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

Bäume gabelförmiger Fraktale  mit veränderbarem Neigungswinkel in einem  Kreis
Trees of  curved fractals with variable angle of inclination in a circle

Goldener Schnitt/Golden ratio

Krone / crown

α = 0.29 (slider from 0.1 to 1.5707963267948966, step 0.01)
D = (-0.017790635795195908, 0.4)
C = (-0.017790635795195908, 0)
f = 0.618033988749895 (slider from 0 to 2, step 0.1)
c = Line(D, C)
n = 1 (slider from 1 to 10, step 1)
B = (-1.0961397994256366, 0.2002880140240463)
E = (1.03873649599788, -0.4223842388078095)
b = OrthogonalLine(B, xAxis)
F = Point(b)
d = OrthogonalLine(F, b)
e = OrthogonalLine(E, xAxis)
G = Point(b)
g = OrthogonalLine(G, b)
list1, list1_2 = W9a(C, D, f, α)
N = 5 (slider from 1 to 50, step 1)
r01 = Sequence(Rotate[list1, 2 * π / N * i, C], i, 1, N)
r02 = Sequence(Rotate[list1_2, 2 * π / N * i, C], i, 1, N)
a = true
A = (0.7763246180187393, 0.6539492268015412)
h = Circle(C, A)

Tool: W1a
A B f a
Input: A, B, f, a
Output: b0

D1: B + Rotate[B - A, -a] * f
C1: B + Rotate[B - A, a] * f
b0: {B, C1, D1}

Tool: W9a
A B f a
Input: C, D, f, α
Output: l0, l09

l01 = W1a(C, D, f, α)
l02 = Sequence(W1a[Element[l01, 1], Element[l01, i], f, α], i, 2, 3)
l03 = Join(Sequence[Sequence[W1a[Element[Element[l02, j], 1], Element[Element[l02, j], i], f, α], i, 2, 3], j, 1, 2])
l04 = Join(Sequence[Sequence[W1a[Element[Element[l03, j], 1], Element[Element[l03, j], i], f, α], i, 2, 3], j, 1, 4])
l05 = Join(Sequence[Sequence[W1a[Element[Element[l04, j], 1], Element[Element[l04, j], i], f, α], i, 2, 3], j, 1, 8])
l06 = Join(Sequence[Sequence[W1a[Element[Element[l05, j], 1], Element[Element[l05, j], i], f, α], i, 2, 3], j, 1, 16])
l07 = Join(Sequence[Sequence[W1a[Element[Element[l06, j], 1], Element[Element[l06, j], i], f, α], i, 2, 3], j, 1, 32])
l08 = Join(Sequence[Sequence[W1a[Element[Element[l07, j], 1], Element[Element[l07, j], i], f, α], i, 2, 3], j, 1, 64])
s01 = Sequence(Segment[Element[l01, 1], Element[l01, i]], i, 1, 3)
a = Segment(D, C)
s02 = Join(Sequence[Sequence[Segment[Element[Element[l02, j], 1], Element[Element[l02, j], i]], i, 2, 3], j, 1, 2])
s03 = Join(Sequence[Sequence[Segment[Element[Element[l03, j], 1], Element[Element[l03, j], i]], i, 2, 3], j, 1, 4])
s04 = Join(Sequence[Sequence[Segment[Element[Element[l04, j], 1], Element[Element[l04, j], i]], i, 2, 3], j, 1, 8])
s05 = Join(Sequence[Sequence[Segment[Element[Element[l05, j], 1], Element[Element[l05, j], i]], i, 2, 3], j, 1, 16])
s06 = Join(Sequence[Sequence[Segment[Element[Element[l06, j], 1], Element[Element[l06, j], i]], i, 2, 3], j, 1, 32])
s07 = Join(Sequence[Sequence[Segment[Element[Element[l07, j], 1], Element[Element[l07, j], i]], i, 2, 3], j, 1, 64])
s08 = Join(Sequence[Sequence[Segment[Element[Element[l08, j], 1], Element[Element[l08, j], i]], i, 2, 3], j, 1, 128])
l09 = Join(Sequence[Sequence[W1a[Element[Element[l08, j], 1], Element[Element[l08, j], i], f, α], i, 2, 3], j, 1, 128])
s09 = Join(Sequence[Sequence[Segment[Element[Element[l09, j], 1], Element[Element[l09, j], i]], i, 2, 3], j, 1, 256])
l0: {a, s01, s02, s03, s04, s05, s06, s07, s08, s09}