Smoothing a random pattern of orientations causes the appearance of
orientation ``vortices.'' These patterns are similar to the
hypercolumn pattern of orientation tuning in monkey visual cortex, and
to the ``pinwheels'' that have been observed in cat area 18. The
generic presence of such patterns in continuous orientation maps is a
consequence of a basic topological theorem (nonretraction of
*R*^{2}-> *S*^{1}), together with the
stochastic properties of random orientation distributions. There as a
close correspondence between experimental results from cat area 18 and
computer simulations based on smoothed random orientations. Several of
the qualitative features of cortical hypercolumn patterns, including
the ``puff-extra'' structure of monkey V-1, are evident in our
simulations. There are two important conclusions from this work. (1)
Experimental observation of orientation ``vortex'' structure in any
visually excitable neural tissue must be evaluated in the light of the
null hypothesis that these patterns are readily formed from smoothed,
random orientation distributions, (2) The underlying explanation for
the ``vortex'' patterns which likely exist in primate and cat visual
cortex is fundamentally topological, and follows directly from the
definition of orientation, and the existence of local correlation of
orientation in cortex.