  The author discusses particular solutions of a second order equation
designated by source equation. This equation is special because the metric of
the space where it is written is influenced by the solution, rendering the
equation recursive. The recursion mechanism is established via a first order
equation which bears some resemblance to Dirac equation. In this paper the
author limits the discussion to solutions with constant norm but makes use of
4-dimensional hypercomplex numbers in matrix representation, a concept that is
formally introduced in a section devoted to that aspect. The particular
solutions that are found exhibit symmetries that can be assigned to spin,
electric and color charges of elementary particles, leaving mass as a free
parameter. Massless particles can also be assigned to special solutions of the
source equation, with the cases of photons, gluons and gravitons clearly
identified, together with another massless particle which does not seem to be
related to anything detected experimentally. Another section deals with
particle dynamics under fields, showing that both gravitational and
electrodynamics can be modelled by geodesics of the spaces whose metric tensors
result from the recursion mechanism. Finally the author suggests two lines of
future work, one deriving fields from densities and currents of masses and
charges and the other one aimed at determining particles' masses.
