Statistical analysis of a multiply-twisted helix

A multiply-twisted helix, in which a one-dimensional array of components is twisted, producing a helix which if twisted itself produces a doubly-twisted helix, and so on, in which there are couplings between adjacent rounds of helices, was investigated using a cellular automaton and the spectral statistics of a quantum particle. A useful distance between the components of the structure is measured using a cellular automaton, the dynamics of which is simulated for a number of initial conditions in order to determine the degree of connectivity between the components. The area of the sphere with radius r, on the basis of the above distance, is shown to be proportional to r2 when r is small. The Anderson transition was investigated based on the spectral statistics of a quantum particle in a multiply-twisted helix with on-site random potentials. As the strength of the on-site random potentials increases, the Anderson transition occurs. Both results support our conclusion that the number of dimensions is always three for every multiply-twisted helix if the couplings between adjacent rounds are strong enough.