To implement behaviors that depend on the run, you are going to need to use the sessionstate method to be able to track whether the page has yet been run for the users session.
OR you could use the get/set query parameters to transition from an initial configuration to the next. After the first run, the app would set the query parameters which would then affect how the app runs a second time by reading the parameters with get and acting accordingly. You could even have some kind of “default” random parameters and when the slider is changed the parameters in the URL get updated.