  Simple ``solar systems'' are generated with planetary orbital radii r
distributed uniformly random in log(r) between 0.2 and 50 AU. A conservative
stability criterion is imposed by requiring that adjacent planets are separated
by a minimum distance of k Hill radii, for values of k ranging from 1 to 8.
Least-squares fits of these systems to generalized Bode laws are performed, and
compared to the fit of our own Solar System. We find that this stability
criterion, and other ``radius-exclusion'' laws, generally produce approximately
geometrically spaced planets that fit a Titius-Bode law about as well as our
own Solar System. We then allow the random systems the same exceptions that
have historically been applied to our own Solar System. Namely, one gap may be
inserted, similar to the gap between Mars and Jupiter, and up to 3 planets may
be ``ignored'', similar to how some forms of Bode's law ignore Mercury,
Neptune, and Pluto. With these particular exceptions, we find that our Solar
System fits significantly better than the random ones. However, we believe that
this choice of exceptions, designed specifically to give our own Solar System a
better fit, gives it an unfair advantage that would be lost if other exception
rules were used. We conclude that the significance of Bode's law is simply that
stable planetary systems tend to be regularly spaced; this conclusion could be
strengthened by the use of more stringent methods of rejecting unstable solar
systems, such as long-term orbit integrations.
