Happy New Year!

There is a well-known cellular-automaton based method for generating images that look like caves.

Each cell is either “empty” or a “wall”. The rule is: if the immediate 9x9 grid centered on a cell has 5 or more walls, that cell should be a wall in the next step. Otherwise, it should be empty.

If you initialize the grid randomly with some density, you can get cavelike patterns.

However, these patterns have an ortholinear aspect to them: something about them is aligned to the axes. This should not be too surprising as the rule looks at a rectangular neighborhood of a point.

If however, we modify the rule to look at a circular neighborhood of a point, and do the analogous thing – become a wall if at least 5/9ths of the neighbors are – we get more organic looking patterns that don’t have this axis-aligned artifact. Nice!