The Fractal Universe

The fractal "Table of Natural Organization" grew out of the attempt to validate the notion that the 4x3 metric of astrology was an intuitive form of the fractal algorithm of the Cosmos, and if true, the Unified Field Theory should also have this same form, as it would necessarily correspond to the same fractal algorithm, but in its rational mode. The Unified Field Theory and astrology, in this view, are just two examples of the same Cosmic ordering principle, fractal algorithm, or General Systems "metric", but one is seen with the intuitive mind, the other with the rational mind. If this viewpoint has any validity, then we should be able to find many other significant examples of the operation of this algorithm in nature.

Once I began looking for 4x3 systems in nature, I found so many examples I decided to arrange them in a table, itself constructed as a 4x3 matrix (later 4x4), in order to effectively tabulate the examples so their significance (or lack thereof) could be carefully accessed in a systematic fashion. The result is the large, 4-part "Table of Natural Organization", which I believe effectively demonstrates the existence of a 4x3 fractal order in Nature expressed both structurally, dynamically, rationally, intuitively, physically, and metaphysically.

Originally in three parts, the fractal table was expanded to a 4th, metaphysical level (sometime around 1987), largely due to the repeated urgings (nagging) of Gus. The 4 parts are: Microphysical, Biophysical, Astrophysical, and Metaphysical - the latter interpreted as wholly the abstract product of the human mind in two modes, intuitive and rational. (Although conservation is a property of energy, the "law of energy conservation" and the "1st law of thermodynamics" - are rational, "metaphysical" constructs of the human mind. The notion of the conservation - "salvation" - of the human soul is similarly an intuitive metaphysical construct.)

Once I had discovered that the Cosmos did indeed have a fractal structure, I was as amazed and puzzled by its existence as anyone else. More than 20 years later, I am still amazed and puzzled. However, lately it has occurred to me that this is by far the simplest and most economical way to build a Universe; the elaboration of a self-similar fractal structure - so similar in principle to resonance - is clearly the path of least energy or least resistance. This is also the way the Tetrahedron model is built from the triangle - the outer 3 lines of the free energy triangle duplicate themselves and produce the 3 interior bound energy lines of the tetrahedron - thus the intrinsic motion of light becomes the intrinsic motion of time, symmetry becomes charge, and free energy becomes mass. The fractal structure of Nature is essentially the "rolling thunder" of the primordial "Word" resonating through the eons on successive levels of fractal expression.

The physical ground from which the 4x3 fractal resonates is evidently the 4-dimensions of spacetime interacting with light (free energy) to produce the three kinds of particles necessary to create matter: hadrons (the quark mass carriers), leptons (the elementary alternative charge carriers), and bosons (the field vectors or force carriers). We see the first expression of the fractal in the 3 families of four elementary particles - 3 quark pairs and 3 corresponding pairs of leptons. These resolve to the ground state proton and electron, the single nucleon of the hydrogen atom, itself a 4x3 structure - 3 quarks carrying four charges (color, flavor, electric, spin).

From hydrogen we next form the alpha particle of the helium nucleus, 4 nucleons each of 3 quarks, a particle so stable it becomes the "brick" of the nucleosynthetic pathway. Next we form carbon, 3 alpha particles each of 4 nucleons. Hence the carbon nucleus is a triple 4x3 resonance, beginning with the baryon (baryons are the class of hadrons composed of 3 quarks, such as the proton and neutron (the nucleons)). From the carbon nucleus we move to the carbon electron shell and the organic chemistry of life. The electron shell of carbon is also a 4x3 resonance; 4 valence (bonding) electrons in the 3rd electron shell (1S2, 2S2, 2P2). Furthermore, the bonding pattern of carbon is tetrahedral - 4 triangles (the crystal form of diamond). No other atom in the periodic table has anything like this combination of nuclear and electronic shell 4x3 resonances - 5 in all.

Beyond the tetrahedral bond of carbon, we find that DNA is itself a 4x3 chemical structure - 4 nucleic acids (adenine, guanine, thymine, cytosine) each composed of 3 molecular groups (sugar, phosphate, nitrogenous base). Finally, the genetic code is another 4x3 structure: the 4 nucleic acids code in triplets, producing the amino acids that comprise proteins. Hence we see how thoroughly the 4x3 Cosmic fractal algorithm is embedded in biology. This is the clue to how the ancients could have intuited the 4x3 fractal structure of the Cosmos: they were intuiting the structure of their own genetic and physical constitutions. At higher levels of biological organization, we lose sight of the molecular thread, but the dynamic and gross structural elements of the 4x3 fractal remain evident.

Each of the 4 realms is characterized by a dominant 4x3 expression of the fractal; in the biological realm, this is obviously the molecular structure of DNA and its genetic code. In the microphysical or atomic realm, it is the 3 quarks and 4 charges of the atomic nucleus, plus the 4 quantum numbers of the electron shell and the 3 components of atoms (electron, proton, neutron). At the astrophysical level, it is the 4x3 force field of gravity - in Einstein's words - four 3rd order equations (the changing rate of gravitational acceleration in x, y, z, t). Another major expression at the astrophysical level is the nucleosynthetic pathway, dependent upon the stability of the alpha particle, the helium nucleus. The 4x3 nuclear resonance of the nucleosynthetic pathway fails with chromium 48, which is highly radioactive, requiring 4 extra neutrons to achieve stability (chromium 52). The resonance settles at iron 56, one alpha particle beyond chromium, after which no more energy can be extracted from nuclear fusion. When the 4x3 resonance fails, so does the release of excess binding energy.

Finally, at the metaphysical level of human thought, we find numerous examples from the intuitive "world systems" of religion, mythology, and occult traditions, including (in religion) the 4 sacred creatures which surround the throne of the Trinity, (in mythology) the 4 riders of the apocalypse and the 3 fates, (in the occult) the 4 elements and 3 qualities of astrology and the 4 trigrams of the I-Ching. In the rational mode we have the four forces of physics combined with 3 energy states in the unified field theory, and numerous examples in the fractal hierarchy table previously cited. It is reflected in the body plan of humans and most terrestrial vertebrates - 3 major body divisions and functions (cephalic - perception; thoracic, metabolic; pelvic, reproductive) x 4 limbs; and even in our calendar of 4 seasons x 3 months.

The existence of a 4x3 fractal algorithm operating at every level in nature is one of the more astonishing discoveries in all of General Systems. The series of fractal papers are not technically challenging and are generally self-explanatory; hence readers should have no trouble understanding them, and I will let them speak further for themselves.