Just got my second in a series of 3 demonstrations published on Wolfram http://demonstrations.wolfram.com/ParticleGeneratorBasedOnTheE8LieAlgebra/
Just got my second in a series of 3 demonstrations published on Wolfram http://demonstrations.wolfram.com/ParticleGeneratorBasedOnTheE8LieAlgebra/
This free Mathematica Computable Document Format (.CDF) demonstration takes you on an integrated visual journey from the abstract elements of geometry, algebra, particle and nuclear physics, and on to the atomic elements of chemistry. http://theoryofeverything.org/TOE/JGM/ToE_Demonstration.cdf (0.5Mb)
It requires the free Mathematica CDF plugin.
This is an image of the electron diffraction pattern of an icosahedral Zn-Mg-Ho quasicrystal with an overlay of a 5-Cube projection from the 240 vertices of the split real even E8 Lie Group.
The basis vectors for the E8 projection are shown (1:1 with the ring of gray vertices with the last 3 of 8 dimensions 0).
There are 2480 overlapping edge lines from the 240 E8 vertices. They have norm’d unit length calculated from the 5 non-zero projected dimensions of E8. Of these, 32 inner vertices and 80 edges belong to the 5D 5-Cube (Penteract) proper. Edges are shown with colors assigned based on origin vertex distance from the outer perimeter.
The vertex colors of the 5-Cube projection represent E8 vertex overlaps. These are:
InView vertices={color{overlap,count},…}Total
{LightGreen{1,20},Pink{5,20},Gray{10,10},Orange{20,1}}51
All vertices={color{overlap,count},…}Total
{LightGreen{1,20},Pink{5,100},Gray{10,100},Orange{20,20}}240
A related projection of a 6D 6-Cube (Hexeract) into a perspective 3D object using the Golden Ratio [Phi]. This particular projection is used to understand the structure of QuasiCrystals. The specific basis vectors are:
x = {1, [Phi], 0, -1, [Phi], 0}
y = {[Phi], 0, 1, [Phi], 0, -1}
z = {0, 1, [Phi], 0, -1, [Phi]}
There are 64 vertices and 192 unit length edges forming pentagonal symmetry along specific axis (as well as hexagonal symmetries on other axis).
An emulation (w/particle labels) of an E8 embedding from Lisi’s Dec. 2010 Scientific American article. There are 2 rings of 12 groups of 8 fermions (with 2 overlapping in the center) and 4 rings of 12 bosons.
Another article in SciAm
I created an emulation of the article pic (bottom)
and added a well known Lisi projection (middle),
and one of my own clearly showing 2 rings of 12 groups of 8 Fermions and 4 Boson rings of 12 :
I finally made it into a notable publication (or at least my image has 😉
Sep. 2010 Scientific American Article “Rummaging for a Final Theory”