You can send the message seededWith: to any random expression. So for example, you could use:
(0.1 s tick randomWalkStartingFrom: 0 stepSize: 0.1 reset: 0) seededWith: 12345678
which starts at 0 and drunkenly walks toward 0.265 in about 8 seconds (so you could multiply the whole thing by 4 to make sure it gets up to 1).
If, instead, you want random numbers that start near zero, then get larger over time and reach 1 at a specific time, you could add random jitter to a straight line. For example, in:
| up down |
up := 1 ramp: 10 s.
down := 1 - (1 ramp: 10 s).
up * (1 + ((0.1 s random) * down))
the variable up is a line that goes from 0 to 1 in 10 seconds. The variable down starts at 1 and ends up at 0 by 10 seconds. Then you add some random jitter to the basic shape of up. The amount of jitter you are adding starts at the maximum and shrinks over time so that, by 10 s, you have no jitter and will really land on 1.
If you end up experimenting with these, please let us know which one gets closest to what you have in mind and what tweaks you added to get there.