Self-Affine Variants of the Sierpinski Carpet
Variants of several classic fractals can be generated by applying scaling factors in each dimension. This produces polygon-shaped holes in the figure. This Demonstration shows the results of affine transformations on the Sierpinski carpet.
Snapshot 1: moving the controller changes the shape of the interior hole from a square to a rectangle.
Snapshot 2: further iterations are constructed from affine transformations of the initial shape.
Snapshot 3: with the scaling factors and , the figure is the classic Sierpinski gasket.
 G. A. Edgar, Measure, Topology, and Fractal Geometry, New York: Springer-Verlag, 1990 p. 187.