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Chaos and Evolution: Fractal example

A fractal

This is a fractal. The points within the fractal are coloured white. The fractal is defined by an iterative (repeating) formula. On each iteration of the formula, any given point will change position, as shown below:

Point A is within the fractal and cycles forever within it, but Point B is outside it, so the iterations bring it out to infinity.

Here we see two points—Point A and Point B. Notice that Point A is within the fractal (white area) but Point B is not. Notice how the points are moving—each arrow represents a single iteration.

As we can see, Point A cycles around and around in a loop; Point B, however, moves away from the fractal and doesn't return. This relates to how the fractal itself is calculated. The points considered to be within the fractal are those that cycle around in a loop forever (e.g. Point A). But, the points outside the fractal are those that travel out towards infinity (e.g. Point B).

Now let's consider a point at the centre of the fractal:

The centre of the fractal.

It's situated at zero, so the iterations don't cause it to move at all. Consequently, it stays fixed forever at the centre of the fractal.

Now let's introduce chaos:

Chaos causes a point within the fractal to move a small distance in a random direction.

The chaos causes the point to move a small distance in a random direction. This chaotic movement is in addition to the movement caused by the iterations.

And now that Chaos has caused the point to move away from the centre, the iterations of the fractal's formula will be causing it some further movement. Below we see this movement; since chaos is continuing to take effect, a small chaotic movement is added to each iteration:

The chaotic and iterative movements combine to move the point around.

Now that the point is experiencing longer movements, there is a possibility that it will move outside the fractal and bomb out to infinity. As long as there is chaos, there will always remain this possibility of extinction. However, we may minimise the chance of extinction occurring.

The point circulates at the fractal's edge.

The chance of bombing out is minimised when the point moves near the fractal's intricate boundary and finds a niche—one in which it can cycle around and around in a tight path, with only a minimal chance of it slipping out and leaving the fractal.

Notice that while the point's movement appeared to be quite simple during the iterations right after it left the origin, its movement later assumed a greater complexity when it found its niche at the boundary. This represents a process of evolution whereby a simple system becomes complex.

Of course, there was a large chance that the point wouldn't find a niche, and would end up travelling to infinity. But if we start with very many points, then it's likely that a few of them will find good niches, and survive in those niches over thousands and millions of iterations.

This would mean that the fractal's formula had favoured a few points out of the many points that it could choose from. And this is how natural selection works—chaos creates a large range of slightly different options, and the Cubic Laws of the Universe select the ones that are best.

Now, let's consider Good and Evil, the Good and Evil that exist within true cubic morality. How does the fractal symbolise Good and Evil? Answer: the points that stay within the fractal for many iterations are good, while the points that quickly leave the fractal and bomb out are evil.

Below, we see that Point A represents good and Point B represents evil.

Point A is within the fractal and cycles forever within it, but Point B is outside it, so the iterations bring it out to infinity.

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