(*This is MATHEMATICA code for drawing the usual VonKoch snowflake.After the code has been loaded,typing `KochSnowflake[n]' will draw the nth generation of the snowflake*)g=0.5;
w=.002;
KochSnowflake[n_Integer?NonNegative,g_,w_]:=Graphics[{GrayLevel[g],Thickness[w],FixedPoint[(#1/.Line[{start_,finish_}]:>doline[start,finish])&,{Line[{{0,0},{1/2,Sqrt[3]/2}}],Line[{{1/2,Sqrt[3]/2},{1,0}}],Line[{{1,0},{0,0}}]},n]}];

Show[AspectRatio->Automatic,PlotRange->All]

doline[start_,finish_]:=Module[{vec,normal},vec=finish-start;
normal=Reverse[vec]{-1,1}Sqrt[3]/6;
{Line[{start,start+vec/3}],Line[{start+vec/3,start+vec/2+normal}],Line[{start+vec/2+normal,start+2 vec/3}],Line[{start+2 vec/3,finish}]}]


vk[n_]:=Show[KochSnowflake[n,0,.005],AspectRatio->Automatic,PlotRange->All]

vk[4]