911:Geometry
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Contents 
Intro
(todo)
Wave dynamics
(To fix: "waving" is a verb. Waves need a medium. Adapt/integrate the various wave theories to/in the concepts of the electromagnetic "rope theory")
 Universal patterns:
 Periodicity: Cyclic energy flows (in, neutralcenter, out)
 Sympathetic vibrations <> Resonance (todo: "law of octaves" observations in various energymass spectra)
 Complexity through simplicity (fractal recurrence, infinite states, few rules)
 Relativity (no absolute, true beginning and end are elusive  "the serpent bites its tail")
 Equilibrium dynamics (Entropy functions from the smallest to the largest scales)
 Meaning/intention and its information communication process (see also: Semiotics)
 Communication and Language (in its broadest sense):
 Symbolism (the coding of the concepts of communication into a more narrow band of possibilities):
 Forms of communication: kinetic, phonetic, optical (with subsets: symbolic signs, letters), nonoptical spectrum
 Electromagnetic waves are the basis for any form of communication
 Information gathering / processing / rendering
Vortices flows.png
"A vortex can spin in only one direction. Parity demands that for every vortex there must be a countervortex. This is why all dynamic structures are created, like men and women, in equal and opposite numbers. Two vortices spinning in the same direction flow in opposite directions along their interface, Therefore, if pushed together. they will annihilate each other. This is why when particle meets antiparticle, they are transformed into radiant energy. The closer two vortices spinning in the same direction are pushed together, the more energy is brought into opposition along their interface. Therefore, all vortices rotating in the same direction will tend to move away from each other until they are spaced equally apart." [1] 
Wave flow basics.png
Standing wave flow basics [2] 
"universal ratio mathematics [4] 

"Chladni figures for circular plate, sorted by number of (diameters, circles) in each pattern. These patterns can appear at any orientation on the plate. Each distinct pattern has a unique vibration frequency. The vibration frequency therefore offers a rotation invariant representation of the pattern present on the plate." [5] (See also: Cymatics) 
Harmonic resonance theory [6] 
Wave behavior
 Waves (Category:Waves): "Disturbances which propagate through space and time, usually with transference of energy."
 Wave mechanics/theories:
 Standing wave: "A wave that remains in a constant position. This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling in opposite directions."
 Running wave:
 Soliton
 Swave:
 "The Swave, secondary wave, or shear wave, sometimes called an elastic Swave, is one of the two main types of elastic body waves, so named because they move through the body of an object, unlike surface waves. The Swave moves as a shear or transverse wave, so motion is perpendicular to the direction of wave propagation: Swaves, like waves in a rope, as opposed to waves moving through a slinky, the Pwave."
 Pwave:
 "Pwaves are a type of elastic wave, also called seismic waves, that can travel through gasses (such as sounds), elastic solids and liquids, including the Earth. Pwaves can be produced by earthquakes and recorded by seismometers. The name Pwave stands for primary wave, as the Pwave is the fastest among the elastic waves, compared to the Swaves. In isotropic and homogeneous solids, the polarization of a Pwave is always longitudinal; thus, the particles in the solid have vibrations along or parallel to the travel direction of the wave energy."
 Transverse wave
 Longitudinal wave
 Rayleigh wave:
 "They are distinct from other types of seismic waves, such as Pwaves and Swaves, which are both body waves, or Love waves, another type of surface wave. Rayleigh waves are generated by the interaction of P and S waves at the surface of the earth. The Rayleigh wave travels with a velocity that is lower than the P, S, and Love wave velocities. Emanating outward from the epicenter of an earthquake, Rayleigh waves travel along the surface of the earth at about 10 times the speed of sound in air"
 Swave:
 Soliton
 See also:
 de Broglie hypothesis and Bohm interpretation
 Wave mathematics:
Wave phenomena
 Natural frequency
 Resonance (See also: "The Frequency Resonsant")
 Entrainment
 Electromagnetic radiation
 Absorption
 Diffraction
 Interference
 Redshift [43] and Blue shift
 Doppler effect
 Gravitational lens
 Holography
 Coandă effect
 Countercurrent exchange
 Lorentz force
 Eddy current (Foucault current)
 Biefeld–Brown effect (video's)
 Electrohydrodynamics
 Centrifugal force and Torque
 Brownian motion
Music theory
 Auditory sensations:
 Science of music:
 "Musical Mathematics", Cristiano M.L. Forster
 Dmitri Tymoczko research
 Rythm:
Selforganizing systems
Dynamical systems
 Video lecture: "Chaos, Fractals and Dynamical Systems"
 Dynamics:
 Attractor: "is a set to which a dynamical system evolves after a long enough time. That is, points that get close enough to the attractor remain close even if slightly disturbed."
 Bifurcation theory: "bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behaviour."
 Complex analysis (topics)
 Complex plane (mathematics)
Cymatics
 "Cymatics is the study of wave phenomena. It is typically associated with the physical patterns produced through the interaction of sound waves in a medium."
 See also:
 Examples:
Natural shapes:
Synthetic shapes:
Picture of tortoise beside cymatic sound pictures at 1021 Hz, 2041 Hz, 1088 Hz and 1085 Hz. [8] 
Magnetohydrodynamics shapes:
Ferrofluid in a rotating and axial magnetic field (video). 
 Synergetics
 "Synergetics is an interdisciplinary science explaining the formation and selforganization of patterns and structures in open systems" ... "As a consequence, selforganization means an enormous reduction of degrees of freedom (entropy) of the system which macroscopically reveals an increase of 'order' (patternformation). This farreaching macroscopic order is independent on the details of the microscopic interactions of the subsystems. This is why Synergetics explains the selforganization of patterns in so many different systems in physics, chemistry, biology and even social systems."
 Tensegrity  an applied mechanical concept of synergetics.
Crystallization
 Various notes:
 Snowflake photos (by Mark Cassino)
 To research:
 Piezoelectricity and other (derived) electromagnetic functions of crystals.
 The large selenite crystals of the Naica Mine ("Crystal Cave of Giants") in Mexico. (see also: [44])
Snow crystals 
Fractals
 Fractal generation classes:
 Escapetime Fractals: Mandelbrot set, Julia set, Nova fractal.
 Iterated Function Systems: Cantor set, Koch snowflake, Sierpinski carpet.
 Random Fractals
 "In random fractals, we see dendritic fractals demonstrate the fundamental natural property of diffusionlimited aggregation (DLA). DLA is best illustrated in the physical manifestations of fern growth, ice crystals, tree branch growth and electrical discharges." [45]
 Strange attractors
 Generated by iteration of a map or the solution of a system of initialvalue differential equations that exhibit chaos.
 See also:
 video: "Fractals in Science, Engineering and Finance (Roughness and Beauty)"
 Multifractal system
 "Grand Unified Fractal Theory"
 "The Thumb Print of God: A Spiritual Exploration Through Fractal Mathematics"
 flickr.com: fractalists pool
 jmckennonmth212s09.wordpress.com
 FractalAnimation.com
 "Study of Chaotic Motions"
Structure of a leaf [10] 
Cellular automata
 Various notes:
 See also:
"Rule 110" cellular automaton, which is Turing complete. 
Information concepts
 Modes and attributes:
 Entropy: "It quantifies the information contained in a message, usually in bits or bits/symbol. It is the minimum message length necessary to communicate information."
 Geometry
 Symmetry, Selfsimilarity, Similarity (asaboveasbelow, "binarytriplets")
 Chirality: "In geometry, a figure is chiral if it is not identical to its mirror image, or more particularly if it cannot be mapped to its mirror image by rotations and translations alone. A nonchiral figure is called achiral."
 Symmetry, Selfsimilarity, Similarity (asaboveasbelow, "binarytriplets")
 Recursion: "a transformation in which the transformation being used is applied within its own structure."
 Duplication
 Variation
 Transformation
 Other informational topics:
 Patterns
 Information theory  pioneered by Claude Elwood Shannon
 Kolmogorov complexity  by Andrey Kolmogorov
 Animal behaviour and Kolmogorov complexity: "Dialog with black box  Using Information Theory to study animal language behaviour", by Zh. I. Reznikova
 Gödel's incompleteness theorems  by Kurt Gödel
 Turing machine  by Alan Turing
Mathematics
Highlevel divisions of mathematics.
Truth
Quantity
 Numeral system (see also: Grapheme)
Structure
 Algebra
 Linear algebra
 Associative algebra
 Clifford algebra ("is a very convenient representational and computational system for geometry. It is going to be the way computer science deals with geometrical issues. It contains, in a fully integrated manner, linear algebra, vector calculus, differential geometry, complex numbers and quaternions as real geometric entities, and lots more. This powerful language is based in Clifford algebra." [46]). See also: "Why do I like Clifford Algebras?".
 Set theory
 Abstract algebra
 Boolean algebra
 Group
 Category of groups (types of groups: finite, infinite, discrete, continuous, multiplicative, additive, abelian, cyclic, simple, solvable)
 Group theory
 Abelian group
 Galois theory ("Using Galois theory, certain problems in field theory can be reduced to group theory, which is in some sense simpler and better understood.")
 Group theory
 Category of groups (types of groups: finite, infinite, discrete, continuous, multiplicative, additive, abelian, cyclic, simple, solvable)
 Ring theory
 Hypercomplex number
 Polynomial
Space
 Geometry
 Symmetry
 Classical geometry
 Classical geometry
 Möbius transformation (see also: video: [47])
 Euclidean geometry (see also: "A mathematician sculpts solids point by point")
 Euclidean space (see also: Topological space)
 Euclidean plane geometry
 Euclidean solid geometry
 Pythagorean theorem
 Bisected hexagonal tiling
 Euclidean space (see also: Topological space)
 Classical geometry
 Trigonometry
 Topology
 Topological space
 Continuous function
 Topological algebra (see also: abstract algebra)
 Geometric topology
 Manifold
 Lie group
 E8 (see also: "An Exceptionally Simple Theory of Everything", disinfo hype?)
 Lie group
 Manifold
Change
 analysis
 Mathematical optimization
 Complex analysis (topics)
 Harmonic analysis
 Computational complexity theory
 Numerical analysis
 Calculus (calculus is the study of change)
 Net (intended to unify the various notions of limit and generalize them to arbitrary topological spaces)
 Probability theory
Metamathematics
Applied mathematics
Geometry
 Various:
 video: "Geometry of Life" (part 14)
 History of geometry
 'Sacred' geometry
 Tetractys (see also: Quincunx)
 "Sacred geometry, Metatron's cube and the platonic solids"
 Metatron
 Platonic solids
 Doubling the cube ("The Delian Problem")
 Noncommutative geometry
 'Magic' shapes
 Magic square
 see also: Sudoku
 Magic circle
 Magic square
Spirals
 Various notes:
 See also:
 Numerology: Phi
 Energy: Electromagnetism
 Occult symbolism: Energy spiral
 Occult symbolism: Serpent
 "The Mystic Spiral: Journey of the Soul" (see Literature list below)
 "In the Garden"
 "Electrofractal Universe"
 Vortex (contraction => center => expansion)
 See also:
Natural spirals
 Todo:
 'images' of DNA, telomere and enzyme helix structures.
 Blood flow vortexes
 Solar Parker spiral
Pinwheel Galaxy (see also: Spiral galaxy) 

North pole of planet Mars 
Waterspout.jpg


Sea life near vents at volcano V1 in the Tonga Arc. [13] 
Ram horns 

Red cabbage internal spiral [15] 

Nautilus shell 
Vine tendril 

Daisy flower (parabolic spiral) [18] 

Pine cone (bottom) 
Pine cone (side) 

(see previous) [20] 

"Cross section through an axoneme of Actinosphaerium near the axopod base. Two spiral rows of microtubules are coiled about a central axis in a precise geometrical arrangement. Scale marker 1 µm." [22] 
Paraffin carborundum crystal [24] 
Scientific spirals
Spiral periodic table [25] 
"All direction is curved, all motion is spiral" by Walter Russell (1871–1963) 
"Ten octaves of integrating light" by Walter Russell (1871–1963) 
Cultural spirals
 Various notes:
 See also:
 Swastika:
 "The Swastika" (by Thomas Wilson Curator, Department of Prehistoric Anthropology, U.S. National Museum, 1894)
 See also Fylfot
 abrahadabra.com forum: Reclaiming Ancient Symbols: The Swastika
 "The Swastika" (by Thomas Wilson Curator, Department of Prehistoric Anthropology, U.S. National Museum, 1894)
Altar at the Tarxien temple complex in Malta. (estimated at ~2800 BC.). 

The Playing Board of the Egyptian Game Mehen 
Newgrange passage tomb entrance stone (with trispiral and single spiral engravings), Ireland (estimated at ~3500 BC.). See also: [27], More images from that site. 

Reask stone, near Kerry, Ireland. [30] 
Väskinde cemetery (Sweden) [31] 

The marble pedestal patterns on the imperial guardian lion (also called a "Fu Lion", "Foo Dog", "Lion of Buddha".) at the Forbidden City, China. 

Nazca Lines monkey, Peru. 

Swastika examples 

Trojan, Onchan (Isle of Man), and Roman artwork 

Cyprus Roman Mosaic (~50BCE) 

Vatican staircase 
Thule Society emblem 

Emblem of the Nazi SS Panzer Division "Wiking" 
US Naval Construction Force Base. Coronado island, San Diego, California USA. [34] 
Drawing by M.C. Escher 
Advertisement of Coka Cola in the early 20d Century. [35] 
Abstractions
 Various notes:
 See also:
 "Vortex Simulations" (research paper) (based on Contouradvective semiLagrangian algorithms)
 See also:
See: Energy 

"Schematic of dominant unisonal vortex with an elongated dualcore vortex eye in a progressive vortical paradigm arrangement with vortical spokes and vortical spiral arms" [36] 

Hopf fibration (or "Hopf map") describes a 3sphere (a hypersphere in fourdimensional space) in terms of circles and an ordinary sphere. Discovered by Heinz Hopf in 1931. Hopf found a manytoone continuous function (or "map") from the 3sphere onto the 2sphere such that each distinct point of the 2sphere comes from a distinct circle of the 3sphere. [37] 
"A basic one dimensional depiction of the "Tube Torus" shape is formed by ratcheting the Seed of Life and duplicating the lines in its design. In Physics, the Tube Torus is considered a basic structure in the study of Vortex forms. Some say the Tube Torus contains a code of vortex energy that describes light and language in a unique way, perhaps as something of an Akashic Record." [38] 
Vortex math.jpg
Marko Rodin's vortex mathematics. 
Fermat spiral (see also: "Spiral Mandela's") 
Fibonacci sequence in the Sunflower 

Ulam spiral (or "Ulam rose", see also the next image) ranging from number 1 to 121. All points starting from the center are numbered from one and go in a anticlockwise spiral outwards. Note how the points tend to line up along diagonal lines. 
Ulam spiral ranging from number 1 to 3,996,001. Prime numbers are white; composites are black. Note how the points tend to line up along diagonal lines. [39]. See also: video's. 
Riemann surface for the square root function. 
Riemann surface for the cube root function. 
Seed of Life
 Various notes:
 "The Seed of Life is formed from seven circles being placed with sixfold symmetry, forming a pattern of circles and lenses, which acts as a basic component of the Flower of Life's design."
 "The first circle at the center including its twelve petals, is called The Germ Of Life and the second concentric circle is called The Seed Of Life. The third concentric circle holds the very important Flower Of Life and the fourth, The Fruit Of Life." [48]
Flower of Life
 Various notes:
 The center of each circle is on the circumference of six surrounding circles of the same diameter. The pattern looks flowerlike, hence the name. The Flower of Life pattern contains the basis of Metatron's Cube. From this pattern, all five of the Platonic solids can be derived.
 The Flower of Life is a geometrical figure composed of multiple evenlyspaced, overlapping circles, that are arranged so that they form a perfect pattern with a sixfold symmetry like a hexagon. It is their ultimate secret!! [49]
 "The Flower of Life is a geometric pattern inscribed on many of the world's great Pyramids, Temples and Cathedrals dating back over 6000 years." [50]
 "Flower of Life symbols: Found in India & other locations"
 "Sacred Geometry: Flower of Life"
... as interference ripples from its center. 
3Dspherical Flower of Life [40] 
Natural analogies:
The process of mitosis in cell division. 
Tree of life
 Various notes:
 video: "Extreme Kabbalah: The Tree of Life" (todo: research this 2D/3D node representation thesis)
Tree of Life derived from the Flower of Life. 

The Caduceus on the Tree of Life. 
Earthly representations if the tree of life?
Polyhedron
Uniform polyhedron
Platonic solids
 See also:
 Stella octangula (derived from 2 intersecting Tetrahedra)
 Merkabah (Two intersected Tetrahedra)
 video: "13 Masonic Secrets, Part 8 of 13"
 Merkabah (Two intersected Tetrahedra)
 Compound of five tetrahedra
 Stella octangula (derived from 2 intersecting Tetrahedra)
Icosahedron 
Octahedron 
Tetrahedron 

Merkabah  which is formed by two intersecting Tetrahedra. 
Hexahedron 
Dodecahedron 
Metatron cube
 The Metatron cube (derived from the "Flower of Life") holds all the 5 Platonic solids.
 See: [51] & [52]
 See: Occult symbolism XV: District of Columbia ( Washington, D.C. masonic street plan. )
Literature
 1924:
 Marcotone: The Science of ToneColor [53], Edward Maryon
 1967:
 1982:
 1994:
 Homage to Pythagoras: Rediscovering Sacred Science, Christopher Bamford (and others: Robert Lawlor, ...), ISBN 0940262630
Links
 Geometric Properties of Masonic Symbols
 Plasma Cosmos Planet (blog aggregation on various cosmology topics)
 Goldenmean.info (Dan Winter)
 Charles Gilchrist (videos)
 2dcurves.com
 Hyperflight.com
 Vedic mathematics (see also: JainMathemagics.com)
 Geometrycode.com
 "Systems of Proportion in Design and Architecture"
 "Museum of Harmony and the Golden Section: Mathematical connections in Nature, Science and Art"
 3D visualization of wave spectrumusage
 Reconciliation of Science and Religion (blog)
 Heliotropodeluz.wordpress.com
 Coralcastlecode.com
 Sacredscience.com
 Sacredgeometry.com
 Halexandria.org
 Humanresonance.org
 Tony Smith
 "Stuff and Style of the Universe"
 "Patterns in Nature"
 James Furia's geomusic (video's, audio interview)
 Pyramidmatrix.com (by Carl P. Munck)
 "Phi Sound Healing"
 2012forum.com
 "Ripening, Maturity and Cosmic Influences"
 "Isomorphiclike Magic Stars"
 "Freemasonry Geometry"
 Flowfieldcycle visualizations:
Various:
 Cyclesresearchinstitute.org
 Foundation for the Study of Cycles
 oregonite.blogspot.com
 biogenesislab.blogspot.com
 Trivortex.com (Brian David Andersen)
 Earthmatrix.com
 Spaceandmotion.com
 RexResearch.com
 Feandft.com
 Metaspherical.com
 thecleaver.blogspot.com
 Holographic Universe
 Spirasolaris.ca
 Lawofone.info
 Lambdoma.com
 "Stoa del Sol"
 Borderlands.com
 unamity.com ("Millennium Twain")
 EarthHarmonics.blogspot.com
 "The prehistoric alignment of world wonders"
 Ray Tomes' Cycles in the Universe
 Biowaves.com
 Crop Circle Language
 Atlascoelestis.com (Catholic astronomy image archive)
 Soundhealingnetwork.org
 Sacred Geometry and Illumination