I have a memory of playing a video game in an arcade. It must have been the late 70s or early 80s. The game had remarkably simplistic graphics but was still fun to play.
The idea, as I recall it, was that you played a dot on the border of the rectangular screen. Your goal was to move into the interior of the rectangle (with a line following along behind you) and try to enclose as much area as possible (using the line following behind you to draw a shape, some of whose borders would be part of the border of the original rectangular area. And then you could keep going, using your new shapes to help you draw larger and larger shapes.
To keep it from being easy, there was an enemy who would wander around inside the rectangle, trying to hit you. If he did, you died and your current drawing was lost. If I recall correctly, the enemy was sort of a moving line segment, looking sort of like the Mystify screensaver that Windows provides.
I recall it being pretty cool in a wonderfully frustrating way, especially on those rare occasions when I could trap the line segment monster in a tiny part of the board, leaving me free to do whatever I wanted.
Obviously, with only thoughts like “line segment monster” and “drawing shapes”, I haven’t had any success searching for the name of this game online.
There was an “updated” version of Qix (I am not talking about “Qix II”) - I think it was in the mid-1990s - but they replaced the lines with some object that quickly moved from one area of the screen to another and occasionally shot things in all directions. IIRC, the filled-in areas displayed part of a larger picture rather than the blue/brown areas of the original.
Wikipedia claims a new version is available on XBox Live.