Spheriphor = Tetrahelix + Triskele + Trimurti + Jewel in the Lotus

I created the geometry for the Spheriphor digital art work as an investigation into spherical spirals, but this figure has also led me down deep into multiple levels of insight meditation. If you have been following my blog, you may know that I believe that the root essence of existence is the spiral. I talked about this with my Maori artist collaborator Kura Puke (for I. She also believes spirals to be at the heart of all things.
 

Just recently, during a Vipassana meditation session, I had an insight that emerged from contemplation of the tetrahelix (spiral based on the tetrahedron). I visualized the tetrahelix emerging from a set of 3 vectors that propagate through space. These 3 vectors are the primary (active) system of all phenomena. There is a set of 3 complementary vectors that are secondary (reactive), and together with the primary set of 3 vectors, the tetrahedron (minimum system of Universe) is formed (as per Bucky's Synergetics).
 

Then, I arrived at an internal visualization of the relationships between the 3 primary vectors. This visualization involved a spiraling propagation through space based on 3 parameters: length, angle and twist. I could see that these 3 parameters were the true 3 dimensions of Universe (as opposed to width, height and depth). I made a mental note to create an mathematical computer generated visualization based on this concept.
 

Then all of a sudden the visualization shifted to the Hindu Trimurti. My mental energy shifted from left hemisphere to right hemisphere; the wonders of the corpus callosum.
 

From Wikipedia:

The Trimurti (English: 'three forms') is a concept in Hinduism in which the cosmic functions of  creation  ,  maintenance  , and  transformation  are personified by the forms of Brahmāthe maintainer or preserver Vishnu the creator and Śhiva the destroyer or transformer. These three deities have been called "the Hindu triad" or the "Great Trinity", often addressed as "Brahma-Vishnu-Maheshwara."

Next came the realization of the equivalence of Hindu and Tibetan Buddhist trinities:

1. Vishnu = Sunyata
2. Brahma = Amitabha
3. Shiva = Chenrezig

 

The visualization then shifted again. This time the triad transformed into the Mani; the most beneficial mantra, "Om Mani Padme Hum". I saw the following: 

1. the clear light of creation (Om) radiating from within 
2. the jewel maintaining (Mani) all phenomena
3. sitting on a lotus transforming (Padme) all dualistic views
4. within my human heart (Hum) the most fortunate of all incarnations

In this meditation I attained the most in-depth understanding of the Mani that I have ever realized.

The visualization which emerged from my contemplation of the tetrahelix now circled back to my 4 colored, Triskele version of the Spheriphor. The Spheriphor contains both the 3-way symmetry of the Trimurti and the 4-colored aspects of the Mani. The Spheriphor is truly an all-encompassing spherical-metaphor that represents the complete Hindu-Buddhist psycho-cosmology. 

 
Spheriphor by Tom Greenbaum

 

You can view my Spheriphor study at http://karmatetra.com/ISDE5/spheriphor_study03.htm

Also on the Spheriphor Study 03 page are alternative views of the figure based on a spherical octahedron. The 3 views are based on vertex, face-centered and edge centered perspectives:

• http://karmatetra.com/ISDE5/Images/Spheri-Spiral_50.jpg  My 4 colored Triskele (Celtic triple spiral) version. Do you think that the Celtic mystics were actually peering into the vertex of a spherical octahedron wrapped in spirals like I was?  Also, Hans-Peter Welke fell in love with this image and asked me for permission to use it for the cover of his brochure on the "Corporate Identity Development Process"  See the attachment for the brochure. Hans-Peter credits me for the image on the last page.
• http://karmatetra.com/ISDE5/Images/Spheri-Spiral_52.jpg
• http://karmatetra.com/ISDE5/Images/Spheri-Spiral_49.jpg

 

I would love to make this figure out of glass. I have thought of possible ways to make it out of glass, but it would be a major challenge.

Synergetics Geometry Studio

MISSION STATEMENT 
A STUDIO where positive IN-tention and pure, unstained action of body, speech and mind, occurs spontaneously IN the moment, aligning effortlessly with the natural rhythmic cycling of the IN-wardly spiraling, self-IN-terfering, associative material energies, and the OUT-wardly spiraling, radially expanding, dis-associative, light energies, provided by Earth, Sun, Moon, planets, stars and galaxies, IN harmony with the most subtle vibrations of cosmic consciousness, universal law, truth, beauty, symmetry and awareness of the IN-terconnectedness of self and all other beings.

A STUDIO where such positively intended vectors of body, speech and mind, forming a minimum, triangular, right-hand spiral unite with a minimum, triangular left-hand spiral comprised of the vectors of truth, beauty and symmetry to form a Synergetic abstract tetrahedral minimum system, which being the IN-tuitive, IN-tellectual heart of the STUDIO, divides the entire universe at this locus into three consideration sets:

1. The micro-cosmic volume of un-manifest no-thing-ness and all beings taking refuge IN-side the STUDIO
2. An integrated, holistic, creative-living system comprised of structural, architectural, mechanical and elemental valving sub-systems of the STUDIO itself
3. The macro-cosmic other-ness of all energies and beings, both positive and negative, OUT-side the STUDIO.

A STUDIO where the micro-cosmic volume of un-manifest no-thing-ness IN-side the STUDIO resonates with the positively IN-tended right-hand spiraling vectors of body, speech and mind of the beings IN-habiting the STUDIO, resulting in un-IN-hibited and IN-spired re-structuring of material and energetic natural resources with-IN the STUDIO, thus re-forming the resources IN-to ART-SCIENCE-TECHNOLOGY physical artifacts that re-flect the left-hand spiraling vectors of truth, beauty and symmetry, which ultimately re-IN-forces the abstract tetrahedral minimum system at the heart of the STUDIO.

A STUDIO where such positively IN-tended right-hand spiraling vectors of body, speech and mind of the beings STUDIO IN-habitants spontaneously, and safely IN-teract with material and energetic natural resources with-IN the STUDIO to creatively form spiral-orbital re-structurings of these resources, thereby un-knotting the self-IN-terfering, associative physical structures of the material resources through the controlled application of sacred spiral radiating, dis-associative energies, ultimately forming artifacts that re-flect truth, beauty and symmetry which may then be propagated and distributed OUT-side the STUDIO to benefit unlimited numbers of beings.

A STUDIO where the creative activities of STUDIO IN-habitants are supported by the structural, architectural, mechanical and elemental valving sub-systems of the STUDIO, which itself is an IN-spired artifact (tool for creative living), IN harmony with IN-habitants' physical and meta-physical requirements, thereby forming a REFUGE that both protects and nurtures while simultaneously enabling the safe and un-IN-hibited manipulation of material and energetic resources for the purpose of positively IN-tended artifact development.

A STUDIO where the macro-cosmic other-ness of all energies and beings, both positive and negative, OUT-side the STUDIO are brought IN-to the compassionate awareness and creative consideration of STUDIO IN-habitants, and because the STUDIO IN-habitants' physical and meta-physical positive growth requirements are met elegantly and efficiently IN harmony with the planet's regenerative systems, the STUDIO IN-habitants spontaneously, with wisdom, IN-telligence and skillful means, safely leverage the un-bounded, IN-spiraling associative and OUT-spiralling dis-associative cosmic energies, carefully applied to physical and energetic resources, empowered by the structural, architectural, mechanical and elemental valving sub-systems of the STUDIO, to form ART-SCIENCE-TECHNOLOGY physical artifacts to be distributed to beings OUT-side the STUDIO, in a manner which reflects the axioms of truth, beauty and symmetry at the abstract of heart of the STUDIO, forming a sacred bond of realized IN-terconnectedness with those beings receiving the artifacts OUT-side the STUDIO, ultimately expanding the STUDIO's positive vibrations at the most subtle level of cosmic consciousness, following planetary lines of energy, causing sympathetic vibrational modes in all planetary GREAT CIRCLE wave lines, thereby healing planetary dis-harmony, resulting in planet-wide peace and happiness.

30 Transcendent Virtues
by Tom Greenbaum

Spirals: Geometry Of Awareness

If you have visited my website http://www.karmatetra.com/ you may have noticed that I am fond of spirals. What is it about spirals that evokes the imagination? The Golden Spiral has inspired philosophers, poets, architects, physicists, astronomers and biologists. We see spirals in nature; from the recorded trails of exotic subatomic particles, to flowers and galaxies. Spirals are everywhere.

Recently, I have been exploring spirals on the surface of spheres. I have published a study on generating these spirals on my website. See Spheriphor Study 03 for details and images. As far as I know this is the only spiral of its kind. There must be other people who have created a geometric design where spirals symmetrically cover the surface of a sphere - so if the reader knows of any, please comment here and let me know where they can be found.

I do a lot of my work in POV-Ray. I have provided sample code on my website for generating some of the images. I even provide information on how to run the code. If the reader is willing to follow a few step-by-step instructions, then it should be fairly simple to reproduce the images.

The image shown in the beginning of this post is titled Golden Spiral Sunset Sailing. It is a 3D rendering of a series of rectangles arranged whimsically in the space above a tranquil body of water. A spiral reminiscent of the Golden Spiral flows through the rectangular structure like the sails of a fanciful sailboat. More spiral digital art to come in future posts ...