  This paper shows how to evolve numerically the maximum entropy probability
distributions for a given set of constraints, which is a variational calculus
problem. An evolutionary algorithm can obtain approximations to some well-known
analytical results, but is even more flexible and can find distributions for
which a closed formula cannot be readily stated. The numerical approach handles
distributions over finite intervals. We show that there are two ways of
conducting the procedure: by direct optimization of the Lagrangian of the
constrained problem, or by optimizing the entropy among the subset of
distributions which fulfill the constraints. An incremental evolutionary
strategy easily obtains the uniform, the exponential, the Gaussian, the
log-normal, the Laplace, among other distributions, once the constrained
problem is solved with any of the two methods. Solutions for mixed ("chimera")
distributions can be also found. We explain why many of the distributions are
symmetrical and continuous, but some are not.
