“Floor plan”, a cellular automaton
Recall “Rain” and “Inferno”, two cellular automata almost defined by the same rule; they only differ in the choice of the parameter θ, which is θ = N/24 for “Rain” and θ = N/12 for “Inferno”. If we let θ = −N/12, we obtain a new cellular automaton, which I call “Floor plan”. In general, this rule creates period-18 “floor plans”. A single such floor plan (for N = 24) is shown below:
Although the image appears to be two-colour, it actually isn’t. By posterizing it to two colours, however, a true maze is obtained. And as far as mazes are concerned, this is a pretty nice one. Below a larger maze is shown and its main connected component is highlighted: