  The variability observed in many complex gamma-ray bursts (GRBs) is
inconsistent with causally connected variations in a single, symmetric,
relativistic shell interacting with the ambient material ("external shocks").
Rather, the symmetry of the shell must be broken on an angular scale much
smaller than Gamma^{-1} where Gamma is the bulk Lorentz factor for the shell.
The observed variability in the external shock models arises from the number of
causally connected regions that (randomly) become active. We define the
"surface filling factor" to be the ratio of the area of causally connected
regions that become active to the observable area of the shell. From the
observed variability in 52 BATSE bursts, we estimate the surface filling factor
to be typically 0.005 although some values are near unity. We find that the
surface filling factor is about 0.1 Delta T/T in both the constant Gamma phase
(which probably produces the GRB) and the deaccelerating phase (which probably
produces the x-ray afterglows). Here, \Delta T is a typical time scale of
variability and T is the time since the initial signal. We analyze the 2 hr
flare seen by ASCA 36 hr after the GRB and conclude that the surface filling
factor must be small (0.001) in the x-ray afterglow phase as well. Explanations
for low surface filling factor can either require more or less energy (by a
factor of about 1000) compared to that expected for a symmetric shell.
