reposted from rongtolas.com
What IS a fractal, anyway? The edges of the concept had been explored since the late 19th century, but not really recognized. The word fractal was coined by Benoit Mandelbrot in 1975, a tag for mathematical constructs with non whole-number dimensions. Not “2-D”, but perhaps instead four-thirds D. Or any other fraction. As defined, fractal refers to a state, not really a thing, but we shall misuse the term here like everyone else usually does.
Euclidian geometry attempts to translate natural form into permutations of lines, but the universe is in fact fractal. To cite the classic example, the coastline of, well, anywhere, is of INFINITE length- even though that is impossible, it is true. The “distance” measured depends upon the scale at which you measure it. The smaller the scale, the longer the line, until you are wrapping around the molecules of the rocks. For more detailed information, go read Rudy Rucker, George Cantor, or James Gleick’s excellent book Chaos, to whom I give credit for the example in the next paragraph. The connection between fractals and Mars, I’ll give you here. It may cause your brain to itch a little.
There is something mathematicians call a Koch line, or Koch snowflake. Draw a triangle (I could show you, but I want you to do this in your mind), and then add another triangle, one third as big, on each side. Voilà. A Star of David. Now, on each exposed side of those add-ons, do the same thing. Repeat. You could keep adding ever smaller triangles forever, without any bumping into each other. Nature does just that, with one difference- the unit isn’t really a triangle. More on that later.
Now consider the letter A - it represents a particular specific sound, but no two people actually pronounce it exactly the same way. We have a fixed alphabet, and a fixed mathematical nomenclature, but by convention and agreement only. Some languages, especially the older ones, don’t have fixed-letter vowels at all (more on that point later). And the Martian mathematics doesn’t rely on our Euclidian geometry of lines and fixed solids.
ow could that possibly work, you ask? Going back to Nature, and the fractal, one needs only to look at clouds to understand. Clouds, as Mandelbrot points out, are not failed spheres, but rather growth patterns of infinite branching. From a sufficient distance, the variations smooth out until we see a shape, but it would also be fair to call that a perceptual illusion. The efforts of mathematicians like Mandelbrot to translate these processes into conventions that fit into equations has led to the concept of self-similarity, which is a virtual pattern of symmetry, instead of a fixed measurement. As above, so below, the same rules of relationship apply (where have I heard that before?), and there are myriads of sets of rules interacting, defined by the perspective of the observer. So...it is possible to define and describe something purely in terms of its predictable patterns of interaction. Not the contents, but the box, and not a tangible box, but its virtual expression. “Interaction” in this context becomes a thing, a nodal point of similarity/symmetry, and even a few such points can define an object . The process is subjective, yet still accurate, rigorous and consistent. Mathematicians love these abstractions. Well, maybe “Love/Hate” is more accurate. Go ahead, scratch. I’ll wait.
We are conditioned to look at the world as being built up from the small to the large, multiplying the inside (building block) toward the outside (boundary). But that “outside” is a perpetual guesstimate. Moreover, if you measure a mile using a six inch pencil as a unit, errors will inevitably creep in, even though the math, on paper, is perfect. As long as you are operating in the realm of theory, you are safe- you are merely measuring the measurement, and can fudge (inside joke there, sorry) the results as required. Once you start applying that little stick to the terrain, all bets are off. You are no longer in total control of the parameters. The Martian saw the world as a shaman does, from the outside to the inside, resonant and symmetrical, and symmetry does not suffer the prejudice of scale that static measurement does. Bigger is not only not better, it is irrelevant. A comparison can be drawn with an observation made by quantum physicist Richard Feynman about gravity. He noted that gravity can be considered a “push” instead of a “pull” with equal validity. The whole universe is pushing you away, and you erroneously perceive the resistance of the ground against your feet as some characteristic of your own mass. Actually, gravity affects you because you are conscious. I do not imply that you should float away if you pass out. A rock, even though it is, in that context, unconscious, falls because it is a passenger in your Reality. But we are getting ahead of ourselves.
Let’s look at some examples of the Martian world view. Here is a building complex in the Cydonia region, taken from one of the first JPL-released Mars Global Surveyor images of the area. The spot is just to the left of the so-called “D&M Pyramid”, if you wonder about such things. Note the profile of a face in the main building outline. Also note that the groups of small towers are not, in fact alike, but all different in shape...yet similar.
The rooftop domes are seemingly shapeless, random amorphous blobs. In fact, they are the shapes they are because of the spots they occupy. As are all the other parts. If you try to envision the Oriental idea of feng shui as a very narrow interpretation of this, you can come close to, well, grokking the situation.
Here is another area, over to the right side on the first image: As you can see, the same patterns of style occur at this scale too, without any of the elements actually being the same.
“Wherever you go, there you are.”
- Buckaroo Banzai
This world view is more than an arbitrary design style. There are side effects to a truly integrative perspective, one being a tremendous amount of synchronicity, as if harmonic resonance could reach across countless dimensions to bring things and events into sync. Which is precisely what does happen. Mars, even in ruins, is well ordered in ways that the Terran perspective can barely comprehend. Here are some groupings of surface details, at different scales, with no attempt whatsoever on my part to align anything . Note how you can extend and transition from one to the next in almost any fashion without effort. The “flow state” of the fractal design persists even in rubble.
