List of oscillators with subperiod combinations

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This page intends to list all known oscillators of periods up to 144 containing each combination of subperiods. Only non-trivial, non-pseudo-object cases are counted; a page for trivial cases may be created in future.

Blue This oscillator is the smallest possible example for the subperiod combination of this period.
Green This oscillator is the smallest known example for the subperiod combination of this period.
Yellow This oscillator may be the smallest known example for the subperiod combination of this period; checking of other pattern collections may be advisable.
Orange Whether this subperiod combination is known for this period is unknown; checking of pattern collections advisable.
Red This subperiod combination is currently unknown for this period.
Gray This subperiod combination is provably impossible for this period.

Prime periods

Oscillators of prime period can either be fully strictly volatile or have stator cells; trivial cases cannot exist. Period 1 is included here for completeness, despite 1 not being a prime number.

p 1, p SV
1 4
2 3 12
3 12 140
5 15 68
7 28 none known
11 33 none known
13 34 128
17 36 none known
19 92 none known
23 54 none known
29 54 none known
31 48 none known
37 58 none known
41 170 none known
43 70 none known
47 84 none known
53 94 none known
59 86 none known
61 134 none known
67 228 none known
71 92 none known
73 68 none known
79 80 none known
83 62 none known
89 164 none known
97 164 none known
101 116 none known
103 180 none known
107 86 none known
109 156 none known
113 86 none known
127 74 none known
131 ? none known
137 ? none known
139 ? none known

Squares of primes

These are the only numbers which have exactly three divisors; only one subperiod is possible other than 1, and trivial cases cannot exist. Here, q represents sqrt(p).

p 1, q, p 1, p q, p SV
4 12 18 12 416
9 37 29 none known none known
25 88 30 none known 128
49 158 44 none known none known
121 check 156 none known none known

Four divisors

This includes oscillators whose periods are a product of two primes, and those whose periods are a cube of a prime. q1 represents the greater of the two divisors, and q2 the lesser.

p 1, q1, q2, p 1, q1, p 1, q2, p 1, p q1, q2, p q1, p q2, p SV
6 56 24 121 16 42 28 check 52
8 45 18 32 15 30 84 34 12
10 46 37 check 24 none known none known none known none known
14

47

62 94 44 check 16 none known none known
15 31 58 27 19 220 80 152 12
21 54

83

62 32 none known none known none known none known
22

52

45 36 48
26 70

150

60

144

none known none known none known none known
27

120

73

118

56 none known none known none known none known
33 46

72

77

60 236
34 620 74 none known none known none known none known
35 58 74 84 44 none known none known none known none known
38 42 44 none known none known none known none known
39 46 340 78 82 none known none known none known none known
46 28 41 114
51 90 86 84 none known none known none known none known
55 49

108

98

134 none known none known none known none known
57 112 228 none known none known none known none known
58

310

68 54 none known none known none known none known
62 110 66 78 92 none known none known none known none known
65 52 138 176 none known none known none known none known
69 103

184

196 none known none known none known none known
74 84 96 none known none known none known none known
77 67 78 none known none known none known none known
82 48 116 none known none known none known none known
85 68 96 none known none known none known none known
86 76 168
87 84 none known none known none known none known
91 68 84 none known none known none known none known
93 60 228 none known none known none known none known
94 54 none known none known none known none known
95 141 228 none known none known none known none known
106 66 115 none known none known none known none known
111 91 292 none known none known none known none known
115 93 96 none known none known none known none known
118 119 208 none known none known none known none known
119 72 none known none known none known none known
122 102 none known none known none known none known
123 228 none known none known none known none known
125 228 none known none known none known none known
129 38 none known none known none known none known
133 84 none known none known none known none known
134 208 none known none known none known none known
141 103 228 none known none known none known none known
142 208 none known none known none known none known
143 69 122 none known none known none known none known

Tesseracts of primes

These are the only numbers which have exactly five divisors. q1 represents the prime cubed, q2 the prime squared and q3 the prime itself.

p 1, q1, q2, q3, p 1, q1, q2, p 1, q1, q3, p 1, q2, q3, p 1, q1, p 1, q2, p 1, q3, p 1, p q1, q2, q3, p q1, q2, p q1, q3, p q2, q3, p q1, p q2, p q3, p SV
16 35 86 27 78 28 check 96 34 51 122 55 48 32 440 check 21
81 check 550 check check check check 146 228 none known none known none known none known none known none known none known none known

Six divisors

12, 18, 20, 28, 32, 44, 45, 50, 52, 63, 68, 75, 76, 92, 98, 99, 116, 117, 124

For the square number the period is divisible by, a1 is that number, and a2 is its square root. b is the remaining factor, and ab is a times b.

For fifth powers, a1, a2, ab, and b represent x^4, x^3, x^2, and x respectively.

Has stator cells

wait where did 18 go

p 1, a1, a2, ab, b, p 1, a1, a2, ab, p 1, a1, a2, b, p 1, a1, a2, p 1, a1, ab, b, p 1, a1, ab, p 1, a1, b, p 1, a1, p 1, a2, ab, b, p 1, a2, ab, p 1, a2, b, p 1, a2, p 1, ab, b, p 1, ab, p 1, b, p 1, p
12 31 33 33
20 30
28 46
32 68 45 48 66
44 45 70 72
45 52 29
50 188 58
52 83 35
63 64
68 38
75 42 49
76 57 52
92 44
98 105 105
99 75
116 68
117 76
124 60

Volatility 1

If a period is not listed (e.g. 75), no volatility 1 oscillators of that period are known.

p a1, a2, ab, b, p a1, a2, ab, p a1, a2, b, p a1, a2, p a1, ab, b, p a1, ab, p a1, b, p a1, p a2, ab, b, p a2, ab, p a2, b, p a2, p ab, b, p ab, p b, p p
12
20
32
45
92
99

Hexeracts of primes

64

Eight divisors

24, 30, 40, 42, 54, 56, 66, 70, 78, 88, 102, 104, 105, 110, 114, 128, 130, 135, 136, 138

Nine divisors

36, 100

Ten divisors

48, 80, 112

Twelve divisors

60, 72, 84, 90, 96, 108, 126, 132, 140

Fifteen divisors

144

Sixteen divisors

120

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