  (abridged) Observations of exoplanets indicate the existence of several
correlations in the architecture of planetary systems. Exoplanets within a
system tend to be of similar size and mass, evenly spaced, and are often
ordered in size and mass. Small planets are frequently packed in tight
configurations, while large planets often have wider orbital spacing. Together,
these correlations are called the peas in a pod trends in the architecture of
planetary systems. In this paper these trends are investigated in theoretically
simulated planetary systems and compared with observations. Whether these
correlations emerge from astrophysical processes or the detection biases of the
transit method is examined. Synthetic planetary system were simulated using the
Generation III Bern Model. KOBE, a new computer code, simulates the geometrical
limitations of the transit method and applies the detection biases and
completeness of the Kepler survey. This allows simulated planetary systems to
be compared with observations.
  The architecture of synthetic planetary systems, observed via KOBE, show the
peas in a pod trends in good agreement with observations. These correlations
are also present in the theoretical underlying population, from the Bern Model,
indicating that these trends are probably of astrophysical origin. The physical
processes involved in planet formation are responsible for the emergence of
evenly spaced planets with similar sizes and masses. The size--mass similarity
trends are primordial and originate from the oligarchic growth of
protoplanetary embryos and the uniform growth of planets at early times. Later
stages in planet formation allows planets within a system to grow at different
rates, thereby decreasing these correlations. The spacing and packing
correlations are absent at early times and arise from dynamical interactions.
