Otter Results

Here you can find the code and detailed results reported in the paper Busy beaver Machines and the Observant Otter Heuristic (or How to Tame Dreadful Dragons), Theoretical Computer Science 646:61-85, September, 2016. The relevant code consists of the files below. The full list of results is below. The results are also available in a Prolog-readable file, or (due to the width being wider than a typical page) as two Latex tables.

Number Dimension Ones Hops Steps Otters Otter Steps Time OtterLess Hops OtterLess Time OtterExtra Hops OtterExtra Time
1 2x4 84 6445 284 2 3706 0.04 6445 0.01 -- --
2 2x4 90 7195 287 2 4576 0.04 7195 0.01 -- --
3 2x4 90 7195 287 2 4576 0.04 7195 0.01 -- --
4 2x4 2050 3932964 737 8 3885112 0.15 3932964 0.18 -- --
5 3x3 31 2315619 824059 52 420 140.28 2315619 13.15 -- --
6 3x3 5600 29403894 1050 16 29254992 0.19 29403894 0.71 -- --
7 3x3 13949 92649163 467 7 92440736 0.07 92649163 0.63 -- --
8 3x3 2050 3932964 737 8 3885112 0.15 3932964 0.18 -- --
9 3x3 36089 310341163 859 17 310094944 0.13 310341163 3.03 -- --
10 3x3 32213 544884219 739 8 544398352 0.15 544884219 1.58 -- --
11 3x3 43925 (10 digits) 1248 14 (10 digits) 0.27 (10 digits) 4.86 -- --
12 3x3 107900 (10 digits) 872 14 (10 digits) 0.20 (10 digits) 5.09 -- --
13 3x3 43925 (10 digits) 1258 14 (10 digits) 0.27 (10 digits) 5.09 -- --
14 3x3 1525688 (12 digits) 1305 29 (12 digits) 0.35 (12 digits) 74.85 (12 digits) 0.28
15 3x3 2950149 (13 digits) 827 13 (13 digits) 0.13 (12 digits) 73.87 (13 digits) 0.13
16 3x3 95524079 (16 digits) 1149 17 (16 digits) 0.19 (12 digits) 73.37 (13 digits) 0.14
17 3x3 374676383 (18 digits) 4520 60 (18 digits) 0.70 (12 digits) 77.25 (12 digits) 0.44
18 5x2 4098 47176870 526 11 47010381 0.12 47176870 0.40 -- --
19 5x2 4098 11798826 510 10 11695761 0.07 11798826 0.21 -- --
20 5x2 4097 23554764 1456 74 23480937 0.28 19988787 77.40 23468894 0.27
21 5x2 4097 11798796 498 10 11721789 0.09 11798796 0.22 -- --
22 5x2 4096 11804910 550 9 11686386 0.10 11804910 0.21 -- --
23 5x2 4096 11804896 544 9 11686386 0.10 11804896 0.21 -- --
24 5x2 1915 2133492 393 4 2076796 0.05 2133492 0.07 -- --
25 5x2 1471 2358064 931 41 2312068 0.16 2358064 6.15 -- --
26 5x2 501 134467 290 6 121176 0.04 134467 0.03 -- --
27 2x5 90604 (10 digits) 1561 9 (10 digits) 0.30 (10 digits) 8.03 -- --
28 2x5 64665 (10 digits) 1283 10 (10 digits) 0.23 (10 digits) 7.56 -- --
29 2x5 97104 (10 digits) 1362 17 (10 digits) 0.21 (10 digits) 12.14 -- --
30 2x5 458357 (12 digits) 3640 84 (12 digits) 0.61 (11 digits) 77.29 (11 digits) 0.58
31 2x5 668420 (12 digits) 1879 12 (12 digits) 0.36 (12 digits) 59.31 -- --
32 2x5 1957771 (12 digits) 852 12 (12 digits) 0.13 (12 digits) 74.43 (12 digits) 0.13
33 2x5 1137477 (12 digits) 1559 47 (12 digits) 0.30 5999830 76.38 15516871 0.14
34 2x5 2576467 (13 digits) 1836 41 (13 digits) 0.45 (12 digits) 73.92 (12 digits) 0.41
35 2x5 4848239 (14 digits) 916 32 (14 digits) 0.25 (12 digits) 75.72 (12 digits) 0.21
36 2x5 143 26375397569930 ?? ?? ?? ?? ?? ?? ?? ??
37 2x5 4099 15754273 958 10 15654122 0.17 15754273 0.43 -- --
38 2x5 3685 16268767 765 13 16171476 0.15 16268767 0.46 -- --
39 2x5 11120 148304214 947 15 148035978 0.18 148304214 1.37 -- --
40 2x5 36543045 (15 digits) 1685 27 (15 digits) 0.30 (12 digits) 78.99 (12 digits) 0.22
41 2x5 114668733 (16 digits) 961 18 (16 digits) 0.16 (12 digits) 73.88 (12 digits) 0.11
42 2x5 398005342 (17 digits) 648 19 (17 digits) 0.11 (12 digits) 71.27 (12 digits) 0.07
43 2x5 620906587 (17 digits) 919 20 (17 digits) 0.15 (12 digits) 72.85 (13 digits) 0.11
44 2x5 (10 digits) (18 digits) 815 20 (18 digits) 0.15 (12 digits) 72.60 (12 digits) 0.09
45 2x5 (10 digits) (18 digits) 823 20 (18 digits) 0.15 (12 digits) 72.11 (12 digits) 0.09
46 2x5 (12 digits) (22 digits) 862 26 (22 digits) 0.16 (12 digits) 72.71 (13 digits) 0.08
47 2x5 (31 digits) (62 digits) 8587 168 (62 digits) 1.74 (12 digits) 76.80 (12 digits) 0.25
48 2x5 (106 digits) (212 digits) 24367 593 (212 digits) 4.54 (12 digits) 75.46 (12 digits) 0.21
49 2x5 (106 digits) (212 digits) 26169 593 (212 digits) 4.80 (12 digits) 75.95 (12 digits) 0.23
50 2x5 (353 digits) (705 digits) 81738 1993 (705 digits) 15.20 (12 digits) 78.16 (12 digits) 0.20
51 6x2 136612 (11 digits) 1498 15 (11 digits) 0.25 (11 digits) 7.86 -- --
52 6x2 95524079 (16 digits) 1514 16 (16 digits) 0.23 (12 digits) 78.61 (13 digits) 0.17
53 6x2 17485734 (14 digits) 1929 25 (14 digits) 0.30 (12 digits) 80.22 (13 digits) 0.25
54 6x2 36109969 (16 digits) 2256 83 (16 digits) 0.38 39940703 76.13 173556244 0.17
55 6x2 36109970 (15 digits) 1000 14 (15 digits) 0.15 (13 digits) 77.64 (14 digits) 0.13
56 6x2 (10 digits) (20 digits) 5817 215 (20 digits) 1.11 19943326 77.26 29765228 0.26
57 6x2 (11 digits) (21 digits) 1734 21 (21 digits) 0.26 (13 digits) 77.50 (14 digits) 0.14
58 6x2 (14 digits) (26 digits) 2155 27 (26 digits) 0.32 (13 digits) 76.99 (14 digits) 0.14
59 6x2 (14 digits) (28 digits) 12634 408 (28 digits) 2.25 39848493 79.99 57854154 0.42
60 6x2 (20 digits) (38 digits) 4197 153 (38 digits) 0.73 54760346 76.58 252160142 0.11
61 6x2 (22 digits) (43 digits) 33228 1075 (43 digits) 5.73 39839230 81.07 43619704 0.57
62 6x2 (48 digits) (96 digits) 20493 643 (96 digits) 3.55 48524764 77.41 92937448 0.20
63 6x2 (48 digits) (96 digits) 19203 641 (96 digits) 3.32 32668321 82.85 41281924 0.17
64 6x2 (50 digits) (99 digits) 28242 380 (99 digits) 4.61 (12 digits) 79.83 (12 digits) 0.42
65 6x2 (61 digits) (120 digits) 12321 332 (120 digits) 1.88 (13 digits) 76.50 (13 digits) 0.16
66 6x2 (50 digits) (100 digits) 29547 389 (100 digits) 4.79 (12 digits) 77.90 (12 digits) 0.42
67 6x2 (463 digits) (926 digits) 265475 12330 (926 digits) 52.02 19932648 73.94 25237532 0.54
68 6x2 (866 digits) (1731 digits) 244643 14334 (1731 digits) 48.22 22225873 75.71 39845896 0.14
69 6x2 (882 digits) (1763 digits) 288760 2211 (1763 digits) 44.48 (13 digits) 77.09 (13 digits) 0.23
70 6x2 (1440 digits) (2880 digits) 406270 8167 (2880 digits) 65.16 (12 digits) 80.84 (12 digits) 0.20
71 6x2 (10567 digits) (21133 digits) 1927565 99697 (21133 digits) 456.05 19959284 76.63 36213129 0.13
72 6x2 (18268 digits) (36535 digits) 6195809 30345 (36535 digits) 1154.03 (12 digits) 79.13 (13 digits) 0.48
73 3x4 17323 262759288 379583 17778 122527994 65.83 50789361 98.93 50798489 28.62
74 3x4 (27 digits) (53 digits) 9187 358 (53 digits) 1.98 6005442 73.57 11408546 0.18
75 3x4 (141 digits) (282 digits) 50694 801 (282 digits) 9.43 (12 digits) 76.52 (12 digits) 0.43
76 3x4 (435 digits) (869 digits) 103962 3493 (869 digits) 21.69 19983565 80.35 55369106 0.12
77 3x4 (629 digits) (1257 digits) 168263 1488 (1257 digits) 33.00 (12 digits) 76.21 (12 digits) 0.32
78 3x4 (1302 digits) (2602 digits) 96341 2163 (2602 digits) 18.78 (13 digits) 71.21 (14 digits) 0.10
79 3x4 (2356 digits) (4711 digits) 3178530 107045 (4711 digits) 559.23 11974138 75.92 12292474 0.46
80 3x4 (2373 digits) (4745 digits) 944360 13465 (4745 digits) 156.75 (12 digits) 74.23 (12 digits) 0.25
81 3x4 (6519 digits) (13037 digits) 731258 13667 (13037 digits) 140.72 (12 digits) 71.51 (13 digits) 0.17
82 4x3 15008 250096775 1594 27 249578940 0.37 250096775 1.94 -- --
83 4x3 (714 digits) (1427 digits) 375816 20051 (1427 digits) 68.39 13319120 72.58 17502670 0.21
84 4x3 (810 digits) (1619 digits) 924926 34272 (1619 digits) 167.45 6264241 74.35 8863780 0.45
85 4x3 (987 digits) (1974 digits) 497189 7887 (1974 digits) 92.18 (12 digits) 72.28 (12 digits) 0.40
86 4x3 (3861 digits) (7722 digits) 1759075 44810 (7722 digits) 313.82 15567444 75.15 24601805 0.20
87 4x3 (4562 digits) (9123 digits) 1511192 25943 (9123 digits) 295.55 (12 digits) 77.07 (12 digits) 0.26
88 4x3 (4932 digits) (9864 digits) 1524523 57368 (9864 digits) 300.73 19934942 81.68 37620302 0.16
89 4x3 (6035 digits) (12069 digits) 1319358 34262 (12069 digits) 224.82 (12 digits) 75.49 (12 digits) 0.16
90 4x3 (7037 digits) (14073 digits) 1695880 25255 (14073 digits) 300.14 (12 digits) 74.43 (13 digits) 0.21
91 4x3 (7037 digits) (14073 digits) 1695879 25255 (14073 digits) 315.79 (12 digits) 73.11 (13 digits) 0.21
92 2x6 10574 94842383 948 11 94674070 0.22 94842383 1.23 -- --
93 2x6 10249 98364599 712 13 98206675 0.18 98364599 1.04 -- --
94 2x6 15828 493600387 1263 15 492945078 0.25 493600387 2.83 -- --
95 2x6 (28 digits) (55 digits) 5059 149 (55 digits) 1.01 (12 digits) 74.71 (12 digits) 0.18
96 2x6 (822 digits) (1644 digits) 139554 2733 (1644 digits) 31.66 (12 digits) 77.38 (13 digits) 0.26
97 2x6 (4932 digits) (9864 digits) 1083249 49142 (9864 digits) 201.36 13328142 77.74 48673870 0.11
98 2x6 (4934 digits) (9867 digits) 770686 16394 (9867 digits) 156.34 (12 digits) 72.78 (13 digits) 0.25
99 7x2 22961 197700005 241 8 197585144 0.07 197700005 1.31 -- --
100 8x2 (45 digits) (90 digits) 2670 94 (90 digits) 1.47 (12 digits) 71.64 (13 digits) 0.14