# Plot Julia - Fractal

I want to obtain the following figure, but I did not manage to obtain it, any suggestion?

julia[c_, z_, m_] :=
ListPlot[{Re[#], Im[#]} & /@
Nest[Flatten[(Map[w, #] /. k -> c), 1] &, {z}, m],
AspectRatio -> Automatic, Prolog -> PointSize[250]];

julia[0.4 + 0.7 I, 2 + I, 15]


• Did I do something wrong? Commented Jul 18, 2020 at 21:16
• Can you please type your code so that those who wish to help you can copy and paste it? Commented Jul 18, 2020 at 21:18
• From what I see your w and k are blue meaning they are undefined, this may be the source of your issues. But please edit your post with your code in a typed, copy and paste-able format, so that others may test and see what the problem is. You can use markdown code formatting to make it more clear that it is code as well. Commented Jul 18, 2020 at 21:22
• you need to define your w that is, according to your code, a function of z with some constant k. I don’t think your numbers are right for w[z_]:=z^2+k, however. Commented Jul 18, 2020 at 23:53
• @Halsey12: JuliaSetPlot[-1, ColorFunction -> None]
– Moo
Commented Jul 19, 2020 at 12:13

Just to make the result a bit closer to the image you showed:

JuliaSetPlot[-1, ColorFunction -> None,
AxesOrigin -> {0, 0}, Axes -> True, Frame -> False,
PlotStyle->Black,ImageSize -> Large,
Ticks -> {Automatic, {-0.75, -0.25, 0.25, 0.75}},
BaseStyle -> 14]


(Added PlotStyle -> Black to make result like original question's image.)

• Not sure why this would get a downvote, great answer! I forgot about this function! +1 Commented Jul 19, 2020 at 23:28
• @murray, add the PlotStyle->Black option to set the curve to black. Commented Jul 20, 2020 at 1:51
• @creidhne: Of course! I thought I had tried that but got some unexpected result; I was quite wrong. Commented Jul 20, 2020 at 14:56