Complex Networks, Simple Rules: Life, The Universe and Everything!

More videos and papers about these systems are:

Complex Networks, Simple Rules
Searching For Complex Systems - Live
Complex Network Growth And Chaos From A Simple Rewrite Model
Complex Networks from Simple Rules (paper)

Explore the systems online with Wolfram Demonstrations

In this videos I try to explain some of the reasons I am so interested in the dynamics of network rewrite systems (that generate complexity via simple rules).

I discuss the systems using my first ever 3D printed shapes -the complex network grown up to step 300, and the hyperbolic network grown up to time step 900.

Looking at these kind of toy models can teach us lots of interesting things about emergent properties, such as -when and where are the most complex parts of the universe expected to be observed.

The systems are also interesting from a topological viewpoint, since they both begin with a cube (a planar graph), and quickly become non-planar. In fact, if one things of the systems as an evolving surface then one can literally see the formation of things like cross-caps which stop the system being orientable.

More importantly, the unpredictability of these systems teaches us to expect unpredictability in the life evolution of individual biological organisms, species, and the entire universe.

We also discuss how such systems could be used to model memory, be having the structure represent a neural network, while the writer's position represents the place the thinker is focused upon.

We show how the network grows after the first 300 time steps and use 3D (rotatable) graphics to show the intricate network developed after 100000 time steps.

The question of whether this system ever falls into a repetitive growth pattern may well be undecidable.

Many of my works an videos are inspired by Stephen Wolfram's `A New Kind Of Science'

By looking at the other programs of this type collected on my website, one can find many systems which exhibit chaos emergence and, which can model the growth of many biological organisms (e.g., plants).

The other `curly rule' produces a non-planar network (corresponding to a non-trivial topological surface), and essentially this network corresponds to hyperbolic space.

This is more evidence for the wide range of difference spaces/geometries that can be made by these systems,

[RichardSouthwell]

I talk about one of my favourite models every in layman's terms, and explain implications for cosmology, biology, complexity, and learning. I love this complex network so m/uch I had to 3D print it!

[TheRealFlenuan]

To add to your point about the origins of the complexity of the universe, many physicists have found comfort in the hypothesis that there are infinitely many universes, each with its own "set of rules", if you will, and that the complexity of each universe not only arises from the probability waves already shown to exist via experimentation and mathematically outlined in the theories of Heisenberg uncertainty, string theory, and so-called "superparticle" pairing, but also from the infinite set of possible "rules" (or rather physical laws and constants) by which a universe can operate. I believe that no amount of experimentation within our universe can show that other universes that are completely separate from our perspective within spacetime exist, but for now this particular multiverse hypothesis is the only explanation for why the universe is not a uniform sphere of energy but the complex system it is today.

[TheRealFlenuan]

Also, I think that this concept relates very well to cellular automata—complexity arising from simple rules and simple starting figures is nearly ubiquitous within the field!

[kiwanoish]

Have you thought of just dedicating a computer to keep a couple of these systems running towards "infinity"? I've actually had plans like this but never came to it. I've always thought there must be someone out there that had one running for a while.

[bullpup]

Hey I think Stephen Wolfram just stole your idea...

[troyhayder]

Now you have six six six views....

Ain't i awesome?