Yes, not only is it fractional, it is irrational. In fact, it is log3/log2 = 1.58, approx.
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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.
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Yes. If you mark the odd numbers in Pascal's Triangle, it would form Sierpinski's Gasket.
Sierpinski gasket
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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.