The Jaccia and Jacciata Cellular Automata

Overview

Jaccia and Jacciata are cellular automata inspired by the Announcement of Scientific Proof that Slime Molds are Intelligent Maze Solvers.

Basically, the slime mold solves the maze by:

• initially being everywhere in the maze
• there being food at the entrance and exit of the maze
• minimizing its surface area by retreating from anywhere it can't get food.

Jaccia operates the same way. In the Jaccia automaton, slime cells survive if they have immediate neighbours in at least two cardinal directions that provide sustenance, i.e. are either food or other slime cells. The result is the same: paths of slime cells that lead down dead ends have one end which provides no sustenance and dies off. Eventually, only paths of slime cells that reach from food to food (or uninterrupted circular paths of slime cells) remain. Jacciata is a more involved automaton which finds only the shortest path.

Properties

Jaccia has the property that, when started from this condition (entire maze filled with slime cells), the automaton will eventually reach a fixed point (steady state) which contains all possible orthogonal paths from food to food. (Orthogonal paths means, a diagonal isn't considered a path.)

Jacciata is similar, but has the property that when it reaches a fixed point, it will contain the shortest path from food to food, if such a path exists and is unique. If no such path exists, or is not unique, the result is undefined. It is otherwise similar to Jaccia.

Definition

Both Jaccia and Jacciata are defined in ALPACA v1.0. Jaccia is defined in the file jaccia.alp and Jacciata in jacciata.alp. The ALPACA definition is authoritative; what is given here is merely advisory.

Both automata use basically the same set of symbols. An initial Jaccia playfield generally serves as an initial Jacciata playfield with the same kind of solution.

• - empty space
• # - wall (purely decorative)
• : - slime mold
• F - food
• S - "start" food (needed in Jacciata, optional in Jaccia)
• - - exploratory head (Jacciata only)
• ? - exploratory body (Jacciata only)
• @ - solved (Jacciata only)

Discussion

Jacciata's definition is not very elegant, especially when compared to Jaccia. In order for it to work, the two sources of food need to be labelled differently (S and F), there needs to be a "head" of an exploratory shoot that looks for solutions, and so on. It could probably be made more elegant with some work.

[New in 1.1] The definition of these automata in ALPACA 0.94 suggested some possible improvements to ALPACA, particularly the definition of neighbourhoods different from the assumed von Neumann neighbourhood, and their use in the count operator. The Jaccia and Jacciata descriptions were rewritten in ALPACA 1.0, and do now take advantage of these features in order to be written more succinctly. (The ASCII appearance of slime mold cells was also changed, from the ridiculous % to the more aesthetically pleasing :. This actually happened half a month after 1.1 was released, so should technically be 1.2, but this change is so difficult to account for and will surely break your toolchain, so I ain't gonna bother with another version bump.)

Happy intelligence! Such as it is.
Chris Pressey
April 11, 2009
Bellevue, WA