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

Fig. 1 Fig. 2

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]

Thanks in advance.

  • $\begingroup$ Did I do something wrong? $\endgroup$
    – Halsey12
    Jul 18, 2020 at 21:16
  • 2
    $\begingroup$ Can you please type your code so that those who wish to help you can copy and paste it? $\endgroup$ Jul 18, 2020 at 21:18
  • 2
    $\begingroup$ 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. $\endgroup$ Jul 18, 2020 at 21:22
  • 1
    $\begingroup$ 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. $\endgroup$ Jul 18, 2020 at 23:53
  • 1
    $\begingroup$ @Halsey12: JuliaSetPlot[-1, ColorFunction -> None] $\endgroup$
    – Moo
    Jul 19, 2020 at 12:13

1 Answer 1


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.)

Julia plot with axes and ticks

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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.