File:Tesseract.ogv

Summary[edit]

Detail Description:
It has 6 sets of rotations of 90 frames each. All of these rotate in steps through ${\displaystyle \theta =i2\pi /steps}$ on the horizontal (H) projection vector. The 6 sets of H,V,Z projection basis vectors are: ${\displaystyle ((\theta ,0,0),(\theta ,\theta ,0),(\theta ,{\frac {1}{2}},{\frac {1}{2}}),(\theta ,0,{\frac {3\pi }{4}}),(\theta ,{\frac {\pi }{2}},{\frac {\pi }{4}}),(\theta ,{\frac {\theta }{2}},{\frac {\theta }{4}}))}$.

4D perspective projection is accomplished by dividing x,y,z vertex dimensions by w+1 after 4D rotation (but before projection to 3D).
This is constructed from VisibLie_E8 found on TheoryOfEverything.org archive copy at the Wayback Machine with the following settings:
(* This is an auto generated list from e8Flyer.nb *)
new := {
scale = 0.1;
limitToRange = False;
cylR = 0.022;
favorite = 9;
showAxes = False;
showEdges = True;
eGrad = 0;
edgeVal = {1, 32};
edgeDimTrim = 4;
perspective = False;
nDcamera = 1;
range := nDcamera;
xyVwPnt = {0, 1};
zVwPnt = 1;
steps = 10;
pListName = "C4=4Cube";
p3D = " 3D";new;

Additional scripting within e8Flyer.nb to generate movie frames is also used.

Licensing[edit]

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