Spiralen In Quadraten
Author: Prof. Dr. Dieter Riebesehl
Date: März  2011

Einstellungen für die Spirale

Schrumpfungsfaktor
der Quadrate

A = (-3.68, 4.14)
a = Line(A, yAxis)
B = Point(a)
Vieleck1, a_1, b, c, d, C, D = Polygon(A, B, 4.0)
A' = Rotate(A, 270.0*°, C)
B' = Rotate(B, 270.0*°, C)
C' = Rotate(C, 270.0*°, C)
D' = Rotate(D, 270.0*°, C)
Vieleck1', a', b', c', d' = Polygon(A', B', C', D')
B''_1 = Dilate(B', 0.3, B')
k = 0.5 (slider from 0 to 1, step 0.01)
A'' = Dilate(A', k, B''_1)
B'' = Dilate(B', k, B''_1)
C'' = Dilate(C', k, B''_1)
D'' = Dilate(D', k, B''_1)
Vieleck1'', a'', b'', c'', d'' = Polygon(A'', B'', C'', D'')
A''' = Rotate(A'', 270.0*°, C'')
B''' = Rotate(B'', 270.0*°, C'')
C''' = Rotate(C'', 270.0*°, C'')
D''' = Rotate(D'', 270.0*°, C'')
Vieleck1''', a''', b''', c''', d''' = Polygon(A''', B''', C''', D''')
E = Dilate(A''', k, B''')
F = Dilate(B''', k, B''')
G = Dilate(C''', k, B''')
H = Dilate(D''', k, B''')
Vieleck2, e, f, g, h = Polygon(E, F, G, H)
E' = Rotate(E, 270.0*°, G)
F' = Rotate(F, 270.0*°, G)
G' = Rotate(G, 270.0*°, G)
H' = Rotate(H, 270.0*°, G)
Vieleck2', e', f', g', h' = Polygon(E', F', G', H')
E'' = Dilate(E', k, F')
F'' = Dilate(F', k, F')
G'' = Dilate(G', k, F')
H'' = Dilate(H', k, F')
Vieleck2'', e'', f'', g'', h'' = Polygon(E'', F'', G'', H'')
E''' = Rotate(E'', 270.0*°, G'')
F''' = Rotate(F'', 270.0*°, G'')
G''' = Rotate(G'', 270.0*°, G'')
H''' = Rotate(H'', 270.0*°, G'')
Vieleck2''', e''', f''', g''', h''' = Polygon(E''', F''', G''', H''')
I = Dilate(E''', k, F''')
J = Dilate(F''', k, F''')
K = Dilate(G''', k, F''')
L = Dilate(H''', k, F''')
Vieleck3, i, j, k_1, l = Polygon(I, J, K, L)
p = CircleArc(C', B'', B)
q = CircleArc(C''', F, B'')
r = CircleArc(G', F'', F)
t = CircleArc(K, L, J)
I' = Rotate(I, 270.0*°, K)
J' = Rotate(J, 270.0*°, K)
K' = Rotate(K, 270.0*°, K)
L' = Rotate(L, 270.0*°, K)
Vieleck3', i', j', k', l' = Polygon(I', J', K', L')
I'' = Dilate(I', k, J')
J'' = Dilate(J', k, J')
K'' = Dilate(K', k, J')
L'' = Dilate(L', k, J')
Vieleck3'', i'', j'', k'', l'' = Polygon(I'', J'', K'', L'')
c_1 = CircleArc(K'', L'', J'')
I''' = Rotate(I'', 270.0*°, K'')
J''' = Rotate(J'', 270.0*°, K'')
K''' = Rotate(K'', 270.0*°, K'')
L''' = Rotate(L'', 270.0*°, K'')
Vieleck3''', i''', j''', k''', l''' = Polygon(I''', J''', K''', L''')
M = Dilate(I''', k, J''')
N = Dilate(J''', k, J''')
O = Dilate(K''', k, J''')
P = Dilate(L''', k, J''')
Vieleck4, m, n, o, p_1 = Polygon(M, N, O, P)
d_1 = CircleArc(O, P, N)
b_1 = Segment(A, E)
e_1 = Segment(A'', C')
Q = Intersect(e_1, b_1)
min = -7.2 (slider from -13 to 5, step 0.1)
max = 4 (slider from -5 to 7, step 0.1)
s = 3.22 (slider from -5 to 10, step 0.01)
u = CurveCartesian(x(Q) + s * k^(-2.0 * α / 3.141592653589793) * cos(α), y(Q) + s * k^(-2.0 * α / 3.141592653589793) * sin(α), α, min, max)
f_1 = CircleArc(L', J, F'')