I wrote a short essay for a related class about how neural networks might (or might not) be able to help speed up emergent simulations, and I may try and test this idea in my tree simulation project. Here is my essay if you are interested; please let me know what you think!
In computer graphics demos there is a fairly common method of rendering water ripples based on a CA; each cell has a height value, and every frame its height value is set to the damped inverse of its previous height value + the average height of its neighbors. This results in fairly realistic-looking ripples that propogate outwards as expected.
A tutorial for achieving this effect can be found here
In my game I am implementing a fairly similar effect for water ripples
In class I feel we are giving Wolfram much more credit than he is due. The idea of molecular determinism (that everything is a result of a starting condition and a set of rules) has been around for over a century, and even the idea of the universe functioning like a giant cellular automaton was first suggested by Konrad Zuse in 1967. Maybe next he will talk about his brilliant new idea that DNA has a double helix structure, or that energy and mass are different sides of the same coin.
Aside from that, I am not convinced of the importance of the idea that the universe is a giant CA. This seems like a fairly typical example of using new technology as an analogy for everything. Back when the steam engine was new, Freud had a great idea that the mind worked by building up and venting pressure. Then when telephones became popular, the mind became a giant switchboard. Filling in scientific voids with the latest technology is tempting, but not necessarily valid or important.
Rule 30 seems to result in a repeating pattern that transfers information along a diagonal with a slope other than 1, though the repeating pattern composing this line is based on lines of slope 1. Here
is a picture of it from Wolfram's book.
The ideas behind emergence are very important for computer game design, because we try and simulate real phenomena based on simpler rules, so in a sense we are trying to reverse-engineer emergent patterns. For example, in my current project I am trying to simulate (in real time) fairly complicated physical objects such as bodies, ropes, weapons, or cloth. My current solution is to deconstruct the object into its component points and constraints, and then apply Isaac Newton's laws of motion.
While this is a much simpler approach than that used in most games, it is yielding very promising results, and may turn out to actually be faster and more flexible than other more popular approaches to physics simulation.