Infinity Gene's central gimmick is "evolution." Starting as a touch-controlled version of Space Invaders, the game changes in every stage, with various "evolutionary paths" depending on your performance. Every few levels, the backgrounds change; you get new weapons like an auto-aiming laser, and new abilities like moving around the whole screen instead of along a single axis; sometimes the scoring system changes, adding new bonuses and new ways to build the score.
Over time, the game resembles Space Invaders less and modern shooters more. The enemies fly in and around the screen in formation, only occasionally settling into the traditional columns. They come in wildly different sizes and shapes. They shoot a variety of beams and bombs at you, even occasionally creating roadblocks across the length of the screen.
In a smart move for the phone format, Infinity Gene keeps the levels short, which has the side effect of making the evolutions occur very rapidly. As the game becomes more complex and more difficult, it retains a lovely art style with all-white sprites inspired in equal parts by vintage Invaders and vector graphics, and simple gradient backgrounds.
If the existing levels aren't enough, Infinity Gene generates unique levels from the music stored on your phone, with enemies appearing on the screen in time to the beat. I love the idea of an infinite variety of randomly-generated levels, but I should warn you that, for whatever reason, these tended to be a lot more difficult than the normal game. Even mellow songs like Cibo Matto's "Sugar Water" turned out impossible waves of Invaders. I guess it's going to take practice before I can shoot my way through a slow jam.
Unless you don't enjoy shooters (or, more plausibly, you don't enjoy touch-controlled shooters), it is impossible not to recommend Space Invaders Infinity Gene. It's beautiful to look at, smartly designed for short sessions while remaining challenging, and features infinite variety. And all for the same five dollars you could spend on the iPhone port of the original Space Invaders.