## An isolated cell must be paired in the x and y-direction

For discussion of other cellular automata.

### An isolated cell must be paired in the x and y-direction

Can anybody make an automata so that the closest lit cell to an isolated lit cell moves to pair in the x-direction (one of the cells directly to the left or right of that cell) and y-direction (one of the cells directly up or down of that cell) of the isolated cell. That is, if there is a single isolated cell some distance from a cloud of randomly lit cells, the closest lit cell in the cloud moves towards the isolated cell (and the isolated cell moves towards that cell as well, like gravity). But as the closest one in the large cloud moves, the other ones in the cloud would pair that one in the x-direction and y-direction (not diagonal) of that moving cell, so that the entire cloud would tend to move towards the isolated lit cell. And all the cells in the cloud would move to the closest isolated cell in the cloud, or on the boundary of that cloud, they would move to isolated cells some distance from the cloud.

I'm wondering if there are several large squares of mostly lit cells, with narrow boundary running between the squares, so you have a larger grid, the squares themselves would act like diffusion, while balls of lit squares would appear at the four corners of 4 large squares, then the ball would begin to gyrate, because there is competition on where it would move to pair another ball in the left or right direction at another crossing, and a smaller ball would shoot out, say in the left direction. Also, as the larger ball disintegrates, it would form a boundary of two moving rows of teeth in that example (the x-direction), with the ball just touching the teeth and being propelled along. Also the teeth would change shape a bit as the two rows of teeth move past each other. That's a triangular billiard ball, and since the two rows are moving and the teeth are changing shape, it may be a quantum circuit.
ntdsc

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### Re: An isolated cell must be paired in the x and y-direction

Are you looking for a CA that would make each ON cell gravitate towards the nearest other ON cell?
Such a CA certainly exists, but Golly can only simulate custom rules with radius 1, and the tricks used in certain rules to simulate higher radii are required to use clever information gathering and compression techniques to provide information to cells.
A custom applet would be able to do this just fine, although that's a bit outside my area of expertise .
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### Re: An isolated cell must be paired in the x and y-direction

I think the activity with the large squares and narrow boundaries between squares would do the same with one of the rules of a normal automata.... I found this: https://en.wikipedia.org/wiki/Block_cel ... plications
There are elastic collisions on that page in a billiard ball, and that is what I was referring as a ball breaks up and a smaller ball shoots down, and I suppose collides elastically, except I'm trying to get the ball to bounce down between two rows of triangular "teeth", that is a nonlinear calculation, and if the teeth change shape and move, it might be quantum,
ntdsc

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### Re: An isolated cell must be paired in the x and y-direction

I know that if you have a large completely filled square of lit squares, according to the above rule, and an isolated lit square to the left, then a square of 4 lit squares will move out of the large square to pair, and there will be an "indention" in the large square, so the large square doesn't move here. The reason a square of 4 squares pops out is that you'd have to have an additional rule so that when the closest square moves away from the large square to pair the isolated square, the one directly behind it moves to pair, because that maximizes pairing. If the one above moved only, it would not be paired in the x-direction.

What is possibly quantum here is if you have banding of parallel lines of lit squares of differening density ie squares will move away from a larger square to pair and like an electron cloud, you'll see various densities of lit squares in bands that tend to the shape of the larger square. ie you'll see a large square, then to the left, a low density long vertical line, a higher density vertical line, etc. for some distance away from the large central square.
ntdsc

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