numbers in order: 2 -- 2^2^0 4 -- 2^2^1 16 -- 2^2^2 256 -- 2^2^3 65,536 -- 2^2^4 yes, 8 is 2^2^1.5849... and here's proof: 8 = 2^2^x 2^3 = 2^2^x 2^3 and 2^2^x are both powers of 2, so we can take the exponent and solve it. 2^3 = 2^2^x then becomes 3 = 2^x 3 = 2^x to find x, we must get log₂(3), which is how you find the exponent. log₂(3) = x log₂(3) = 1.5849... yes that is the dimension of the Serpinski Triangle
