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.
Exponential growth is a core game mechanic of Katamari, as the player must keep the katamari growing in proportion to its size to unlock new ways of exploring a level at different scales. The result is an aesthetic experience that is as mathematical as it is entertaining.