As a self taught programmer I'm finding it difficult to enter into the game industry as a game programmer. Ultimately I want to be a game engine programmer and I have a couple scrap projects for which I play around with certain game/game engine concepts. These projects are just 2d games for which I have some simple animations and other things working. The problem is these are unfinished projects and I figure it might be good to show I can complete a project as well.
So for an aspiring game engine programmer, what sort of self contained or smaller projects could one feasibly complete in a reasonable amount of time (6mo - 1yr) and still impress a would be employer in this area? Are there things you have completed in the past that help get you a job or really impressed your peers?