Sierpinsky

Sierpinsky's triangle-fractal

The construction starts with two copies of scheme Ā.
Select the tool [User-Defined \ Fractal-Socket _ _ ].
1) Click on the upper-most (smallest) triangle of scheme Į (which is a leaf of the relation-tree)
2) Click on the surrounding triangle (biggest one) of scheme Ā
Repeat some times the previous steps. Before to start working, we set, from the [Settings] menu, the points to be invisible.

The construction (of scheme B) is done by defining the middles of the sides of the big triangle and building (with the triangle-tool) the three triangles with vertices at two middles and one vertex of the big triangle. The procedure could be generalized by taking not the middles, but three arbitrary points on the sides and constructing similarly smaller triangles. Another generalization could be the division of a quadrangle and more general the division of a polygon.

http://users.math.uoc.gr/~pamfilos/