In the following, the author's sine wave sequence appears first followed by Sherrill's sequence. The emphasis on the direction of movement comes from the derivation of the sequences. It may be possible that movement is bi-directional, but cycles themselves have uni-directional aspects that will emerge in some circumstances.
Sine wave sequence
12 33 44 01 43 34 11 19 24 02 23 20 12
Sherrill's sequence
01 44 33 12 20 23 02 24 19 11 34 43 01
Sine Wave Sequence
12 33 44 01 43 34 11 19 24 02 23 20 12
Sherrill's Sequence
02 24 19 11 34 43 01 44 33 12 20 23 02
Sine Wave Sequence
48 29 08 03 42 27 21 30 14 50 32 28 48
Sherrill's Sequence
03 08 29 48 28 32 50 14 30 21 27 42 03
Sine Wave Sequence
22 27 41 04 07 29 47 28 31 49 13 30 22
Sherrill's Sequence
04 41 27 22 30 13 49 31 28 47 29 07 04
Sine Wave Sequence
08 39 48 05 09 26 14 38 21 35 16 45 08
Sherrill's Sequence
05 48 39 08 45 16 35 21 38 14 26 09 05
Sine Wave Sequence
13 25 10 06 47 40 07 46 15 36 22 37 13
Sherrill's Sequence
06 10 25 13 37 22 36 15 46 07 40 47 06
Sine Wave Sequence
13 25 10 06 47 40 07 46 15 36 22 37 13
Sherrill's Sequence
07 19 24 36 55 49 13 33 44 06 59 04 07
Sine Wave Sequence
08 39 48 05 09 26 14 38 21 35 16 45 08 (moves right to left)
Sherrill's Sequence
08 03 60 05 43 34 14 50 56 35 23 20 08
Sine Wave Sequence
20 53 57 09 05 11 34 54 51 16 35 12 20 (moves left to right)
Sherrill's Sequence
09 57 53 20 12 35 16 51 54 34 11 05 09
Sine Wave Sequence
33 12 06 10 58 54 19 11 36 15 52 53 33 (moves left to right)
Sherrill's Sequence
10 06 12 33 53 52 15 36 11 19 54 58 10
Sine Wave Sequence
12 33 44 01 43 34 11 19 24 02 23 20 12 (moves right to left)
Sherrill's Sequence
11 46 15 02 16 45 12 25 10 01 09 26 11
Sine Wave Sequence
12 33 44 01 43 34 11 19 24 02 23 20 12 (moves right to left)
Sherrill's Sequence
12 25 10 01 09 26 11 46 15 02 16 45 12
Sine Wave Sequence
13 25 10 06 47 40 07 46 15 36 22 37 13 (moves right to left)
Sherrill's Sequence
13 33 44 06 59 04 07 19 24 36 55 49 13
Sine Wave Sequence
08 39 48 05 09 26 14 38 21 35 16 45 08 (moves right to left)
Sherrill's Sequence
14 50 56 35 23 20 08 03 60 05 43 34 14
Sine Wave Sequence
33 12 06 10 58 54 19 11 36 15 52 53 33 (moves left to right)
Sherrill's Sequence
15 36 11 19 54 58 10 06 12 33 53 52 15
Sine Wave Sequence
20 53 57 09 05 11 34 54 51 16 35 12 20 (moves left to right)
Sherrill's Sequence
16 51 54 34 11 05 09 57 53 20 12 35 16
Sine Wave Sequence
28 47 45 17 25 21 27 22 26 18 46 48 28 (moves left to right)
Sherrill's Sequence
17 45 47 28 48 46 18 26 22 27 21 25 17
Sine Wave Sequence
28 47 45 17 25 21 27 22 26 18 46 48 28 (moves left to right)
Sherrill's Sequence
18 26 22 27 21 25 17 45 47 28 48 46 18
Sine Wave Sequence
33 12 06 10 58 54 19 11 36 15 52 53 33 (moves right to left)
Sherrill's Sequence
19 07 02 15 62 31 33 13 01 10 61 41 19
Sine Wave Sequence
20 53 57 09 05 11 34 54 51 16 35 12 20 (moves right to left)
Sherrill's Sequence
20 42 61 09 01 14 34 32 62 16 02 08 20
Sine Wave Sequence
48 29 08 03 42 27 21 30 14 50 32 28 48 (moves right to left)
Sherrill's Sequence
21 35 64 50 18 57 48 05 63 03 17 51 21
Sine Wave Sequence
22 27 41 04 07 29 47 28 31 49 13 30 22 (moves right to left)
Sherrill's Sequence
22 52 18 04 64 06 47 58 17 49 63 36 22
Sine Wave Sequence
26 41 27 23 02 08 45 31 28 43 01 14 26 (Moves left to right)
Sherrill's Sequence
23 27 41 26 14 01 43 28 31 45 08 02 23
Sine Wave Sequence
46 07 02 24 27 42 25 13 01 44 28 32 46 (Moves left to right)
Sherrill's Sequence
24 02 07 46 32 28 44 01 13 25 42 27 24
Sine Wave Sequence
46 07 02 24 27 42 25 13 01 44 28 32 46 (Moves right to left)
Sherrill's Sequence
25 12 06 44 57 18 46 11 36 24 51 17 25
Sine Wave Sequence
26 41 27 23 02 08 45 31 28 43 01 14 26 (Moves right to left)
Sherrill's Sequence
26 18 52 23 35 12 45 17 58 43 05 11 26
Sine Wave Sequence
28 47 45 17 25 21 27 22 26 18 46 48 28 (moves right to left)
Sherrill's Sequence
27 23 04 18 50 44 28 43 49 17 03 24 27
Sine Wave Sequence
28 47 45 17 25 21 27 22 26 18 46 48 28 (moves right to left)
Sherrill's Sequence
28 43 49 17 03 24 27 23 04 18 50 44 28
Sine Wave Sequence
63 03 60 29 59 04 64 50 56 30 55 49 63 (Moving left to right)
Sherrill's Sequence
29 60 03 63 49 55 30 56 50 64 04 59 29
Sine Wave Sequence
63 03 60 29 59 04 64 50 56 30 55 49 63 (Moving left to right)
Sherrill's Sequence
30 56 50 64 04 59 29 60 03 63 49 55 30
Sine Wave Sequence
58 43 49 31 33 56 52 23 04 41 19 60 58 (Moving left to right)
Sherrill's Sequence
31 49 43 58 60 19 41 04 23 52 56 33 31
Sine Wave Sequence
51 55 34 32 50 44 57 59 20 42 03 24 51 (Moving left to right)
Sherrill's Sequence
32 34 55 51 24 03 42 20 59 57 44 50 32
Sine Wave Sequence
33 12 06 10 58 54 19 11 36 15 52 53 33 (moves right to left)
Sherrill's Sequence
33 13 01 10 61 41 19 07 02 15 62 31 33
Sine Wave Sequence
20 53 57 09 05 11 34 54 51 16 35 12 20 (moves right to left)
Sherrill's Sequence
34 32 62 16 02 08 20 42 61 09 01 14 34
Sine Wave Sequence
08 39 48 05 09 26 14 38 21 35 16 45 08 (moves left to right)
Sherrill's Sequence
35 21 38 14 26 09 05 48 39 08 45 16 35
Sine Wave Sequence
13 25 10 06 47 40 07 46 15 36 22 37 13 (moves left to right)
Sherrill's Sequence
36 15 46 07 40 47 06 10 25 13 37 22 36
Sine Wave Sequence
59 57 53 37 63 36 55 51 54 40 64 06 59 (Moves left to right)
Sherrill's Sequence
37 53 57 59 06 64 40 54 51 55 36 63 37
Sine Wave Sequence
56 35 64 38 54 58 60 05 63 39 53 52 56 (Moving left to right)
Sherrill's Sequence
38 64 35 56 52 53 39 63 05 60 58 54 38
Sine Wave Sequence
56 35 64 38 54 58 60 05 63 39 53 52 56 (Moving left to right)
Sherrill's Sequence
39 63 05 60 58 54 38 64 35 56 52 53 39
Sine Wave Sequence
59 57 53 37 63 36 55 51 54 40 64 06 59 (Moves left to right)
Sherrill's Sequence
40 54 51 55 36 63 37 53 57 59 06 64 40
Sine Wave Sequence
58 43 49 31 33 56 52 23 04 41 19 60 58 (Moving left to right)
Sherrill's Sequence
41 04 23 52 56 33 31 49 43 58 60 19 41
Sine Wave Sequence
51 55 34 32 50 44 57 59 20 42 03 24 51 (Moving left to right)
Sherrill's Sequence
42 20 59 57 44 50 32 34 55 51 24 03 42
Sine Wave Sequence
26 41 27 23 02 08 45 31 28 43 01 14 26 (Moves left to right)
Sherrill's Sequence
43 28 31 45 08 02 23 27 41 26 14 01 43
Sine Wave Sequence
46 07 02 24 27 42 25 13 01 44 28 32 46 (Moves left to right)
Sherrill's Sequence
44 01 13 25 42 27 24 02 07 46 32 28 44
Sine Wave Sequence
26 41 27 23 02 08 45 31 28 43 01 14 26 (Moves right to left)
Sherrill's Sequence
45 17 58 43 05 11 26 18 52 23 35 12 45
Sine Wave Sequence
46 07 02 24 27 42 25 13 01 44 28 32 46 (Moves right to left)
Sherrill's Sequence
46 11 36 24 51 17 25 12 06 44 57 18 46
Sine Wave Sequence
22 27 41 04 07 29 47 28 31 49 13 30 22 (moves right to left)
Sherrill's Sequence
47 58 17 49 63 36 22 52 18 04 64 06 47
Sine Wave Sequence
48 29 08 03 42 27 21 30 14 50 32 28 48 (moves right to left)
Sherrill's Sequence
48 05 63 03 17 51 21 35 64 50 18 57 48
Sine Wave Sequence
22 27 41 04 07 29 47 28 31 49 13 30 22 (moves left to right)
Sherrill's Sequence
49 31 28 47 29 07 04 41 27 22 30 13 49
Sine Wave Sequence
48 29 08 03 42 27 21 30 14 50 32 28 48 (moves left to right)
Sherrill's Sequence
50 14 30 21 27 42 03 08 29 48 28 32 50
Sine Wave Sequence
51 55 34 32 50 44 57 59 20 42 03 24 51 (Moving right to left)
Sherrill's Sequence
51 16 40 32 46 48 57 09 37 42 25 21 51
Sine Wave Sequence
58 43 49 31 33 56 52 23 04 41 19 60 58 (Moving right to left)
Sherrill's Sequence
52 22 26 41 38 10 58 47 45 31 39 15 52
Sine Wave Sequence
61 09 37 53 39 15 62 16 40 54 38 10 61 (Moving left to right)
Sherrill's Sequence
53 37 09 61 10 38 54 40 16 62 15 39 53
Sine Wave Sequence
61 09 37 53 39 15 62 16 40 54 38 10 61 (Moving left to right)
Sherrill's Sequence
54 40 16 62 15 39 53 37 09 61 10 38 54
Sine Wave Sequence
59 57 53 37 63 36 55 51 54 40 64 06 59 (Moves right to left)
Sherrill's Sequence
55 62 32 40 07 29 59 61 42 37 13 30 55
Sine Wave Sequence
56 35 64 38 54 58 60 05 63 39 53 52 56 (Moving right to left)
Sherrill's Sequence
56 30 14 38 41 61 60 29 08 39 31 62 56
Sine Wave Sequence
51 55 34 32 50 44 57 59 20 42 03 24 51 (Moving right to left)
Sherrill's Sequence
57 09 37 42 25 21 51 16 40 32 46 48 57
Sine Wave Sequence
58 43 49 31 33 56 52 23 04 41 19 60 58 (Moving right to left)
Sherrill's Sequence
58 47 45 31 39 15 52 22 26 41 38 10 58
Sine Wave Sequence
59 57 53 37 63 36 55 51 54 40 64 06 59 (Moves right to left)
Sherrill's Sequence
59 61 42 37 13 30 55 62 32 40 07 29 59
Sine Wave Sequence
56 35 64 38 54 58 60 05 63 39 53 52 56 (Moving right to left)
Sherrill's Sequence
60 29 08 39 31 62 56 30 14 38 41 61 60
Sine Wave Sequence
61 09 37 53 39 15 62 16 40 54 38 10 61 (Moving right to left)
Sherrill's Sequence
61 59 20 53 33 56 62 55 34 54 19 60 61
Sine Wave Sequence
61 09 37 53 39 15 62 16 40 54 38 10 61 (Moving right to left)
Sherrill's Sequence
62 55 34 54 19 60 61 59 20 53 33 56 62
Sine Wave Sequence
63 03 60 29 59 04 64 50 56 30 55 49 63 (Moving right to left)
Sherrill's Sequence
63 39 48 29 47 40 64 38 21 30 22 37 63
Sine Wave Sequence
63 03 60 29 59 04 64 50 56 30 55 49 63 (Moving right to left)
Sherrill's Sequence
64 38 21 30 22 37 63 39 48 29 47 40 64