  The parallel computational complexity of the quadratic map is studied. A
parallel algorithm is described that generates typical pseudotrajectories of
length t in a time that scales as log t and increases slowly in the accuracy
demanded of the pseudotrajectory. Long pseudotrajectories are created in
parallel by putting together many short pseudotrajectories; Monte Carlo
procedures are used to eliminate the discontinuities between these short
pseudotrajectories and then suitably randomize the resulting long
pseudotrajectory. Numerical simulations are presented that show the scaling
properties of the parallel algorithm. The existence of the fast parallel
algorithm provides a way to formalize the intuitive notion that chaotic systems
do not generate complex histories.
