Portraits 400 Years of Hellenistic Portraits Andreas Pangerl
Table C1. Portraits of ω-Limit Orbits of rule...
34
Table C1. Portraits of ω-Limit Orbits of rule L Distinct Orbit ID number i Number of Period-T attractors Number of Period-T Isles of Eden Period T Bit-strings (coded by integer ) for Period-T Orbit of Length L Bernoulli Parameters Robustness Coefficient ρ i β σ τ 3 1 1 0 1 x 0 ( ) + 0 1 2 ρ 1 = 1 4 1 1 0 1 x 0 ( ) + 0 1 2 ρ 1 = 0.75 2 0 2 2 x 0 ( ) + 2 1 0 x 1 ( ) x 0 ( ) 5 1 1 0 1 x 0 ( ) + 0 1 1 ρ 1 = 0.375 2 5 0 2 x 0 ( ) + 0 2 1 x 1 ( ) x 0 ( ) 18 n Maximum Transient Length δ max 0 3 3 0 69 81 12 0 0 12 0 0 3 20 3 20 6 9 12 18 24 5 17 10
Transcript of Table C1. Portraits of ω-Limit Orbits of rule...
Table C1. Portraits of ω-Limit Orbits of rule
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
3 1 1 0 1 x0( ) + 0 1 2 ρ1 = 1
4
1 1 0 1 x0( ) + 0 1 2 ρ1 = 0.75
2 0 2 2
x0( )
+ 2 1 0x1( )
x0( )
5
1 1 0 1 x0( ) + 0 1 1 ρ1 = 0.375
2 5 0 2
x0( )
+ 0 2 1x1( )
x0( )
18
nMaximum TransientLength
δmax
0
33
0
69
81
12
00
12
0 0
3
20
3
20
6
9
12
18
24
5
17
10
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
6
1 1 0 1 x0( ) + 0 1 4 ρ1 = 0.7188
2 3 0 2
x0( )
+ 3 1 1x1( )
x0( )
7 1 1 0 1 x0( ) + 0 1 5 ρ1 = 1
8
1 1 0 1 x0( ) + 0 1 5 ρ1 = 0.5156
2 4 0 6
x0( )
+ 4 3 2x5( )
x0( )
3 0 2 2
x0( )
+ 2 1 0x1( )
x0( )
nMaximum TransientLength
δmax
51
204
3
108
0
0
40
5
0 0
5
40
10
17
20
34
0
0
3
108
6
105
12
210
24
165
51
204
102
153
20
Table C2. Portraits of ω-Limit Orbits of rule
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
3 1 1 0 1 x0( ) + 0 1 2 ρ1 = 1
4
1 1 0 1 x0( ) + 0 1 2 ρ1 = 0.625
2 0 2 2
x0( )
+ 2 1 0
x1( )
3 0 2 1x0( )
+ 0 1 0
5 1 1 0 1 x0( ) + 0 1 6 ρ1 = 1
61 1 0 1 x0( ) + 0 1 5 ρ1 = 0.9688
2 0 2 1x0( )
+ 0 1 0
22
nMaximum TransientLength
δmax
0
0
3
0
0
6
5
10
21
42
0
3
0
5
0
0
21
=0.125
=0.03125
!3 = 2!!
116
"
12 12
9
!2 = 2!!
164
"
20
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
7
1 1 0 1 x0( ) + 0 1 6 ρ1 = 0.8906
2 0 1 7x0( )
+ -3 1 0x6( )
3 0 1 7x0( )
+ -3 1 0x6( )
8
1 1 0 1 x0( ) + 0 1 8 ρ1 = 0.6016
2 4 0 6
x0( )
+ 4 3 2
x5( )
nMaximum TransientLength
δmax
0
11
0
3
13
49
0
11
49
3
252
104
252
6
249
13
104
0
!3 = 1!!
7128
"
!2 = 1!!
7128
"
=0.0547
=0.0547
!2 = 4!!
14256
"
=0.218812
243
24
231
20
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
8
3 4 0 4
x0( )
+ 4 2 2x3( )
4 0 2 2
x0( )
+ 2 1 0x1( )
z
5 0 2 7x0( )
+ 0 1 0
nMaximum TransientLength
δmax
55
216 216
10
177
20
99
40
198
51
204
51
204
102
153
85 85
170
=0.1563
=0.0156
!4 = 2!!
2256
"
!3 = 4!!
10256
"
!5 = 2!!
1256
"
=0.0078
20
Table C3. Portraits of ω-Limit Orbits of rule
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
3 1 1 0 1 x0( ) + 0 1 3 ρ1 = 1
4
1 1 0 1 x0( ) + 0 1 2 ρ1 = 0.25
2 0 2 2
x0( )
+ 2 1 0
x1( )
3 0 2 4
x0( )
+ 2 2 0x3( )
5 1 1 0 1 x0( ) + 0 1 6 ρ1 = 1
54
nMaximum TransientLength
δmax
0
0
3
6
1
14
0
3
0
1
12 12
9
14
2
13
0
!3 = 2!!
416
"
=0.5
0
20
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
6
1 1 0 1 x0( ) + 0 1 5 ρ1 = 0.5313
2 6 0 4
x0( )
+ 0 4 1x3( )
7
1 1 0 1 x0( ) + 0 1 2 ρ1 = 0.0703
2 7 0 4
x0( )
+ 0 4 6
x3( )
nMaximum TransientLength
δmax
0
0
1
0
1
126 126
2
125
0
4
123
8
119
1
62
2
61
4
59
8
55
16
47
32
31
=0.4688
16
111
32
95
64
63
1
62
!2 = 6!!
564
"
!2 = 7!!
17128
"
=0.9297
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
8
1 1 0 1 x0( ) + 0 1 3 ρ1 = 0.0781
2 2 0 4
x0( )
+ 2 2 4x3( )
z
3 4 0 4
x0( )
+ 4 2 2x3( )
4 4 0 6
x0( )
+ 4 3 4x5( )
nMaximum TransientLength
δmax
00
17
238
17
238
34
221
5
248
10
241
20
227
40
199
3
252
6
249
12
243
24
231
5
248
3
252
!2 = 2!!
24256
"
=0.1875
!3 = 4!!
14256
"
=0.2188
!4 = 4!!
28256
"
=0.4375
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
8
5 0 1 8x0( )
+ 3 1 0x7( )
6 0 1 8x0( )
+ -3 1 0x7( )
7 0 2 2
x0( )
+ 2 2 0x1( )
x0( )
x3( )
nMaximum TransientLength
δmax
2929
232 232
4646
197 197
51
204
51
204
102
153
!5 = 1!!
8256
"
=0.0313
!6 = 1!!
8256
"
=0.0313
!7 = 2!!
2256
"
=0.0156
20
Table C4. Portraits of ω-Limit Orbits of rule
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
31 1 0 2
x0( )+ 0 2 1 ρ1 =0.625
x1( )
2 0 3 1x0( )
+ 0 1 0
4
1 1 0 2x0( )
+ 0 2 2 ρ1 = 0.5x1( )
2 0 4 1x0( )
+ 0 1 0
3 0 2 2
x0( )
+ 0 2 0x1( )
73
nMaximum TransientLength
δmax
0
7
3
5
0
3
7
6
0
15
0
15
3
6912
3
1
4
1
4
2
8
!2 = 3!!
18
"
=0.375
!2 = 4!!
116
"
=0.25
!3 = 2!!
216
"
=0.25
20
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
5
1 1 0 2x0( )
+ 0 2 2 ρ1 = 0.5313x1( )
2 5 0 2
x0( )
+ 0 2 0x1( )
61 1 0 2
x0( )+ 0 2 5 ρ1 = 0.6719
x1( )
2 3 0 1x0( )
+ 0 1 2
nMaximum TransientLength
δmax
0
0
0
0
63
5445
31 31
!2 = 5!!
332
"
=0.4686
63
27 27 !2 = 3!!
764
"
=0.3281
33
11 11
6122417
22132621
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
7
1 1 0 2x0( )
+ 0 2 5x1( )
2 0 7 2
x0( )
+ 0 2 0x1( )
3 7 0 3
x0( )
+ 0 3 2x2( )
4 0 7 1x0( )
+ 0 1 0
nMaximum TransientLength
δmax
00
127 127
33
43 43
6122448
86459053
9665
10685
2011
35
11
35
22
70
44
13
88
26
49
52
98
104
69
81
27 27
54108895110277
!1 = 1!!
44128
"
=0.3438
!2 = 7!!
2128
"
=0.1094
!3 = 7!!
9128
"
=0.4922
!4 = 7!!
1128
"
=0.0547
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
8
1 1 0 2x0( )
+ 0 2 2 ρ1 = 0.0625x1( )
2 4 0 6
x0( )
+ 4 3 1x5( )
3 8 0 3
x0( )
+ 0 3 1x2( )
4 0 4 1x0( )
+ 0 1 0
nMaximum TransientLength
δmax
00
255 255
5
87
51
5
87
10
174
51
102204153
!2 = 4!!
10256
"
=0.1563
1
84
248
1688116
20
93
40
186
80
117
160
234
65
213
130
171
!3 = 8!!
5256
"
=0.1563
!4 = 4!!
1256
"
=0.0156
1
84
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
8
5 8 0 3
x0( )
+ 0 3 2x2( )
6 8 0 2
x0( )
+ 0 2 2x1( )
x0( )
nMaximum TransientLength
δmax
33
75 75
27
91
27
91
!5 = 8!!
12256
"
=0.375
!6 = 8!!
6256
"
=0.1875
6
150
12
45
24
90
48
180
96
105
192
210
129
165
54
182
108
109
216
218
177
181
99
107
198
214
141
173
Table C5. Portraits of ω-Limit Orbits of rule
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
3 1 4 0 1x0( )
+ 0 1 1 ρ1 = 1
4 1 1 0 1 x0( ) + 0 1 1 ρ1 = 1
5
1 1 0 1 x0( ) + 0 1 1 ρ1 = 0.0625
2 5 0 3
x0( )
+ 0 3 1x2( )
6 1 4 0 1
x0( )
+ 0 1 1x0( )
90
nMaximum TransientLength
δmax
0
0
0
0
356
0 0
0 0
3
20
6
9
12
18
24
5
17
10
!2 = 5!!
632
"
=0.9375
27
5445
27
!1 = 4!!
464
"
=0.25
3
20
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
6 2 6 0 2
x0( )
+ 3 1 1
x1( )
x0( )
x1( )
7 1 7 0 7
x0( )
+ 0 7 1x6( ) !1 = 7!
!14128
"
=0.7656
nMaximum TransientLength
δmax
55
30
51
60
39
!2 = 6!!
864
"
=0.75
4040
15
57
15
57
10
17
20
34
6
86
12
45
3
43
3
43
24
90
48
53
96
106
65
85
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
7 2 2 0 7
x0( )
+ 3 1 1x6( )
x0( )
x6( )
3 1 0 1 x1( ) + 0 1 1 ρ3 =0.0157
8 1 1 0 1 x1( ) + 0 1 4 ρ1 = 1
!2 = 2!!
14128
"
=0.2188
nMaximum TransientLength
δmax
2929
3939
00
23
92
23
92
00
20
Table C6. Portraits of ω-Limit Orbits of rule
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
3 1 1 0 2x0( )
+ 0 2 1 ρ1 = 1x1( )
4
1 0 4 1x0( )
+ 0 1 0
2 0 4 2
x0( )
+ 2 1 0
x1( )
x0( )
x1( )
3 0 1 2x0( )
+ 1 1 0x1( )
nMaximum TransientLength
δmax
0
7
3
2
0
3
7
1 1
8
105
4 4
14
7 7
11
13 13
5 5
10 10
6912
!1 = 4!!
116
"
!2 = 4!!
216
"
!3 = 1!!
216
"
=0.125
=0.25
=0.5
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
4 4 0 1 2x0( )
+ 0 2 0x1( )
5
1 0 1 2x0( )
+ 0 2 0 ρ1 = 0.0625x1( )
2 0 5 6
x0( )
– 0 6 0x5( )
61 1 0 2
x0( )+ 0 2 2
x1( )
2 1 0 2x0( )
+ 1 1 2x1( )
7 1 0 1 2x0( )
+ 0 2 0 ρ1 = 0.0156x1( )
nMaximum TransientLength
δmax
0
0
63
15
0
15
0
=0.125!4 = 1!
!216
"
0
31
1
18
21
42
0
127
2
5
4
10
8
20
16
9
0
31
1
18
63
21
42
0
127
!2 = 1!!
3264
"
!1 = 1!!
3264
"
!2 = 5!!
632
"
=0.5
=0.5
=0.9375
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
7
2 0 7 14
x0( )
– 0 7 0x13( )
3 0 1 14x0( )
+ 1 7 0x13( )
4 0 1 14x0( )
+ -1 7 0x13( )
8
1 0 1 2x0( )
+ 0 2 0 ρ1 = 0.0078x1( )
2 0 1 2x0( )
+ 1 1 0x1( )
3 0 4 1x0( )
+ 0 1 0
nMaximum TransientLength
δmax
1
36
1
36
2
72
4
17
8
34
16
68
32
9
64
18
11
78
11
78
13
23
13
23
!4 = 1!!
14128
"
!3 = 1!!
14128
"
!2 = 7!!
14128
"
=0.0194
=0.0194
=0.7656
0
255
0
255
85
170
85
170
5151
102204153
!2 = 1!!
2256
"
=0.0078
!3 = 4!!
1256
"
=0.0156
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
8 4 0 4 2
x0( )
+ 2 1 0
x1( )
x0( )
x1( )
x0( )
x1( )
x0( )
nMaximum TransientLength
δmax
17
68
17
68
34
136
119
221
119
187
238
187
!4 = 4!!
2256
"
=0.0313
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
8 5 0 48 4
x0( )
+ 0 4 0
x3( )
x0( )
x3( )
x0( )
x3( )
x0( )
nMaximum TransientLength
δmax
1
146
1
146
2
37
4
74
8
148
16
41
32
82
64
164
128
73
3
72
3
72
6
144
12
33
24
66
48
132
96
9
192
18
129
36
11
35
11
35
22
70
44
140
88
25
176
50
97
100
194
200
133
145
!5 = 48!!
4256
"
=0.75
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
8 5 0 48 4
x0( )
+ 0 4 0
x3( )
x0( )
x3( )
x0( )
x3( )
x0( )
nMaximum TransientLength
δmax
13
76
13
76
26
152
52
49
104
98
208
196
161
137
67
19
134
38
23
43
23
43
46
86
92
172
184
89
113
178
226
101
197
202
139
149
7
253
7
253
14
251
28
247
56
239
112
223
224
191
193
127
131
254
!5 = 48!!
4256
"
=0.75
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
8 6 0 12 4
x0( )
+ 4 2 0
x3( )
x0( )
x3( )
x0( )
x3( )
x0( )
nMaximum TransientLength
δmax
5
39
5
39
10
78
20
156
40
57
15
150
15
150
30
45
60
90
120
180
27
245
27
245
54
235
108
215
216
175
!6 = 12!!
4256
"
=0.1875
20
Table C7. Portraits of ω-Limit Orbits of rule
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
3 1 1 0 1 x0( ) + 0 1 2 ρ1 = 0.875
2 0 1 1 x0( ) + 0 1 0 ρ2 = 0.125
4
1 1 0 1 x0( ) + 0 1 3 ρ1 = 0.6875
2 0 2 2
x0( )
+ 2 1 0x1( )
3 0 1 1 x0( ) + 0 1 0 ρ1 = 0.0625
5
1 1 0 1 x0( ) + 0 1 2 ρ1 = 0.3438
2 5 0 2
x0( )
+ 0 2 1x1( )
3 0 1 1 x0( ) + 0 1 0 ρ3 = 0.0313
146
nMaximum TransientLength
δmax
0
6
0
9
77
0
3
12
15
0
3
12
15
!2 = 2!!
216
"
=0.25
00
31 31
3
20
6122417
10 5 18 9
3
20
!2 = 5!!
432
"
=0.625
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
6
1 1 0 1 x0( ) + 0 1 4 ρ1 = 0.7031
2 3 0 2
x0( )
+ 3 1 2x1( )
3 0 1 1 x0( ) + 0 1 0 ρ3 = 0.0156
7 1 1 0 1 x0( ) + 0 1 6 ρ1 = 0.9922
2 0 1 1 x0( ) + 0 1 0 ρ2 = 0.0078
8
1 1 0 1 x0( ) + 0 1 7 ρ1 = 0.5429
2 4 0 6
x0( )
+ 4 3 2x5( )
nMaximum TransientLength
δmax
00
6363
5
40
5
40
10
17
20
34
!2 = 3!!
664
"
=0.2816
127127
0 0
0 0
3
180
3
180
6
105
12
210
24
165
!2 = 4!!
28256
"
=0.4375
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
83 0 2 2
x0( )
+ 2 1 0x1( )
4 0 1 1 x0( ) + 0 1 0 ρ1 = 0.0039
nMaximum TransientLength
δmax
51 51
204
255
204
255
102
153
!3 = 2!!
2256
"
= 0.0156
Table C8. Portraits of ω-Limit Orbits of rule
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
3 1 2 0 1x0( )
+ 0 1 1 ρ1 = 1x1( )
4
1 0 4 1
x0( )
+ 0 1 0x0( )
x0( )
2 0 2 2
x0( )
+ 2 1 0x1( )
x0( )
x1( )
3 0 4 2
x0( )
– 0 2 0x1( )
nMaximum TransientLength
δmax
0
7
0
6
0
0
7
5
9
150
15 15
10
5
12
33
12
1
11
2
7
11
1
4
14
8
13
!1 = 4!!
116
"
!2 = 2!!
216
"
=0.25
=0.25
!3 = 4!!
216
"
=0.5
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
5
1 0 1 1x0( )
+ 0 2 0x1( )
2 0 10 3
x0( )
+ 0 3 0
x2( )
x0( )
x2( )
6 1 4 0 1
x0( )
+ 0 1 2 ρ1 = 1x0( )
x0( )
nMaximum TransientLength
δmax
0
15
0
15
3
23
6
15
12
30
24
29
17
27
3
23
1
13
2
26
4
21
8
11
16
22
1
13
!1 = 2!!
132
"
=0.0625
!2 = 10!!
332
"
= 0.9375
00
6363
2121
42
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
7
1 0 2 1x0( )
+ 0 1 0x0( )
2 0 14 7
x0( )
+ 0 7 0
x6( )
x0( )
x6( )
3 0 2 7
x0( )
+ 1 2 0x6( )
x0( )
x6( )
nMaximum TransientLength
δmax
0
127
0
127
2
55
4
110
8
93
16
59
32
118
64
109
1
91
1
91
3
108
6
89
12
51
24
102
48
77
96
27
65
54
3
108
13
104
13
104
23
57
23
57
!1 = 2!!
1128
"
= 0.0156
!2 = 14!!
7128
"
= 0.7656
!3 = 2!!
7128
"
= 0.1094
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
7 4 0 2 7
x0( )
+ -1 2 0x6( )
x0( )
x6( )
8
1 0 4 1
x0( )
+ 0 1 0x0( )
x0( )
2 0 2 2
x0( )
+ 2 1 0x1( )
3 0 4 2
x0( )
– 0 2 0x1( )
nMaximum TransientLength
δmax11
49
11
49
29
83
29
83
= 0.1094
!4 = 2!!
7128
"
85
170
85
0 0
255 255
51
204
102
153
51
204
17
187
34
119
17
187
68
238
136
221
!1 = 4!!
1256
"
!2 = 2!!
2256
"
!3 = 4!!
2256
"
= 0.0156
= 0.0156
= 0.0313
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
8 5 0 48 4
x0( )
+ 0 4 0
x3( )
x0( )
x3( )
x0( )
x3( )
x0( )
nMaximum TransientLength
δmax
1
109
1
109
2
218
4
181
8
107
16
214
32
173
64
91
128
182
3
183
3
183
6
11
12
222
24
189
48
123
96
246
192
237
129
219
11
220
11
220
22
185
44
115
88
230
176
205
97
155
194
55
133
110
!5 = 48!!
4256
"
=0.75
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
8 5 0 48 4
x0( )
+ 0 4 0
x3( )
x0( )
x3( )
x0( )
x3( )
x0( )
nMaximum TransientLength
δmax
13
179
13
179
26
103
52
206
104
157
208
59
161
118
67
236
134
217
23
212
23
212
46
169
92
83
184
166
113
77
226
154
197
53
139
106
31
191
31
191
62
127
124
254
248
253
241
251
227
247
199
239
143
223
!5 = 48!!
4256
"
=0.75
LDistinct Orbit
ID number
iNumber of Period-Tattractors
Number of Period-TIsles ofEden
Period
T
Bit-strings (coded by integer )
for Period-T Orbitof Length L
BernoulliParameters
RobustnessCoefficient ρiβ σ τ
8 6 0 12 4
x0( )
+ 4 2 0
x3( )
x0( )
x3( )
x0( )
x3( )
x0( )
nMaximum TransientLength
δmax
5
216
5
216
10
177
20
99
40
198
15
105
15
30
210
60
165
120
75
39
175
39
78
95
156
190
57
125
!6 = 12!!
4256
"
=0.1875
105
175
![violation of the OZI rule in ω φ - CORE · The OZI rule was tested in several experiments and is remarkably well fulfilled in many reactions (for a review, see. e.g. Refs. [4]](https://static.fdocument.org/doc/165x107/5e4a79d36cb28f324a0eb13f/violation-of-the-ozi-rule-in-core-the-ozi-rule-was-tested-in-several-experiments.jpg)
