  A Monte Carlo code (ARTIS) for modelling time-dependent three-dimensional
spectral synthesis in chemically inhomogeneous models of Type Ia supernova
ejecta is presented. Following the propagation of gamma-ray photons, emitted by
the radioactive decay of the nucleosynthesis products, energy is deposited in
the supernova ejecta and the radiative transfer problem is solved
self-consistently, enforcing the constraint of energy conservation in the
co-moving frame. Assuming a photoionisation dominated plasma, the equations of
ionisation equilibrium are solved together with the thermal balance equation
adopting an approximate treatment of excitation. Since we implement a fully
general treatment of line formation, there are no free parameters to adjust.
Thus a direct comparison between synthetic spectra and light curves, calculated
from hydrodynamic explosion models, and observations is feasible. The code is
applied to the well known W7 explosion model and the results tested against
other studies. Finally the effect of asymmetric ejecta on broad band light
curves and spectra is illustrated using an elliptical toy model.
