2017 Look At Outer Profile Shapes - Almost Like Polygons

2011 Fractal Cognition: 2011 Reticulating Fractal Star: Fractal flowering of tetrahedron subdivisions-- The color coded tetrahedron-stars are arrayed and patterned. ( The natural, 60º, perspective view happens to generally appear spherical in overall shape. While the totally flat, plane view, as seen from any of the 3d, (three plane), orthogonal-axes, appears as an equilateral, platonic cube. The natural human perception field can be nominally described as a 60º cone of visibility, (or good focal resolution of human eye).

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The center most tetrahedrons are the normal, two-interpenetrating tetrahedron star, which protrudes  8 exposed tetrahedrons in tan color below. Next "layer of fractal tetrahedrons are colored a semitransparent green. Finally the outer, multicolored set of tetrahedrons align in a generally, truly cubic alignment, (in plane views).

The outline traced through point-alignments of star-tetrahedron-sets, happen to work out in the form of a wire-frame-pattern dubbed the "vector equilibrium". Established by Bucky (Buckminster Fuller of synergetic fame). I inserted a screen shot from google, see next image below. Many significant patterns can so work out. My pattern happens to contain more sub patterns, using a triangular version of 'beveling' the sharp corners.

Click here to see spherical arrangements placed in the same order.

Buckminster Fuller has applied the term 'frequency' to instances of insertions, of multiple sub divisions of a particualr geometric order, which reflect or repeat the overall order.  The mathematical term 'recursive' or 'recursion' might also apply to this principle. As in fractal geometry,  where the overall geometric form is repeated in each of the composite parts.



I have been curious about fractals based on precise platonic solids, especially tetrahedrons.

Fractal flowering of tetrahedron subdivisions--Successively budding, only upon the freshest buds, at each new level.   Tetrahedrons symmetrically protrude from successive protrusion levels. Protrude in the same manner as the original star tetrahedron, but only from the new star faces.

Each new level of tetrahedrons protrudes only from the previous level of protruded tetrahedrons, in the above model. I had intended to reticulate the budding flower 7 times (or a full octave). Except that the 4th budding or sudivision is already difficult to see.  Also,my fully- 3d models of this, deserve more work.

Next model below, added selective sets of protrusions, (to fill out the cubic aspect).

I like the way that the recursive protrusions actually outline what has been named the vector equilibrium.

Next is a compact animation of progressively-scaled models integrating the 4 levels of star point tetrahedrons.

A fly-around and fly through animation is planned to real this aspect:.  I lost track of this powerful rendering feature-- As my formZ software (version 7 beta) has advanced considerably. I'm still acquiring thew interface changes as of May 2012. The fact of aligned arrangements of tetrahedrons, which thereby form a vector equilibrium, as discussed by Bucky (Bucknminster Fuller/ Synergetics).

In the next model below, the recursive protrusions are kept parallel to base tetrahedrons.

Some of my connections made with universal patterns are presented on http://projectavalon.net/forum4/forum.php)  

Recursive Tetrahedrons ~ Face Centered

Ancient examples like the Cistene Chapel floor plan, suggest structural fractals of repetition or recursion. Earlier examples can be found in ancient art samples, which lack verification through precise computer modeling.



Next i managed to get formZ "automation" to add recursive cubes in diagonal alignment.

I think there are many potential experiments for this sort of geometry. Computerized geometry inspires some visual effects. Careful scaling consideration of applications can apply to antennae or resonance circuitry. Only if one can actually experiment, much more than visual rendering--

Recursive cube with environmental rendering


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