911:Geometry

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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, neutral-center, out)
    • Sympathetic vibrations <-> Resonance (todo: "law of octaves" observations in various energy-mass 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), non-optical 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]

  • Frequency (speed), amplitude (force) and phase (cycle start/end pattern) [3]

  • "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

  • 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
        • S-wave:
          • "The S-wave, secondary wave, or shear wave, sometimes called an elastic S-wave, 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 S-wave moves as a shear or transverse wave, so motion is perpendicular to the direction of wave propagation: S-waves, like waves in a rope, as opposed to waves moving through a slinky, the P-wave."
        • P-wave:
          • "P-waves 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. P-waves can be produced by earthquakes and recorded by seismometers. The name P-wave stands for primary wave, as the P-wave is the fastest among the elastic waves, compared to the S-waves. In isotropic and homogeneous solids, the polarization of a P-wave 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 P-waves and S-waves, 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"

Wave phenomena


Music theory

Self-organizing systems

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."

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."


Natural shapes:

  • Water drop

  • Redwood tree rings


Synthetic shapes:

  • [7]

  • Picture of tortoise beside cymatic sound pictures at 1021 Hz, 2041 Hz, 1088 Hz and 1085 Hz. [8]

  • AMOEBA water writing device [9]


Magnetohydrodynamics shapes:

  • 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.

Crystallization

Fractals

  • Structure of a leaf [10]

Cellular automata

Information concepts

  • Modes and attributes:

Mathematics

High-level divisions of mathematics.

Truth

Quantity

Structure

Space

Change

Metamathematics

Applied mathematics

Geometry

Spirals

Natural spirals

Scientific spirals

  • Spiral periodic table [25]

    Note: "This arrangement of the elements focuses on the increasing atomic number in an ordered sequential fashion." ... "hydrogen is at the center and all elements radiate out from it." [26]

    See also: Languages: Electrochemical

  • "All direction is curved, all motion is spiral" by Walter Russell (1871–1963)

  • "Ten octaves of integrating light" by Walter Russell (1871–1963)

  • (see previous)

Cultural spirals

Abstractions

  • See: Energy

  • Bi-polar vortex2.jpg

  • 2D and 3D elips

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

  • Fibonacci spiral.jpg
  • Fibonacci spiral 2.jpg

  • Hopf fibration (or "Hopf map") describes a 3-sphere (a hypersphere in four-dimensional space) in terms of circles and an ordinary sphere. Discovered by Heinz Hopf in 1931. Hopf found a many-to-one continuous function (or "map") from the 3-sphere onto the 2-sphere such that each distinct point of the 2-sphere comes from a distinct circle of the 3-sphere. [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.

  • 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 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. [39]. See also: video's.

  • Riemann surface for the square root function.

  • Riemann surface for the cube root function.

  • 3d Fibonacci spiral.jpg

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 001c.jpg
  • Flower of Life 001.jpg

  • Seed of Life

  • Note the 2D representation of a cube.

  • 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 [40]

Natural analogies:

Tree of life

Earthly representations if the tree of life?

Polyhedron

Uniform polyhedron

Platonic solids

  • Platonic solids.jpg

  • 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." [42]

  • 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."

Metatron cube
  • Metatron.gif
  • Fruit-of-Life Platonic-Solids.jpg
  • Metatron cube.gif

Literature

Links

Various:

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