I consider anisotropic cosmological dynamics in Einstein-Gauss-Bonnet gravity. It is shown that a natural outcome of such evolution is a splitting of initially totally anisotropic space into a product of two isotopic sub spaces. If the expanding sub space is 3-dimensional, this scenario could explain the appearance of our world within multidimensional Universe. Moreover, non-zero spatial curvature of “inner” sub space can stabilise it, leading to effective Friedmann dynamics for the expanding sub space.