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This is fantastic! It would probably be mesmerizing to watch the pattern emerge in an accelerated animation, GIF or video. Not sure if this is possible.
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Dear Sander,
great idea to use the “chaos game” this way - I already had a lot of fun playing around with this nice idea! Thanks for sharing !!!
Here I just have a remark: I noticed that instead of applying the respective randomizing function on single points, it can be applied on the whole region (using TransformedRegion). The result then would be a clean region or a vector graphic:
(* MaxCellMeasure: to be chosen as big as possible! *)
reg = RegionResize[DiscretizeGraphics[Text[Style["\[Wolf]", Bold, 20]], _Text, MaxCellMeasure -> 3.1], 0.7];
pts4 = {{-1, -1}, {1, -1}, {1, 1}, {-1, 1}};
regs = Flatten[Table[NestList[TransformedRegion[#, (RandomChoice[pts4] + #)/2. &] &, reg, 6], 3000], 1];
regsd = DeleteDuplicates[regs];
(* in case a region is wanted: *)
(* totalReg=RegionUnion[regsd]; *)
obj = Reverse[MeshPrimitives[#, 2] & /@ regsd];
Graphics[obj, ImageSize -> 700]
But doing it this way one definitely would need a more systematic approach instead of randomly choosing a transformation and then deleting duplicates …
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=wolfes.png&userId=32203
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Hi Henrik,
Yes! This is indeed another way. However you will not be able to see the ‘density’ of the points. For the square it is more-or-less trivial, but there are chaos games where the density itself gives very rich patterns. Yours would converge much fast though 
Cheers!
Sander
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Hi Sander,
yes, yes - I totally agree: The chaos game relies on points! As I said - I was just playing around. To me it was rather surprising that Region and friends still work in that less simple context.
Best regards from Germany!
Henrik
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