911:Geometry

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“The cube and the sphere are the sole working tools of creation“ - Walter Russell

Contents

Intro

Life cycle

Design

  • Idea, conception, intention, functions, properties.

Creation

Evolution

Recycling

  • Radiation, disintegration, exhaling, magneto-positive force.

Logic

Topology

Dimensions

Hyperspace

“The mind is a maximum hypersurface and thought a trajectory on it and the Amygdala and Hippocampus are Hopf maps of it.“ - Chris McKinstry

Interaction

Transformation

  • Object iteration:
    • Addition and multiplication (todo: note the difference between pure types and mixed type multiplication)
    • Subtraction and division (todo: note the difference between pure types and mixed type multiplication)

Self-organizing systems

Cymatics


  • Natural shapes (circles):

Water fluid surface/drop

Tree rings

Agate geode crystal [1]

Rock formation (ItalKali mine, Sicily) [2]

Fungus [3]

See also: Liesegang rings


  • Natural shapes (stripes):

Sand dunes [4]

Cloud street [5]


  • Artificial shapes:

[6]

Picture of tortoise beside cymatic sound pictures at 1021 Hz, 2041 Hz, 1088 Hz and 1085 Hz. [7]

AMOEBA water writing device [8]


Magnetohydrodynamics shapes:

Ferrofluid in a rotating and axial magnetic field (video).

  • Synergetics
    • "Synergetics is an interdisciplinary science explaining the formation and self-organization of patterns and structures in open systems" ... "As a consequence, self-organization means an enormous reduction of degrees of freedom (entropy) of the system which macroscopically reveals an increase of 'order' (pattern-formation). This far-reaching macroscopic order is independent on the details of the microscopic interactions of the subsystems. This is why Synergetics explains the self-organization of patterns in so many different systems in physics, chemistry, biology and even social systems."
    • Tensegrity - an applied mechanical concept of synergetics.

Crystals

  • Periodicity:
    • Periodic
    • Aperiodic: "Regular crystals have translational symmetry, where the same unit part is repeated over and over again with no rotation. Quasicrystals have rotational symmetry, where the same unit part is repeated over and over, but with a rotation about an angle. Quasicrystals are structural forms that are both ordered and nonperiodic. They form patterns that fill all the space but lack translational symmetry. The term and the concept were introduced originally to denote a specific arrangement observed in solids which can be said to be in a state intermediary between crystal and glass. Producing Bragg diffraction, they share a defining property with crystals, but differ from them by lacking a simple repeating structure. Mathematical artefacts known as "aperiodic tilings" were invented in the early 1960s, but some twenty years later physical experiments gave conclusive evidence of their material existence. Within the field of crystallography and solid state physics the discovery has produced a paradigm shift which is indeed a minor scientific revolution." [52]

The large selenite crystals of the Naica Mine ("Cave of the Crystals") in Mexico.

Tibetan quartz crystal cluster [9]

Pyrite [10]

Bismuth crystal

Snowflake [11]

(see previous)

Fractals

  • Fractal generation classes:
    • Escape-time Fractals:
      • Mandelbrot set
        • '3D'-rendering: [53], [54]
        • "While the Mandelbrot set as usually defined is 2D, each point has an associated Julia set, where instead of the additive constant, the starting point is varied (the original Mandelbrot set always uses zero as starting point). Together, they give a 4-dimensional set, where two dimensions are given by the starting point (zr, zi), and the other two by the additive constant (cr, ci). The original Mandelbrot set is a cut through this 4D set at the plane zr=zi=0, while the Julia sets are cuts orthogonal to theat, at planes with constant cr and ci." [55]
      • 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 diffusion-limited aggregation (DLA). DLA is best illustrated in the physical manifestations of fern growth, ice crystals, tree branch growth and electrical discharges." [56]
    • Strange attractors
      • Generated by iteration of a map or the solution of a system of initial-value differential equations that exhibit chaos.

Structure of a leaf [12]

Cellular automata

"Rule 110" cellular automaton, which is Turing complete.

Mathematics

High-level divisions of mathematics.

Truth

Quantity

Structure

Space

Change

Metamathematics

Applied mathematics

Forms

Sphere

(todo)

  • Sphere versus cube:
    • only curves / no curves
    • one face / multiple-faces
    • dynamic / static
    • non-dense stacking / dense stacking
  • Sphere to/from cube conversion:

Cube

(todo)

  • To research: sphere-to-cube transforms (eg. using 4 plains of equal pressure)
  • Line (a straight curve)
    • ...

Spiral

“It don't mean a thing, If it ain't got that swing“ - Duke Ellington & Irving Mills

Natural spirals

Light is an torqued, spirally waving 'rope' composed of coupled electric and magnetic fields oscillating in synchrony at very high frequencies. The electric and magnetic fields oscillate perpendicular to each other and perpendicular to the direction the light is traveling.

This model of light shows all the observed phenomena associated with light and the rest of the electromagnetic-radiation spectrum.

Electro-magnetically induced metal/water vortex experiment (video)

Note: The two modes of spinning depend upon the +/- current wiring. The flow of energy creates a vortex movement.

Adult galaxy

Comet tail interaction with the Sun (to research) [13]

Solar prominence plasma (video)

Sunspots showing a spiraling vortex shape, itself consisting of twisting plasma filaments. [14]

Earth's magnetic field vortexes [15]

North pole of planet Mars

Cyclone

Waterspout

Pāhoehoe lava

Breaking sea wave tunnel

Scalp hair [16]

Ram horns

Sea life near vents at volcano V-1 in the Tonga Arc. [17]

Spider web

Nautilus shell

See also: Pheidian spirals research.

Savoy cabbage

Red cabbage internal spiral [18]

Romanesco broccoli [19]

Umbilical cord

Cochlea of the Human inner ear [20]

Seahorse

Vine tendril

Cactus

Cactus

Datura stramonium [21] (video)

Rose

Daisy flower (parabolic spiral) [22]

Pine cone (bottom)

See also: Occult symbolism: Pine cone

Pine cone (side)

Whirly fingerprint

Note: "In the Henry system of classification, there are three basic fingerprint patterns: Loop, Whorl and Arch. They constitute 60-70, 25-35 and 5 percent of all fingerprints, respectively." [23]

German wasp antenna detail

Bismuth crystal

Spirogyra (green algae) [24]

(double helix variant)

Charophyceae (green algae) [25]

Protoconch [26]

"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." [27]

Graphite crystal [28]

Paraffin carborundum crystal [29]

DNA

Cultural spirals

Osiris pine cone staff (representing Consciousness). Egyptian Museum, Turino, Italy.

Note: the spiraling serpents (representing the Kundalini life force and DNA).

Altar at the Tarxien temple complex in Malta. (estimated at ~2800 BC.)

Mycenaean Tholos 'tomb' chamber ceiling decoration at the Orchomenos site in Greece. [30]

Newgrange passage tomb entrance stone (with trispiral and single spiral engravings), Ireland (estimated at ~3500 BC.). See also: [31], More images from that site.

Newgrange "Triple Spirals of Life" [32]

Newgrange [33]

Reask stone, near Kerry, Ireland. [34]

Väskinde cemetery (Sweden) [35]

Martebo stone with runic inscriptions, Gotland, Sweden.

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

Nüwa and Fu Xi (an ancient painting about Chinese mythology) [36]

Yin and Yang

Nazca Lines monkey, Peru.

Meso-American

Swastika examples

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

Roman floor mosaic

Cyprus Roman Mosaic (~50BCE)

Note: 4-pointed star, 6-pointed star and Double square

Baalbeck Jupiter temple in Lebanon [37]

(see previous)

Vatican staircase

Note: the octagon ceiling.

Santa Cantalina cathedral decoration, Peru

Theosophical Society seal (founded 1875)

Note: the Ouroboros, Ankh and Merkaba.

Thule Society emblem

Emblem of the Nazi SS Panzer Division "Wiking"

US Naval Construction Force Base. Coronado island, San Diego, California USA. [38]

(see previous)

Drawing by M.C. Escher

[39]

Abstractions

See: Energy

Fermat spiral (see also: "Spiral Mandela's")

Fibonacci sequence in the Sunflower

"Primes in a sunflower"

See also: Primes

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 anti-clockwise 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. [40]. See also: video's.

Riemann surface for the logarithmic function. [41]

Riemann surface for the square root function.

Riemann surface for the cube root function.

3D Fibonacci spiral (animated video)

Hopf flux

  • Alternative names:
    • Hopf fibration ("hopf torus", "hopf map", "hopf bundle", "hopf flux")
    • Vortex (in the broader sense, meaning not just the central tunnel)
    • Solenoid (in the broader sense, meaning not just the central tunnel)
    • Universal formative field (Walden)
    • Ψ ("The field denoting the scalar field of the cosmic plenum" - Ervin László)
    • Tube Torus
    • Light rope
    • ...

Energy: EM principles

[42]

Infinity symbol (see also: Lemniscate).

"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." [43]

Marko Rodin's vortex mathematics.

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." [61]

"animation showing how a slant cut torus reveals a pair of circles, known as Villarceau circles in R3." [44]

Seed of Life

Note the 2D representation of a cube.

6-pointed star of Saturn

Remains Of Ancient Pebble Mosaic Floor Ornament Of Late Hellenistic Period At Roman Agora The Archaeological Site Of Kourion In Cyprus

Flower of Life

Flower of Life

Note the 2D representation of a cube.

... as interference ripples from its center.

3D-spherical Flower of Life [45]

Natural analogies:

The process of mitosis in cell division.

There are 4 types of cell division: binary fission for the simpler Prokaryotic cell types, and cytokinesis, mitosis and meiosis for Eukaryotic cell types.

(see previous)

(see previous)

(see previous)

cell nucleus division [46]

Tree of life

Tree of Life derived from the Flower of Life.

(see previous)

The Caduceus on the Tree of Life.

Polyhedron

Uniform polyhedron

Platonic solids

  • Tetrahedron (This shape is found in chemical elements: (todo). For any tetrahedron there exists a sphere such that the tetrahedron's vertices lie on the sphere.)

Icosahedron

"The icosahedron is bounded by twenty equilateral triangles. It has the largest volume for its surface area and represents the property of wetness. The icosahedron corresponds to water."

Octahedron

"The octahedron is bounded by eight equilateral triangles. It rotates freely when held by two opposite vertices and corresponds to air."

Tetrahedron

"The tetrahedron is bounded by four equilateral triangles. It has the smallest volume for its surface and represents the property of dryness. It corresponds to fire." [47]

Merkabah - which is formed by two intersecting Tetrahedra.

Hexahedron

"The hexahedron is bounded by six squares. The hexadedron, standing firmly on its base, corresponds to the stable earth."

Dodecahedron

"The dodecahedron is bounded by twelve equilateral pentagons. It corresponds to the universe because the zodiac has twelve signs corresponding to the twelve faces of the dodecahedron."

Hyper platonic solids
  • Todo: the process of higher-dimensional projection (and its movement visualization)

Metatron cube

Derived from the "Flower of Life") holds all the 5 Platonic solids. See also: [48]

(see previous)

(see previous)

Hyper Icosahedron

Research

Researchers

(todo)

Literature

Video

(todo)

Links

Various:

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