This code shows how to create 3D printable Mandelbrot and filled Julia sets.
You are welcome to use this code for non-commercial purposes. If you do so, please send me an email and let me know how it goes!
Evelyn Sander, esander@gmu.edu GMU, 2016-2017

MandelbrotSetPlot[MaxIterations->20]

MandelbrotSetPlot[{-0.65+0.47I,-0.4+0.72I},MaxIterations->100]

data=Table[MandelbrotSetDistance[#]/4&[x+I*y],{y,-1.5,1,.02},{x,-2,.6,.02}];
ListPlot3D[data, Filling->Bottom]

data=Table[MandelbrotSetDistance[x+I*y, "Interior",MaxIterations->40],{x,-2.,1.,.031},{y,-1.5,1.5,.031}];
ListPlot3D[data,Mesh->None,PlotRange->Full,Filling->Bottom]

data=Table[Max[MandelbrotSetDistance[#,"Interior"],MandelbrotSetDistance[#]/4]&[x+I*y],{y,-1.5,1,.02},{x,-2,.6,.02}];
ListPlot3D[data, Filling->Bottom]

a =ListPlot3D[MandelbrotSetIterationCount[Table[x+I*y,{x,-2,1,0.01},{y,-1.5,1.5,0.01}],MaxIterations->20]+1,Mesh->False,Filling->Bottom]

JuliaSetPlot[0.365-0.37I,PlotLegends->Automatic]

ListPlot3D[JuliaSetIterationCount[0.365-0.37I,Table[x+I*y,{x,-2,1,0.01},{y,-1.5,1.5,0.01}],MaxIterations->20]+1,Mesh->False,Filling->Bottom]

Graphics3D[
Table[{ Sphere[Append[#,-δ^2 100], δ]& /@ JuliaSetPoints[0.365-0.37I,"ClosenessTolerance"->δ]},
{δ, 0.1, 0.01, -0.01}]]

Export["mandel.stl",a]