Here is an example of a simple generative art game implemented as a single HTML file using JavaScript. The game runs in a browser and can be played on a smartphone. The game involves creating unique patterns and compositions by interacting with pictograms. Please note that this is just a basic example, and you can enhance it further as per your requirements.
In this game, a canvas element is created with an ID of "gameCanvas". Whenever the canvas is clicked, a circle with a random color is drawn at the clicked position on the canvas. The getRandomColor function generates a random color for each circle.
You can further expand and modify this game by adding different shapes, levels, or any other features you desire.