Mathematica 67
ListPlot@NestList[(#+RandomChoice@{{0,0},{2,0},{1,2}})/2&,{0,0},8!]
Mathematica 92
Graphics@Polygon@Nest[Join@@(Mean/@#&/@#~Tuples~2~Partition~3&/@#)&,{{{0,0},{2,0},{1,1}}},3]
chyanog
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