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!