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The gravitational orbit of any moon, planet, star or galaxy forms a helix, when you view it traveling through a time dimension. A 3-dimensional helix is a ‘slice’ of the 4-dimensional shape of the orbit of a planet; X is a time dimension, Y and Z are space dimensions. One 2D slice of a 3D helix is a circle, another is a wave. One 3D slice of a 4D helix is a sphere; a planet in a specific moment of time.
Interesting patterns are revealed when you start thinking about the 4-dimensional shapes of objects through time. One example I enjoy is the fractal nature of gravitational orbits. Consider the 4D shape of the orbit of the Moon around the Earth through time; a helix. The helix of the Moons orbit is ‘wrapped’ around the helical orbit of the Earth around the Sun. The helices of the Earth and Moon are further ‘wrapped’ around the orbit of the Sun around the center of our Galaxy. When Galaxies orbit each other another iteration is possible. Because gravity causes the same behavior at different physical scales, a fractal pattern is generated. Viewed from the ‘side’, with one space and one time dimension, orbits are fractal waves. Viewed from the ‘top’ (two space dimensions) they are fractal circles. A 3D slice in spacetime (XYZ) shows a helical fractal. The true 4D object is a fractal hyperhelix.
Another beautiful fractal in time is biology. Every time a cell divides it creates a bifurcation or a ‘branch’. The same thing happens whenever an organism reproduces, or at each speciation event. All life is part of the same 4-dimensional fractal tree, extending back in time to the moment of abiogenesis. When you consider your 4-dimensional shape it becomes clear that we are all part of the same fractal organism, wrapped on the spherical surface of a hyperhelix!
I have a difficult time explaining this concept, if you don’t understand it’s because I’m not doing a good enough job explaining. I can see it perfectly in my mind, and I wish I could create visuals to show exactly what I mean. If there are any visual artists (paper or CG) who understand and would like to help spread this concept, please contact me. The same goes for any mathematicians who can clarify this!
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Fractals have always (consciously or otherwise) been an innate part of design (seriously – they’re found everywhere in nature).
In Fabergé Fractals by Tom Beddard, the artist used WebGL 3D Fractal Creator to create a vibrant fractal that, no matter how many different ways you slice it, offers an interesting new architecture every time.
See more of Tom Beddard’s fractal-inspired digital art on Subblue.com.
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DIY Model Kit - Star Orb Dodecahedron - Sacred Geometry
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Working on this one right now!!!

The Flower of Life and the 64 Tetrahedron grid: the mother and father of the geometry of the fabric space… The flower of life is shown in “2D” in this image and is actually a “3D” structure like the 64 tetrahedron grid above it: 64 tetrahedrons with a sphere around each tetrahedron, creating a perfectly space-filling 3D flower of life lattice. This same pattern continues inward and outward, both bigger and smaller toward infinity. It is the theorized underlying geometric structure of everything in the entire universe… The Resonance Project - https://www.facebook.com/TheResonanceProject
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