The Sierpinski gasket is a base motif fractal where the base is a triangle. After subdivision in 4 equal triangles the motif is to remove the middle triangle:
Waclaw Sierpinski (1882-1969), a Polish mathematician, described the construction to give an example of a curve simultaneously Cantorian and Jordanian, of which every point is a point of ramification.
The fractal dimension of the curve is equal to log 3/ log 2, i.e. about 1.58496 1).
1) Fractal dimension = log N / log e, where N is the number of line segments
and e the magnification.
2) W.K. Ching, M. Erickson, P. Garik, P. Hickman, J. Jordan, S. Schwarzer, and L. Shorem Overcoming Resistance with Fractals: A New Way to Teach Elementary Circuits, in The Physics Teacher, Vol 32., No. 9 (December 1994), p546-551.