>>1Sounds like normie wrote all this:
Binary is type of encoding not language.
NAND gates are simplest electronic elements.
Turing machines are pretty mainstream part of CS.
Fractal generators are popular.
"combintors" are part of functional paradigm.
Malbolge and brainfuck are most popular esoteric language(they are both extremely simple)
Hypercomputation is a theoretical computation class.
Game of Life is known widely, i've wrote several pattern rules for it here:
http://w11.zetaboards.com/frozenbbs/forum/4223812/ (i recommend Glitch City and Glitch Maze first)