Neighborhood of a cell
A cell’s neighborhood consists of those cells adjacent to it. If you lived inside a two dimensional grid, your neighborhood would be those cells that you could see around you.
In a Cellular automaton, your state in the next generation of the simulation depends on the state of your neighborhood. This is kind of like how you might put up Christmas lights because you notice that your neighbors’ houses are covered in lights. Or, maybe you’re the type of person who purposefully keeps your home dark during the holiday season, just to be contrary to your neighbors (those jerks)1. In either case, your state depends on the state of your neighborhood, just like the state of a cell in a cellular automaton depends on the state of its neighborhood.
Depending on the cellular automaton, the neighborhood can vary in size and shape. The neighborhood shape determines your view out onto the lovely world of the grid.
In addition, the neighborhood shape defines a local network of influence. You can imagine that each cell in your neighborhood is connected by a wire to you, and that wire represents the cell’s influence on you.
Thinking about a neighborhood in this way can be useful if you want to understand the 2D grid as a graph with nodes and edges. (Idea: What if a neighborhood varied over time and space?)
Notice that we haven’t yet described how your state might depend on your neighborhood’s state — that’s up to the rules of whatever cellular automaton you might be running. See Conway’s Game of Life for a classic example of how the concept of a neighborhood is used with specific rules.
In Feedback Crystal Studio, the rules of the neighborhood can be rapidly swapped for other rules to create variations over time. In this context, the rules are defined by a Kernel, which is the same terminology used for Convolutions
Or, maybe like me, you don’t own a home at all. But let’s fantasize that we are home owners for the sake of the analogy. ↩︎