CoCalc -- span_4_surjective.txt

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A (one dimensional) cellular automaton is a function1 F : Σ → Σ with the property that there is a K > 0 such that F (x)i depends only on the 2K + 1 coordinates xi−K , xi−K+1, . . . , xi−1, xi, xi+1, . . . , xi+K . A periodic point of σ is any x such that σ^p (x) = x for some p ∈ N, and a periodic point of F is any x such that F^q (x) = x for some q ∈ N. Given a cellular automaton F, a point x ∈ Σ is jointly periodic if there are p, q ∈ N such that σ^p (x) = F^q (x) = x, that is, it is a periodic point under both functions.

This project aims to explore the nature of one-dimensional Cellular Automata, in the hope of finding the structure of cellular automata through its periodic points.

Shared Project -- M498ES23-Cellular-Automata

LEMMA Research Project / span_4_surjective.txt

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License: MIT
ubuntu2004

1
510, 765, 1020, 1275, 1530, 1785, 2040, 2295, 2550, 2805, 3060, 3315,
2
3570, 3825, 3885, 4335, 4590, 4845, 5100, 5355, 5610, 5865, 6120,
3
6375, 6630, 6885, 7140, 7230, 7395, 7650, 7710, 7770, 7905, 8160,
4
8415, 8670, 8925, 9180, 9435, 9690, 9945, 10200, 10455, 10605, 10710,
5
10965, 11220, 11475, 11565, 11730, 11985, 12240, 12495, 12750, 13005,
6
13116, 13164, 13203, 13212, 13251, 13515, 13628, 13763, 13770, 13875,
7
14025, 14028, 14280, 14460, 14535, 14790, 14796, 14908, 15043, 15045,
8
15300, 15411, 15443, 15452, 15523, 15532, 15564, 15810, 15900, 16065,
9
16320, 16575, 16830, 17085, 17340, 17595, 17850, 18105, 18360, 18615,
10
18795, 18870, 19125, 19215, 19275, 19380, 19635, 19890, 20145, 20400,
11
20655, 20910, 21165, 21420, 21675, 21846, 21849, 21850, 21861, 21862,
12
21865, 21866, 21909, 21910, 21913, 21914, 21925, 21926, 21929, 22101,
13
22102, 22105, 22106, 22117, 22118, 22121, 22122, 22165, 22166, 22169,
14
22170, 22181, 22182, 22186, 22440, 22695, 22869, 22870, 22873, 22874,
15
22885, 22886, 22889, 22890, 22933, 22934, 22937, 22938, 22949, 22953,
16
22954, 23070, 23125, 23126, 23129, 23141, 23142, 23145, 23146, 23160,
17
23189, 23190, 23193, 23194, 23206, 23209, 23210, 23460, 23715, 23970, \
18
24225, 24480, 24735, 24990, 25245, 25500, 25755, 25941, 25942, 25945, \
19
25946, 25957, 25958, 25961, 25962, 26005, 26006, 26009, 26021, 26022, \
20
26025, 26026, 26197, 26198, 26201, 26202, 26213, 26217, 26218, 26261, \
21
26262, 26266, 26277, 26278, 26281, 26282, 26520, 26775, 26965, 26966, \
22
26969, 26970, 26981, 26982, 26986, 27029, 27033, 27034, 27045, 27046, \
23
27049, 27050, 27221, 27222, 27225, 27226, 27237, 27238, 27241, 27242, \
24
27286, 27289, 27290, 27301, 27302, 27305, 27306, 27465, 27540, 27795, \
25
27945, 28050, 28305, 28560, 28815, 29070, 29325, 29580, 29835, 30090, \
26
30345, 30600, 30810, 30840, 30855, 31110, 31365, 31620, 31800, 31875, \
27
32130, 32385, 32640, 32895, 33150, 33405, 33660, 33735, 33915, 34170, \
28
34425, 34680, 34695, 34725, 34935, 35190, 35445, 35700, 35955, 36210, \
29
36465, 36720, 36975, 37230, 37485, 37590, 37740, 37995, 38070, 38229, \
30
38230, 38233, 38234, 38245, 38246, 38249, 38293, 38294, 38297, 38298, \
31
38309, 38310, 38313, 38314, 38485, 38486, 38489, 38490, 38501, 38502, \
32
38506, 38549, 38553, 38554, 38565, 38566, 38569, 38570, 38760, 39015, \
33
39253, 39254, 39257, 39258, 39269, 39273, 39274, 39317, 39318, 39322, \
34
39333, 39334, 39337, 39338, 39509, 39510, 39513, 39514, 39526, 39529, \
35
39530, 39573, 39574, 39577, 39578, 39589, 39590, 39593, 39594, 39780, \
36
40035, 40290, 40545, 40800, 41055, 41310, 41565, 41820, 42075, 42325, \
37
42326, 42329, 42341, 42342, 42345, 42346, 42375, 42389, 42390, 42393, \
38
42394, 42406, 42409, 42410, 42465, 42581, 42582, 42586, 42597, 42598, \
39
42601, 42602, 42645, 42646, 42649, 42650, 42661, 42662, 42665, 42666, \
40
42840, 43095, 43349, 43353, 43354, 43365, 43366, 43369, 43370, 43413, \
41
43414, 43417, 43418, 43429, 43430, 43433, 43434, 43606, 43609, 43610, \
42
43621, 43622, 43625, 43626, 43669, 43670, 43673, 43674, 43685, 43686, \
43
43689, 43860, 44115, 44370, 44625, 44880, 45135, 45390, 45645, 45900, \
44
46155, 46260, 46320, 46410, 46665, 46740, 46920, 47175, 47430, 47685, \
45
47940, 48195, 48450, 48705, 48960, 49215, 49470, 49635, 49725, 49971, \
46
50003, 50012, 50083, 50092, 50124, 50235, 50490, 50492, 50627, 50739, \
47
50745, 51000, 51075, 51255, 51507, 51510, 51660, 51765, 51772, 51907, \
48
52020, 52284, 52323, 52332, 52371, 52419, 52530, 52785, 53040, 53295, \
49
53550, 53805, 53970, 54060, 54315, 54570, 54825, 54930, 55080, 55335, \
50
55590, 55845, 56100, 56355, 56610, 56865, 57120, 57375, 57630, 57765, \
51
57825, 57885, 58140, 58305, 58395, 58650, 58905, 59160, 59415, 59670, \
52
59925, 60180, 60435, 60690, 60945, 61200, 61650, 61710, 61965, 62220, \
53
62475, 62730, 62985, 63240, 63495, 63750, 64005, 64260, 64515, 64770, \
54
65025
55

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