To explain this before going further, fractals are not identical clone copies of each other, even in the geometric sense. A child is a fractal unit of its parents, genetically the same, yet a different chemistry--figuratively speaking. The same child and parents are yet fractal levels of a family tree and at the same time--units of a larger community fractal, and may be a fractal unit of a religious group or political affliliation within that set. This same child, parents, the community are all fractals of county, state, national fractals and may be fractal units of sets within any of these larger fractals--organizations, spiritual affiliations, clubs, special interest groups, schools, workplaces, etc. and etc. Aside from this fractal set, this same child is a fractal unit of the mammal set which is a fractal of the animal set, which is a fractal unit of the organic set, which is a unit fractal of the biosphere named Earth. From this bioshere is also an inorganic set--rocks, minerals and metals, plus elements such as water, fire and wind. All within one world. Or is it one world?
Let's go back to the individual fractal set-- a human being. This one individual is very much like the fractal units of every individual human being, yet is distinctly different in many dimensions--genetically, in a biological dimension. But each individual also resides in many dimensional worlds--some in academic worlds, some in spiritual worlds, some in political worlds, some in worlds of dispair and some in worlds of optimism. Some individuals share like worlds and are polarized by some worlds. Galaxies share the same diversity. Though all galaxies are such by definition and attribute, they are not all identical. Even as 75% to 85% of large galaxies are spiral or lenticular (Bennet 592), they may have differing attributes, origins and makeup, though they all behave as galaxies. As a human and other primates all stem from a like fractal set where their genetic makeup is nearly identical it is very evident the vast difference between them. Likewise, as a whirlpool and a galaxy may share some fractal properties, the differences are quite evident in a scale sense and in a physical sense, but it's the shared properties that should be examined, particularly when bonded by the same Golden Mean. Also, note the subtleness, as well.
Just as primates and humans are near genetically identical, the biggest differences are quite profound. Humans operate quite differently than chimps. Where a whirlpool, or a tornado, may have a funnel that draws objects down into it and then spewing them out; a galaxy may simply be doing the same but in a different manner. Whereas in a whirlpool or hurricane, the draw is relatively constant, a galactic funnel may be that of building an amount of intensity before releasing bursts, as excited-state electrons hold and release photons in atoms.
Simply put, the swirling of a spiral galaxy starts when a giant molecular cloud is drawn together by gravity, resulting in the matter forming substructures, "not unlike bumps in our own atmosphere (Goodman 50)" with the densest matters "collapsing into spherical nuclear reators known colloquially as stars (Goodman 50)." In time, the gravitation center of a galaxy draws more mass to it, the gravitational force becomes greater until the density of mass is so great that compression heats the core spewing cosmic winds back into space. "Galactic" whirlpools? Does this happen on an even larger scale? More on this later.
Closer to home, our solar system possesses some interesting Golden Mean properties. The "red eye" storm on Jupiter have mirror Golden Spirals within it. Also, the distances of planetary orbits working out from the Sun displays a Golden Mean proportion. "The distance from the sun to Mercury plus Mercury's distance to Venus equals the distance between Venus and Earth. The Phi relationship is most clearly defined by the planets nearest the sun, but the ideal gradually breaks down toward the outer planets (Schneider 127)." Roughly. The orbital "averages" are more spectacular, particularly those of the inner planets with their averages no less than 0.076 of perfect Phi, 1.61803. Interestingly, Earth sits at a 1.608 orbital average. The orbital relationships work out as follows [based on AU distances (Bennet 213)]:
|PLANET AU / PLANET AU
|Mercury 0.387 / Venus 0.723
|Venus 0.723 / Earth 1.00
|Earth 1.00 / Mars 1.52
|Mars 1.52 / Asteroid Belt (center) 2.75
|Asteroid Belt 2.75 /Jupiter 5.20
|Jupiter 5.20 / Saturn 9.53
|Saturn 9.53 /Uranus 19.20
|Uranus 19.20 / Neptune 30.10
|Neptune 30.10 / Pluto 39.50
All figures are remarkably close to Phi. It may be that these orbits simply are still on their way to a perfect Phi relationship.
We have glimpsed some of the interweaving and fractalizing relationships that nature utilizes in many facets -- from the subatomic to galactic proportions; within the structures of life, the universe and to the very psyche of mankind. Now, let's examine this closer. For an example of the Fibonacci Sequence and the Golden Mean in a biological sense, let's look at the genealogy of a drone honeybee. Honeybees experience parthenogenenis, unfertilized females give birth to males, whereas fertilized females always give birth to other females. Each branch in the tree accumulates in a Fibonacci growth pattern and each branch resembles the whole. Also, notice the golden proportions in this branching.
Just as fractals are evident in the patterns of genealogy, this individual family tree is but a branch of the hive fractal. The hive fractal but a branch of the entire honeybee population, and this but a fractal of the bee genus. One can visualize a picture of honeybee populations around the world from this one family tree. How can we be certain? Nature utilizes the infinite, fractal proportions of the Golden Mean through the Fibonacci Sequence. Even the honeybee's body is in golden proportion. And, so are human's.
Examine the Phi relationships in the overall body and the face, and the hand. Build Phi calipers to verify these golden proportions. The ancients believed man was a microcosm of the whole universe. I believe they were on to something.