  We investigate the probability of observing a given pattern of $n$ rises and
falls in a random stationary data series. The data are modelled as a sequence
of $n+1$ independent and identically distributed random numbers. This
probabilistic approach has a combinatorial equivalent, where the data are
modelled by a random permutation on $n+1$ objects. The probability of observing
a long pattern of rises and falls decays exponentially with its length $n$ in
general. The associated decay rate $\alpha$ is interpreted as the embedding
entropy of the pattern. This rate is evaluated exactly for all periodic
patterns. In the most general case, it is expressed in terms of a determinant
of generalized hyperbolic or trigonometric functions. Alternating patterns have
the smallest rate $\alpha_{{\rm min}}=\ln(\pi/2)=0.451582\dots$, while other
examples lead to arbitrarily large rates. The probabilities of observing
uniformly chosen random patterns are demonstrated to obey multifractal
statistics. The typical value $\alpha_0=0.806361\dots$ of the rate plays the
role of a Lyapunov exponent. A wide range of examples of patterns, either
deterministic or random, is also investigated.
