolsky.](http://www.math.toronto.edu/yampol/preprints/STOC07.pdf) (which, apparently, appeared in STOC '07). They don't give an explicit example, but give an algorithm to construct (arbitrarily close) approximations thereto.


