On the Aesthetics of Sierpinski Gaskets Formed from Large Pascal’s Triangles

The mathematical characterization of patterns in Pascal’s triangle is useful and can be achieved by a variety of brute-force computations, but sometimes at a cost of the loss of an intuitive feeling for the regularities and irregularities in the structure. The graphic and mathematical approach described here reveals a visually striking and intricate class of patterns that make up a family of regular fractal networks known as Sierpinski gaskets. The figures indicate self-similarity of the gasket structures for several orders of dilational invariance.