A mathematician, explaining the Chaos Game
Fractals… They’re all over in biology. They’re one solution that natural selection has come up with over and over again.
NOVA, Fractals the Hidden Dimension
A good friend has spent the past few weeks on jury duty – a death penalty, double murder trial. It’s been a hard, very emotional period for her. But, she’s approached it as happening for some reason and so she tends to look upon the trial as an opportunity for growth. Her husband, on the other hand, feels things simply happen. The trial is an odious even she has been pulled into and there is no reason for the disasters that befall us. Our task is simply to survive the pain and move on down the road. His philosophy has uncovered my friend’s own doubts regarding her spiritual beliefs.
His doubts also reflect statements I sometimes hear from nondualists: There is no reason or ultimate cause. Things simply happen.
I think we all wrestle with this question. Sometimes we simply voice it as, “Why me?”
I find one answer to this question through the science of Chaos Theory and Fractals. It’s simple and very graphic. Fractals are beautiful complex patterns. Each pattern is defined by an equation. The equations are meant to be solved repeatedly with each iteration generating a point. When these points are plotted graphically, their location pops up randomly. It is from this random deposition of points upon a piece of paper that the beautiful fractal pattern eventually emerges.
You can watch this process for the pattern called a Sierpinski Triangle here.
You can view an emergence of this pattern in 21 seconds here.
[The game is following these rules: Number the vertices of an equilateral triangle 1, 2 and 3. Start with a random initial point in the plane and plot this point. Randomly pick a number: 1, 2 or 3. From the initial point, move half the distance towards that numbered vertex. This point is plotted and becomes our new initial point. Repeat this process thousands of times.]
Fractal geometry is the geometry which describes the chaotic systems we find in Nature. Scientifically speaking, Life and the Universe itself are complex systems. Such systems are Chaotic in behavior and Chaos Theory presents these simple, defining features of every chaotic system:1. Chaotic systems may appear to be random but they are not. They are deterministic with equations ruling their behavior.
2. Chaotic systems are very sensitive to the initial conditions making them very unpredictable. A very slight change in the starting point can lead to enormously different outcomes. The famous Butterfly Effect and the difficulty in predicting weather are examples.
3. Chaotic systems appear to be disorderly, but they are not. Beneath the seemingly random behavior are a sense of order and beautiful patterns. The orderly systems predicted by classical physics are actually the narrow situation.
And thus, in the Chaos Game we find that the picture that is generated through this random process is not random at all. And I think this is exactly how are lives are. We may not see the reason for the situation that we're in. But, that does not mean there is no intelligence or reason underlying the surface appearance of events.
Chaos and order are deeply, deeply linked. In fact, I view them as different sides of the same coin.
You can call this phenomenon an expression of the Laws of Nature or the intelligence of God. I think it just depends upon whether you are coming from your head or heart, and your ability to look deeply inside yourself, deeply inside the universe.