The basic hypothesis the author sets up is that the foundations of physics lie in mathematical aesthetics. In fact, the author considers a field theory in Cartesian space under the following assumptions: (1) Data are specified at a single point rather than on a hypersurface. (2) All tensors are treated in a uniform way so far as change is concerned. (3) Integrations depend on the path, and in determining the field no integration path is favored over any other integration path. (4) There exists a unique change function \(\Gamma^ i_{jk}\) at each point. In the past the author emphasized lattice solutions with the purpose of trying to shed light on certain basic physical concepts which are present even when the system is simple. In this paper the author does not use lattice systems as a base, but considers more general origin point data and finds a solution that has no regular appearance and is called chaotic. The numerical calculation done in connection with this system is the most extensive and uses the most accurate grids in the work up to date. Results are checked by using different grid sizes. The author also found a three-dimensional space-time system not based on any obvious lattice system and such that trajectories cannot be followed in time since maxima (minima) appear and disappear.