Overlapping resonant perturbations of Tokamak equilibrium magnetic fields can produce volumes with 'stochastic' field lines. The common assumption of a diffusive field line spreading in such volumes has not been found to be generally valid. Because numerical errors can feign stochasticity, a new mapping technique has been applied. Examples of overlapping perturbations have been evaluated by statistical means. Very long correlations contradict simple diffusion models. Increasing the perturbation amplitudes to large values does not necessarily enhance stochasticity, but new ordered structures in phase space can appear.