Conway's Game of Life, using floating point values instead of integers

      1/3_____1/2/3
      /|      /|
     / |     / |
    1------1/2 |
    |  3____|__2/3
    | /     |  /
    |/      | /
    0-------2

It branches out along the three axes:

1) Add mutual gravitation, giving you the theory of Newtonian celestial mechanics (in which gravity acts instantaneously)

2) Add relativistic effects, giving you Einstein's theory of special relativity (there is a finite upper limit to all communication, the speed of light)

3) Add quantization, giving you 1920s era quantum mechanics, as described by the Schrodinger equation.

We know how to combine any two of these:

1/2) Combining gravitation and relativistic effects gives you Einstein's theory of General Relativity. In this theory, gravitational effects travel at the speed of light.

2/3) Combining relativity and quantum mechanics gives you quantum field theory and the Standard Model. This encompasses the Dirac equation, which is a quantum relativistic theory of fermions (i.e. matter particles).

1/3) Combining gravity and quantum mechanics gives you... well, it's kind of boring and we don't talk about it much, but you get a quantum theory with gravitation, but no relativistic effects. No one really studies this.

Combining all three is the holy grail of physics:

1/2/3) Often called `quantum gravity` or the `theory of everything`, this is the as yet nonexistent theory that can explain both very small and very massive (in the sense of having a large mass) objects, like black holes or the early universe.