As we were doing some logic during the last few lectures (see the post about reasoner), I decided that I wanted to do something usefull with this highly interessting stuff. So as I already had an engine to evaluate propositional logic expressions it was an easy thing to accomplish the following idea:
Consider the following matrix constituting our “world” and initial population:
with 
and ![i,j \in [1,n]](http://blog.32leaves.net/wp-content/cache/tex_2998418c60234b7445f26468cba5e1e8.gif)
To compute a new “generation” the aliveness (1 being alive, 0 dead) of each element is determined by evaluating a certain propsitional expression:
with 
being the valuation of the proposition and 
being the proposition itself.
with 
Have a look at the screenshot to get a better idea on what the program is doing or run it using Java webstart below (may not work on MacOSX or Windows).
