You can ask the computer to return a random number millions of times per second. If you can think of how to use those values in algorithms that make decisions you can do very interesting things. Here are some examples...
You can have a set of dots in a certain place and use randomness to move them. You can't know what path a point will take but you can get an idea of the stain that hundreds of them will leave.
You can use the computer to paint the result of a system of equations. By adjusting the coefficients of the equations randomly you sometimes find strange attractors.
Sometimes you can randomly draw a velocity vector and then let the law of universal gravitation do the drawing.