Sierpinski fractal [triangles, tetrahedra]: Johannes Kepler, Edo Kaal, Stephen Puetz 'Universal Wave Series' (UWS)

• His concept was the early stages of an intent to replace Quantum Mechanics (QM). It only had 1 arbitrary parameter, if I remember correctly, compared to something like 20 for QM?
• Almost immediately this seemed to tie into many [recent, longstanding] topics of interest to me.
• Did most of the Quantum Mechanics (QM)-Sierpinski literature pop up AFTER the NPS presentation, or during the 20+ years that the amateur was developing hus concepts? There is NO indication of any credit given to an amateur who may have figured out the basis [BY HIMSELF, BEFORE] all of the professional scientists listed below??? Or maybe this theme reaches back almost to Boskovitch in the mid 1700s, as a long-established componenet of energy quanta, thence QM?

	etsy.com second generation Sierpinski tetrahedron VI, beaded art
	Johanna L. Miller 19Nov2018 Quantum mechanics in fractal geometry (<Sierpinski triangle>), Physics Today ...Ingmar Swart, Cristiane Morais Smith, and colleagues at Utrecht University in the Netherlands have taken a step toward experimentally studying quantum physics in a fractional-dimensional system. On a (111) surface of copper they placed carbon monoxide molecules (black indentations in the figure) to corral the surface electrons into a simplified Sierpinski triangle. Howell: it seems to me that Kaal has a fractal-like basis to his "Structured Atom Model" (SAM), albeit with many component parts, and therefore more complex than many well-known fractal patterns? Perhaps the use of fractals in hollywood CGI images is somewhat similar, but taken to artistic extreme?
	Shajesh, Parashar, Cavero-Peláez, Kocik, Brevik 13Nov2017 Casimir energy of Sierpinski triangles, Phys. Rev. D 96, 105010 Using scaling arguments and the property of self-similarity we derive the Casimir energies of Sierpinski triangles and Sierpinski rectangles. The Hausdorff-Besicovitch dimension (fractal dimension) of the Casimir energy is introduced and the Berry-Weyl conjecture is discussed for these geometries. We propose that for a class of fractals, comprising compartmentalized cavities, it is possible to establish a finite value to the Casimir energy even while the Casimir energy of the individual cavities consists of divergent terms. Howell: This does remind me of our recent "pyramids" emails. However, keep in mind that pyramids tend to have a square (or rectangular) base, not triangular like a tetrahedron. For example [Bosnia, Egypt, Mesopotamia, Central America, China (dirt, not stone)]. Even so, the energy-focussing properties of pyramid [material, geometry] may distantly relate to things like the Casimir effect?
	Johannes Kepler Howell: I seem to remember that Johannes Kepler always sought a tetrahedron concept as the proper way to explain planetary motions, even after he formulated Kepler's Laws?
	Great Pyramid of Giza can focus electromagnetic energy through its hidden chambers Andrey Evlyukhin, ... the international research team looked into the relationship between the shape of the Great Pyramid of Giza and its ability to focus electromagnetic energy. To do this, the team led by ITMO University in Saint Petersburg, Russia, created a model of the pyramid, one of the seven wonders of the ancient world, to accurately measure it electromagnetic response. Howell: This does remind me of our recent "pyramids" emails. However, keep in mind that pyramids tend to have a square (or rectangular) base, not triangular like a tetrahedron. For example [Bosnia, Egypt, Mesopotamia, Central America, China (dirt, not stone)]. Even so, the energy-focussing properties of pyramid [material, geometry] may distantly relate to things like the Casimir effect?

• page 2 of paper: "... Section 2 provides background information on how Pascal’s triangle is related to the Sierpinski triangle when the numbers are taken modulo a prime. ..."
• Bannink & Buhrman's "modulo power of 3" immediately reminds me of Stephen J. Puetz's "Universal Wave Series". Puetz and co-author Glenn Borchardt struggled to explain the amazing power of their factor-of-three powers series actross, well, almost all well-known cycles. I haven't done the check yet, but it seems to me that their OR[half, double] series is just due to frequency-beating of their primary factor-of-3 series.