  In 2004 Vasiga and Shallit studied the number of periodic points of two
particular discrete quadratic maps modulo prime numbers. They found the
asymptotic behaviour of the sum of the number of periodic points for all primes
less than some bound, assuming the Extended Riemann Hypothesis. Later that same
year Chou and Shparlinski proved this asymptotic result without assuming any
unproven hypotheses.
  Inspired by this we perform experiments and find a striking pattern in the
behaviour of the sum of the number of periodic points for quadratic maps other
than the two particular ones studied previously. From simulations it appears
that the sum of the number of periodic points of all quadratic maps of this
type behave the same. Finally we find that numerically the distribution of the
amounts of periodic points seems to be Rayleigh.
