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Trying to plot "fuzzy" values vs time

Stella is a little continuous time system simulation product.

Like so many simulation packages it asks for exact values for all
coefficients and plots spidery thin lines representing the behavior of
the model.

I would like to put together a prototype demonstration, using
Mathematica 3.0, that would like to demonstrate a user interface where
coefficients had, for example, a normal distribution and where graphs
of the behavior over time were plotted as a fuzzy band.  Perhaps this
could be done using dots, more closely spaced where the probability was
high and less closely spaced where the probability was low.

I have been experimenting, trying to craft up a plotting function that
would convey the uncertainty in a value over time but not by covering
the graph with confidence bars.

Anyone have any examples or ideas that I might learn from?

many thanks

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