\fgcolor{ff0000}{f}= \frac{\sqrt[2]{ 5} -1 }{2 } =0.618033988749895

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

Baum bogenförmiger Fraktale im Kreis 
Trees of curved fractals in a circle

Installation

Delete

N=:

replication

set

Goldener Schnitt
Golden ratio   →

Der Goldene Triplex-Baum
The Golden Tree Triplex

h = 0.02 (slider from 0 to 0.1, step 0.01)
D = (-4.668304153261257E-4, 0.880655262689391)
C = (-0.01462194976380915, 0.014621949763809039)
f = 0.618033988749895 (slider from 0 to 2, step 0.1)
n = 10 (slider from 1 to 10, step 1)
N = 3 (slider from 1 to 20, step 1)
B = (1.9853780502361908, -0.48537805023619096)
E = (2.105449999206294, -1.303882461904766)
cc = Circle(C, B)
inputBox1 = Textfield(N)
Name2: "" + (LaTeX[Autor]) + ""
gr = 2.7 (slider from 0 to 9, step 0.1)
bl = 2.9 (slider from 0 to 13, step 0.1)
rot = 1 (slider from 0 to 1, step 0.1)
l1_1, l1_2, l1_3 = W08(C, D, f, h)
r01 = Sequence(Rotate[l1_1, 2 * π / N * i, C], i, 1, N)
r02 = Sequence(Rotate[l1_2, 2 * π / N * i, C], i, 1, N)
r03 = Sequence(Rotate[l1_3, 2 * π / N * i, C], i, 1, N)

Tool: W1
l(B,C,D)
Input: A, B, f
Output: b0

C1: B + Rotate[B - A, 60*°] * f
D1: B + Rotate[B - A, 300*°] * f
b0: {B, C1, D1}

Tool: W41
A,B,h
Input: E, F, h
Output: Vieleck1

e = Segment(E, F)
i = LineBisector(E, F)
j = LineBisector(E, (E + F) / 2)
H = Point(i, 0.5 + h)
G = Point(j, 0.5 + 1.5 * h)
G' = Mirror(G, e)
G'' = Mirror(G', i)
G'_1 = Mirror(G, i)
Vieleck1 = Polygon({G, E, G', G'', F, G'_1, H})

Tool: W08
A,B,f,h
Input: C, D, f, h
Output: l101, ss1, ss2

l1 = W1(C, D, f)
l2 = Sequence(W1[Element[l1, 1], Element[l1, i], f], i, 2, 3)
l31 = Join(Sequence[Sequence[W1[Element[Element[l2, j], 1], Element[Element[l2, j], i], f], i, 2, 3], j, 1, 2])
l41 = Join(Sequence[Sequence[W1[Element[Element[l31, j], 1], Element[Element[l31, j], i], f], i, 2, 3], j, 1, 4])
l51 = Join(Sequence[Sequence[W1[Element[Element[l41, j], 1], Element[Element[l41, j], i], f], i, 2, 3], j, 1, 8])
l61 = Join(Sequence[Sequence[W1[Element[Element[l51, j], 1], Element[Element[l51, j], i], f], i, 2, 3], j, 1, 16])
l71 = Join(Sequence[Sequence[W1[Element[Element[l61, j], 1], Element[Element[l61, j], i], f], i, 2, 3], j, 1, 32])
l81 = Join(Sequence[Sequence[W1[Element[Element[l71, j], 1], Element[Element[l71, j], i], f], i, 2, 3], j, 1, 64])
l91 = Join(Sequence[Sequence[W1[Element[Element[l81, j], 1], Element[Element[l81, j], i], f], i, 2, 3], j, 1, 128])
l101 = Join(Sequence[Sequence[W1[Element[Element[l91, j], 1], Element[Element[l91, j], i], f], i, 2, 3], j, 1, 256])
s9 = Join(Sequence[Sequence[Segment[Element[Element[l91, j], 1], Element[Element[l91, j], i]], i, 2, 3], j, 1, 256])
s10 = Join(Sequence[Sequence[Segment[Element[Element[l101, j], 1], Element[Element[l101, j], i]], i, 2, 3], j, 1, 512])
s01 = Sequence(W41[Element[l1, 1], Element[l1, i], h], i, 1, 3)
s02 = Join(Sequence[Sequence[W41[Element[Element[l2, j], 1], Element[Element[l2, j], i], h], i, 2, 3], j, 1, 2])
s03 = Join(Sequence[Sequence[W41[Element[Element[l31, j], 1], Element[Element[l31, j], i], h], i, 2, 3], j, 1, 4])
s04 = Join(Sequence[Sequence[W41[Element[Element[l41, j], 1], Element[Element[l41, j], i], h], i, 2, 3], j, 1, 8])
s05 = Join(Sequence[Sequence[W41[Element[Element[l51, j], 1], Element[Element[l51, j], i], h], i, 2, 3], j, 1, 16])
s06 = Join(Sequence[Sequence[W41[Element[Element[l61, j], 1], Element[Element[l61, j], i], f * h], i, 2, 3], j, 1, 32])
s07 = Join(Sequence[Sequence[W41[Element[Element[l71, j], 1], Element[Element[l71, j], i], f * h], i, 2, 3], j, 1, 64])
s00 = W41(C, D, h)
ss1: {s9, s10}
s08 = Join(Sequence[Sequence[W41[Element[Element[l81, j], 1], Element[Element[l81, j], i], h], i, 2, 3], j, 1, 128])
ss2: {s00, s01, s02, s03, s04, s05, s06, s07, s08}