It now has 3D clipping (and slicing) plane control sliders on the the left side controls within a new multiplexed slider control. I also added the 2D I-Ching and 2D/3D Sanskrit Sri Yantra visualizations.
Category Archives: Physics
Pascal Triangle and Mod 2-9 Sierpinski Maps
I decided to take a quick dive into an interesting idea from Peter Williams related to how the modulus of binomial numbers are related to the Pascal Triangle. I’ve added this to the VisibLie_E8 viewer as well.
Here is a screenshot:
Here is the code I wrote to produce the output below:
Mod 9:
Mod 8:
Mod 7:
Mod 6:
Mod 5:
Mod 4:
Mod 3:
Mod 2:
New features and options – Lite version, MIDI Music, Hebrew/English Nearest Word Gematria
I created a “Lite” version (4-10 Mb) of the VisibLie_E8 CDF/NB/Intereactive application, so now you can interact with the main E8 and particle physics panes w/o loading the full 100 Mb version (which contains multiple versions of parametric spherical harmonics for atoms, Molecule/DNA protein data, 4 gematria word value indexed Hebrew/Greek Bibles, solar system and Universe simulation dynamics, etc.)
I added some demonstration capability to the Chords (Beauty of Math/Music) pane. It now has full instrumentation for creating MIDI tones along with the various tones in available chords.
I added a cool Nearest Word Graph to the Gematria pane. This uses the Wolfram curated LanguageData / DictionaryLookup to find Hebrew and English words that are close in spelling (no Greek available yet)-:
I also added a more extensive cross index of common (or “interesting”) words found in the Hebrew/Greek Bibles used in the Gematria pane. These are:
More 3D Conway’s Game of Life videos and pics
Universal Time’s Arrow as a Broken Symmetry of an 8D Crystallographic E8 folding to self dual H4+H4φ 4D QuasiCrystal spacetime
Animations of Wolfram’s Cellular Automaton rule 224 in a 3D version of Conway’s Game of Life.
While this does not yet incorporate the E8 folding to 4D H4+H4φ construct, the notion of applying it, as the title suggests, to a fundamental particle physics simulation of a “Quantum Computational Universe” or an emergent (non)crystallographic genetic DNA (aka. Life) is an interesting thought…
Watch a few notional movies, some in left-right stereo 3D. Best viewed in HD mode.
More to come, soon!
These are snapshots of all the different initial conditions on the rule 224. Each set of 25 has a different object style and/or color gradient selection.
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
Music related
Gematria
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
Adding sociology and psychology panes to VisibLie_E8 MyToE Demonstration
These are more personal interest than hard math/science as the other panes – but they are, IMO, interesting asides.
The 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 psychology pane deals with the idea of the mathematical beauty of music.
The list of 18 panes is now:
1) Math:____ Chaos/Fibr/Fractal/Surface: Navier Stokes/Hopf/MandelBulb/Klein
2) Math:____ Number Theory:_________ Mod 2-9 Pascal and Sierpinski Triangle
3) Math:____ Geometric Calculus:______ Octonion Fano Plane-Cubic Visualize
4) Math:____ Group Theory:__________ Dynkin Diagram Algebra Create
5) Math:____ Representation Theory:___ E8 Lie Algebra Subgroups Visualize
6) Physics:__ Quantum Elements:______ Fundamental Quantum Element Select
7) Physics:__ Particle Theory:_________ CKM(q)-PMNS(ν) Mix CPT Unitarity
8) Physics:__ Hadronic Elements:______ Composite Quark-Gluon Select Decays
9) Physics:__ Relativistic Cosmology:___ N-Body Bohmian GR-QM Simulation
10) Chemistry: Atomic Elements:_______ 4D Periodic Table Element Select
11) Chemistry:Molecular Crystallography: 4D Molecule Visualization Select
12) Biology:_ Genetic Crystallography:___ 4D Protein/DNA/RNA E8-H4 Folding
13) Biology:_ Human Neurology:________ OrchOR Quantum Consciousness
14) Psychology:Music Theory & Cognition: Chords, Lambdoma, H4, and Tori
15) Sociology: Theological Number Theory: Ancient Sacred Text Gematria
16) CompSci: Quantum Computing:______ Poincare-Bloch Sphere /Qubit Fourier
17) CompSci: Artificial Intelligence:_______ nD Conway’s Game Of Life
18) CompSci: Human/Machine Interfaces:_ nD Human Machine Interface
A 3D projection of E8 (binary coordinates) to Pascal triangle related columns
This uses “binary” vertices of E8 (all 0’s or 1’s) from the Pascal triangle / Clifford algebra construction.
Notice the 8 excluded “generator” vertices are the axis 1-8, which show the projection orientation {X,Y,Z} vectorx. These sometimes are added to the 240 vertex “dimension count” of E8. There are a number of overlaps in the vertices in some columns, which are indicated by the color of the vertex.
Just for good measure, here is a 2D 16×16 matrix projection of the same “binary” E8 vertices. It shows the particle physics label with the E8 vertex number.
E8 Particle Assignment Triality Symmetries
E8 Particle Assignment Triality Symmetry
An .html version of a .ppt (or .pps or .pdf) that explains the detail of the particle assignment symmetries contained in MyToE.
A complete algorithmically assigned particle list is here.
Playing around visualizing non-crystallographic DNA/RNA
I’ve got interaction between the DNA/RNA protein visualizations (e.g. “1F8V- PARIACOTO VIRUS REVEALS A DODECAHEDRAL CAGE OF DUPLEX RNA) with the VisibLie_E8 projections of crystallographic E8 to non-crystallographic H4 (and to dodecahedral H3 in 3 dimensions, of course).
These pics are a simple (naive) merge of the D6 projected using the E8 to H4 folding matrix and the Protein DB at http://www.rcsb.org/ for 1F8V).
