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?

What exactly do you mean by game engine developer? Graphics, audio, AI, physics or editors/tools?
A company most likely needs at least one specialist(!) for each of these fields, instead of one person being able to do everything a bit. So if you want to do graphics mainly, then show that you can work in at least one of these well: OpenGL, DirectX, Vulkan, Metal.

Instead of trying to make something new, it might be more reasonable to finish your existing projects. Or at least redo them in a way that you can present them. However keep in mind what you want your main focus to be. If you do graphics you won't need to make a whole game necessary. Instead rendering a complex scene with dynamic lighting etc. and high fps should be fine too. Bonus points if the demo software is cross platform and can be run on a device with limited capabilities (smartphone, older console).

I don't know if it's the kind of project you're looking for, but take a look at this suggestion to write an ARM disassembler from mmozeiko.

Thanks for the suggestions.

LaresYamoir
What exactly do you mean by game engine developer? Graphics, audio, AI, physics or editors/tools?
A company most likely needs at least one specialist(!) for each of these fields, instead of one person being able to do everything a bit.

Ya, this has been my biggest problem. I can't really identify any one field specifically yet. I enjoy the entire process of making a game and the ability to control everything my game is built on is very appealing to me. I guess I'll really have to try and either narrow my scope down a bit or see about starting my own thing or working for a smaller startup that may need a more generalist programmer.