why do cellular automata only check their immediate neighbors? what if you made one that checks more like a random walk through a small tree of nearby cells, to determine its rules. like it checks its neighbors and checks half of its neighbors-neighbors randomly, then picks one of those to check a random 3rd neighbor. total all those to check for a rule. You could make a lot more rules that way. If you make rules that mostly preserve matter it might look more organic. like rules that teleport pieces into empty neighbors, or teleports some pieces from one end of a connected tree to another. basically you could make snakes or bendy bushes or mazes or molecules designed into the rules.
Most CA use only the immediately adjacent neighbor cells in order to keep the number of neighborhood configurations manageable. If the neighborhood extends out further, you can certainly get richer behavior, but the number of configurations generally grows exponentially. But I like your idea of using a neighborhood that branches outwards without trying be include all neighbor cell within the branch radius. This keep the number of configurations from exploding, which is important since the rule-set must be able to specify the next state of the central cell for all possible configurations (by either an equation or look-up table). Notice that the branching neighborhood that you suggest is itself fractal. Seems like this could be more appropriate, and more realistic than an adjacent-neighbors-only approach.
You make puns with Imp Unity! Pedantic topology: A standard torus (a "2-torus") is the 2-D surface of a 3-D object. It's technically the surface of a ring doughnut, not the interior of a ring doughnut. A 3-D torus ("3-torus") would be the surface of a 4-D object. Similarly, technically, a sphere is the 2-D surface of a ball. The ball is a 3-D object.
Thanks for the clarification -- yes, I now see how I abused the terminology. A torus is a surface, not the volume enclosed by said surface. And the dimensionality of that surface is the key, not that of the volume. So the topology of the surface inhabited by the cells in my cellular automata is "2-torus". Glad to get this straightened out. Although I am mostly self-taught when it comes to maths, I do love geometry & topology.
why do cellular automata only check their immediate neighbors? what if you made one that checks more like a random walk through a small tree of nearby cells, to determine its rules. like it checks its neighbors and checks half of its neighbors-neighbors randomly, then picks one of those to check a random 3rd neighbor. total all those to check for a rule. You could make a lot more rules that way. If you make rules that mostly preserve matter it might look more organic. like rules that teleport pieces into empty neighbors, or teleports some pieces from one end of a connected tree to another. basically you could make snakes or bendy bushes or mazes or molecules designed into the rules.
Most CA use only the immediately adjacent neighbor cells in order to keep the number of neighborhood configurations manageable. If the neighborhood extends out further, you can certainly get richer behavior, but the number of configurations generally grows exponentially.
But I like your idea of using a neighborhood that branches outwards without trying be include all neighbor cell within the branch radius. This keep the number of configurations from exploding, which is important since the rule-set must be able to specify the next state of the central cell for all possible configurations (by either an equation or look-up table).
Notice that the branching neighborhood that you suggest is itself fractal. Seems like this could be more appropriate, and more realistic than an adjacent-neighbors-only approach.
현실 셀룰러 오토마타는 매우 높은 에너지가 만든 규칙으로 돌아가니 현실에 외계인이 흔해도 할말이 없음.
You make puns with Imp Unity!
Pedantic topology: A standard torus (a "2-torus") is the 2-D surface of a 3-D object. It's technically the surface of a ring doughnut, not the interior of a ring doughnut. A 3-D torus ("3-torus") would be the surface of a 4-D object. Similarly, technically, a sphere is the 2-D surface of a ball. The ball is a 3-D object.
Thanks for the clarification -- yes, I now see how I abused the terminology. A torus is a surface, not the volume enclosed by said surface. And the dimensionality of that surface is the key, not that of the volume. So the topology of the surface inhabited by the cells in my cellular automata is "2-torus". Glad to get this straightened out. Although I am mostly self-taught when it comes to maths, I do love geometry & topology.
@@hexagon-multiverse You've got it!😉