Abstract. 
We study the complexity of stable waves in unidirectional bistable coupled
map lattices. Numerical calculations reveal that, grouping traveling
patterns into sets according to their velocity, at most one set has
positive topological entropy for fixed parameters. The chaotic set's
velocity has a mode-locking structure in parameter space and the entropy
shows non-monotonous features. By using symbolic dynamics, we analytically
determine velocity-dependent parameter domains of existence of pattern
families with positive entropy. These estimates show excellent agreement
with numerical results.