Just another variation

Projects: 
Here is my updated version that allows up to four ants and has the option to halt the process when any two ants cross paths. The display will restart by pressing go again. A couple of (I thought) interesting points: The initial coordinates are set up to match the ones that Kathy drew our attention to. This model is difffernt from Kathy's though in that it is not set up to be paralell like hers is. The result is much the same effect, except for two differences. 1) The internal pattern that is left in the centre when the ants start to move out in a circle are mirror images. 2) Because my world is larger, the ants don't wrap and bump into each other, and so they don't cycle. Lastly, a comment on the behaviors of 1 or more ants. I believe that 1 will never backtrack, 2 always will and more than 2 may or may not given the right conditions, but are more likely not to

Comments

PaulGrobstein's picture

Nice work (but fix the link? it isn't working). Like/appreciate the "believe" (translated as "my observations suggest"?). One "will never". We have a "halting problem" here; can one prove "never"? For worlds of particular sizes? Two "always will" ... if the world is small enough? Observations (with halting problem) or proof? More than two .... ?

So we have mix here of some summarizable patterns and Chaitin's "just the way it is"? Maybe that's the way "reality" is, and forms of inquiry need to be reconceived accordingly?

Kathy Maffei's picture

One thing I noticed right off the bat was that the pattern your model makes is a mirror image to mine, and mine runs clockwise (on expansion) while yours runs counter-clockwise. The only thing I can think of to explain this is the parallel computing. The reason why yours doesn't cycle is because your world isn't square. If it was, I'm sure the ants on the right & left would meet up at the same time as the top & bottom ants do, and they would all switch places, change directions, and spiral back inward as they do on my model. Instead, your top & bottom wraps before the left & right, so only 2 ants reverse, crashing into the other two. Very pretty, but maybe it doesn't cycle (I didn't watch long after that). I made my world square for the purpose of encouraging more interesting (to me) symmetrical patterns. Also, I should mention that this set-up performs 2 distinct patterns in a cycle - after spiraling inward and cleaning up the 1st one, it creates different center pattern, spirals outward in a slightly different circlular pattern (also clockwise), and then back in again to start over with the 1st pattern.