Sure, I can create a simple generative art game using JavaScript enclosed in HTML script tags. Here's an example of how it can look like:
When you open this HTML file in a browser on your smartphone, it will display a canvas element with randomly generated circles and squares of various colors. You can refresh the page to generate a new artwork each time.
Note: This is a basic example of generative art using random shapes and colors. You can modify and enhance it further based on your preferences and requirements.