The Universe as a Fractal

Today I will attempt to show that the universe in its entirety can be thought of as a fractal.









First off, we need to establish what a fractal is, and what this means for the universe. A simple example of a fractal would be the Sierpinski Triangle:



To make this triangle, we start with an equilateral triangle - a triangle whose sides are all equal in length, and angles are all 60 degrees. Within this triangle, we draw a smaller, upside-down triangle by connecting the midpoints of each of the original triangle's sides. We then have 4 smaller triangles that all interlock into the shape of one large triangle. We can repeat this process within each of the small triangles to create even more triangles. Indeed, we can do this infinitely.

Now, what's interesting about fractals - including this one - is that each triangle contains all of the information that the whole system does. Given a Sierpinski triangle that continues infinitely in both directions (increasing and decreasing in magnification), you can choose a triangle at any level of magnification and the formula to produce the rest is exactly the same. It doesn't matter where you choose to begin, you will always find the same pattern. This phenomenon is known as self-similarity.

But how does this apply to the universe? I will borrow a concept from Buddhist monk Thich Nat Han called interbeing to illustrate this idea:

Think about a wooden chair. You may look at it and say "this is a chair". The chair is, in fact, everything but a chair. Contained within the information of that chair is the information of the sun, which grew the tree that the chair was made from. The person who made the chair is also within the chair. The lumberjack who cut down the tree, as well as his breakfast that morning are in the chair. Indeed, everything in the universe is within that chair except for the chair itself. The chair is empty of a separate identity. The only way to define the chair is by describing everything but the chair. But then, things other than the chair - your desk, for example - contain the chair within them. But they are in the chair! This makes it difficult to come to a concrete definition of anything.

For those who are more technically inclined, on a smaller scale things are indeed intimately related. The phenomenon of quantum entanglement, where subatomic particles communicate at great distances instantaneously shows that information is indeed exchanged between particles on a level that is imperceptible to us. It has also been shown that shortly after the big bang everything in the universe was entangled.

So, within each piece of the universe exists all of the information of the universe as a whole. Does that sound familiar?

Of course, your chair certainly doesn't look like everything else - it looks like a chair. But the Sierpinski triangle is a simple example of a fractal. The Mandelbrot set, for example, exhibits vast complexity, and there are certainly perspectives of its visual representation that look nothing like the original. But they do represent the same formula, despite their different appearances. What I am suggesting is that the universe, in all its complexity and beauty is realized through a single fractal formula.

Fractal patterning is often found in nature, such as the growth patterns of ferns and other plants, as well as the human circulatory system. Recent studies even suggest that genetic code has a fractal nature.

















A fractal fern

Well, I hope that this has been informative. Later I will describe some further implications of a fractal model of the universe.