Wolframite here: these would make a good summer school project for our summer school (plug: the 2013 one is coming up, apply at https://www.wolframscience.com/summerschool/ if you're interested in this kind of stuff and want to do a 3-week project).
In fact I studied the space-filling behavior of precisely these 2D Turing machines in 2009. For low numbers of states and colors you can enumerate them exhaustively and calculate the distribution of space-filling efficiency (log-normal, if anyone is interested).
The full spectrum of behavior is quite fascinating to catalog. All these kinds of simple computational system have a character and 'zaniness' all their own.
Putting on a more scientific hat, it might be interesting to look at block-entropy measures and find interesting rulesets that way.
In fact I studied the space-filling behavior of precisely these 2D Turing machines in 2009. For low numbers of states and colors you can enumerate them exhaustively and calculate the distribution of space-filling efficiency (log-normal, if anyone is interested).
The full spectrum of behavior is quite fascinating to catalog. All these kinds of simple computational system have a character and 'zaniness' all their own.
Putting on a more scientific hat, it might be interesting to look at block-entropy measures and find interesting rulesets that way.
P.S. To the author: this is a great implementation! Really nice to play with. Check out http://reference.wolfram.com/mathematica/ref/TuringMachine.h... for the one built into the Wolfram Language.