How to generate random color dot on screen at x interval of time in Flutter

So I'm trying to make an app where when clicked on Play button random color dots start to appear on screen at any location but I can't get around to how to implement that in flutter any help would be appreciated.

I know that I need to use random class which is built-in method but how to generate color dots using that?

Btw one color should appear at a given time and next color should appear after X seconds

Below is an image attached to what kind of effect I want on pressing play button.