"Darren Garrison" wrote in message
...
I want some sort of low ground cover that can be used over a whole yard
where I do not have other
plants and does not need mowing at all. Oxalis ("false shamrock") looks
promising, but descriptions
also say that it is "non-invasive", and I want something that WILL be
invasive to my whole yard, to
the exclusion of "normal" grass. Anyone have any tips?

Try Ivy. You can keep rooting offshoots and placing them where you want.
Snake heaven too.