Tag Archives: H4

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!
outAI2

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.
AI 1-25

AI 26-50

AI 51-75

AI 76-100

AI 101-125

AI 126-150

AI 151-175

AI 176-200

AI 201-225

AI 226-250

AI 251-253

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).

outE80prot

DNAscreen

outDNA

outDNAprot

E8, H4, Quasi-Crystals, Penrose Tiling, Boerdijk-Coxeter Helices and an AMS blog post on the topic

This pic is an overlay of an image from Greg Egan on the AMS blog VisualInsight on top of one I created several years ago for the quasicrystal wikipedia page.

It uses my E8-H4 folding matrix to project E8 vertices to several interesting objects. The 5 dimensional 5-cube (Penteract) and the related 3D the Rhombic-Triacontahedron, as well as this 2D overlay on the Ho-Mg-Zn electron diffraction pattern.

Ho-Mg-Zn_E8-5Cube-baez-egan-overlay

E8 vertices projected to 2D pentagonal projection
E8-5Cube

5-cube in 3D
5-cube-2

6-cube edges projected to the Rhombic-Triacontahedron using 3 of 4 rows of my E8-H4 folding matrix.
6Cube-QuasiCrystal-low

Rhombic-Triacontahedron with inner edges removed
RhombicTricontahedron

The Boerdijk-Coxeter helix is also related to these structures through the Golden Ratio.

Edges on the outer ring of the E8 Petrie projection related to Boerdijk-Coxeter helix.
helix2Db

Same as above in 3D with the tetrahedral cell faces and 3D vertex shape-color-size based on quantum particle parameters from a theoretical physics model.
cells6004b

Same as above also showing the inner E8 ring Boerdijk-Coxeter helix.
inner-outerP
Platonic solids
E8-3D-Platonic-2

Analyzing individual Fermi 4 particle "cell interactions" in 3D on Boerdijk–Coxeter helix rings

cell-interaction

inner-outerP

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

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

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