FRACTRAN at first sight is just a sequence of fractions, but it demonstrates that many registers can be encoded into a single number.
The FRACTRAN prime game has a certain charm.
Modern computers do computations based on a small number of simple operations, and Brainfuck demonstrates that number can be VERY small.
A BF Quine was a challenge.
Conway's game of life shows what happens when a finite state machine is fixed, and the programmer can only change the input.
I wouldn't even try to make a GOL program, but random configurations are interesting to watch.