A more complete, updated version of this article appears in Chapter 2 of the Simple Explanation book. Jump to that article by clicking here.

This blog's author recently gave an easy-to-understand 20-minute talk on this topic. Here's the blog article where you can view the Simple Fractal Model video.

In 1975, mathematician Benoit Mandelbrot coined the term “fractal” in the first published paper on fractal geometry. Despite some resistance from the mathematical community, it was soon discovered that fractal geometry is unparalleled at measuring and modeling the world of natural phenomena.

This blog's author recently gave an easy-to-understand 20-minute talk on this topic. Here's the blog article where you can view the Simple Fractal Model video.

In 1975, mathematician Benoit Mandelbrot coined the term “fractal” in the first published paper on fractal geometry. Despite some resistance from the mathematical community, it was soon discovered that fractal geometry is unparalleled at measuring and modeling the world of natural phenomena.

Here's the definition of fractals from Wikipedia: “A fractal is 'a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,' a property called self-similarity... Because they appear similar at all levels of magnification, fractals are often considered to be infinitely complex (in informal terms). Natural objects that are approximated by fractals to a degree include clouds, mountain ranges, lightning bolts, coastlines, snow flakes, various vegetables (cauliflower and broccoli), and animal coloration patterns.”

If you would like to see fractals in action, the NOVA documentary, “Fractals,: Hunting the Hidden Dimension," gives an excellent overview of fractals.

*At this point in the article, if you haven't already, you really should read the Basic Principles of the Simple Explanation of Absolutely Everything found in Chapter One of the Simple Explanation book, in order to acquaint yourself with the concepts and terminology.*

• It has a fine structure at arbitrarily small scales.

• It is too irregular to be easily described in traditional Euclidean geometric language.

• It is self-similar (at least approximately or stochastically).

• It has a Hausdorff dimension which is greater than its topological dimension.

• It has a simple and recursive definition.

**To put the**

*Simple Explanation*in fractal terms, our universe is populated by simple, recursive, self-similar structures of consciousness at arbitrarily small scales.As explained in Chapter 2 of the

*Simple Explanation*, as our universe expanded, over and over and over again, pale echoes of God’s mind attached themselves to the particles streaming out of the Big Bang. These self-replicating Units of Consciousness (UCs) can be described as fractal emanations of the originating fractal formula--the Universal UC.

Whereas Mandlebrot's best-known fractal, the Mandlebrot Set, looks like this, |

the fractal associated with the Simple Explanation of Absolutely Everything looks like this. |

One interesting feature of fractal patterns is that no matter how closely you look, or how many calculations are performed, the pattern continues to replicate on smaller and smaller, and larger and larger, scales.

In the

In the *Simple Explanation*, the enclosure of our material Universe is a Very Large toroidal pattern at the "outside" edge of creation. This would be the Universal pattern at its largest fractal scale, the Universal UC, akin to the singular void at the center of the Mandlebrot set. Drilling downward from greatest to smallest, the Units of Consciousness associated with sub-atomic particles are the smallest fractal expressions of the Universal set. These smallest material instantiations of creation pass from the realm of pure consciousness through causal energy to material instantiation through calculations of the Universal fractal formula. The crossover from pure consciousness to material instantiation occurs at the edge of an infinite series of ever smaller fractal divisions proceeding downward from the lower limit of material instantiation (Planck's constant), and then energetically finer and finer until energy is finally suspended in the infinite stillness of non-being,*the Metaverse*.*Simple Explanation*, the zero point at the center of the universal toroid is the source point where the pure undifferentiated consciousness of the metaverse is concentrated to singular manifestation. This is the crossover location between the undifferentiated unity and material creation. Some call it the Womb of Creation. From this zero-point, all organizing principles and laws enter our Universe and replicate their patterns upwardly through creation, from the very smallest sub-atomic particles to the largest galaxies, and then beyond, to the Very Large.

These replicating patterns and their hierarchical structure is explained more fully in the two articles, "My Self, the Governor of Whoville" and "Nested Hierarchies." In personal terms, my Self UC is a fractal division of the Universal UC, and so is every UC associated with everything in my body. The fractal calculations occur at every hierarchical jump of organizational complexity.

The spiritual implication of this fractal model is this: the Universal UC ("God," "The Creator," "The Mother of 10,000 Things") may be visualized as both immanent and transcendent. Immanent within every one of my body's UCs, at the tiniest fractal crossover point at the center of each UC. Transcendent at the outer edge of the Very Large, where our Universal UC fractally nests against the infinite, undifferentiated Metaversal UC ("God the Father," "Sat," "Pure Consciousness," the "Undifferentiated Unity"). We humans are suspended thusly, a particular fractal emanation of, and located within, creation, yet patterned directly from pure consciousness.

I find fractals fascinating and intriguing. I think the application of fractal physics to your Simple Explanation is thought provoking and profound. Drawing upon my knowledge of fractals and quantum mechanics, please allow me to provide my thoughts as they relate to this portion of your cosmology.

ReplyDeleteI think you can state that there are dimensional fractals and non-dimensional fractals, the latter being a metaphysical state. Both occur on a continuum from small to large in scope. I say scope, because I am not referring exclusively to relative size. You could propose that consciousness fractally becomes more complex as you move from the smallest to the largest entities. Similarly, starting at the molecular level and proceeding to supra-toroidal level fractals, it is reasonable to believe that fractals reflect the way the universe replicates itself into continuously complex levels of organization. A good example of that is the relationship of the atom to a solar system, to a galaxy, and to a universe. I don’t believe that evidence of fractals at the subatomic level will be found. At the level of electrons, protons, and neutrons and their component particles in the Standard Model of particle physics, these particles are essentially locations of energy that oscillate according to String Theory. The oscillations for each subatomic particle are unique and therefore I don’t believe there would be a fractal pattern at this level of material instantiation.

I hope my remarks are reasonable and useful.

David--excellent comment. Thanks for your input!

ReplyDeleteI like the way you note a difference between dimensional and non-dimensional fractals. Yes, the dimensional fractals are easy to see at the larger scales, even the large toroids emanating from our position in space (see the article in the topical index to the right, "Scientists find Torus of Dark Matter..." At the sub-atomic level, the toroidal fractal pattern may only partially manifest as the forces and fields peculiar to each very small "thing." Or the toroidal pattern may be entirely non-dimensional, merely the Word or Pattern required to uphold Order in the Universe.

Today I'm going to write a follow-up article to this one concerning dimensional vs. non-dimensional fractals in the Simple Explanation.

Insightful comments, Dave! I would question your distinction between dimensional and non-dimensional fractals. I believe the distinction is one of convenience and not one of proposed reality. I believe the universe as a whole is all metaphysical and thereby non-dimensional. There is merely a continuous level of organization from top to bottom. Planck's Constant may define the lower level of material instantiation, but such a level may only be a matter of convenience rather than a matter of reality. String Theory may well be an attempt to describe the fractal complexity of atomic and subatomic particles whose existence may well be only metaphysical and non-dimensional. As Cyd says, the toroidal pattern may be entirely non-dimensional.

ReplyDeleteBill here is pointing out that the universe shows itself to be entirely metaphysical when you get down to the quantum level at and below Planck's constant. What we refer to as "dimensional" is more a matter of convenience than reality, as the domain/dimension of sense perception. In the cosmology of the Simple Explanation (Ch. 1), consciousness is non-dimensional, dwelling in fullness in the Metaverse. Our fractal units of consciousness are also non-dimensional, all nesting in the same no-place, each energetically focused on a bit of the "dimensional" Universe.

ReplyDeleteI am so glad you are able to put into simple words what I experienced mystically some months ago. I had been trying to find words to explain what I experienced and here you are offering them to me on a silver platter. I experienced my very moment as an infinite toroid. As I attempted for hours to find an "escape"to this geometrical form, I found myself ending up at the same place and time. I was profoundly touched and traumatized by the event. But months later I believe I can make sense of it. Thank you once again.

ReplyDeleteDMT/LSD creates geometric images i know its sounds like hippe stoner stuff but wen theres an unbiased study about these triptomines it alwas comes up with biger questions in no way im saying lsd has enething to do with the universes big questions but somethings going on in the brain wen its on triptomines and eneone whos experienced dmt/lsd has the same crazy hippie im not condoning drug use skrewed my life up with the stuff dont use enemore but still beleve more unbiased study are needed

DeleteI wrote the following as a result of reading your January 8 comments, Cyd. Perhaps you can consider how these comments work with your cosmology.

ReplyDeleteDimensions, Time, Energy, and the Metaphysical in a Massless Universe:

I believe that dimensions may be a convenient place for us to experience the metaphysical world above the level of the Planck constant. Without dimensions, we are rather like in a womb of limited perception, whereas the universe is outside this environment. Do you agree that the physical laws of our known universe that create the environment for our metaphysical experience originate in laws assigned prior to the valuation of Planck’s constant? The energy and characteristics of strings are non-dimensional; that is the reason that the universe as we know it could originate at a point without dimension. The aggregations of these non-dimensional points of energy in space have pushed the envelope of space outward creating dimensionality. Since time is a byproduct of the existence of dimensions, then time began concurrent with the advent of dimensions as the first moment in a sequence of events within space. The creation of a potential for energy to exist, did not occur at any dimensional location or moment in time. In order to have energy, there must be an offsetting potential of non-energy. A good example of this is lightning. If there isn’t a difference in charge between the earth and the atmosphere (the potential), there cannot be a discharge of electron flow. At moment 0 of the universe, an almost infinite amount of energy was created at the initial, non-dimensional point (prior to expanding and creating dimensions) because there was potential energy as a result of an off-setting state of equivalent non-energy. In this paradigm, energy isn’t something created and introduced into a budding dimensional universe, but is a location where there is a potential for energy to exist. I think this opposite-energy potential or “dark matter” originates at the edge of the expanding dimensional universe, or in your model, at the non-dimensional location being absorbed by an expanding toroidal space. As the edge is pushed outward, dark matter is left behind within our dimensional universe. The density of the dark matter acts through gravity to attract stars and galaxies and accelerate them toward the outer boundary of the universe. This attractive affect has been erroneously referred to as a cosmological constant of repulsion among planetary bodies that accounts for the expansion of space at an ever increasing rate as the universe thins out and the rate of expansion due to inertia continues to wane. Furthermore, because space continues to expand at an accelerating rate, this lends support to the proposition that energy continues to flow from the initial point where the universe began its expansion.

If the metaphysical world is without form or substance, this may or may not describe our known universe. Since matter at the subatomic level independent of our senses has no mass, and since matter above that level has form and substance based on perception from our senses, we could surmise that the universe is both metaphysical and non-metaphysical depending upon our relative frame of reference. For the convenience of explaining and engineering our world, E=MC2, is a useful tool but mass is simply a construct that makes the formula work to describe the relationship of these variables. Perhaps an irony better than a massless universe, is a universe that is both metaphysical and non-metaphysical at the same time, since the original state of our universe pre-dated time.

Awesome description, dpuett! Beautifully stated. Let me respond by first answering your question.

ReplyDeleteYou asked, "Do you agree that the physical laws of our known universe that create the environment for our metaphysical experience originate in laws assigned prior to the valuation of Planck’s constant?" I would answer, "yes," but the directionality goes the other way, that the metaphysics comes before the physics. I'm basically an idealist, so I tend to think that nothing exists prior to consciousness, and that our apparent material universe is really a projection of our shared imaginations. Most scientists are probably materialists, believing that, obviously there is a physical universe, and they set about to describe it and predict its workings. To a materialist, the mystical experience may be just another way of perceiving and describing the material universe.

So yes, I totally agree with you that the physical laws of the known universe predate the inception of Planck's constant. Since Planck's constant describes the lower limit of material instantiation, then laws that come prior to our material universe came first. These would be the "fundamental forces" I'm trying to unravel in those toroid articles.

I'll respond to your dark energy model in a separate Comment.

Now, let me restate dpuett's beautifully articulated Comment as I understand it. dpuett--tell me if this is right:

ReplyDeleteWhat we call "dark matter" is an attribute of the dimensionless place that lies outside our material universe of time, energy, and space. As lightening manifests an electrical polarity between earth and sky, energy manifests a polarity between our universal space and a substrata of dark matter outside the universe. As the boundary of matter pushes outward into newly expanding space, the dark matter that originally lay outside now lies inside, being unaffected by the expansion. This "trapped" dark matter is erroneously attributed to gravity, but is actually the onward process of dark matter/matter manifestation.

Is this what you are saying?

David, your continuing comments are exceptional and stimulating! I especially liked your discussion of dark matter! Of course, Cyd, your discussions and commentary continue to be exceptional and consistent with a "Simple Explanation!" I could become wordy here but want to stay simple! Cyd, you can see by my earlier comments that I hold an Idealism position on the nature of the universe just as you do. But perhaps I go a step further. I believe that all distinctions made about the nature of the universe are only either epistemological or mathematical, not ontological. The universe, in reality, will always be metaphysical and non-dimensional at all levels. In reality, there never was a Big Bang. In reality, there never was matter, energy, space, or time. There was no actual creation of anything. As conscious beings, we are merely trying to "understand" the" Mind Of God." Cyd, your toroidal and fractal explications are an attempt to examine, in our limited way, how Consciousness makes sense of Itself!

ReplyDeleteCyd,I want to follow up my last comments with what I meant by epistemological and ontological distinctions. In a nutshell (or is it a toroid!), is the universe as you present it truly toroidal and fractal (i.e.ontologically real) or is the universe as you present it the best representation of the universe of our "limited and meme clouded" consciousness (i.e.epistemological and mathematical models only)? What do you think?

ReplyDeleteWell, Bill, I'm not sure. It seems to me that, ontologically speaking, the fractal aspect somehow has to be "true," since nature continually follows this form. As to whether the universe is actually toroidal, this I don't know. OTOH, epistemolocially, the toroids as well as the fractals do an excellent job of modeling the universe.

ReplyDelete