## Exponential growth in Katamari Damacy

*Katamari Damacy* is a wonderful game: simple, fun, delightfully bizarre, and deceptively mathematical. *Katamari* and its sequels follow the tiny Prince of All Cosmos as he rolls a magical sticky ball (called a katamari) around Japan. As things stick to the katamari, it becomes bigger, enabling it to pick up larger and larger objects. Eventually, the Prince builds up a massive enough katamari to roll up people, cars, buildings, islands, rainbows, and just about everything else in the game.

*Katamari*’s core game mechanic is the exponential growth model. As long as the stage has plenty of objects to pick up, the katamari grows at a rate roughly proportional to its size. *Katamari* delivers an aesthetic experience that conveys the essential intuitions behind exponential functions, similar to short films like *Powers of Ten*.

In the above chart, I explore how closely katamari size tracks an exponential curve. I watched five Let’s Play videos of different YouTubers playing the final level of *Katamari Damacy* and plotted their progress. Sure enough, each run traces an approximately straight line on the logarithmic scale, indicating exponential growth.