Sacred Geometry in Nature
Sacred geometry is the nexus point between physics and mysticism. It is the realm where infinities live within finite forms, and the chaos of creation is brought to order.
The true beauty of sacred geometry is that it satisfies both the right and left brain. Elegant expressions of compelling proportional relationships simultaneously activate the intellectual and artistic functions, merging the rational with the abstract.
Sacred geometry arises from the desire to express philosophical truths through concrete means. It offers a scientific method for philosophical inquiry, complete with hypotheses, experiments, and repeatable results.
The best way to study the fundamental shapes of nature is to draw them yourself. In order to fully appreciate this article, I would encourage you to procure paper, pencil, compass and straight edge in order to perform at home the experiments here described.
Now, we will embark on a journey through creation as it arises in spheres, lines, and spirals. Fair warning: visceral engagement with these shapes can be irrationally rewarding; what begins as strictly formulaic may soon become more magical than ever expected.
Seed, Flower, Fruit
By way of introduction, let us consider the life cycle of any fruit-bearing tree.
Down from the ancestors a seed reaches Earth, is buried, and germinates. Its cells divide and the seed expands into a baby plant. A stable trunk grows up and the tree eventually flowers, portending of abundant fruits to come.
When ripe, a fraction of fruits fall to the earth. The flesh rots into compost that then feeds the new seeds now underground, just waiting for the day when the process starts anew.
This cycle ought to be painfully familiar to anyone with even the briefest human experience. Like plants, people are born, grow up, bear fruit, decay, and then die in order to feed that which is being born. This exact pattern is mirrored by the most fundamental processes of sacred geometry.
Our journey begins with a single circle, which may also be drawn or imagined as a sphere. This is not yet a seed, but its mere potential. This first circle is an abstract concept that serves as the perpetual center point and container for all that comes next.
If you are drawing along, this is a good time to bust out your compass and draw a circle — probably smaller than you might initially like — in the center of your paper.
The first movement on the road to fruition is duplication. Keeping the compass set to precisely the same radius, place its point anywhere along the circumference of the first circle and draw a second circle so that its edge passes through the center point of the first.
You are now looking at a shape known as vesica piscis, the womb of creation or literally, “the bladder of a fish.” This shape represents the union of opposites, the resolution of polarity. Two distinct entities overlap to create a unified space wherein a distinct third entity can arise. Need I explain why this shape is associated with femininity?
Here we have all the information needed to generate two equilateral triangles within the “womb,” where the circles overlap. Draw a line connecting the center points of the two circles. Now connect each center point directly to the point where the circles cross paths. You now have two equilateral triangles on either side of a horizontal (x) and an implied vertical (y) axis.
From here, we can infer the existence of six equidistant points around one of the circles. A protractor is a useful tool to maintain precise measurements at this juncture, although a straight-edge is sufficient and ultimately, a compass is all you need.
Now then, place the point of the compass on each of these new points and draw five more circles. You are now looking at something like this:
This conglomeration of circles is called the Seed of Life. When someone mentions sacred geometry, the Seed arises first in my mind’s eye. It is extremely common to see derivations of this structure in visionary art, corporate logos, and new age tattoos.
Despite its pervasive usage, the shape is so fundamental to the structure of the cosmos that humans will never grow weary of its perfect harmonics. Would you or anyone deny that this pattern is infinitely pleasing?
It is so interwoven into our lives that we may not even notice the depth of its symbolism. Where else do we encounter the concept of six encircling one?
The days of the week come to mind, based as they are upon the six days of creation followed by a single day of rest. Similarly, there are six heavenly bodies (Mercury, Venus, Moon, Mars, Jupiter, Saturn) visible to the naked eye, all encircling the central sun.
In addition, many traditions identify seven chakras, where the heart-center is encircled by three upper and three lower chakras. Likewise, there are seven perceptible colors in the rainbow, with green at the center and red or violet at either end of the spectrum.
There are plenty more of these examples available if you care to investigate further on your own, but evolution is ongoing and so are we.
From Seed to Flower
Once germinated, the seed becomes a plant and achieves its utmost beauty in the form of a flower. In sacred geometry, this is shown by adding another ring of six circles around the Seed, so that we now have twelve encircling one.
(Remember: you can always add a circle around the outside to contain the entire shape. Just like the infinitesimally tiny dot at the very center, it doesn’t influence the overall energetics of the form).
Is this a familiar shape? Does it have any applications in nature or human culture?
Common examples include the twelve signs of the zodiac that encircle our perspective here on Earth and the twelve hour-markers on the face of a clock. The famous Jesus of Nazareth is said to have had twelve disciples, the same way King Arthur led twelve knights of the round table. We recognize twelve months in a year, and there is often a thirteenth full moon hidden within those solar months.
According to John Michell in How the World is Made, twelve “is the root number in the code of proportions that governs the solar system… In some remote, unknown age the zodiac was divided into twelve sections so that the sun passed through one zodiacal house or sign in 2160 years, which is… the same as the diameter of the moon in miles…”
Far beyond any possibility of coincidence, such alignments reveal the divine intelligence inherent to creation. Such mysterious rationality and beautiful order cannot be the result of so many mere happy accidents.
The fact that the Flower of Life is found carved or otherwise encoded into the remnants of ancient civilizations the world over only adds to the power of this image to inspire us toward further study of the fixed forms that give rise to reality as we know it.
In any healthy organism, flowering precedes the production of fruit. After the flower expresses its irrepressible beauty and fragrance, it wilts and all that energy redirects to generate the next generation.
Plants are super intelligent but basically immobile. As such, they have strategies to spread their seeds. Primary among these is to hide seeds within a delicious morsel so that some animal might pass by, consume the fruit and in its droppings, drop the seed in a far off the fertile ground. Thus the species is propagated, arriving in fresh territory already encased in the best kind of compost.
The fruit of one’s labor, loins, or karma refers to the tangible output of a period of incubation; to the cumulative and far-reaching effect of a collection of causes.
The fruit is the distillation of all previous efforts and growth. That which has been expanding now sheds superfluous forms to become highly concentrated in order to create new forms. To obtain excellent fruits, one must prune the tree.
The glorious complexity of the Flower is reduced in order to produce the Fruit of Life. This little death serves that which is being born.
Now simplified, the Fruit becomes the creative framework from which the infinite potential of Metatron’s Cube springs to life.
Home Geometers, if you haven’t already, draw a fresh Fruit of Life, separate from your other scribbles. Use a new paper if need-be.
Now, connect the center points of the thirteen circles that compose the Fruit, and you’ll discover a web of interlocking lines that are the two-dimensional representation of the three-dimensional polyhedra that are the complete structural basis for human experience. This multidimensional shape-stack is called Metatron’s Cube.
Esoterically, Metatron is an archangel, one of the energetic entities that oversee our particular corner of creation. Among the archangels, Metatron is understood to be the architect, the transcendent genius of shape and proportion. Metatron governs the specific logistics by which consciousness is able to take form.
Dear reader, at our shared level of experience, the most fundamental forms we can grasp are the five Platonic solids. The tetrahedron, octahedron, cube, icosahedron, and dodecahedron are the building blocks of our reality. These polyhedra are the only shapes in existence that have uniform numbers of sides, side lengths, and internal angles. They are the only perfectly symmetrical three-dimensional forms possible.
The five Platonic Solids correspond to the five elements and our five senses; they define the relationships between planetary orbits and atomic structures; they are the tools of Metatron; they are the vehicle whereby the Many arise from the One. The Platonic solids are the primary focus of a different article on the Gaia network.
Two Kinds of Spirals
If you’ve drawn along with us this long, congratulations — you have now sketched an outline of everything that is or could be. There is, however, one more dynamic we must acknowledge before reaching completion, and that is the quality of spin.
At each successive stage in the evolution from seed to flower, we simply added one more ring of circles around the center. This linear style of the spiral is called Archimedean, after the great Archimedes of Syracuse.
Archimedean spirals progress in a linear fashion, the way paper towel is wrapped around cardboard, or a rope is a coiled layer by layer. This is contrasted to a Phi, or Golden spiral, which expands proportionally according to the Fibonacci sequence. The Phi spiral is in fact far more common in nature, observable in phenomena such as whirlpools, tornadoes and spiral galaxies.
An excellent exercise to experience the difference between these two types of spirals is given on page 120 of A Beginner’s Guide to Constructing the Universe, by Michael Schneider.
In essence, the instructions are to cut two strips of paper and decide on a unit of measurement (inches, finger-breadths, it doesn’t matter). Beginning at one end of the first strip, measure and mark units of sequentially increasing value (1, 2, 3, 4…). For example, if the first section is one inch, then the second section is two inches, and so on. Then fold a right angle at each mark on this strip, and feel an Archimedean spiral unfold in your very own hands.
Do the same thing with the second strip of paper, except that here the length of each section is determined by the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13…). Again, make a right angle at each mark and compare the results. When finished, you’ll have earned a direct and profound understanding of the two types of spirals that exist in nature.
Traces of the Creator
This essay tracks the organic evolution of potential energy into actuality using the simplest shapes available. These are the building blocks of sacred geometry.
These are concrete representations of abstract, otherwise inconceivable ideas. Simple shapes, lines, and curls generate a journey through the dimensions, perpetually approaching zero or infinity, the One and Many.
To discern the patterns by which creation unfolds and retracts is to approach the Creator directly. By participating in the process yourself, literally tracing the steps of the Creator, you have initiated yourself into a mystery tradition whose only limits are your own imagination.
This is truly universal knowledge, and according to Drunvalo Melchizedek, “It’s outside of any race or religion. It is a pattern that is intimately part of nature. If you go to distant planets where there is consciousness, I’m sure you’ll find the same image.”
Go on, then!
What are Fractals?
If you look around you right now, depending on where you are, you’re likely to see to two distinct types of shapes: 1) blocky, linear and smooth if you’re in a manmade environment; or 2) branching, uneven and irregular shapes if you’re in a natural one. Why is there such a difference between the appearance of manmade and natural spaces? Why does one tend to look smooth, while the other looks rough? It comes down to one word: fractals.
A Brief History of Fractals
At the beginning of the 20th Century, mathematicians Pierre Fatou and Gaston Julia discovered fractal patterns while looking at complex mathematical systems. Back then, these objects defied linear analysis; they were considered aberrations or scary mathematical monsters, with infinite depth and complexity. They weren’t very popular and were forgotten until the late Belgium mathematician Benoit Mandelbrot discovered them again while working at IBM labs in Armonk, New York in 1980.
Fractals Contain Imaginary Numbers
To distinguish fractals from ordinary objects, you should know that fractal sets are created by algorithms that, in addition to ordinary integer numbers, also contain so-called “imaginary numbers”. This allows fractals to behave in much more complex ways, and describe more complex systems than ordinary numbers.
The Behavior of Fractals
Mandelbrot was the person who coined the word fractal. He used it to describe the behavior of financial markets and telephone line noise. The word fractal is derived from the word Greek “fractus,” meaning “fractured.” Mandelbrot noticed that telephone line noise is similar, whether you look at it over the course of an hour, a minute, or a second: you still see the same wave-form shape. In this sense, you can describe telephone line noise with a numerical dimension that applies at any time scale. The dimension defines the visual “roughness” of the signal; in other words, the dimension translates to how choppy it looks.
This is a very different type of geometrical logic than the one we were taught in school, where objects have a definite length and size. This is because, in school, we’re dealing with abstract objects that we imagine are perfectly linear and smooth. Nothing in the real world really looks like that!
If you take a look at almost anything natural under a microscope, you’ll see it’s full of fissures, pits and holes.
That’s because natural things are seldom perfectly flat beyond a certain scale. The closer you look, the more defects you’ll see.