B-Schieb mich

$ \copyright\; Roman\;Chijner,\;Heidelberg,\;2013 $

Goldenes Fünfecksfraktal  (9 Schritte)
Golden section in pentagonal fractal (9 steps)

Goldener Schnitt
Golden ratio   →

f=\frac{\sqrt{5}-1}{2}

f→II

n=

B→II

schieb mich

f = 0.6180339887498949 (slider from 0 to 5, step 0.1)
B = (0, 2.58969)
A0 = (0, 0)
l10 = Sequence(Rotate[B, 2 * π / 5 * i, A0], i, 1, 6)
l00 = Sequence(Rotate[l10, i * π] * f^(i), i, 0, 16)
v02: Element[l10, 1] - A0
An2: A0 + (2 + f + f^(2) + f^(3)) * v02
v03: Element[l10, 2] - A0
v01: Element[l10, 5] - A0
A04: B + (1 + f) * v01
An1: A0 + (2 + f + f^(2) + f^(3)) * v01
An12: (An1 + An2) / 2
A02: A0 + (1 + f) * v01
v05: Element[l10, 4] - A0
An1c1 = Translate(An12, Vector[v01 * f^(2) - f^(3) * v05 + f^(2) * v02])
An1c1' = Mirror(An1c1, Line[A0, An12])
Pl13: A04 - f * v05
An1c = Translate(An1, Vector[v01 * f^(2) - f^(3) * v05 + f^(2) * v02])
An1c2: (An1c1' + An1c) / 2
Pl22: A02 + (1 + f^(2)) * v01 - f^(3) * v05 + f^(2) * v02
Pl23: Pl22 - f^(2) * v05
Pl33: Pl23 - f^(2) * v03
v04: Element[l10, 3] - A0
Pl34: Pl33 - f^(4) * v04
Pl36: Pl34 + (f^(4) + f^(5)) * v02
Pl37: Pl36 - f^(4) * v03
Pl41: Pl36 - f^(4) * v04
Pl42: Pl36 - f^(4) * v05
Pl35: Pl34 + f^(3) * v01
Pl40: Pl35 - f^(4) * v04
Pl38: Pl35 - f^(4) * v03
Pl39: Pl38 + f^(5) * v01
VK761 = Translate(Polygon[Element[l00, 8]], Pl39)
VK763 = Rotate(VK761, 1.2566370614359172, Pl38)
l74K = Sequence(Rotate[VK763, 2 * π / 5 * i, Pl40], i, 0, 3)
VK764 = Rotate(Element[l74K, 4], 1.25664, Pl37)
l75K = Sequence(Rotate[VK764, 2 * π / 5 * i, Pl41], i, 0, 3)
VK765 = Rotate(Element[l75K, 4], 1.25664, Pl42)
lVr1: {VK761, Mirror[VK761, Line[Pl22, An1c]]}
lVr1a = Rotate(lVr1, 1.25664, Pl13)
l73Ks: {{l74K, l75K, VK765, lVr1a}, Mirror[{l74K, l75K, VK765, lVr1a}, Line[Pl23, An1c2]]}
VK762 = Mirror(VK761, Line[Pl22, An1c])
A05: A0 + (2 + f + f^(2) + f^(3) + 2 * f^(5) + f^(7) + f^(8)) * v01
A: A05 - f^(5) * v03
Ar1: A + f^(5) * v05
A05aa: A0 + v01 * (2 + f + f^(2) + f^(3) + 2 * f^(5) + f^(7) + f^(8)) - f^(7) * v03
Ar2: A + f^(5) * v01
VK75 = Translate(Polygon[Element[l00, 8]], Ar2)
VK72 = Translate(Polygon[Element[l00, 8]], Ar1)
PP1: Ar1 - f^(5) * v02
VK73 = Rotate(VK72, -1.25664, PP1)
Ar3: Ar1 - f^(6) * v03
V81 = Translate(Polygon[Element[l00, 9]], Ar3)
Pl24: Pl22 - f^(2) * v03
Pl31: Pl24 + f^(3) * v01
Pl32: Pl31 - f^(4) * v03
V62 = Translate(Polygon[Element[l00, 7]], Pl32)
l65 = Sequence(Rotate[V62, 2 * π / 5 * i, Pl31], i, 1, 2)
l62 = Mirror({l65, V62}, Line[Pl22, An1c])
l61 = Mirror({Sequence[Rotate[V62, 2 * π / 5 * i, Pl31], i, 1, 2], l62}, Line[Pl34, Pl37])
PPP1: B + (1 + f + f^(2) + f^(3) + f^(6)) * v01
A12: B + (1 + f + f^(2) + f^(4) + f^(6) + f^(8)) * v01
V80 = Rotate(V81, 1.2566370614359172, Ar1)
PPP1a = Translate(PPP1, Vector[v01 * f^(2) - f^(3) * v05 + f^(2) * v02])
VZ10 = Translate(Polygon[Element[l00, 12]], A12)
lZ11 = Sequence(Rotate[VZ10, 2 * π / 5 * i, An1], i, 1, 5)
lZ10 = Sequence(Rotate[Dilate[lZ11, (1 + f)^(i), An1], π / 5 * i, An1], i, 0, 6)
lZ32 = Join(Translate[lZ10, Vector[v01 * f^(2) - f^(3) * v05 + f^(2) * v02]])
A10: B + (1 + f + f^(2) + f^(4) + f^(6)) * v01
V10 = Translate(Polygon[Element[l00, 2]], A02)
V01 = Polygon(l10)
V04 = Dilate(V10, f^(2), An1)
V30 = Translate(Polygon[Element[l00, 4]], A04)
V10_1 = Dilate(V10, f^(8), An1)
VZ11 = Dilate(V10, f^(10), An1)
A08a: B + (1 + f + f^(2)) * v01
A08: B + (1 + f + f^(2) + f^(4)) * v01
V12'' = Translate(Polygon[Element[l00, 12]], An1)
V00 = Polygon(l10)
V65 = Translate(Polygon[Element[l00, 7]], A)
V64 = Translate(Polygon[Element[l00, 7]], PP1)
VK71 = Translate(Polygon[Element[l00, 8]], A05)
An5: A0 + (2 + f + f^(2) + f^(3)) * v05
An4: A0 + (2 + f + f^(2) + f^(3)) * v04
An3: A0 + (2 + f + f^(2) + f^(3)) * v03
lZ31 = Sequence(Element[lZ32, i], i, 1, 25)
V12c'' = Translate(V12'', Vector[v01 * f^(2) - f^(3) * v05 + f^(2) * v02])
AA2 = 0
lZ20 = Translate(lZ10, An12 - An1)
An1c2_1 = Translate(An2, Vector[v01 * f^(2) - f^(3) * v05 + f^(2) * v02])
PPPP1a1: (An1c2_1 + An1c1) / 2
lZ51 = Translate(lZ31, An1c1' - An1c)
lZ31a = Translate(lZ31, An1c1 - An1c)
lZ40 = Translate(lZ31, An1c2 - An1c)
lZ33 = Sequence(Element[lZ32, i], i, 1, 30)
lZ30s: {lZ31, Mirror[lZ31, Line[A0, A05]]}
lZ41s: {lZ40, Mirror[lZ40, Line[A0, A05]]}
lZ50: {lZ51, Mirror[lZ51, Line[A0, A05]]}
Pl1: A0 + v01
Pl11: A0 - v04 / f
Pl12: A0 + (1 + f^(2)) * v01 - f^(3) * v05 + f^(2) * v02
Pl14 = Rotate(Pl13, 288*°, A02)
Pl15: A02 + v02 / f
Pl16: Pl11 + v01 * f
Pl16' = Rotate(A04, 288*°, A02)
Pl16'' = Rotate(Pl16, 72*°, Pl11)
l32: {Translate[Polygon[Element[l00, 4]], Pl16''], Translate[Polygon[Element[l00, 4]], Pl16]}
l31: {Translate[l32, Pl13 - Pl11], V04, Mirror[Translate[l32, Pl13 - Pl11], Line[A0, A05]]}
Pl21: A04 - f^(2) * v04
V40 = Translate(Polygon[Element[l00, 5]], Pl21)
l40 = Sequence(Rotate[V40, 2 * π / 5 * i, Pl22], i, 0, 3)
l40a = Mirror(l40, Line[A0, B])
Pl25: Pl13 + f * v02
l41 = Sequence(Rotate[Element[l40, 4], 2 * π / 5 * i, Pl25], i, 1, 3)
V42 = Rotate(Element[l41, 3], 1.25664, Pl16)
l41s: {{l40, l41, V42}, Mirror[{l40, l41, V42}, Line[A0, B]]}
V41 = 0
V55 = Translate(Polygon[Element[l00, 6]], Pl31)
l54 = Sequence(Rotate[V55, -2 * π / 5 * i, An1c], i, 0, 2)
l54' = Mirror(l54, Line[An1c2, Pl23])
V53 = Translate(Polygon[Element[l00, 6]], Pl36)
V63 = Translate(Polygon[Element[l00, 7]], Pl37)
V61 = Mirror(Element[Element[l61, 2], 2], Line[Pl23, An1c2])
l64 = Mirror({l65, l61, l62}, Line[An1c2, Pl23])
V63' = Mirror(V63, Line[Pl23, An1c2])
V54 = Mirror(V53, Line[Pl23, An1c2])
l55 = Sequence(Rotate[V55, -2 * π / 5 * i, Pl24], i, 0, 2)
V52 = Rotate(Element[l55, 3], -1.2566370614359172, Pl21)
V56 = Rotate(V53, 1.25664, Pl34)
l51 = Sequence(Rotate[V53, -2 * π / 5 * i, An1c2], i, 0, 3)
l52 = Translate(l51, An12 - An1c2)
V51 = Rotate(Element[l52, 1], 1.25664, An12)
l50s: {Mirror[{V51, l52, l54', l51, l54, l55, V52}, Line[A02, A08]], {V51, l52, l54', l51, l54, l55, V52}}
Ar4: Ar1 - f^(6) * v04
Ar5: Ar4 + f^(9) * v02
PP1r: PP1 + Ar2 - A
V82 = Rotate(V81, -1.2566370614359172, PP1r)
PP1r2: PP1r - f^(5) * v03
l71K = Sequence(Rotate[VK73, -2 * π / 5 * i, PP1r2], i, 0, 3)
l70Ks: {{VK73, VK72, VK75, l71K}, Mirror[{VK73, VK72, VK75, l71K}, Line[A0, A05]]}
PP1r3: PP1r2 + f^(5) * v02
l81 = Sequence(Rotate[V82, -2 * π / 5 * i, PP1r3], i, 0, 3)
PP1r4: PP1r2 + v01 * f^(5)
l82 = Sequence(Rotate[Element[l81, 4], -2 * π / 5 * i, PP1r4], i, 1, 3)
l80s: {{Sequence[Rotate[V80, 72° * i, Ar2], i, 0, 3], V81, V82, l81, l82}, Mirror[{Sequence[Rotate[V80, 72° * i, Ar2], i, 0, 3], V81, V82, l81, l82}, Line[A0, A05]]}
l66s: {{V64, V65}, Mirror[{V64, V65}, Line[A0, A05]]}
Kl10 = Sequence(Rotate[Translate[Polygon[Element[l00, 2]], A02], 2 * π / 5 * i], i, 1, 5)
Kl21 = Sequence(Rotate[Translate[Polygon[Element[l00, 3]], Pl11], 2 * π / 5 * i], i, 1, 5)
Kl22 = Sequence(Rotate[Translate[Polygon[Element[l00, 3]], Pl13], 2 * π / 5 * i], i, 1, 5)
Kl23 = Sequence(Rotate[Translate[Polygon[Element[l00, 3]], Pl14], 2 * π / 5 * i], i, 1, 5)
Kl31 = Sequence(Rotate[l32, 2 * π / 5 * i], i, 1, 5)
Kl32 = Sequence(Rotate[l31, 2 * π / 5 * i], i, 1, 5)
Kl40 = Sequence(Rotate[l41s, 2 * π / 5 * i, A0], i, 1, 5)
Kl50 = Sequence(Rotate[l50s, 2 * π / 5 * i], i, 1, 5)
KZ10 = Sequence(Rotate[lZ10, 2 * π / 5 * i, A0], i, 1, 5)
KlK90 = Sequence(Rotate[l80s, 2 * π / 5 * i, A0], i, 1, 5)
lV09 = Rotate(Dilate[lZ11, (1 + f)^(3), An1], 0.6283185307179586, An1)
lV10 = Rotate(Dilate[lZ11, (1 + f)^(2), An1], 1.2566370614359172, An1)
lV11 = Rotate(Dilate[lZ11, 1 + f, An1], 0.6283185307179586, An1)
KZ20 = Sequence(Rotate[lZ20, 2 * π / 5 * i, A0], i, 1, 5)
KZ30 = Sequence(Rotate[lZ30s, 2 * π / 5 * i, A0], i, 1, 5)
KZ40 = Sequence(Rotate[lZ41s, 2 * π / 5 * i, A0], i, 1, 5)
KZ50 = Sequence(Rotate[lZ50, 2 * π / 5 * i, A0], i, 1, 5)
KZ50_1 = Rotate(B, 1.25664, A0)
l72Ks: {{VK761, VK762, l73Ks}, Mirror[{VK761, VK762, l73Ks}, Line[A04, An1]]}
Ko1 = Sequence(Rotate[V12'', 2 * π / 5 * i, A0], i, 1, 5)
Ko2 = Sequence(Rotate[{V12c'', Mirror[V12c'', Line[An1, A0]]}, 2 * π / 5 * i, A0], i, 1, 5)
An1a = Sequence(Rotate[An1, 2 * π / 5 * i, A0], i, 1, 4)
V66 = Mirror(Element[Element[l66s, 2], 1], Line[Pl13, Pl23])
l66ss: {{V64, V65, V66}, Mirror[{V64, V65, V66}, Line[A0, A05]]}
Kl60 = Sequence(Rotate[{{l61, V61, V62, V63, l62, l65, l64, V63', l66ss}, Mirror[{l61, l66ss, V62, V61, V63, l62, l65, l64, V63'}, Line[B, A02]]}, 2 * π / 5 * i, A0], i, 0, 4)
C = (9.84632, -2.96112)
c = Circle(A0, C)
VK766 = Mirror(Rotate[Element[Element[l70Ks, 2], 1], 3.76992, Pl32], Line[Pl13, Pl23])
KlK70 = Sequence(Rotate[{l70Ks, VK71, l72Ks, VK766}, 2 * π / 5 * i, A0], i, 1, 5)
An12a = Sequence(Rotate[An12, 2 * π / 5 * i, A0], i, 0, 4)
n = 9 (slider from 1 to 9, step 1)
Name2: "" + (LaTeX[Name1]) + ""
inputBox1 = Textfield(n)
a = false