  We study dynamical effects of introducing noncommutativity on string
worldsheets by using a matrix model obtained from the zero-volume limit of
four-dimensional SU($N$) Yang-Mills theory. Although the dimensionless
noncommutativity parameter is of order 1/N, its effect is found to be
non-negligible even in the large $N$ limit due to the existence of higher
Fourier modes. We find that the Poisson bracket grows much faster than the
Moyal bracket as we increase $N$, which means in particular that the two
quantities do not coincide in the large $N$ limit. The well-known instability
of bosonic worldsheets due to long spikes is shown to be cured by the
noncommutativity. The extrinsic geometry of the worldsheet is described by a
crumpled surface with a large Hausdorff dimension.
