Two rules. If the ant is on a white cell: turn right, flip the cell black, move forward. If on a black cell: turn left, flip the cell white, move forward. That's everything. No memory. No goal. No design.
For several thousand steps, the pattern looks like noise — asymmetric, unpredictable, building and destroying itself. Then, around step 10,000, something changes. The ant begins constructing a periodic highway: a diagonal structure that repeats every 104 steps, extending indefinitely. Order from nowhere. Nobody has proven why this happens.
With multiple ants, the dynamics shift entirely. They interfere, reset each other's paths, build and destroy together. Sometimes they still find highways. Often they don't. The rules are the same. The outcomes aren't.