(For clarity for future posters:
thepenguin means the total amount of matter is conserved; yes, you can change a zero cell into a million plus matter and a million minus matter, but their sum is still zero)
Argh.
Just give me the text of the homework assignment already.
Or whatever you got from the person asking to solve it.
Because you still don't specify the rules of your automaton! It either does nothing (option one, a bit boring), or it "resembles thermodynamics" (HOW, exactly? are there rates of diffusion? what are they?), or you have these force vectors that act in unspecified ways on the cell's contents, on neighbors' contents, as well as each other (to these vectors even add? do they act on what's two cells away?)
Compare and contrast to
an actual cellular automaton specification:
- square grid
- each cell has eight neighbors
- each cell can be alive or dead
- any live cell with fewer than two live neighbours dies, as if caused by under-population.
- any live cell with two or three live neighbours lives on to the next generation.
- any live cell with more than three live neighbours dies, as if by overcrowding.
- any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.
And yep, while it's rather counterintuitive to do so,
one can construct a Turing machine based on those rules. It can compute XOR and anything else.