Sorry for the late response.

Emergence, as a mathematical concept, can actually be modeled in computer programming. Typically involving AI.

The first example you could use is something like "The Game of Life". The first thing it introduces you to is the idea that highly complex systems can develop from extremely simple rules. You set baseline parameters, and things can grow wildly and in highly unexpected ways, even to the point of a permanent pattern developing.

That can show you that an order can emerge without the strict imposition of all patterns from a programmer ahead of time.

From there, if we try to ask a computer to model a most optimal function through trial and error, and we give it the ability to identify which result was "best" so that it can be carried on to the next series of tests, as time progresses the computer will create a highly efficient model to do what we ask, even if the behavior is totally unexpected and/or wouldn't have been programmed.

This is how most AI Learning works by giving a computer a set of objectives, and trialing them out.