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

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

Baum-Fraktal als Netz dreieckförmiger  Strukturen
Fractal tree as a network of triangular structures

Goldener Schnitt
Golden Ratio  →

n=:

f = 0.618033988749895 (slider from 0 to 5, step 0.1)
N = 3 (slider from 3 to 20, step 1)
B = (-0.007231503418699798, 1.2909286789273329)
A0 = (0, 0)
l1 = W1(A0, B, N, f)
lr020 = Sequence(W1[Element[l1, 5], Element[l1, i], N, f], i, 1, 2)
lr030 = Join(Sequence[Sequence[W1[Element[Element[lr020, i], 5], Element[Element[lr020, i], j], 3, f], j, 1, 2], i, 1, 2])
lr040 = Join(Sequence[Sequence[W1[Element[Element[lr030, i], 5], Element[Element[lr030, i], j], 3, f], j, 1, 2], i, 1, 4])
lr050 = Join(Sequence[Sequence[W1[Element[Element[lr040, i], 5], Element[Element[lr040, i], j], 3, f], j, 1, 2], i, 1, 8])
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])
V020 = Sequence(Polygon[Sequence[Element[Element[lr020, i], j], j, 1, N + 1]], i, 1, N - 1)
Kl010 = Sequence(Rotate[V10, 2 * π / N * i, A0], i, 1, N)
Kl020 = Sequence(Rotate[V020, 2 * π / N * i, A0], i, 1, N)
l00 = Sequence(Rotate[l10, i * π] * f^(i), i, 0, 10)
V050 = Sequence(Polygon[Sequence[Element[Element[lr050, i], j], j, 1, 4]], i, 1, 16)
V040 = Sequence(Polygon[Sequence[Element[Element[lr040, i], j], j, 1, 4]], i, 1, 8)
lr060 = Join(Sequence[Sequence[W1[Element[Element[lr050, i], 5], Element[Element[lr050, i], j], 3, f], j, 1, 2], i, 1, 16])
V060 = Sequence(Polygon[Sequence[Element[Element[lr060, i], j], j, 1, 4]], i, 1, 32)
lr070 = Join(Sequence[Sequence[W1[Element[Element[lr060, i], 5], Element[Element[lr060, i], j], 3, f], j, 1, 2], i, 1, 32])
V070 = Sequence(Polygon[Sequence[Element[Element[lr070, i], j], j, 1, 4]], i, 1, 64)
lr080 = Join(Sequence[Sequence[W1[Element[Element[lr070, i], 5], Element[Element[lr070, i], j], 3, f], j, 1, 2], i, 1, 64])
V080 = Sequence(Polygon[Sequence[Element[Element[lr080, i], j], j, 1, 4]], i, 1, 128)
lr090 = Join(Sequence[Sequence[W1[Element[Element[lr080, i], 5], Element[Element[lr080, i], j], 3, f], j, 1, 2], i, 1, 128])
V090 = Sequence(Polygon[Sequence[Element[Element[lr090, i], j], j, 1, 4]], i, 1, 256)
lr100 = Join(Sequence[Sequence[W1[Element[Element[lr090, i], 5], Element[Element[lr090, i], j], 3, f], j, 1, 2], i, 1, 256])
V100 = Sequence(Polygon[Sequence[Element[Element[lr100, i], j], j, 1, 4]], i, 1, 512)
V030 = Sequence(Polygon[Sequence[Element[Element[lr030, i], j], j, 1, 4]], i, 1, 4)
Kl030 = Sequence(Rotate[V030, 2 * π / 3 * i, A0], i, 1, 3)
Kl040 = Sequence(Rotate[V040, 2 * π / 3 * i, A0], i, 1, 3)
Kl050 = Sequence(Rotate[V050, 2 * π / 3 * i, A0], i, 1, 3)
Kl060 = Sequence(Rotate[V060, 2 * π / 3 * i, A0], i, 1, 3)
Kl070 = Sequence(Rotate[V070, 2 * π / 3 * i, A0], i, 1, 3)
Kl080 = Sequence(Rotate[V080, 2 * π / 3 * i, A0], i, 1, 3)
Kl090 = Sequence(Rotate[V090, 2 * π / 3 * i, A0], i, 1, 3)
Kl100 = Sequence(Rotate[V100, 2 * π / 3 * i, A0], i, 1, 3)
A = (4.64855483622231, -1.2531338774506917)
d = Circle(A0, A)
Name2: "" + (LaTeX[Autor]) + ""
n = 11 (slider from 1 to 11, step 1)
inputBox1 = Textfield(n)

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}})