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Self-Affine Variants of the Sierpinski Carpet

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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.

Contributed by: Robert Dickau (September 2018)
Open content licensed under CC BY-NC-SA

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 and , the figure is the classic Sierpinski gasket.

Reference

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

Snapshots

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