  We show relative to strong hypotheses that patterns of compact cardinals in
the universe, where a compact cardinal is one which is either strongly compact
or supercompact, can be virtually arbitrary. Specifically, we prove if V is a
model of ``ZFC + Omega is the least inaccessible limit of measurable limits of
supercompact cardinals + f :Omega-->2 is a function'', then there is a partial
ordering P in V so that for Vbar = V^P, Vbar_Omega models ``ZFC + There is a
proper class of compact cardinals + If f(alpha) = 0, then the alpha-th compact
cardinal isn't supercompact + If f(alpha) = 1, then the alpha-th compact
cardinal is supercompact''. We then prove a generalized version of this theorem
assuming kappa is a supercompact limit of supercompact cardinals and
f:kappa-->2 is a function, and we derive as corollaries of the generalized
version of the theorem the consistency of the least measurable limit of
supercompact cardinals being the same as the least measurable limit of
non-supercompact strongly compact cardinals and the consistency of the least
supercompact cardinal being a limit of strongly compact cardinals.
