@Sinuhe Perea , the tutorial that you have produced is all using simple discrete lattice geometries. Those topological invariants that make the pseudo-particles, the skyrmions...the mobius strip.
sizes = Range[2, 7];
Grid[{
{"Increasing size of the quiver geometries ->"},
{"Linear (Z)",
Sequence @@ Table[LineQuiver[n, ImageSize -> 130], {n, sizes}]},
{"Cyclic/periodic (Zn)",
Sequence @@ Table[CycleQuiver[n], {n, sizes}]},
{"Triangular",
Sequence @@
Table[TriangularQuiver[n, ImageSize -> 85], {n, sizes}]},
{"Cubic",
Sequence @@ Table[CubicQuiver[n, ImageSize -> 150], {n, sizes}]},
{"Bundle E=BxF", TrivialBundleGraph[12, 4, ImageSize -> 300]},
{"Mobius strip", MobiusStrip[12]}},
Alignment -> Left
]
![Increasing Size, Quiver Geometries](https://community.wolfram.com//c/portal/getImageAttachment?filename=GridIncreasingSizeQuiverGeometries.png&userId=2553367)
Manipulate[{Length[
FindAllBundleSections[QuiverBundleGraph[bss, fbr]]], fbr^bss,
N[Length[FindAllBundleSections[QuiverBundleGraph[bss, fbr]]]/
fbr^bss, 4]},
Style["Possible/Total States, Ratio" Dynamic[bss] Dynamic[fbr], 10,
Bold], {{bss, 4, "n=Base size"}, 3, 10, 1,
ImageSize -> Tiny}, {{fbr, 3, "m=Fibre size"}, 2, 10, 1,
ImageSize -> Tiny}]
MatrixForm[
Table[N[Length[FindAllBundleSections[QuiverBundleGraph[i, j]]]/
j^i], {i, 2, 7}, {j, 2, 7}]]
@Sinuhe Perea QuiverBundleGraph produces such massive quantities that you could be an Ambassador of Wolfram. It's like how Spongebob broke the laws of physics.
![QuiverBundleGraph Manipulate](https://community.wolfram.com//c/portal/getImageAttachment?filename=ManipulateFindAllBundleSectionsQuiverGraph.png&userId=2553367)
![MatrixForm QuiverBundleGraph](https://community.wolfram.com//c/portal/getImageAttachment?filename=MatrixFormQuiverBundleGraph.png&userId=2553367)
QuiverBundleGraph, corresponds to the poetic interpretation of @Jonathan Gorard we saw his lambda calculus in C++, it was so good to see how even primes are odd.
Manipulate[Module[{hh, sky}, hh = \[Pi]/2*hel;
sky = Flatten[
Table[
{
{st Cos[\[Theta]] - Cos[\[Theta] + hh] Sin[-\[Pi] st]/20,
st Sin[\[Theta]] - Sin[\[Theta] + hh] Sin[-\[Pi] st]/20,
-Cos[-\[Pi] st]/20},
{st Cos[\[Theta]] + Cos[\[Theta] + hh] Sin[-\[Pi] st]/20,
st Sin[\[Theta]] + Sin[\[Theta] + hh] Sin[-\[Pi] st]/20,
+Cos[-\[Pi] st]/20}
},
{st, 0, 1, 0.05},
{\[Theta], 0, 2 \[Pi], 0.1}
], 1];
Show[
{
Graphics3D[{
RGBColor[1, 0.19, 0.59, 1],
Arrowheads[0.01],
Arrow[Tube[#, 0.001]
]} & /@ sky]
},
ImageSize -> 500,
Boxed -> False]
], Style["Domain wall transformation to skyrmion", 12, Bold],
{{hel, 0.01, "Character, 0=Neel, 1=Bloch"},
0, 1, 0.01, ControlPlacement -> Top}
]
![Domain Wall Transformation](https://community.wolfram.com//c/portal/getImageAttachment?filename=Domainwalltransformation.png&userId=2553367)
It's this physical-inspired system, the domain walls @Sinuhe Perea how is it elastic? There's a focus on quantum processes and not states. And looking back at the isomorphisms in the Ruliad they are smooth and continuous lovely treatment that you have produced, @Sinuhe Perea .