Sure, here's an example of a simple generative art game implemented as a single HTML file using JavaScript. The game allows you to create art by clicking on the screen, and each click generates a randomized colorful shape.
You can save the above code as an HTML file and open it in a web browser, preferably on a smartphone, to play the generative art game. Each click on the screen will generate a random shape (square, circle, or triangle) with a random color. Have fun creating your own generative art!