# The pathing problem [an interesting 'though experiment"]

the other day i was fiddling on a cellular automata thing i found (ncase.me/sim/?s=blank), i made lots of cool sims using it but i also came across a interesting problem and or thought experiment.
it is as follows: How would you make some sort of pathing system or projectile if the thing your making cannot ‘see’ more then one tile away and doesnt have any form of direction?
any discussion on the matter is welcome, but the base problem is on a grid and the choices for sight are either just the sides or the sides and diagonals.
feel free to ask questions like methods i have previously thought of and commands you can use and such.

Something like this?

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What exactly do you mean by a “sort of pathing system”?

Various forms of cellular automata are known to be Turing complete, which, in principle (but in a very cumbersome and abstract sense), allows for arbitrary computation.

As for “projectiles”, there are many shapes that move under various forms of cellular automata systems, but I’m not too sure what you mean.

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not really? im not exactly sure what you mean by that
it is a cellular automata i suppose, though.

some way to get a ‘thing’ to near a specific spot. like getting ants to food, perhaps?

also, yes, this program is probably Turing complete as it can run Conway, but you can also add things to it.

yes, spaceships and other forms are actually one way to move in a specific direction, so it is one solution. by projectile, i (somewhat) mean a minimized as much as possible collection or singular object that can figure out where to go. it might make more sense if you were to try the thing.

idk like maybe sim a slime mold

You can do this sort of thing physically by using a potential difference (chemical or electrical)

But this doesn’t follow the “doesn’t have a direction” condition because you always have an underlying gradient forcing a preferred direction. It’s just that the “specific path” to get to the minimum doesn’t matter so much.

In your case, the only way would be to either brute force it (always turn left in a maze) or random walk until you get to the desired endpoint and then just go with the first solution. Both have the issue of massive time complexity, so optimization problems never go with this solution.

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