__A Sacred Geometry __

With their sleek and gently inward-flowing curves and lines, one can’t help but revel in the splendor, intrigue, poise, and beauty of nature’s center-oriented patterns. Their simple and unencumbered designs solidify their position as robust providers of form and function in a world subject to vying influences.

Centerpatterns come in practically any size, shape, texture, form, and function. Their shape underlies things the size of atoms and universes. Their parts can be as directly connected as the spokes of a wheel to its hub, or as loosely connected as nations of people about shared feelings of national pride. Their form can be as tightly bound as the crystals of a snowflake, or as loosely formed as ants circling an ant hill. Their boundaries can be as sharply defined as a property line or as loosely defined as the extended volume of air converging on your lungs.

But in all instances, they are unified by their shared overall alignment to a common center – they share a center-oriented shape.

It’s impossible to define a fixed set of categories encompassing all Centerpattern forms –after all, how many orientations, angles, and arrangements can “things” take around a central point? However, there are primary Centerpatterns favored throughout nature.

__Circles and Spheres__

Centers and spheres hold a special place in myth and philosophy due to their flawless and ‘perfect’ forms. They also provide a sort of “ideal” definition of a Centerpattern, as the following definition attests: “A center is the point that is equally distant from every point on the circumference of a circle or sphere.3”

It’s interesting to note a sort of ideal whole is formed by spheres with all the points on its surface (i.e. its parts) being exactly equal in distance to a common center (at the center of sphere). We see this Centerpattern in our sun, dinner plates, planets, balls, and wheels.

__The Sections of a Conical__

Conical sections hold an exceptionally unique place in science and math. In fact their merging of math, geometry (space), and physical processes speak of the interconnectivity all things share. The fact their forms are fully center-oriented also lets us know just how deeply intertwined the tenets of the Centering Principle are ingrained into the very fabric of the universe.

From a Centering Principle perspective, we first note the overall shape of a conical section forms an exemplary center-oriented design with their head-to-head cones forming a perfectly arranged dualistic geometry. But this same ‘crisp’ center-oriented design is also found in all the various ‘cuts’ of a conical section (which as you’ll remember from geometry, are generated by ‘slicing’ the cones with a planar section). Conical sections not only include the evocative forms of circles we just examined, they also include the highly balanced and aesthetically pleasing center-oriented forms of ellipses, parabolas, and hyperbolas which are coincidently defined by and perpetuated by core foci.

More than idealized mathematical and geometric concepts, conical sections also match ‘real’ world functions including the patterns of planetary orbits, the shape of parabolic satellite dishes (used to ‘capture’ electromagnetic radiation), as well as the path of a ball traces as it flies overhead.

__Concentric Circles__

Probably the first Centerpattern design we unwittingly marveled over as children where concentric circles. For me it was watching waves spread radially outward from rocks thrown into a pond. Later it was counting the rings of a tree’s cross-section to ascertain its age and origin.

The pleasing natural symmetry of concentric circles and their Centerpattern claim to fame can be gleaned from their definition in the Merriam Webster Dictionary as “circles having a common center.”

Other examples in nature and life include the growth pattern of teeth, various fruits and vegetables (like onions), Mandalas, the shape of B-Z reactions in metabolic processes, the rings of Saturn, and the arrangement of seating rows in sporting arenas such as football stadiums, as well as the shell-like arrangement of electrons orbiting an atom.

__Spirals__

If nature elected a mascot it would surely be spirals. This because spirals reflect many of nature’s most appealing structures. The proportions of their outwardly fanning segments also imitate a myriad of nature’s interrelationships and growth patterns.

Defined as “winding around a center or pole and gradually receding from or approaching it3”, spirals are ubiquitous in nature as sunflowers, shells, galaxies, a ram’s horn, crashing waves, the aerotora of the heart, and the ear’s cholera. The power of spirals extends beyond just their geometric manifestations extending into philosophical considerations such as emotions, the rates of growth and decay systems, and the ‘strange attractors’ of chaotic system in the new science of Chaos. Their peculiar property of endlessly spiraling forever inward toward a center that’s never attained also speaks of the intrigue and mystery surrounding centers.

__Radials__

Like the spokes of a bicycle wheel directly connected to a common hub, radials highlight the connectivity of a group of parts (of larger whole) to a common center. Radials are wonderfully abundant in nature. Botanists for instance consider that most of the 300,000 species of plants in existence have some degree of radial configuration. Other naturally occurring radial designs include roulette wheels, dartboards, the flow of goods from distribution hubs, innumerable jewelry designs, spider webs, flowers, starfish, and Internet connectivity diagrams.

__Branches__

Nature, biology, and man’s institutions are jam-packed with branching and arterial distribution systems. Trees, leaves, lungs, veins, arteries, skeletal systems, roots, rivers, family trees, organizational charts, parking lots, computer directory systems, and roads and highway systems –all fall within the definition of branching arterial systems.

However, possibly because of their popular representation as two-dimensional objects, branching systems are often not recognized as center-oriented patterns. This is an illusion –braches are actually center-oriented systems gone wild! In fact branching systems comprise a ‘center-oriented-ness’ at all their various degrees of scale all of which are tied together in an efficient hierarchal structure (i.e. reflect a fractal hierarchal structure). This structure and the internal interrelations it generates literally ‘multiplies’ efficiency and is likely the reason why arterial branching systems seem to be nature’s design of choice in living systems.

This fantastic fractal-like organization can be seen at all scales of branching systems. For instance if you look at the smallest part of a tree (it’s twigs) you’ll notice all its twigs attach to a common larger branch (we’ll call it Small Branch). This common branch (Small Branch) is the center of a larger whole formed by the combination of all the twigs.

Now take the Small Branches we just examined and follow it to where it joins with other Small-Sized Branches. What you’ll find is they meet at next larger sized branch (we’ll call it the Medium Branch). Cumulatively the Small Branches form a whole about their common center (which in this case is the Medium Branch they all connect to).

By continuing this practice you eventually come to the entire tree with all its branches ultimately connected to its biggest center, which is the trunk of the tree.

Through this example you can begin to see how the parts reflect the whole (and indeed how the whole reflects the part). We can also begin to understand how fractal geometry ‘works’.

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References

2 Nua, Jin. *The Center Ordering Principle*, 2013.

3 “circle.” *Merriam-Webster.com*. Merriam-Webster, 2011. Web. 27 June 2013.

4 “spiral.” *Merriam-Webster.com*. Merriam-Webster, 2011. Web. 27 June 2013.

5 Leung, A. *Limiting Behavoir for a Predator-Prey Model with Diffusion and Crowding Effects. *Journal Math Biology, 6, 1978: 87.

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