Self-Affine Variants of the Sierpinski Carpet

iterations

i

1

2

3

4

(x scale, y scale)

	0.333
0.333

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.

Details

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

1/3

and

1/3

, the figure is the classic Sierpinski gasket.

References

[1] G. A. Edgar, Measure, Topology, and Fractal Geometry, New York: Springer-Verlag, 1990 p. 187.

Permanent Citation

Robert Dickau

"Self-Affine Variants of the Sierpinski Carpet" from the Wolfram Demonstrations Project http://demonstrations.wolfram.com/SelfAffineVariantsOfTheSierpinskiCarpet/
Published: September 6, 2018