Centipede was another genre defining game by Atari. It was similar to Space Invaders in that you operated from the bottom the screen at things coming towards you. The differences are higher speed, more varied objects and the ability to move vertically to some degree. It was one further step towards the vertical scrolling shooters that would soon come along.
In Centipede, the goal is to destroy centipedes and other bugs that infest your garden. The centipede weaves its way back and forth across the screen, changing directions whenever it encounters a mushroom. Periodically other menaces will come along like the spider that bounces across the screen, the scorpion that crawls across or the flea that dive bombs you.
There were many home ports of centipede. The Atari 5200 version, which is essentially the same as the Atari 8-bit computer version, is a very good port and was a nice step up graphically from the Atari 2600 version. For the best experience you can use a trackball instead of a joystick to mimic the arcade experience.
There have been a number of releases of the arcade version of Centipede and the Atari 7800 version has been released via the Atari Flashback consoles. However, as far as I am aware there has never been a re-release of the Atari 5200 or Atari 8-bit versions. To play these you will have to track down some original hardware and software or resort to emulation. If you have never played centipede, you should definitely try at least one version. The arcade version is best of course but the vast majority of home ports are very good as well.
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