Projected from E8 to 6-Cube and then to Rhombic Triacontahedron using 3 of 4 rows of the E8-to-H4 folding matrix.
and a Tesseract for good measure…
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!
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.
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).
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.
E8 vertices projected to 2D pentagonal projection
5-cube in 3D
6-cube edges projected to the Rhombic-Triacontahedron using 3 of 4 rows of my E8-H4 folding matrix.
Rhombic-Triacontahedron with inner edges removed
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.
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.
Same as above also showing the inner E8 ring Boerdijk-Coxeter helix.
Platonic solids
Analyzing individual Fermi 4 particle "cell interactions" in 3D on Boerdijk–Coxeter helix rings
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
Outer (Ring 4) of H4 in 3D with physics vertices
Ring 3 of H4 in 3D with physics vertices
Ring 2 of H4 in 3D with physics vertices
Inner (Ring 1) of H4φ in 3D with physics vertices
Combined 4 rings of H4 in 3D with physics vertices
Outer (Ring 4) of H4φ in 3D with physics vertices
Ring 3 of H4φ in 3D with physics vertices
Ring 2 of H4φ in 3D with physics vertices
Inner (Ring 1) of H4φ in 3D with physics vertices
Combined 4 rings of H4φ in 3D with physics vertices
Combined 8 rings in 3D with physics vertices
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
Outer (Ring 4) of H4 in 3D with physics vertices
Ring 3 of H4 in 3D with physics vertices
Ring 2 of H4 in 3D with physics vertices
Inner (Ring 1) of H4φ in 3D with physics vertices
Combined 4 rings of H4 in 3D with physics vertices
Outer (Ring 4) of H4φ in 3D with physics vertices
Ring 3 of H4φ in 3D with physics vertices
Ring 2 of H4φ in 3D with physics vertices
Inner (Ring 1) of H4φ in 3D with physics vertices
Combined 4 rings of H4φ in 3D with physics vertices
Combined 8 rings in 3D with physics vertices