App-side, a radio button group would probably be the easiest (and most user-friendly) way to do that. In the API function, this wouldn't be difficult to implement at all. We could add a third input to the input association list
"random"->"Boolean"
then use that in conjunction with another If command:
If[#random,
ArrayPlot[CellularAutomaton[#rule, RandomInteger[1, 100], #steps]],
ArrayPlot[CellularAutomaton[#rule, {{1}, 0}, #steps]]
]
replacing the single ArrayPlot command that currently exists in the API.
Edit: If you use RandomInteger[1, #steps] instead, it will make the resulting evolution a square every time. This might save you some really poorly shaped images.
