"Patterns
of Nature"
Sacred Geometry
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Phi ratioed compound curves within a sunflower
The
mathematical laws of our universe and its primary particles constitute
a template for fluent transmutation of energy into form, and vice
versa. To the keen observer, their identity is revealed in the recurring
growth geometry of natural objects such as flowers and seashells.
Below are listed several of the better known.
Phi
ratio (golden mean/section): 1.61803
Fibonacci series: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 ...
Lucas numbers: 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123 ...
Feigenbaum number: 4.699
Most
essentially these point to a universal basis for beauty, as acknowledged
in their work by renaissance painters. In his book, "The Cosmic
Christ", theologian Mathew Fox equates it with the oft-used Biblical
term "glory", representing the power and spendor of the
Godhead itself, as radiated throughout all creation.
The
Call of Beauty
In practical
usage the Phi curve, Phi rectangle, pentagram and vesica picis appear
most often as a recurring design element.
The Phi spiral folds inward and outward endlessly upon itself, the
mathematics of self-transcendence and infinity as represented on the
dome of a shrine in Tehran, Iran.
These
values are a key to selecting harmonious relationships between objects
or elements of any dynamic force that may be constructed numerically.
A long history exists, in all major cultures, of their use to incorporate
inspiring dimensions (beauty) within paintings, sculpture and religious
architecture. It is only recently, largely through New Age spin-offs,
that this "sacred geometry" has come to the attention of
fringe science, and the wider public.
Harmonious Phi rectangular grid of the Great
Mosque of Kairounan, Tunisia.
The actual meaning of the occult phrase, "squaring the circle",
is none other than Phi. BTW the opposite of a circle is a point, not
a square.
(Unwanted)
harmonics are dampened at, or near, the proportion of Phi ratio. As
apparent on the Color Therapy page,
these two are mathematically anithetical. This property is exploited
in the dimensions of speaker enclosures, as well as these specialized
chambers for "resonant macrosonic synthesis" of intense
sound waves.
Acoustic
Resonator Having Mode-Alignment-Canceled Harmonics
Similar forms were employed in the overunity generators of the Austrian
inventor Viktor Schauberger. Phi ratio, widely observed in nature,
is the key to implosive, as opposed to explosive, power. The properties
of vortices, with their inherent Phi ratioed structure, are discussed
on the Power Spot page.
The
humble egg is an example of nature's grand design. It resists pressure
from the outside, but cracks from within at the slightest peck. A
protective container for life. Double Phi spirals form a heart shape;
the symbol of nurturing.
Golden
Number Website
Sacred
Geometry - Robert Lawlor
The
Power of Limits - György Docz
Fibanocci
and Phi in Music: The Golden Proportion in Musical Form
Make
Your Own Golden Section Calipers
Phi Matrix software
Dan Winter Implosion Group
Website
Sacred
Geometry - Deciphering the Code
Phi
Ratio Mixing
An obvious
application to bioelectronics is energetically affinitizing two or
more synthesized frequencies. For example, if we assume the primary
Earth resonance of 7.8Hz is beneficial, than mixing it with 7.8 x
1.61803, being 12.6Hz, would augment the effect. Addition of every
similarly related value is increases this activity exponentially,
eg. 20.4, 33, 53.5, etc.
Signals
structured around Phi ratio are better absorbed by living systems,
which are anatomically resonant with this proportion. This property
also allows for integration (internalization) of opposing incidental
forces, thereby extracting life force from environmental stimuli.
Similar
functions can be performed with the other "universal" number
sets listed at the top of the page.
Another
advantage of mixing individual ELF's into a complex waveform is that
it raises the frequency content of the signal, thereaby allowing sub-audio
influences to collectively pass through audio componentry, without
utilizing modulation as described in the section below. However, this
is obviously unsuited to instances where a "pure" ELF is
deemed preferable.
Top: Single ELF. Bottom: five mixed ELF's.
In situations
where it is beneficial to apply multiple frequencies simultaneously,
ie. as in transmitting the entire Schumann spectrum simultaneously,
mixing is even more advantageous. Below is just such a device, designed
by the Author, utilizing a PIC microprocessor as the signal source,
and a 20mA output amp. Also shown, for technical interest, is a strip
board (Veroboard) layout of its circuitry. Note: connections to the
emitter and 4 x "AAA" cells are not shown.
It is
also possible to work backward, as in finding an ELF that is Phi compatible
with a preferred audio frequency. For example, according to Hans
Cousto, 136.1Hz is a higher octave of the Earth year. It is also
the auspicious mystical seed syllable "OM". By successively
multiplying it by 0.61803, we derive 7.58Hz, which fortuitiously corresponds
nearly enough to the primary Schumann resonance of 7.8.
Overtones
& Octaves
While
somewhat unrelated to sacred geometry, another method is the use of
"overtones", whereby each frequency has the same separation
from the next. A clue to the import of this can be seen in the Earth's
natural Schumann resonances, which
are evenly spaced about 5.9Hz apart.
Conventional
octaves, eg. multiplying or dividing a frequency by a whole integer,
also have limited value as dynamic reinforcement; especially when
at least three are combined.
Phi
Ratio Modulation
Here
is an application that allows us to introduce another valuable technique.
Let's say we want to generate 7.8Hz in audio editiing software to
feed an external amplifier that will power a bio-active emitter. But
PC soundcards typically will not pass anything below 20-30Hz. The
solution is to output the 7.8Hz as MODULATION upon an audio frequency
"carrier". How to choose an affinitive value? Simply multiply
7.8 x Phi (1.61803) until within the requisite audio range, ie. 86.5Hz
140Hz, etc.
Frequencies
derived in this way can be endlessly compounded into complex, but
still fully harmonious, signals. In other words, we have abided by
the self-referential imperative of high cosmic order, thereby ensuring
mutually augmentative (non-destructive) interaction.
The fundamental
options are amplitude modulation (AM), frequency modulation (FM),
as shown above, or the two combined.
Due to
differing receptivities, such as those exemplified in the above MRI
scan, the author prefers AM for evoked somatic
responses and FM for neural entrainment.
Since the latter is typically of uniform amplitude, overall inductivity
is also higher. According to the primary methodology of this website,
these would all be broadcast as silent energy waves. However, you
can audibly compare their respective qualities in the two mp3 files
below. For multi-sensory experience, Windows Media Player can be set
to full screen mode. This simulates an audiovisual
entrainment machine, as per the linked page.
AM
FM
The above
techniques embody the four benefits of audio modulation: 1) preservation
of the entraining attributes of an ELF, 2) harmonic reinforcement
of same, 3) added signal density, via the carrier wave, for improved
progagation and absorption, and 4) enlistment of consumer software,
PC sound cards and audio equipment for signal generation and processing.
Procedures utilizing the latter are disclosed elsewhere on this website,
and represent an easy entry point for low budget experimenters.
And here is AM and FM being implemented simultaneously.
AM+FM
Combined
The characteristc
Phi curve, illustrated at thetop of this page, can also be used as
a modulation envelope for any carrier frequency, and additionally
a basis for degrees of phase separation in compounded carriers to
thereby embed geometry within the signal. For further details on wave-shaping,
visit the Emotional Waves page.
Irrespective
of sacred geometry, any higher frequency can, of course, be enlisted
as a carrier based upon some known compatible attribute. For a few
examples of
those in the audio band, see the Frequency
Therapy page.
Additional
to this, direct recordings from nature can be mixed or modulated with
ELF's as carriers. Here is a track of forest sounds, with compressed
dynamic range, blended with a 7.8Hz sinewave. Since the former is
in stereo, left and right channels differ. This provides a captivating
"psychedelic-like" effect. Listen
to MP3
Pentagram
Phi ratio,
and its characterisitic spiral, are implicit in the mathematical proportions
of the Pentagram.
Street plan of Washington DC and Islamic tiling hint at a culturally
shared appreciation for sacred geometry.
Universe
is Finite: Dodecahedron-shaped - National Geographic
Vesica
Piscis
The Vesica
Piscis, or "the fish", is formed by the intersection of
two circles or spheres. When this is done at Phi ratio across their
diameters, as illustrated above, a hexagon is "miraculously"
born from what was previously a pentagonal identity. Hence, it is
also the union of two triangles; one pointing downward, the other
upward. Both operations represent the union of nature and will, feminine
and masculine, water and fire; a theme repeated in the "yantas"
of Hinduism and Buddhism. Ancient religions viewed such hermaphroditic
transformations as a higher vehicle for human consciousness, accessible
through equivalent ceremonial motifs related to the accumulation/sublimation
of primal (sexual) energy.
Spherical
wave intersections, as per Walter Russell; infinitely contracting
and expanding. Next is the iconography of the Christian church. Both
allude to a Phi (love) mediated superposition of matter and spirit.
The cross of cruxifiction, drawn above correctly in Phi ratio, symbolizes
both the human trials and point of release relative to worldly existence.
It is
worth noting, that Ruth Drown, an originator of radionic therapy and
practicing Kabbalist, used a string of overlapping wire circles as
the output antenna of her "Homo Vibra Ray" instrument.
Vesica
Piscis Sacred Geometry
Magic
Squares & Sigils
Another
source of transcendent proportion is based upon an arrangement of
numerials within adjoining squares such that their total adds to the
same value in each column; vertically, horizontally and diagonally.
Depending upon how they are combined, the patterns derived (sigils)
are good canidates for purpose-tuned antenna; to be energized as described
on the Shape Shifting page.
Magic
square from Albrecht Durer etching. A 1-9 square showing a sigil for
39714. For an instrumented version, see the Malcolm Rae card illustrated
on the Radionics page.
Magic
Squares
Magic
Square - Wolfram
Brief
Introduction to Sigils
Sigils,
Magick Squares and Planetary Seals - Detailed instructions
Sigils
Based Upon the Pythagorean Theorum
Sigils
representing palnetary forces.
Units
of Measurement
Advance
of science has uncovered a number of universal
constants. One implication is that they somehow figure in the
templating of the cosmos, and, therefore, may represent low-resistance
conduits for projected energy when incorportated (at lower octaves)
into an electronic signal.
Another
application is in calibrating "sacred" numbers to a meaningful
unit of measurement, as opposed to a man-made construct, for the purpose
of signal generation. There are two methods, external and internal.
First, instead of expressing the value 359 in the arbitrary measure
of "cycles per second" (Hz), reference it by multiplication
to the Planck constant of 6.62 yielding 2.3766KHz. Second, both 6.63
and 359 can be incorporated within the same signal as frequencies.
Euler
number: 2.71828
Fine structure constant: 137
Ratio proton to electron mass: 1.840
Planck constant 6.62606
It is
believed that prior civilizations derived their units of measurement
from both natural and esoteric observations. This was used to create
structures that resonated with higher dynamics.
Egyptian
cubit: 52.367cm
Royal cubit: 52.4002cm
Megalithic
yard: 82.966cm
Rosslyn
Chapel: 1:81 = 0.012345679
It should
be noted that the metric system possesses no correspondence to any
natural law. In other words, everything manufactured using this contrived
system of measurement clashes with cosmic order, and is therefore
energetically deprived. This is in contrast to the old system of feet
and inches. Time, however, still subscribes to an ancient system,
originating with the base
60 numerical system of the Sumerians.
Fractals
Self-similarity
is the resource-efficient method nature has evolved to elaborate highly
complex forms from simple mathematical rules. Its discovery in the
1950's paved the way for game and film terrain generation by computer
algorithm, as seen in the realistic scene above.
Fractal
Landscapes
Generating
Random Fractal Terrain
Self-contacting
Symmetric Fractal Trees and the Golden Ratio
The fractal
proportions of a single tree have been scientifically proven to mirror
the distribution of trees in the entire forest. The implication is
one of mutual support between all naturally evolved entities within
a given ecosystem. This highlights the recursive, or self-observing,
quality of consciousness itself and harkens to the age old Alchemical
dictum, "as above, so below". An analogy in electronic circuit
design is when the output of a signal generator is looped back into
its own modulation input.
To paraphrase
the eminent physicist David Bohm, "Each part (of a fractal hologram)
is in the whole and the whole in each part. The quintessential religious
experience, the experience of mystical oneness and 'supreme identity',
might very well be a genuine and legitimate experience of this implicate
and universal ground."
Fractal
topology can assume a striking resemblence to sacred art and architecture,
as exemplifed by a modern PCB antenna and the Tibetan Buddhist "the
great wheel of bliss".
On
the Design of Wheel Shape Fractal Antenna
Fractal
Antenna
Confluence
Emulation
of nature, in its most basic expression, takes the form of an orchestrated
physical conjunction with what is perceived to be a higher dynamic.
The intent varies from imputed power-by-association, to pre-technological
calculations of impending seasonal change and celestial phenomena.
This is witnessed worldwide in traditional folk dances, religious
ceremonies, and temple achitecture that incorporates astral and solar
alignments for symbolic gesture and sanctification.
A
Tibetan Buddhist mandala, the structure of the cosmos represented
by infinite grains of dyed sand.
Calendrical
features of Stonehenge in England, and zodiacal juxtaposition of Round
Towers in Ireland.
Assorted
Links
Ancient
Architectural Acoustic Resonance
The
Frozen Music of Rosslyn Chapel - Check out the other pages of
this website as well.
Vesica piscis
Rhysmonic
Cosmology
BioGeometry
Research
Incorporation
of the Golden Ratio Phi into the Schrodinger Wave Function
Harmonic Interferrence
Theory
The
Flower of Life
Biblical
Gematria
Little
Guy in the Eye - Occult Geometry
Online Gematria Calculator -
Converts words or phrases to a numerical sequence in several mystical
systems. Radionic rates? Subliminal messaging?
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Signals
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