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Yes, the Sierpinski Gasket has a fractional dimension. It is known as a fractal and has a dimension of approximately 1.58496, which is between a one-dimensional and a two-dimensional object. This is one of the properties that makes the Sierpinski Gasket interesting and unique.
Sierpinski gasket
The Sierpinski triangle (also with the original orthography Sierpiński), also called the Sierpinski gasket or the Sierpinski Sieve, is a fractal and attractive fixed set named after the Polish mathematician Wacław Sierpiński who described it in 1915.
Sierpinski Gasket
Yes. If you mark the odd numbers in Pascal's Triangle, it would form Sierpinski's Gasket.