Dragon Curve Fractal algorithm (essentially): With each segment, replace it with a right angle. Repeat, making the output the input (a feedback loop).
This simple fractal example demonstrates some interesting properties of feedback loops and the side effects they produce:
* Complexity can come from simple processes
* Emergence - something different seems "to come out of nowhere"
* Paradoxes / duality, such as simple-but-complex and rectilinear-but-curvy
Illusions of Scale: Fractals are self-similar and scale-free, characteristics that can make it confusing to understand something's size. Objective analysis requires putting them in context. Geological formations have this nature.
For instance, you have to see the people in these pictures to appreciate how large these crystals are: http://news.nationalgeographic.com/news/2007/04/photogalleries/giant-crystals...
It can be confusing to understand their size without an objective means of comparison. In the case of the Dragon Curve, zooming in you can see nothing but right angles but zooming out you can see curviness. The Mandelbrot Set (link below) is a more amazing example of how one can get lost in the complexity of self-similar, scale-free worlds.
Question to Ponder: At what point does it become curvy? Can you *objectively* say when it is curvy? No, it is subjective. Many questions have this nature: How many pieces of rice form a "heap"? How much evidence is "proof" of something. These thresholds are subjective--illusions of scale.
Tip: If you follow just the bottom-most segment ("the tail"), you can see it shorten and spin, which makes it somewhat obvious what is going to happen.
Blinding Complexity: If you do not focus on some important aspect, you can fail to appreciate what is happening. Understanding nonlinear dynamics (including the power of feedback to create emergent phenomena) can help you to see the oak in the acorn--to see how something will grow or change.
Ubiquity of Fractals: Comlexity is everywhere, and it is always comprised of simpler components. While deterministic fractals like this one may seem like strange geometry, detached from the real world, you can begin to see nonlinear dynamics and feedback everywhere if you start looking for them (you just have to try). Nonlinearity gives rise to self-organization. See the emergence video below. Fractals exist not just in geometry but also in time (attractors in Chaos Theory), size (Fractal Statistics) and networks (scale-free "small-world networks").
Black Swans: Some huge, seemingly "impossible" events are described by recent realizations of "black swan" events. This huge, incredibly complex events are produced by simple rules--nonlinearity and feedback. Because complexity can be so blinding, sometimes people are called crazy for thinking some such events could even occur. Yet black swan events occur much more regularly than one would imagine if one uses a notion of reality that is based on past experience--which is how we normally think! Whereas superstition seemed to play a role in believing or denying the existence of some such events, we now have a rational way to discuss such "impossible" events.
Catching the Dragon by the Tail: In the manner of a feedback loop, write and read your thoughts on these things and other ideas repeatedly. Over time you can see something emerge--a greater understanding of the profundity and beauty of whole new worlds that lies hidden to the casual observer. Being a sage, a visionary, an artist depends on being able to see, to be able to make non-obvious connections. See for yourself.
Personal Wiki: Since late 2001, my strategy of dealing with the complexity of information overload has been to use a personal wiki. Information is infinite and complex (reminiscent of the Mandelbrot set), and some topics are needlessly complex because some people just don't know how to look at them. But whenever you are in a novel situation, it can be difficult to know what to focus on. It is wonderful and beautiful (and ESSENTIAL) to be able to quickly get the output of your last thinking on a particular topic and make it the input of your thinking this time when dealing with extremly complex issues or a lot of information. For this reason, I recommend a personal wiki. Trying to understand some things in great detail would otherwise be seemingly impossible. The more you "go through the feedback loop" of using the system, the more you will gain from the network effect--the emergent value of having such a system. (Don't underestimate this! It seems simple, but in the end you will wonder how life would have been otherwise.)
Emergence video: http://www.pbs.org/wgbh/nova/sciencenow/3410/03.html
http://en.wikipedia.org/wiki/Dragon_curve
http://en.wikipedia.org/wiki/Mandelbrot_Set
http://en.wikipedia.org/wiki/Black_swan_theory
http://en.wikipedia.org/wiki/Personal_wiki
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3D Dragon Curve Animationby Cryogenius1,136 views
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