“In this article I want to show how structure emerges out of iteration. Specifically, I want to create a very simple model of Darwinian evolution and demonstrate with simulations and mathematical proof that patterns emerge naturally ….. when stable patterns emerge in some iterated system, it’s possible to build new systems on top of the old ones. Moreover, these new systems can be seen as independent of the old ones ….. Artificial Life is the use of computer simulations to understand biological-like behavior. Conway’s Game of Life is one of the best known.”

This is an interested read, written by David Eubanks of Johnson C. Smith University. The article discusses the emergence of structures through iteration, leading to eventual “artificial life”. A realistic definition of artificial life would be that “artificial life is the use of computer simulations to understand biological-like behavior.” Knowing this and making use of Collatz iterator, David Eubanks shows how to construct a population that is subject to Darwinian evolution. There is even source code provided, written in Perl, if you’d like to play around with the example. Actually, this isn’t the first time this idea has appeared. Another similar example of using the Collatz sequence to study artificial life can be seen in: An Artificial Life View to the Collatz Problem by Hiroki Sayama.

Collatz Ecologies (highered.blogspot.com)

More Resources:

• Artificial Life (wikipedia.org)
• Conway's Game of Life (wikipedia.org)
• An Artificial Life View to the Collatz Problem (Hiroki Sayama)