Qix: The "Computer Virus" Game is a famous arcade created by Taito in 1981 and ported to many different platforms.
You control a marker that can only moves on the border of the screen or the lines already drawn. To draw a line you have to keep the fire button pressed while moving. Once you draw a rectangle, the area will be filled. Once the screen has been enough colored, you can go ahead to the next level. The monster (Qix, pronounced "kicks") must be avoided. Hitting one of its lines while drawing will consume one of your lives.
GamesNostalgia has packed for you the Amiga version, created by Alien Technology Group for Taito America and possibly one of the best looking.