The Sierpinski curve is a base motif fractal where the base is a square. After subdivision in 3x3 equal squares the motif is to remove the middle square:
The curve is also known as the Sierpinski (universal plane) curve,
Sierpinski square or the Sierpinski carpet.
The curve is the only plane locally connected one-dimensional continuum S
such that the boundary of each complementary domain of S is a simple
closed curve and no two of these complementary domain boundaries intersect.
The fractal dimension of the curve is equal to log 8/
log 3, i.e. about 1.8928 1).
Professor Gerda de Vries of the University of Alberta designed a quilt named ´Sierpinksi Meets Mondrian´, based on the Sierpinski curve. The quilt was made in 2002 in response to the Edmonton & District Quilters' Guild challenge to create a quilt in the theme ´Voices in Cloth´. It was made for the entry category ´A Picture is Worth a Thousand Words´.
1) Fractal dimension = log N / log e, where N is the number of line segments
and e the magnification.