  The use of type Ia supernovae as distance indicators for cosmology has
initiated a search for theoretical arguments supporting the empirical
calibration methods applied. To this end, as a first step, a sound
understanding of the origin of the observed diversity in type Ia supernova
properties is needed. Here we present a first systematic study of effects
resulting from changing some physical parameters of three-dimensional
deflagration models of thermonuclear supernovae. In our study we vary the
progenitor's carbon-to-oxygen ratio and its central density prior to ignition
because both properties are not well determined by stellar evolution theory and
they may change from supernova to supernova. Next we compute for these
explosion models the nucleosynthesis yields in a post-processing step. This, in
addition, allows us to study variations in the progenitor's metallicity by
means of different $^{22}$Ne mass fractions in the initial composition. We find
that the progenitor's carbon-to-oxygen ratio and its central density affect the
energy release of the models and thus the expansion velocity of the supernova.
Moreover, we find that changing the metallicity and the central density changes
the production of radioactive $^{56}$Ni and thus affects the luminosity. In
contrast, the carbon-to-oxygen ratio has little effect on the $^{56}$Ni
production. Implications of the found variations of the explosion energy and
the produced $^{56}$Ni mass for the type Ia supernova diversity are discussed.
