The Padovan sequence links into the Trinity and Base 3 as we have shown in previous posts and in this post we will be going deeper into the Padovan sequence and how it is related to the Fibonacci spiral forming dimensions.
Padovan sequence, Trinity and Base 3
The Padovan sequence is formed out of the trinity 111 and the trinity relates to base 3 and base 3 is formed out of the quantum state of binary and the quantum state can form infinity.
The Padovan sequence and base 3(Binet-like formula)
Triangles with sides in ratio of 1/ρ form a closed spiral
The Padovan sequence numbers can be written in terms of powers of the roots of the equation (x^3)-x-1=0. This equation has 3 roots; one real root p (known as the plastic number) and two complex conjugate roots q and r. Given these three roots, the Padovan sequence can be expressed by a formula involving p, q and r:
P(n)=(ap^n)+(bp^n)+(cr^n)
where a, b and c are constants.
Since the magnitudes of the complex roots q and r are both less than 1 (and hence p is a Pisot–Vijayaraghavan number), the powers of these roots approach 0 for large n, and (P(n))-(ap^n) tends to zero.
For all n>0, P(n) is the integer closest to (p^(n-1))/s, where s = p/a = 1.0453567932525329623... is the only real root of s3 − 2s2 + 23s − 23 = 0. The ratio of successive terms in the Padovan sequence approaches p, which has a value of approximately 1.324718. This constant bears the same relationship to the Padovan sequence and the Perrin sequence as the golden ratio does to the Fibonacci sequence.
Sierpinski triangle, Base 3 and Membrane
The Padovan sequence forms triangles which form the vibrational dimensions because it forms the Fibonacci spiral out of triangles and the spiral forms the Kathara grid which is encoded in another triangular pattern called Pascal's triangle which we have talked about before and a bigger Kathara grid corresponds to a bigger Pascal's triangle and a bigger one means the membrane is more folded and the starting point of the folding is in the 12th dimension and it unfolds to form the lower dimensions(The membrane encases the Zero-point field/God Source).
1.58 is the dimension of Sierpinski triangle. "Arrowhead construction of the Sierpinski gasket" is basically forming a folding like fractal which forms Sierpinski triangle and this is the fractal shape of the membrane and as we know Sierpinski triangle is formed out of Pascal's triangle which shows a connection between the membrane and Pascals triangle and as we know Pascal's triangle is formed out of the zero-point field.
- e^0.5671432904097838729999686622≈1.75(Ω Constant)
- 1.58/0.5671432904097838729999686622≈2.7
- 2.7=e
Sierpinski triangle base 3 can be formed out of Pascal's triangle mod 3 and the dimension of the Sierpinski triangle is 1.5
e which is 2.7 forms the vibrational dimensions. As shown in a previous post the Sierpinski triangle and Cubistic matrix fractal are related to each other and the Cubistic matrix is the structure of(and encases) the zero-point energy and the Cubistic matrix starts of with 27(2.7) cubes because it is base 3. The Cubistic matrix is formed out of the star tetrahedron which can be formed out of 2 of these membranes merged into one and as we know these membranes fractal, fold more and lots more of them merge into one in higher dimensions.
The Cubistic matrix and the Padovan sequence form the Cuboid spiral which we will talk about next.
Cuboid spiral
A spiral can be formed based on connecting the corners of a set of 3-dimensional cuboids. This is the Padovan cuboid spiral. Successive sides of this spiral have lengths that are the Padovan sequence numbers multiplied by the square root of 2.
In mathematics the Padovan cuboid spiral is the spiral created by joining the diagonals of faces of successive cuboids added to a unit cube. The cuboids are added sequentially so that the resulting cuboid has dimensions that are successive Padovan numbers.
The first cuboid is 1x1x1. The second is formed by adding to this a 1x1x1 cuboid to form a 1x1x2 cuboid. To this is added a 1x1x2 cuboid to form a 1x2x2 cuboid. This pattern continues, forming in succession a 2x2x3 cuboid, a 2x3x4 cuboid etc. Joining the diagonals of the exposed end of each new added cuboid creates a spiral. The points on this spiral all lie in the same plane.
The cuboids are added in a sequence that adds to the face in the positive y direction, then the positive x direction, then the positive z direction. This is followed by cuboids added in the negative y, negative x and negative z directions. Each new cuboid added has a length and width that matches the length and width of the face being added to. The height of the nth added cuboid is the nth Padovan number.
Connecting alternate points where the spiral bends creates a series of triangles, where each triangle has two sides that are successive Padovan numbers and that has an obtuse angle of 120 degrees between these two sides.
The Golden root of 432 and the number 168
The Golden root of 432
Before we talk about the golden root(phi root) of 432 lets talk about 432.
432 already has connections to phi because it has connections to sacred geometry as shown in many other posts and in some pages on this wiki and it has connections to vortex maths since its equal to nine. 432 forms what I would like to call the Golden rays because it forms a wheel shape which forms the infinite fractal fruit of life which forms the vibrational dimensions and the Golden rays form the star tetrahedron which is formed out of two Fibonacci(phi) spirals.
- Golden root of 432=33.6
33.6 also shows up when you look into other sacred numbers which we will go into in a bit but first lets look at 1133's connection since 432 forms the 4 octaves which form the tetrahedron grid fractal which is encoded in the infinite fractal fruit of life and 1133 forms the 64 tetrahedron grid and other sacred geometries related to it so how are 33.6 and 1133 related? Well, we showed this ages ago:
- √1133=33.6
So lets move onto 33.6 and the sacred numbers related to it.
168
33.6 is related to 336 and 336 is encoded in sacred geometries related to and encoded in superstrings(E8) and half of 336 is 168 which is very important because it is strongly related to superstrings and is the number that is the bases to Stephen M. Phillips work which is merging Kabbalah and string theory and 168 is strongly related to 3, 6 and 9 relating it to vortex maths and it is related to the numbers 7 and 8 relating it to the 64 tetrahedron grid and relating it to the many sacred geometries related to 7.
Some other interesting connections related to 168 are Robert Grant's constant which is 1.68 sowing that 168 is encoded in geometries which Robert Grant has discovered.
Padovan Fibonacci spiral, Dimensions, Kathara grid and E8 Cubistic matrix
Within the Fibonacci sequence when forming it out of circles it forms a doubling sequence since some numbers have to repeat and this doubling sequence could be the reason as to why the Fibonacci spiral forms a doubling sequence which forms a triangle(Which forms numbers equal to 3, 6 and 9) and it could also be the reason as to why it forms the doubling sequence which forms the Kathara grid and as we know this forms the vibrational dimensions. We have to double the triangle to form the star tetrahedron which encodes all vibrational dimensions and we have to double the star tetrahedron and when we do we form the fruit of life/Metatrons cube/64 tetrahedron grid.
The Kathara grid is formed out of and forms the star tetrahedron(Each triangle formed out of a Fibonacci spiral) and the star tetrahedron can be formed out of the Fibonacci spiral. Why does the Fibonacci spiral form the triangle? The Padovan sequence is the reason why because the Padovan sequence forms triangles which encodes the Fibonacci spiral and the Padovan sequence is formed out of the Trinity.
The 10 spacetime dimension/12 vibrational dimension tree of life is formed out of the vesica pices(Which can be expanded to form the flower of life/cubistic matrix) and as we know the vesica pices which forms the doubling sequence also forms the vibrational dimensions when it fractals(The more vesica pices in the vesica pices the more dimensions it forms this could link into how dimensions are encoded in higher dimensional shapes) and since we doubled the triangle to form the star tetrahedron we can double the vesica pices this means we have doubled the circles which forms the prime number cross and this doubles the Kathara grid(forming the cubistic matrix) so all vibrational dimensions are encoded in this geometry.
Since the double vesica pices forms 2 Kathara grids i thought what if i overlayed 6 kathara grids to form 12 circles and to form something like the cosmic tree of life and i overlayed it over the double star tetrahedron(Because i wanted to create a 64 tetrahedron grid out of Kathara grids) since they both repersent the 12 vibrational dimensions and when i did i noticed something very interesting because 6×12=72 so there are 72 spheres/sephirot and the Kathara grid has 28 pathways so 6×28=168 so overall there are 168 pathways and there are 72+168(240) roots of the E8 lie group(8 Dimensional 64 tetrahedron grid)
There are actually 49 spheres/sephirot and 49=7:7=19:91 and this shows another connection between this geometry and the 64 tetrahedron grid because the 64 tetrahedron grid when each tetrahedron is encased in a sphere to form a 3D flower of life(Cubistic matrix) has 84 vesica pices and the cosmic tetractys is made up of 84 points and the cosmic tetractys corresponds to(is the) cosmic tree of life which is made up of 91 tree of life's.
As you can see in the magnet diagram there are 28 sephirot(28 magnets) making up a tree of life and one Kathara grid corresponds to 13 of the magnets and as you can see i was able to overlay 3 Kathara grids(Trinity) over the magnets(Which formed 27 sephirot) and there are therefor 84 pathways(28 for each Kathara grid) so this shows an interesting connection between 12, 13, 15, 28, 45 and 84 and when we double this to form the diagram i made above we get 56 which as we have seen(creates the 19:91 correspondence) corresponds to the 64 tetrahedron grid.
As shown in 120-cell and Cubistic matrix the Cubistic matrix can be turned into the 120-cell which is interesting because the 120-cell can be derived from the E8 lie group.
Tetractys, Frequencies and E8 Cubistic matrix
Frequencies between 12 and 19 in a triangulart medium form the tetractys now lets work out the average:
- 12+19=31
- 31/2=15.5
This shows a new connection between the 10 spacetime dimensions, 12 vibrational dimensions and pascals triangle tetractys which as we know forms the doubling sequence also pascals triangle tetractys is equal to 15 so this shows another connection also the doubling sequence shows up when you double the fraction:
- 31/2
- 62/4
- 124/8
- 248/16
The number 248 is related to the E8 lie group and the 13, 31 correspondence is the last line of pascals triangle tetractys which is equal to 8 which relates it to the 8th dimension and E8 is an 8 dimensional structure so this shows a correspondence between 31 and E8 also the 19:91 correspondence is related to the 64 tetrahedron grid which is the E8 lie group.
The tetractys when formed in this traingular medium through frequencies looks like it is made out of toruses and the torus is formed out of the double seed of life which encodes the Kathara grid also the E8 lie group is a torus. The torus/sphere encases the cube and corresponds to the cube so every cube in the Cubistic matrix can be a torus/sphere. The spheres are the spheres of the Kathara grid. The tree of life in Kabbalah can actually be extended to have 12 or 13 sephirot.