The Game of Life is just awesome. Here's a picture of me with John Conway where he signed a box of Life cereal for me. John hates the Game of Life because he thinks the mathematics are trivial and he has done so much more important work. I think he should just be happy that he is known for something, unlike most mathematicians!
I wholeheartedly recommend setting generation step to 64 and just sort of mousing around. It's the only way to discover the whole thing is powered by Fred Flintstone shitting on a volcano.
http://copy.sh/life/?gist=f3413564b1fa9c69f2bad4b0400b8090&step=512 this is entrancing
Those constructor type of games fascinate me every time I see something like that. It started with a working microprocessor in Dwarf Fortress, and things like that keep appearing on my radar. I'm now waiting for someone to build a game within a game with that kind of stuff.