On a new class of planar fractals: the Pascal-Sierpinski gaskets

Abstract

A new class of planar fractals called the Pascal-Sierpinski gaskets is described, of which the well known Sierpinski gasket is a special case. Some of these gaskets are true Mandelbrot fractals possessing non-integral dimensions as well as self-similarity; the remaining ones are not self-similar, but appear to have nonintegral dimensions.