Tag Archives: 2D

7 Perfect Sri Yantras in 2D and 3D

Based on an excellent 1998 paper by C.S. Rao I’ve modeled the Sri Yantra in Mathematica and incorporated it into the VisibLie_E8 demonstrations (I will upload that soon).

This is a reference figure to verify the model is correct for concurrency (intersecting lines) and concentricity (inner triangles and Bindu point are centered). There are 4 of 18 other constraints used in the diagrams below numerically and/or symbolically solved within the Mathematica code.

SriYantra-Refernce

Here are 7 of many possible solutions using the 20 constraint rules to produce optimal spherical and plane forms of the Sri Yantra.

Solution 1: Solving constraints (* 1,2,3,4,8 *)
SriYantra1

Solution 2: Solving constraints (* 1,2,3,10,15 *)
SriYantra2

Solution 3: Solving constraints(* 1,2,4,5,10 *)
SriYantra3

Solution 4: Solving constraints (* 1,2,5,6,19 *)
SriYantra4

Solution 5: Solving constraints (* 1,2,6,14,19 *)
SriYantra5

Solution 6: Solving constraints (* 1,2,8,9,20 *)
SriYantra6

Solution 7: Optimum planar
SriYantra7

3D using pyramids and new clipping and slicing functions to take off the front (and back) portions of the symmetric 3D object.
I will produce a version option with conical shapes just for fun (soon).
SriYantra3D1

This is a list of the details behind each constraint function Fn
ConstraintFunctions

Ever wonder what the Bible's social network looks like?

These are 3D hyperbolic tree graphs of some major figures in the Bible. The Hebrew, Greek transliterations for the first verse where they show up are also shown. Mouseover shows the names between the links and the number of times they occur (which changes the thickness of the link).

Another cool new feature I just added is a word translation when you mouse over any word. Clicking on the word or name in the graph changes the statistics to that word.

God
outGematria-god

Jehovah
outGematria-jehovah

Lord
outGematria-lord

Adam
outGematria-adam

Eve
outGematria-eve

Jeshua
outGematria-jeshua

Noah
outGematria-noah

Abraham
outGematria-abraham

Moses
outGematria-moses

Jesus
outGematria-jesus

Gabriel
outGematria-gabriel

Michael
outGematria-michael

Satan
outGematria-satan

Mathematical Navigation of Ancient Sacred Texts

I’ve added some new features in the #15 pane (Gematria). This sociology pane deals with the idea of Old Testament Hebrew and New Testament Koine Greek Gematria. The histogram shows the distribution of words used in the Bible according to their gematria value in Hebrew or Greek. It also presents a clickable 3D hyperbolic tree (graph) of proper names related within verses, as well as a clickable “nearest word” graph. Each word in each book, chapter, verse are select-able by slider or clickable (as are the list of words with the same gematria values).

This combination of UI creates a powerful new way to navigate the bible. Each word in the verse is colored by their value in Hebrew (if Old Testament), Greek and English. It makes use of Wolfram’s curated LanguageData/DictionaryLookup to get a Nearest Word Graph in Hebrew and English. Note: Hebrew is properly presented from right to left.

outGematria-new1

I also decided to attempt to develop visualizations related to the alignment of sociological, theological ancient world history using the recorded sacred texts created at the start of the Bronze age. The time line runs between 4000 BCE and 100 CE and the geopolitical map centers on the cradle of civilization Sumerian (Tigris/Euphrates), and extends from the Egyptian (Nile) to China’s (Yellow), and including Indian (Indus) and Persian cultures.

The list of sacred texts aligned by creation, flood and patriarch figures (e.g. Adam, Eve, Noah, Abraham) and primary deity (e.g. Elohim) were:
1. Egyptian Book Of The Dead
2. Babylonian/Sumerian Kings List/Epic of Gilgamesh/Enuma Elish
3. Hebrew(OT)-Greek(NT) Bible
4. Chinese I Ching
5. Indian Rig Veda
6. Greek Homeric Poems (Illiad/Odyssey)
7. Persian Avesta

SacredTextInfo

Given the amazing advancement of modern science in tracing the genetic lineage of human history along with radioactive dating techniques, it is untenable to interpret these sources literally with any precision. Yet, by understanding their “world view” at the time along with consistently applied “poetic license” across all the texts (e.g. Homer), one can come up with interesting theories for the veracity of their original intentions to document sociologic human history!

For example, it is interesting to note the alignment between the 10 AntiDiluvian (pre-flood) kings in both the Sumerian Kings List and the first 10 patriarchs (starting with Adam) in the Pentateuch. Both have unusually long life-times. When the extremely large (and in most cases rounded) ages of each person are reduced by factors based on the counting system in use (e.g. Sexagesimal (base 60) 10*60^2) for Sumeria and decimal 10^2 or 10^3), the reigns of kings and lifetimes of lineage align as follows:

Genesis2Flood1

See:
Antediluvian Patriarchs and the Sumerian King List
Reinvestigating the Sumerian Kings List

For a modern genetic species analysis visualization, see:
http://www.timetree.org/book.php

timetree_poster_final

See this Dymaxion Map of genetic analysis of human migration from Wikipedia Commons:
Map-of-human-migrations

Here is an old artistic map of World History from HistoMap http://www.davidrumsey.com/. It is largely Biblical in its antidiluvian history. While it is not based on modern scientific evidence, it is an interesting mash-up of information from various sources. A more detailed map (horizontal) is here (right-click the image to download and save-as the 20MB PNG file):
HistoMap

Here is another vertical version from the same website:
histomap1

and another histomap (linear and logarithmic) of the Earth’s Geologic/Evolutionary History (right-click/save-as for a 12MB version):
Evolution

Fun with Conway's "Game of Life" in 3D -> nD and Music

I’ve integrated a few more demonstrations, see below for descriptions and pics..

Conway’s “Game of Life” in 3D -> nD
outAI5

outAI3

outAI2
Music related
outChords2D

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Gematria
Gematria-snap

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outGematria3

The #13 pane (Chords) will address the psychology of the mathematical beauty of music. The 2D pane presents Emmanuel Amiot and Fernand Brunschwig’s  Pythagorean Meantone And Equal Temperament Musical Scales, while the 3D pane shows Drew Lesso’s 3D Lambdoma matrix.

The #14 pane (Gematria) will address Theological Number Theory in the form of Hebrew gematria, H4, and Tori. This sociology pane deals with the idea of Old Testament Hebrew and New Testament Koine Greek Gematria. The histogram shows the distribution of words used in the Bible according to their gematria value in Hebrew or Greek. Each word in each verse is selectable and shown in the distribution. Each word in the verse is colored by their value in Hebrew (if Old Testament), Greek and English.
Note: Hebrew is properly presented from right to left.

The #15 pane (QC) will address Quantum Computing in the context of MyToE. It uses several demonstrations… Qubits On The Poincare-Bloch Sphere,  Quantum Logic Gates Roots Exponents And Eigensystems and Quantum Fourier Transform Circuit by Rudolf Muradian

The #16 pane (AI) will address Artificial Intelligence, an nD version of Conway’s “Game of Life” and Cellular Automata in the context of MyToE. It is an integration of Daniel de Souza Carvalho’s demonstration

outAI2

Boerdijk–Coxeter helix

The Boerdijk–Coxeter helix is a 4D helix (of 3D tetrahedral cells) that makes up the vertices on 4 of the concentric rings of E8 Petrie projection (or the H4 and H4φ rings of the 2 600 cells in E8).

Outer (Ring 4) of H4 in 2D with non-physics vertices of all 8 rings of E8 in the background

helix2Db

inner-outerP

Outer (Ring 4) of H4 in 3D with physics vertices

cells6004b

Ring 3 of H4 in 3D with physics vertices

cells6003b

Ring 2 of H4 in 3D with physics vertices

cells6002b

Inner (Ring 1) of H4φ in 3D with physics vertices

cells6001a

Combined 4 rings of H4 in 3D with physics vertices

cells6001234-small

Outer (Ring 4) of H4φ in 3D with physics vertices
cells6004phib

Ring 3 of H4φ in 3D with physics vertices

cells6003phib

Ring 2 of H4φ in 3D with physics vertices

cells6002phib

Inner (Ring 1) of H4φ in 3D with physics vertices

cells6001phib

Combined 4 rings of H4φ in 3D with physics vertices

cells6001234phi-small

Combined 8 rings in 3D with physics vertices

cells6001234-phi-small

E8's 10 24-cells (H4 and H4φ) made up from 10 8-cell Tesseracts and their dual 16-cell 4-Orthoplexes

I decided to visualize my decomposition of the 10 self-dual 24-cells of E8. These are shown in the Petrie projection of E8 that is split into H4 and H4φ using my E8 to H4 folding matrix. The interesting aspect of this is that the selection of the canonical H4 24-cell determines the other 4 24-cells that make up the 96 vertices of the H4 snub-24-cell by rotating 4 times by π/5. Scaling the vertices by φ on the Petrie projection give the other 5 24-cell+snub-24-cell vertices.

It is also interesting to note that (my modified) Lisi physics particle assignments (with particle/anti-particle pairing) create 30 nicely ordered 4-particle/anti-particle sets that (fairly consistently) distribute over type, spin, generation, and color. These are visualized in 3D with shape, size and color defined by the quantum numbers of the assigned particle. The 3D projection is the same as that of the Petrie with a 3rd Z vector added. For more detail, see my latest paper.

The last set of images (using only the “math version” round black vertices and numeric identifier from the position in the Pascal triangle/Clifford Algebra canonical lexicographic ordering) are the 2D rotations of 24-cells around face-3 of this projection (which turns out to be the orthonormal shape of the H4 600 cells).

snub-pics

out_H4Φ_4_80

out_H4Φ_0_80

out_H4_4_80

out_H4_0_80

out_H4Φ_2_160

out_H4Φ_0_160

out_H4_2_160

out_H4_0_160

out_H4Φ_0_240

out_H4_0_240

out_H4Φ_4_240

out_H4Φ_1_240

out_H4Φ_0_240

out_H4Φ_2_160

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out_H4_4_160

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out_H4Φ_3_80

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