This 2012 page briefly summarizes my modeling of fractal tetrahedrons, as might apply to electromagnetic coils.  For many years now, i have 3d modeled many arrangements, in order to contemplate the reactive fields. Fractal geometry could align the inductive field differently than traditional electro-magnetics.  When arranged into complex arrays, the fractal fields might offer interesting effects. I'm glad to share these concepts with many experimenters trying new, experimental concepts.

The use of 3d geometry software has made possible a multi-path exploration of this subject. The image below represents the sequence of adding smaller, face centered tetrahedrons of differing colors. The green tetrahedrons on the left hand side, were precisely positioned on upon a lager "star tetrahedron" (not shown here). Then the smaller, blue tetrahedrons were all aligned by intersecting blue vertices to green midpoints:

The above scaffolding eventually lead me to the 8X8X8 arrangement, in next image below. (First web posting is here).


After studying the 8X8X8 arrangement, i found that the octahedral aspect ratio could be modified to other 3d aspect ratios.

It might be interesting to reverse engineer the scaffolding on these variations.  Circuit application follow, further below.


The following image has the scaffolding, (larger tetrahedron) shrunk internally, (to show relationships)... Many perspective-angles (or focal lengths) are provided to explore the seeming changes of geometry. Yet the 3d geometry always remains constant in this poster. The term 'equilibrium' was made popular by Bucky Fuller's Synergetics. The octahedron, so it seems, is an ample and earlier term. Yet emphasizing the term 'equilibrium' may have been absent, before Synergetics.  (Or was it simply the lack of powerful geometry software).

Experimental construction reports should be added in time. Although my procrastination record keeps me distracted with many other things, (like making a living).   Geometric modeling procedures are presented first to explore and demonstrate natural 3d layouts. Ultimately, the intent is to wire-build, in real life, with fractal-coil circuits. To experiment with these fractal circuits-- To test effects as resonators or radiators of electromagnetic energy.

Next is an example of circuiting one tetrahedron with multiple turns. These multiple turns are an example of increasing the induction of each coil.


This approach to en circuit a tetrahedron derived from my discovery that a tetrahedron is formed directly by the formula of the helix: When the helix object is facetted with exactly 9 straight segments. (See relevant page on this website).


My preferred building plan is to use a "wire-spot-welder" which could build arrays of tetrahedron modules. (The basic circuit, pictured above was discovered here). The fact is that the tetrahedron above is pictured as a "closed circuit". Such a closed circuit can be cut at any of it's junctions. (At vertices or at midpoints, to allow "connecting" or "welding" in smaller face centered tetrahedron module). In this way incorporate all tetrahedron modules into one circuit. The red and blue tetrahedrons are contemplated as focussed dipole sets:


Experimental modeling with ball magnets could provide interesting insights. Especially if the pole ends are colored red and blue.  The FEA software ought to provide even more interesting magnetic field modeling. Finite Element Analysis (FEA) software with this extended capability has been out of reach. The public is not yet allowed to interact with this level of computing.  In the mean time, currently available 3d modeling has provided me the satisfaction of exploring these concepts. Research into energizing these arrays, itself may take on diverse forms:

What if the octahedral unit is arranged into a fractal matrix of many modules? These fractal matrices or space-packings can be fit into a wealth of diverse networks.  At this point, the concept is introduced only as inspiration.   Inspired thoughts, in this case demands a 3d-welder-printer, to automate construction.  How to build it and what could a fractal-coil do for us? Let us find out!


I learned about the vector equilibrium from the book "synergetics" by Buckminster Fuller. For better or worse, the term "vector equilibrium" was  taken over by the polyhedron shape of the octahedron, as two words, with one meaning.    Therefore, the English language needs a special word to signify "equal in all directions" in referring to any sort of example.  The dandelion is an example of parts all pointing outwardly. We currently have no adjective of adverb or noun which clearly signifies this meaning.   


The models on this page were discovered by use of a tetrahedron as 'scaffolding'. To see where the equally balanced fractals would align. To see what outlines would form: the equilibrium, naturally.   Recently i noticed the Leonardo Davinci connection. Quote from eternal link:

"The stellated octahedron is the only stellation of the octahedron. It was depicted by Leonardo da Vinci in Pacioli's book 'De Divina Proportione' in 1509. A hundred years later was named 'Stella octangula' by Johannes Kepler."

In the 1990's my efforts focussed on visualizing field possibilities for electromagnetically energizing the tetrahedron:


My earliest tetrahedron modeling with a Synergetics forum online.

My earliest work with 3d modeling software.

My exploration of electric and magnetic field relationships, through geometry.

My experiments with feeble currents and coil geometries.

"Morphing-Sphere Spiral"
"Reflex Flame Amplifier"
"Spherical Reflex Coil"
"Plasma Resonator"
"Reflex Vortex Amplifier"
"Multi Axial Coils"

Sunspot Coil Model

Conceptual artist is repressed, for modeling coil art?


Continuation of my printed coil "thought experiments", March 2013, modeling for a transversely wound and folded coil.



Envisaging Transverse Force Fields:   Laminated, parallel coils are considered on this linked page.

Geometric speculation: Relationship of poloidal structure to the tetrahedron.

geometric speculation: poloidal coil structure.

biaxial potential for habitable buildings.

2012 blog on Inductive Coupling Symmetries







Sunspot Coil Model

Pictorial Site Index Page

Conceptual artist is repressed, for modeling coil art?


Note: My 100s of pages on this website,, are placed in the public domain and are furnished "as is" and "open source". My creativity is posted as a free exchange of ideas and as my "service to others". Caution: The author assumes no responsibility for the improper use or improper misuse of the concepts in these web pages. All relevant laws of all kinds and local codes should be verified and observed before any building or experimentation proceeds. Donations to me would be welcome, for me to continue or to up step the progress of these works.  Cooperation might be possible as well, please write.  Bo Atkinson