  The diversity of Type Ia supernova (SN Ia) photometry is explored using a
grid of 130 one-dimensional models. It is shown that the observable properties
of SNe Ia resulting from Chandrasekhar-mass explosions are chiefly determined
by their final composition and some measure of ``mixing'' in the explosion. A
grid of final compositions is explored including essentially all combinations
of 56Ni, stable ``iron'', and intermediate mass elements that result in an
unbound white dwarf. Light curves (and in some cases spectra) are calculated
for each model using two different approaches to the radiation transport
problem. Within the resulting templates are models that provide good
photometric matches to essentially the entire range of observed SNe Ia. On the
whole, the grid of models spans a wide range in B-band peak magnitudes and
decline rates, and does not obey a Phillips relation. In particular, models
with the same mass of 56Ni show large variations in their light curve decline
rates. We identify the physical parameters responsible for this dispersion, and
consider physically motivated ``cuts'' of the models that agree better with the
Phillips relation. For example, models that produce a constant total mass of
burned material of 1.1 +/- Msun do give a crude Phillips relation, albeit with
much scatter. The scatter is further reduced if one restricts that set to
models that make 0.1 to 0.3 Msun of stable iron and nickel isotopes, and then
mix the ejecta strongly between the center and 0.8 Msun. We conclude that the
supernovae that occur most frequently in nature are highly constrained by the
Phillips relation and that a large part of the currently observed scatter in
the relation is likely a consequence of the intrinsic diversity of these
objects.
