something between a point and a line #tibees #fractal #dimension #cantor

Fractals are shapes that exist between dimensions. Let me introduce you to one that exists between zero and one dimension. Take a line of length one, divide it into three parts of length one-third. Just keep the two end segments and throw the rest out, so 'n' is equal to two. Now repeat that process. The remaining fragments are split into three parts of length one over nine. Keep the two ends of each, and you now have four fragments. Continue this process and you will have infinitely many points in a line of zero length. It's called the cantor set. We can use this formula to find the dimension of the cantor set, and it works out to be 0.6309, which is indeed between zero and one, more than a point, but less than a line.