THE PENROSE TILINGS & the GOLDEN MEAN Towards Hyperdimensional Intergeometry

-By Ananda, May 1999-

In order to appreciate the Vortexijah, let us explore the local models that map inter-dimensional transfer.

Since 8 Hz ELF in bio-hemispheric brain synchronization, is mapped by the inset of coherence: the Golden Mean lining up of the doughnut quanta fields, as they bridge through from non-locality (via the room temperature superconductivity of the DNA and microtubeles, who themselves being in the Golden Mean arrangement, most of the time), having been condensed by the Intergeometrical coherence of the Vortexijah Lens; quantum gravity; and then translated into PHI dodecahedron cascades - any new model that is built from the Golden Mean will take us some steps to the Vortexijah in-depth hyperdimensional mathematics.

The Vortexijah Sphere being the union of all geometries and intergeometries, as well as all Penrose Tilings and relatives, and this Multiversal Sphere having a quantum gravitational cousin, the incubator of its first causation.

Roger Penrose, of Oxford, Put forward an astounding notion with anaesthesiologist Stuart Hameroff of the University of Arizona: consciousness arises from quantum-mechanical processes taking place within tubes of protein inside nerve cells, and is, in part Virtual, non-local "no-thing". (See "Quantum states of mind", New Scientist, 20 August 1994).

We have been relaying the above notions in our Vortexijah protocol for numerous years now, and were delighted to discover Dr. Roger Penrose's models relate the same, from a different angle, as he states:

"According to the standard rules of quantum theory, the quantum-gravitational state would involve the super positions of all possible geometries - here space-time geometries, which are four-dimensional things - with complex weighing factors."

(Penrose, 1996, Oxford. Chapter 5, Structure of the Quantum World, pp 378)

So essentially what has Penrose contributed in this field, in simple terms? Here is a condensed overview:

This great British physicist and mathematician, has developed a series of aperiodic tilings, which themselves incorporates the Golden Mean and the five-fold pentagonal symmetry lies inherent in it, and hence is infinitely recursive in its connectivity.

These tilings are composed of two rhombi, both with exceptionally important numbers (embedded in Egypt and Angkor Wat, Cambodia; one has the angle of 36, and the other of 144 degrees. These are in fact two Golden Triangles, base-to-base), and the other one has the angles of 72° and 108° degrees, which again are part of the Unified Field Cartography system, as well as the Unified Field Universal Map, which we have been mathematically generating in our recent work (see ATON).


In his book, The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics, and in Tilings and Patterns by Grunbaum and Shephard,they relate that when a plane is tiled according to the Penrose golden directions, then the ratio of tile A to tile B, is the Golden Ratio.

In working these, it is by the following of sets of the parallel lines within the tiling itself, that the five-fold symmetry is leaps out from the pattern.

Here are just two of the five axes of pentagonal relations, that can extract as distinct entities:


Being a step towards mapping quantum gravity, one would expect more than a Pandora's box, but a treasure chest of other relationships to emerge and join the unusual symmetry. For from the Penrose tilings also emerges a pattern of overlapping decagons, hence mapping the the central 10 equator vertices of the dodecahedron, a map for the gravity grid of Earth, and the top down view of DNA, made from the 10 phosphate sugar pentagons:

Following in the principles of Unity, towards the unified field, this multi-geometrical mandalla has each tile within the overall pattern always contained inside one or the other of the two types of decagons which are embedded within it. And to illustrate the coherent path of the Golden Middle Way, the ratio of the decagon populations are, quite naturally, the ratio of the Golden Mean. The two decagrammes in his relationship are highlighted as follows:


Since the publication of his book in the late 1980's, Dr. Roger Penrose has extensively extended the first Penrose tiling, and other scientists recognizing the significance of his findings, have continued to develop new aperiodic tilings, that are steps on the Golden Mid Way Path towards the Unified Field and the Unified Thoton Holon.

These are not just theoretical findings, they also may be strong signposts to future alchemy, and the Pangaeum of the Arcanum, that perfects the DNA into its coherent superconducting path.

For in the Scientific American, for February 1992, Peter W. Stephens and Alan I. Goldman showed how quasicrystals, alloys, which were formed by melting aluminum, copper, and iron together, generally revealed the same Golden symmetry which is present in the Penrose Tilings.


When one considers that Iron is the only true magnetic element, and when Iron is in a coherent magnetic field, its molecular poles lines up, creating phase conjigation for electrogravity to emerge; and then unite this with Bell Laboratories discoveries that Copper in its oxidated form contained billions of microscopic Giza Pyramids (half octahedrons, who are the Golden section cascade at maximum compactation); and that aluminum can be made to become a semi non-true magnetic element - then these findings are even more significant in making steps towards practical Vortexijah mathematics, for intergeometry and electrogravity.

Especially when we take into consideration the microtubeles equations of Penrose and many others, in behaving like superconductors, or Bose-Einstein condensates, as quantum coherence; and add to this the coherent heart cardio-rhythm data and 8 Hz EEG data - some astonishing models and practical applications can be made.

This is precisely why we are making this creative canvas for post-quantum mechanical paint to synergise these fields and models into discovering the the hidden multiversal laws, and inter-laws, not yet discovered. And most importantly, the consciousness interface with these - stepping towards a unified field model of consciousness, Virtual interactivity with locality, through coherence, and alchemy.

-Ananda, May, 1999.