Date: 24 Februar 2013

Zentrum

f-->II

Goldfraktal mit  fünfzackigem Stern 
Gold Fractal,  five-pointed star

c-->II

max Reihe: innere Pentagramme

(skalierte) äußere Sternchen

max Reihe: äußere Pentagramme

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

Goldener Schnitt
Golden ratio   →

$f=\frac{\sqrt{5}-1}{2}≈ 0.6180339887$

inneres Pentagramm

Sternteilchen

(skalierte) äußere Pentagramme

VZ2

max Reihe: äußere Sternchen

Zentrum Punkte

zackP

innerePentagrammPunkten1

innere Pentagramm Punkte

innere Pentagramm Punkte Mitte

großer Stern

äußeres Pentagramm

bewegliches Sternchen (im Zentrum)

bewegliches Pentagramm (im Zentrum)

Zentrum-Punkt

bewegliche  i-Pentagramme(äußere)

bewegliche i-Sternchen(äußere)

bewegliche max i-Pentagramme(äußere)

kleiner Stern

$ Vierzehn\; mögliche\; Variationen:\; (anklicken)$
$fourteen\; possible\;  variations:\;(click)$

n_{ext} = 7 (slider from 0 to 50, step 1)
f = 0.6180339887498949 (slider from 0 to 2, step 0.01)
B = (0, 1500)
A0 = (0, 0)
N = 5 (slider from 1 to 6, step 1)
ll10 = Sequence(Rotate[B, 2 * π / N * i, A0], i, 1, N + 1)
v2: Element[ll10, 1] - A0
v1: Element[ll10, 5] - A0
An: A0 + (2 + f + f^(2) + f^(3)) * v1
An1: A0 + (2 + f + f^(2) + f^(3)) * (v1 + v2) * f^(3)
ll11 = Sequence(Rotate[An1, 2 * π / N * i, A0], i, 1, N + 2)
Vz1: {Segment[Element[ll11, 1], Element[ll11, 3]], Segment[Element[ll11, 1], Element[ll11, 4]], Segment[Element[ll11, 2], Element[ll11, 4]], Segment[Element[ll11, 2], Element[ll11, 5]], Segment[Element[ll11, 3], Element[ll11, 5]]}
n_{inr} = 17 (slider from 0 to 20, step 1)
ff: 1 / (2 * f)
Vz2: {Segment[Element[ll10, 1], Element[ll10, 3]], Segment[Element[ll10, 1], Element[ll10, 4]], Segment[Element[ll10, 2], Element[ll10, 4]], Segment[Element[ll10, 2], Element[ll10, 5]], Segment[Element[ll10, 3], Element[ll10, 5]]}
lV081 = Sequence(Dilate[Vz1, f^(i), An], i, 1, n_{ext})
lV01 = Sequence(Dilate[A0, f^(i), An], i, 0, n_{ext})
Liste1 = Sequence(Rotate[lV081, 2 * π / N * i, A0], i, 1, 5)
Liste2 = Sequence(Rotate[An, 2 * π / N * i, A0], i, 1, N + 2)
Vieleck1 = Polygon(Liste2)
Liste3 = Sequence(Segment[Element[Liste2, i], Element[Liste2, i + 2]], i, 1, 6)
Liste1a = Sequence(Rotate[lV01, 2 * π / N * i, A0], i, 1, 5)
VVz: {Segment[Element[ll11, 1], Element[ll11, 3]], Segment[Element[ll11, 1], Element[ll11, 4]], Segment[Element[ll11, 2], Element[ll11, 4]], Segment[Element[ll11, 2], Element[ll11, 5]], Segment[Element[ll11, 3], Element[ll11, 5]]}
n_{in} = 6 (slider from 1 to n_{inr}, step 1)
l00abc = Sequence(Polygon[ff^(i) * Rotate[ll11, i * π, A0]], i, 0, n_{inr})
Vieleck2 = Element(l00abc, n_{in})
Liste4 = Sequence(Element[ll11, i] - A0, i, 1, N + 1)
l00abcP = Sequence(ff^(i) * Rotate[ll11, i * π, A0], i, 0, n_{inr})
l00abc1 = Rotate(Dilate[VVz, ff, A0], 3.141592653589793, A0)
Vieleck2P = Element(l00abcP, n_{in})
Liste5 = Sequence(Segment[Element[Vieleck2P, i], Element[Vieleck2P, i + 2]], i, 1, 5)
Liste55 = Sequence(Sequence[Segment[Element[Element[l00abcP, j], i], Element[Element[l00abcP, j], i + 2]], i, 1, 5], j, 1, n_{inr} + 1)
d = true
lV082 = Sequence(Dilate[Liste5, f^(i), An], i, 0, n_{ext})
lV083 = Sequence(Dilate[l00abc, f^(i), An], i, 1, n_{ext})
Liste83 = Sequence(Rotate[lV083, 2 * π / N * i, A0], i, 1, 5)
c = true
e = false
Name2: "" + (LaTeX[Autor]) + ""
Liste82 = Sequence(Rotate[lV082, 2 * π / N * i, A0], i, 1, 5)
V31, h, i_1, j = Polygon(Element[ll11, 1], Element[ll11, 5], Element[Liste2, 1])
V32, k, l, m = Polygon(Element[ll11, 4], Element[ll11, 5], Element[Liste2, 5])
V33, n, p, q = Polygon(Element[ll11, 3], Element[ll11, 4], Element[Liste2, 4])
V34, r, s, t = Polygon(Element[ll11, 2], Element[ll11, 3], Element[Liste2, 3])
V35, a_1, b_1, c_1 = Polygon(Element[ll11, 1], Element[ll11, 2], Element[Liste2, 2])
V30 = Polygon(ll11)
ptgr1 = false
u = false
lV081a = Sequence(Dilate[Vieleck2, f^(i), An], i, 1, n_{ext})
Liste82a = Sequence(Rotate[lV081a, 2 * π / N * i, A0], i, 1, 5)
g = true
v = false
st1 = true
lP1 = true
lP2 = false
lP3 = false
lP5 = false
lP4 = true
Stern1 = false
w = true
Stern2 = true
ptgr2 = true
Zentrum = true
i = 1 (slider from 1 to n_{ext}, step 1)
Liste7 = Sequence(Element[Element[Liste82a, j], i], j, 1, 5)
Liste6 = Sequence(Element[Element[Liste82, j], i + 1], j, 1, 5)
b = true
o = true
Liste8 = Sequence(Element[Element[Liste83, j], i], j, 1, 5)
a = true
z = true
Name02: "" + headline + ""