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Space Filling Curves

Hilbert Squares 
Orders 1 - 5

Space Filling Curves are 1-dimensional (line)

However, they fill the space of higher fractal dimensions

A Hilbert Square fills the space of a 2D regular square

A Hilbert Cube fills the space of a 3D regular cube​​​​

Optimal Cubic Memory Storage

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Order 1 Hilbert Cube

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Order 2 Hilbert Cube

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​​A Hilbert curve can represent linear time (1D time)

Think of every square in the grid, that the curve passes through as a still frame of time. Like a movie reel. Apply this concept to Conway's game of life & you can represent 2D life with 1D time. 

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This concept can also be applied to 3D life using a Hilbert Cube

THE ENTROPY SERPENT ENGULFING EXISTENCE

Omniscience is a space-filling fractal

Hilbert Radiation

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All forms of radiation follow the

Inverse Square Law: Energy twice as far from the source will spread over four times the area.

Hilbert curves have a direct correlation to radiation.

Each progression of the curve takes up four times the surface area and the origin travels twice as far away between each layer.

Hilbert Curve Towers (Not A Hilbert Cube*)

Towers are a series of curves stretched across a pyramid.

 Each frame of the movie is a Frustum (truncated pyramid) 

These "frustum frames" are pathway to map waveforms or particles over time.

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Bipyramids are radiation wave packets

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Check out the toroids article on the geometry page, to learn more about bipyramids/bicones and their relation to waves

5 toroidal moments of time on a line filled with bi-conical gaps 

Hilbert Discs​

Hilbert Cones

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Emptiness is Limitless Potential

Hilbert Discs

Begining & Ending

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OUTSIDE

INSIDE

OUTSIDE inside of INSIDE

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INSIDE is Infinitesimal for Higher Order Curves

BALANCE

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ORDER 3 HBC BICONE

ORDER 9 HBC BICONE

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ORDER 7 HBC BICONE

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ORDER 5 HBC BICONE

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Hilbert Rectangular Prisms

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Tiling a Rhombic Icosahedron With Hilbert Curves

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Diagonal section of menger cube is the Sierpinski Triangle

Sierpinski Triangle Curve

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Planting Branch-Fractals

More Space to fill here
ahahahaha

Entropy Serpent

A Serpent made of Darkness
Emerged from the void and
Swallowed Existence Whole
 
The serpents body weaved to fill space
Inside the serpent
Every moment of the universe
all of time

(Black represents the serpents body)

Free Download (click artwork)

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