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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.

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  • $\begingroup$ Did I do something wrong? $\endgroup$ – Halsey12 Jul 18 '20 at 21:16
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    $\begingroup$ Can you please type your code so that those who wish to help you can copy and paste it? $\endgroup$ – CA Trevillian Jul 18 '20 at 21:18
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    $\begingroup$ 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. $\endgroup$ – CA Trevillian Jul 18 '20 at 21:22
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    $\begingroup$ 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. $\endgroup$ – CA Trevillian Jul 18 '20 at 23:53
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    $\begingroup$ @Halsey12: JuliaSetPlot[-1, ColorFunction -> None] $\endgroup$ – Moo Jul 19 '20 at 12:13
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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

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  • $\begingroup$ Not sure why this would get a downvote, great answer! I forgot about this function! +1 $\endgroup$ – CA Trevillian Jul 19 '20 at 23:28
  • $\begingroup$ @murray, add the PlotStyle->Black option to set the curve to black. $\endgroup$ – creidhne Jul 20 '20 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 '20 at 14:56

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