26
Jun
04

### Inverse Julia Set Fractal

Here is cubic Julia set fractal using the inverse Julia set technique. This technique is good for showing the edges of the set, but some regions are faint because they attract much slower

```(* runtime: 4 seconds *) InvertList[zlist_] := Flatten[Map[(# - zc)^(1/3){1, -(-1)^(1/3) , (-1)^(2/3)} &, zlist], 1]; zc = -0.5 - 0.05 I; zlist = {0}; Do[zlist = InvertList[zlist], {10}]; ListPlot[{Re[#], Im[#]} & /@ zlist, PlotStyle -> PointSize[0.005], AspectRatio -> 1, Axes -> None];```

This can be improved using pruning. The following code was adapted from Mark McClure’s Mathematica code:
```(* runtime: 4 seconds *) InvertList[zlist_] := Flatten[Map[Floor[130(# - zc)^(1/3){1, -(-1)^(1/3), (-1)^(2/3)}]/130 &, zlist], 1]; zc = -0.5 - 0.05 I; zlist = Nest[InvertList, {0}, 8]; zlist2 = zlist; While[zlist2 =!= {}, zlist2 = Complement[InvertList[zlist2],zlist]; zlist = Union[zlist2, zlist]]; ListPlot[{Re[#], Im[#]} & /@ zlist,PlotStyle -> PointSize[0.005], AspectRatio -> 1, Axes -> None];```

## Welcome !

You will find here some of my favorite hobbies and interests, especially science and art.

I hope you enjoy it!

Subscribe to the RSS feed to stay informed when I publish something new here.

I would love to hear from you! Please feel free to send me an email : bugman123-at-gmail-dot-com

• 553,072 hits