I had an idea to extend Langton’s Ant and the generalized Ant Automata by allowing turning of the ant in 45 degree angles rather than just 90 degree angles. I was hoping to get some new unique results.
In the usual ant automaton, when the ant turns right it makes a 90 degree turn (eg from facing west it turns 90 degrees to face north). In my experiment I turn only 45 degrees (so facing west now turns right to face north-west). Otherwise the way the ant behaves is the same for the usual Ant Automaton.
After running a few thousand automated rule numbers the results were nothing spectacular. Mostly blobs without any interesting structures.
A few of the rules did produce highways the same as the regular Ant Automaton in 2D and 3D does.
My next idea was to change the amount the ant turns based on its surrounding 8 neighbors (the left or right turn direction is still based on the rule binary digit as in the usual ant automaton). Each of the 8 neighbors (W,NW,N,NE,E,SE,S,SW) state values are summed and then a turnvalue is found by
turnvalue=neighborcount mod 8+1
This gives a value between 1 and 8 to turn by. 8 means do not turn and keep moving straight ahead. When a turn is made to the left or right, the turn takes that many 45 degree steps. So if the neighbor value comes out to 2, then a right turning ant now turns 90 degrees rather than the usual 45 degrees.
This method did give more interestingly shaped blobs
and also produced some complex highways.
The following rule created a symmetric structure before creating a straight highway.