Mike Williams wrote:

After a while this pattern breaks down because there aren't enough
nearby uninhabited planets.

"After a while" may be "right away."  We have no idea about the
propenderance of habitable planets.  Remember, almost by definition,
"habitable planet" means one with Earth-like life on it (oxygen-nitrogen
atmospheres aren't normal, they indicate a system way out of
equilibrium).

Terraforming all the material in each
colonised solar system helps slightly, but doesn't affect the overall
picture. So by about 20000 years the picture you end up with is
something like a sphere of stars where every possible inch of real
estate is occupied, that's expanding at close to the maximum speed
that
their starships can achieve. If that speed is 0.1% of light speed,
they
fill the whole galaxy in about a hundred million years.

So why aren't they here?

Because we have no idea whether such simplistic models are actually
apprporiate, and really have no strong reason to believe so.

Even in the middle of a Galaxy with very active colonization, you can
get large "dead zones" where the expanding front falters (certainly not
every single colony will _always_ want to send out colony ships).  This
is called percolation theory, a subject studied by none other than our
Geoffrey Landis.

Even in the middle of a Galaxy with active colonization, there may be
reasons why aliens aren't interested in visiting or contacting us. 
There could be any number of reasons for this, from a "prime directive"
to the simple fact that a civilization a million years ahead of us
wouldn't have much to talk with us about.

-- 
   Erik Max Francis && max@alcyone.com && http://www.alcyone.com/max/
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/  \ Nobody can reach me, nobody can touch me; it's a wonderful feeling.
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