# 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? – Halsey12 Jul 18 '20 at 21:16
• Can you please type your code so that those who wish to help you can copy and paste it? – CA Trevillian Jul 18 '20 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. – CA Trevillian Jul 18 '20 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. – CA Trevillian Jul 18 '20 at 23:53
• @Halsey12: JuliaSetPlot[-1, ColorFunction -> None] – Moo Jul 19 '20 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 – CA Trevillian Jul 19 '20 at 23:28
• @murray, add the PlotStyle->Black option to set the curve to black. – creidhne Jul 20 '20 at 1:51
• @creidhne: Of course! I thought I had tried that but got some unexpected result; I was quite wrong. – murray Jul 20 '20 at 14:56