I know how to construct the Koch snowflake:
f[{a:{x1_,y1_},b:{x2_,y2_}}] :=
Partition[{a,(2a+b)/3,{3(x1+x2)+√3(y1-y2),√3(x2-x1)+3 (y1+y2)}/6,(a+2b)/3,b},2,1];
pts=Join@@Nest[Join@@f/@#&,.5{{{0,0},{2,0}},{{2,0},{1,-√3}},{{1,-√3},{0,0}}},5];
Graphics[Polygon @ pts]
and draw a hue disk (How do I draw a Circular Graph colored like this in Mathematica?), but how do I draw a Koch snowflake with hue-based coloring like this? Vector diagrams are better than images.