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This was an error, but looks interesting anyway.

https://plus.google.com/101799841244447089430/posts/Ru92jRS7uNo

#Fractal #Math #Art #Space

https://plus.google.com/101799841244447089430/posts/Ru92jRS7uNo

*_*#Fractal #Math #Art #Space

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Trying to fill it in a little more.

https://plus.google.com/101799841244447089430/posts/DVDKt8QnpKx

#Fractal #Math #Art #Space

https://plus.google.com/101799841244447089430/posts/DVDKt8QnpKx

*__*#Fractal #Math #Art #Space

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A 33 Metadisk group:

Group:

mu = -I/Sqrt[2];

a = N[{{1, 0}, {mu*N[Exp[I*2*Pi/3]], 1}}]

A = N[{{1, 0}, {mu*N[Exp[-I*2*Pi/3]], 1}}]

b = N[{{Sqrt[2] - I*Sqrt[2], Sqrt[3]}, {Sqrt[3], Sqrt[2] + I*Sqrt[2]}}]

B = Inverse[b];

Group:

mu = -I/Sqrt[2];

a = N[{{1, 0}, {mu*N[Exp[I*2*Pi/3]], 1}}]

A = N[{{1, 0}, {mu*N[Exp[-I*2*Pi/3]], 1}}]

b = N[{{Sqrt[2] - I*Sqrt[2], Sqrt[3]}, {Sqrt[3], Sqrt[2] + I*Sqrt[2]}}]

B = Inverse[b];

‹

›

11/13/18

3 Photos - View album

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3-ary tessellation.

https://plus.google.com/101799841244447089430/posts/P4mpJHW3T5F

#Fractal #Math #Art #Space

https://plus.google.com/101799841244447089430/posts/P4mpJHW3T5F

*__*#Fractal #Math #Art #Space

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Four views : one strange looking surface....

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A strange formation wrt a new hybrid version of an older fractal of mine.

#Fractal #Art #Math #Space #Iteration

*__*#Fractal #Art #Math #Space #Iteration

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Kleinian group hyperbolic 3 manifold projection onto 3d parametric coordinates ->33 metadisk:

(* Mathematica*)

Clear[x, y, z, t, p, a, b, A, B, f1a, f2a, f3a, f4a, w, z1]

(* hyperbolic cylinder parametric coordinates*)

x = Cos[t]

manifold*)

(

w = {0.` + (

1.` Cos[t] Cosh[

p])/((0.` + 0.35355339059327356` Cos[t] Cosh[p])^2 + (1.` +

0.6123724356957945` Cos[t] Cosh[p])^2) + (

0.6123724356957945` Cos[t]^2 Cosh[

p]^2)/((0.` + 0.35355339059327356` Cos[t] Cosh[p])^2 + (1.` +

0.6123724356957945` Cos[t] Cosh[p])^2) + (0.` - (

0.35355339059327356` Sinh[

p]^2)/((1.` - 0.6123724356957945` Sinh[p])^2 + (0.` +

0.35355339059327356` Sinh[p])^2)),

0.` + 2.4494897427831783`/(

2.0000000000000004` + (1.4142135623730951` +

1.7320508075688772` Cosh[p] Sin[t])^2) + (

2.9999999999999996` Cosh[p] Sin[t])/(

2.0000000000000004` + (1.4142135623730951` +

1.7320508075688772` Cosh[p] Sin[t])^2) + (

2.4494897427831783` Cosh[p]^2 Sin[t]^2)/(

2.0000000000000004` + (1.4142135623730951` +

1.7320508075688772` Cosh[p] Sin[t])^2) + (0.` - (

0.35355339059327356` Cos[t]^2 Cosh[

p]^2)/((0.` + 0.35355339059327356` Cos[t] Cosh[p])^2 + (1.` +

0.6123724356957945` Cos[t] Cosh[p])^2)),

0.` + (1.` Sinh[

p])/((1.` - 0.6123724356957945` Sinh[p])^2 + (0.` +

0.35355339059327356` Sinh[p])^2) - (

0.6123724356957945` Sinh[

p]^2)/((1.` - 0.6123724356957945` Sinh[p])^2 + (0.` +

0.35355339059327356` Sinh[p])^2) + (0.` - 2.4494897427831783`/(

2.0000000000000004` + (1.4142135623730951` +

1.7320508075688772` Cosh[p] Sin[t])^2) - (

4.000000000000001` Cosh[p] Sin[t])/(

2.0000000000000004` + (1.4142135623730951` +

1.7320508075688772` Cosh[p] Sin[t])^2) - (

2.4494897427831783` Cosh[p]^2 Sin[t]^2)/(

2.0000000000000004` + (1.4142135623730951` +

1.7320508075688772` Cosh[p] Sin[t])^2))}

g2 = ParametricPlot3D[w, {t, -Pi, Pi}, {p, -Pi^2, Pi^2},

ColorFunction -> "CMYKColors", PlotStyle -> Opacity[0.5], Mesh -> False,

Axes -> False, ImageSize -> 1000, Boxed -> False, PlotPoints -> 200,

PlotRange -> All]

Show[{g1, g2}, ViewPoint -> Top]

(

(* Mathematica*)

Clear[x, y, z, t, p, a, b, A, B, f1a, f2a, f3a, f4a, w, z1]

(* hyperbolic cylinder parametric coordinates*)

x = Cos[t]

**Cosh[p];****y = Sin[t]*Cosh[p];****z = Sinh[p];****g1 = ParametricPlot3D[{x, y, z}, {t, -Pi, Pi}, {p, -Pi, Pi},****ColorFunction -> "CMYKColors", Mesh -> False, Axes -> False,****ImageSize -> 1000, Boxed -> False, PlotPoints -> 60,****PlotStyle -> Opacity[0.5], ViewPoint -> {5, 5, 5}]****mu = -I/Sqrt[2];****a = N[{{1, 0}, {mu*N[Exp[I*2*Pi/3]], 1}}]****A = N[{{1, 0}, {mu*N[Exp[-I*2*Pi/3]], 1}}]****b = N[{{Sqrt[2] - I*Sqrt[2], Sqrt[3]}, {Sqrt[3], Sqrt[2] + I*Sqrt[2]}}]****B = Inverse[b];****f1a[z1_] = (a[[1, 1]]*z1 + a[[1, 2]])/(a[[2, 1]]*z1 + a[[2, 2]]);****f2a[z1_] = (b[[1, 1]]*z1 + b[[1, 2]])/(b[[2, 1]]*z1 + b[[2, 2]]);****f3a[z1_] = (A[[1, 1]]*z1 + A[[1, 2]])/(A[[2, 1]]*z1 + A[[2, 2]]);****f4a[z1_] = (B[[1, 1]]*z1 + B[[1, 2]])/(B[[2, 1]]*z1 + B[[2, 2]]);****ComplexExpand[{f1a[x], f2a[y], f3a[z]}]****(**cyclic Möbius projection of hyperbolic cyclinder by the Weeks hyperbolic 3 \manifold*)

(

**Cyclic projection of complex variables: Im[x]→Re[y], \****Im[y]→Re[z],Im[z]→Re[x]**)w = {0.` + (

1.` Cos[t] Cosh[

p])/((0.` + 0.35355339059327356` Cos[t] Cosh[p])^2 + (1.` +

0.6123724356957945` Cos[t] Cosh[p])^2) + (

0.6123724356957945` Cos[t]^2 Cosh[

p]^2)/((0.` + 0.35355339059327356` Cos[t] Cosh[p])^2 + (1.` +

0.6123724356957945` Cos[t] Cosh[p])^2) + (0.` - (

0.35355339059327356` Sinh[

p]^2)/((1.` - 0.6123724356957945` Sinh[p])^2 + (0.` +

0.35355339059327356` Sinh[p])^2)),

0.` + 2.4494897427831783`/(

2.0000000000000004` + (1.4142135623730951` +

1.7320508075688772` Cosh[p] Sin[t])^2) + (

2.9999999999999996` Cosh[p] Sin[t])/(

2.0000000000000004` + (1.4142135623730951` +

1.7320508075688772` Cosh[p] Sin[t])^2) + (

2.4494897427831783` Cosh[p]^2 Sin[t]^2)/(

2.0000000000000004` + (1.4142135623730951` +

1.7320508075688772` Cosh[p] Sin[t])^2) + (0.` - (

0.35355339059327356` Cos[t]^2 Cosh[

p]^2)/((0.` + 0.35355339059327356` Cos[t] Cosh[p])^2 + (1.` +

0.6123724356957945` Cos[t] Cosh[p])^2)),

0.` + (1.` Sinh[

p])/((1.` - 0.6123724356957945` Sinh[p])^2 + (0.` +

0.35355339059327356` Sinh[p])^2) - (

0.6123724356957945` Sinh[

p]^2)/((1.` - 0.6123724356957945` Sinh[p])^2 + (0.` +

0.35355339059327356` Sinh[p])^2) + (0.` - 2.4494897427831783`/(

2.0000000000000004` + (1.4142135623730951` +

1.7320508075688772` Cosh[p] Sin[t])^2) - (

4.000000000000001` Cosh[p] Sin[t])/(

2.0000000000000004` + (1.4142135623730951` +

1.7320508075688772` Cosh[p] Sin[t])^2) - (

2.4494897427831783` Cosh[p]^2 Sin[t]^2)/(

2.0000000000000004` + (1.4142135623730951` +

1.7320508075688772` Cosh[p] Sin[t])^2))}

g2 = ParametricPlot3D[w, {t, -Pi, Pi}, {p, -Pi^2, Pi^2},

ColorFunction -> "CMYKColors", PlotStyle -> Opacity[0.5], Mesh -> False,

Axes -> False, ImageSize -> 1000, Boxed -> False, PlotPoints -> 200,

PlotRange -> All]

Show[{g1, g2}, ViewPoint -> Top]

(

**end**) Post has attachment

A more refined version of the probabilities.

https://plus.google.com/101799841244447089430/posts/fWM7YuabUxQ

#Fractal #Math #Art #Space #Iteration

https://plus.google.com/101799841244447089430/posts/fWM7YuabUxQ

*_*#Fractal #Math #Art #Space #Iteration

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