Filled Julia sets with empty interior are computable. Binder, I., Braverman, M., & Yampolsky, M. Found. Comput. Math., 7(4):405–416, 2007.
Filled Julia sets with empty interior are computable [link]Paper  doi  bibtex   
@ARTICLE{BBY07,
  author = {Binder, I. and Braverman, M. and Yampolsky, M.},
  title = {Filled {J}ulia sets with empty interior are computable},
  journal = {Found. Comput. Math.},
  year = {2007},
  volume = {7},
  pages = {405--416},
  number = {4},
  doi = {10.1007/s10208-005-0210-1},
  file = {BBY07.pdf:BBY07.pdf:PDF},
  fjournal = {Foundations of Computational Mathematics. The Journal of the Society
	for the Foundations of Computational Mathematics},
  issn = {1615-3375},
  keywords = {bib,cca},
  mrclass = {37F10 (03F60)},
  mrnumber = {2352604 (2008i:37084)},
  mrreviewer = {Peter Ha{\"{\i}}ssinsky},
  owner = {Vasco},
  timestamp = {2013.12.01},
  url = {http://dx.doi.org/10.1007/s10208-005-0210-1}
}

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