His definition of the dimension is quite similar to the definition of the dimension of a fractal. His definition also works better than euclidean dimension, e.

His definition of the dimension is quite similar to the definition of the dimension of a fractal. His definition also works better than euclidean dimension, e.g. for a grid on cylinder euclidean dimension will be 3 and his definition will give 2. I think a modification of the definition above to allow minimum dimension of non-euclidean space will be same as Wolframs definition for the cases when dimension of the graph is not fractional number.