n=

f →II

Goldener Schnitt
Golden ratio   →

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

Goldener Schnitt in fünfeckigem Fraktal (5 Schritte)
Golden section in pentagonal fractal (5 steps)

für andere Vielecke

A0 = (0, 0)
B = (-0.007231503418699798, 1.2909286789273329)
N = 5 (slider from 3 to 7, step 1)
f = 0.618033988749895 (slider from 0 to 5, step 0.1)
l1 = W1(A0, B, N, f)
l10 = Sequence(Rotate[B, 2 * π / N * i, A0], i, 1, N + 1)
V00 = Polygon(l10)
V10, a, b, c = Polygon(Sequence[Element[l1, i], i, 1, N + 1])
ll20 = Sequence(W1[Element[l1, N + 2], Element[l1, i], N, f], i, 1, N - 1)
V20 = Sequence(Polygon[Sequence[Element[Element[ll20, i], j], j, 1, N + 1]], i, 1, N - 1)
ll30b = Join(Sequence[Sequence[W1[Element[Element[ll20, i], N + 2], Element[Element[ll20, i], j], N, f], j, 1, N - 1], i, 2, N - 2])
V3 = Sequence(Polygon[Sequence[Element[Element[ll30b, i], j], j, 1, N + 1]], i, 1, 2 * N - 2)
ll40 = Join(Sequence[Sequence[W1[Element[Element[ll30b, i], N + 2], Element[Element[ll30b, i], j], N, f], j, 2, N - 1], i, 1, N - 2])
V40 = Sequence(Polygon[Sequence[Element[Element[ll40, i], j], j, 1, N + 1]], i, 2, 2 * N - 1)
V41 = Mirror(V40, Line[A0, B])
ll50 = Join(Sequence[Sequence[W1[Element[Element[ll40, i], N + 2], Element[Element[ll40, i], j], N, f], j, 2, N - 1], i, 2, 3 * N - 1])
Kl10 = Sequence(Rotate[V10, 2 * π / N * i, A0], i, 1, N)
Kl20 = Sequence(Rotate[V20, 2 * π / N * i, A0], i, 1, N)
Kl42 = Sequence(Rotate[V41, 2 * π / N * i, A0], i, 1, N)
l00 = Sequence(Rotate[l10, i * π] * f^(i), i, 0, 10)
ll30a = Sequence(Element[Element[ll30b, i], N + 2], i, 1, 2 * N - 2)
Kl41 = Sequence(Rotate[V40, 2 * π / N * i, A0], i, 1, N)
V30 = Sequence(Translate[Polygon[Element[l00, 4]], Element[ll30a, i]], i, 1, 2 * N - 2)
Kl30 = Sequence(Rotate[V30, 2 * π / N * i, A0], i, 1, N)
ll51 = Sequence(Element[Element[ll50, i], N + 2], i, 1, 6 * N - 6)
V50: {Sequence[Translate[Polygon[Element[l00, 6]], Element[ll51, i]], i, 2, 4], Sequence[Translate[Polygon[Element[l00, 6]], Element[ll51, i]], i, 7, 13], Sequence[Translate[Polygon[Element[l00, 6]], Element[ll51, i]], i, 16, 6 * N - 8]}
V51: {Mirror[V50, Line[A0, B]], V50}
Kl50 = Sequence(Rotate[V51, 2 * π / N * i, A0], i, 1, N)
n = 5 (slider from 1 to 5, step 1)
inputBox1 = Textfield(n)
d = true

Tool: W1
A B N f
Input: A, B, N, f
Output: l1aa

B1: B + (B - A) * f
l1a = Sequence(Rotate[B, 2 * π / N * i, B1], i, 1, N + 1)
l1aa = Join({l1a, {B1}})