Sure, here's an example of a simple generative art game implemented as a single HTML file, utilizing JavaScript and enclosed in script tags. The game is designed for smartphone operation and uses pictograms. Note that this is just a basic example to get you started:
When you open this HTML file on a smartphone, it will display a canvas with randomly generated lines and circles. Every time you reload the page, the canvas will be regenerated with new random elements, creating a unique generative art piece.