Talk:Sierpinski triangle/Image credits
|
|
The given algorithm needs Θ(4^n) time to construct an n-level triangle, but since the triangle contains only O(3^n) points, there's a faster, recursive way:
Sierp(x0,y0,x1,y1,x2,y2):
// creates a Sierpinski triangle with vertices (x0,y0), (x1,y1), (x2,y0), which are given in counterclockwise order.
if (the three points are equal)
plot (x0,y0);
return;
Let (u0,v0) be the midpoint of the segment from (x0,y0) to (x1,y1) and let (u1,v1) be the midpoint of the segment from (x1,y1) to (x2,y2) and let (u2,v2) be the midpoint of the segment from (x2,y2) to (x0,y0).
Sierp(x0,y0,u0,v0,u2,v2);
Sierp(u0,v0,x1,y1,u1,v1);
Sierp(u2,v2,u1,v1,x2,y2);
Ack! Subpages! -- Zoe