## Complexity from Simplicity – More Support for a Digital Reality

Simple rules can generate complex patterns or behavior.

For example, consider the following simple rules that, when programmed into a computer, can result in beautiful complex patterns akin to a flock of birds:

1. Steer to avoid crowding local flockmates (separation)
2. Steer towards the average heading of local flockmates (alignment)
3. Steer to move toward the average position (center of mass) of local flockmates (cohesion)

The pseudocode here demonstrates the simplicity of the algorithm.  The following YouTube video is a demonstration of “Boids”, a flocking behavior simulator developed by Craig Reynolds:

Or consider fractals.  The popular Mandelbrot set can be generated with some simple rules, as demonstrated here in 13 lines of pseudocode, resulting in beautiful pictures like this:

Fractals can be used to generate artificial terrain for video games and computer art, such as this 3D mountain terrain generated by the software Terragen:

Conways Game of Life uses the idea of cellular automata to generate little 2D pixelated creatures that move, spawn, die, and generally exhibit crude lifelike behavior with 2 simple rules:

1. An alive cell with less than 2 or more than 4 neighbors dies.
2. A dead cell with 3 neighbors turns alive.

Depending on the starting conditions, there may be any number of recognizable resulting simulated organisms; some simple, such as gliders, pulsars, blinkers, glider guns, wickstretchers, and some complex such as puffer trains, rakes, space ship guns, cordon ships, and even objects that appear to travel faster than the maximum propagation speed of the game should allow:

Cellular automata can be extended to 3D space.  The following video demonstrates a 3D “Amoeba” that looks eerily like a real blob of living protoplasm:

What is the point of all this?

Just that you can apply some of these ideas to the question of whether or not reality is continuous or digital (and thus based on bits and rules).  And end up with an interested result.

Consider a hierarchy of complexity levels…

Imagine that each layer is 10 times “zoomed out” from the layer below.  If the root simplicity is at the bottom layer, one might ask how many layers up you have to go before the patterns appear to be natural, as opposed to artificial? [Note: As an aside, we are confusing ideas like natural and artificial.  Is there really a difference?]

The following image is an artificial computer-generated fractal image created by Softology’s “Visions of Chaos” software from a base set of simple rules, yet zoomed out from it’s base level by, perhaps, six orders of magnitude:

In contrast, the following image is an electron microscope-generate image of a real HPV virus:

So, clearly, at six orders of magnitude out from a fundamental rule set, we start to lose the ability to discern “natural” from “artificial.”  Eight orders of magnitude should be sufficient to make natural indistinguishable from artificial.

And yet, our everyday sensory experience is about 36 orders of magnitude above the quantum level.

The deepest level that our instruments can currently image is about 7 levels (10,000,000x magnification) below reality.  This means that if our reality is based on bits and simple rules like those described above, those rules may be operating 15 or more levels below everyday reality.  Given that the quantum level is 36 levels down, we have at least 21 orders of magnitude to play with.  In fact, it may very well be possible that the true granularity of reality is below the quantum level.

In any case, it should be clear to see that we are not even closed to being equipped to visually discern the difference between living in a continuous world or a digital one consisting of bits and rules.