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I like the OP's view on "shaping the space of Game of Life universe" by just defining the getNeighboursOf function. I think that would be a core idea if one wan

I like the OP's view on "shaping the space of Game of Life universe" by just defining the getNeighboursOf function. I think that would be a core idea if one wanted to see Game Of Life as some abstract mathematical object. However, it seems like the title might be a bit too much for what the text really is.

goldenkey 11y ago
The space is entirely decided by interaction. Not how it looks when you decide to turn it into a grid and put it on a screen. For example, if your neighbor function returned edge+vertice neighbors, if you wanted to accurately show the space as homogenous sized cells, on a 2d screen, you would no longer be able to show a grid of squares, a different tesselation or complex surface would be necessary. Literally the only thing that defines space, which is primitively defined by the derivative of neighborment, is what interacts with what. Food for thought if you do like to ponder about this universe :-)
- fibo 11y ago
  The mathematical theory the study space is Topology. A definition of a topology of a space is given by, starting from an underlying set, the definition of the open intervals (there are also other ways, this is the most used one) which gives the notion of continuous functions. Another approach to define a topology is by defining a distance which gives a metric space and the definition of open intervals. Any variant of the GoL I have seen is discrete, every cell has distance one from its adjacent cell. It is the adjacence notion that defines the nearness, hence the space. That is the math that I applyed, to deduce that when you define a function getNeighboursOf, you are actually defining the shape of the space, and also its set (the counter image of the function).
goldenkey 11y ago
The space is entirely decided by interaction. Not how it looks when you decide to turn it into a grid and put it on a screen. For example, if your neighbor function returned edge+vertice neighbors, if you wanted to accurately show the space as homogenous sized cells, on a 2d screen, you would no longer be able to show a grid of squares, a different tesselation or complex surface would be necessary. Literally the only thing that defines space, which is primitively defined by the derivative of neighborment, is what interacts with what. Food for thought if you do like to ponder about this universe :-)

goldenkey 11y ago

The space is entirely decided by interaction. Not how it looks when you decide to turn it into a grid and put it on a screen. For example, if your neighbor function returned edge+vertice neighbors, if you wanted to accurately show the space as homogenous sized cells, on a 2d screen, you would no longer be able to show a grid of squares, a different tesselation or complex surface would be necessary. Literally the only thing that defines space, which is primitively defined by the derivative of neighborment, is what interacts with what. Food for thought if you do like to ponder about this universe :-)

fibo 11y ago
The mathematical theory the study space is Topology. A definition of a topology of a space is given by, starting from an underlying set, the definition of the open intervals (there are also other ways, this is the most used one) which gives the notion of continuous functions. Another approach to define a topology is by defining a distance which gives a metric space and the definition of open intervals. Any variant of the GoL I have seen is discrete, every cell has distance one from its adjacent cell. It is the adjacence notion that defines the nearness, hence the space. That is the math that I applyed, to deduce that when you define a function getNeighboursOf, you are actually defining the shape of the space, and also its set (the counter image of the function).

goldenkey 11y ago