Raw data generated for the article

Replicators.txt: Output of the computer search for replicators that generates Table 1

For n from 1 to 13, the file lists all found replicators of length n+2. Each configuration is

followed by R (replicator) or RF (fraternal replicator). The next line gives a replication time (pq=)

and the two replicating elements at that time, separated by a * to indicate a long string of 0's.

For each n, the replicator counts are also tabulated and entropies are estimated.

p16.doc: A detailed description of the label dynamics for π =16

Output of the complete Stage I label tree for π =16, as introduced just before Fig.5.

Each of the 1050 nodes is numbered, and listed are: its generation, its parent and children

(if any), its representation λ, and its equivalence to other nodes with respect to shifts.

q2p32examples.txt: Complete list of the 26 robust handle-link pairs with π =32

Output of the R-algorithm for π =32, as described just before Example 3. The search finds

27 examples. One is the π=8 link of Example 1d; the other 26 have π=32. For each entry,

the first line includes the handle and link sizes and a possible comment. The following

lines form an .rle pattern specification of a handle-link pair for the entry, ending with !.

The rest of the entry gives binary handle+link data for each of the 32 temporal shifts.

ex1tdata.txt: Complete list of the handle-link pairs with π =32 and σ=64

Output of the R- and M- algorithms for those nodes of the π =32 label tree that may

yield a periodic seed, i.e., for those links with σ=64. The first line of the entry includes the

node index and handle size. If the M-algorithm produces a match, the second line shows its

index row and the rotation size. In this event, the next lines specify the handle-link pair in

.rle format, ending with !. The entry ends with binary handle+link data for each of the 32

shifts. If there is no match, then after the first line only the handle+link data is included.

match.txt: Matching pairs generated by the M-algorithm for π =32

This is simply the previous file restricted to links with a match. Careful case

checking produces six periodic seeds with genuinely distinct links – four

robust and two not – as mentioned in the paragraph before Example 5.

ex1tdata_64_nob7.txt: Output of the S-algorithm for π =64

As described in the paragraphs before Example 4, the data represents a complete search

of special labels with π=64 and 4 intervals of each type. Thus there are 7 boundaries, i.e.,

changes from one type (0 or 1) to the other within the label. For any label trajectory that

results in a handle-link pair, the index of the label, the sizes of the handle and link, and

a coding of the boundary structure are given. In the rare cases when σ=128, much more

complete information is listed. First, the root label is given explicitly. Also, the handle-

link pair in .rle format and all the binary handle+link data are included. In this manner,

one discovers the four additional periodic seeds mentioned just before Example 6.