Remember those weather TV channel hurricane images over central America captured by satellites? E.g. Floyd just off the Florida coast on September 14, 1999 (image at nationalgeographic.com). Well, you are pretty close. Here is an example of an ant colony death spiral, where a group of ants gets separated from their colony and start following each other by scent in a circle, and they do so until they all die of exhaustion. A deadlock. An ant’s circle deadlock.
So in order to teach a computer on how to draw a circle without giving him any clue on how what a circle his, what you have to do is exactly the same thing. You just follow a generative design line of bottom-up distributed pattern formation. And you keep replacing the word “computer” by the word “ant” at the title of this post, as many times you can, back and forth, in a non-explicit manner. Using stigmergy. You just implicitly create simple rules, even ant-like, non-anthropomorphic, which end-up at that exactly behaviour. Yes,… sometimes those “simple” rules are difficult to grab. But you just keep doing it. Not with a simple “trial-and-error” method, of course. We have better tools to do that. In fact, they are present in planet Earth since the Big-Bang: we call it, Evolution. Now, from circles beyond, a full array of problems, even hard ones could be treated. Here are some examples.