How it works

Polymers as tape-processing machines. Two strings react when a recognition site on each can locate the same pattern; the first then acts as a processor reading the second as a tape and writing new strings. Self-replicators exist - a string that copies itself via its complement - and so do parasites: strings carrying the replicator's recognition site but no replication machinery of their own, which get copied for free. It began as a C program (1988) and was later realised in special-purpose parallel hardware.

S

binary heteropolymers; species id p<bitstring>, structure the bitstring (first character = first monomer) · implicit

R

s1 + s2 -> s1 + s2 + s3 (+ s4 ...), if a recognizon of s1 and one of s2 can place the same specific pattern; s3.. are the strings the processor s1 writes while reading the tape s2 · arity 2

A

well-stirred-multiset · products overwrite randomly chosen molecules (Moran displacement), population constant

Parameters

What to look for

• self-replicating strings exist: 0001111100111010111 replicates via its complement (report section 4; tested)
• parasites: strings with the replicator's recognizon but no replication rule, replicated by it (0000000100100010111; tested)
• report section 4 (1.2 x 10^6 steps, random population of 19-mers inoculated with 10% replicator and 10% parasite): quasispecies-like mutant clouds form, the parasite master sequence goes extinct at 750000 steps, the replicating rule survives in other sequences (not reproduced here)
• later lattice and hardware versions (review 3.5.1): hypercyclic cooperating polymer sets, chemoton-like membrane-bounded organizations (not modelled)

Implementation decisions

• The book gives only the scheme; the machine follows the 1988 report. Its doublet tables (section 3, items 4-5) are implemented verbatim. The report does not say where a rule starts relative to its initiator, where the heads start, the initial state or how the written tape is cut into strings. Of the literal choices tried (rule after or at the initiator, overlapping or not, forward or reversed, linear or circular, head at either end, initial state 0 or 1), exactly one family makes the published replicator replicate: a rule is the 12 bits starting at every occurrence of 111 (overlapping, the initiator bits included), both heads start at position 0 of their tapes, the state starts at 0 (1 works too), later rules overwrite earlier ones (the reverse order breaks replication), and released strings are the maximal non-blank runs of the written tape.
• With that decoding 0001111100111010111 does not copy itself in one step but through its complement: s + s -> s + s + c(s) and s + c(s) -> s + c(s) + s (two alternating rules write, per tape symbol, 1 and then the opposite of the read symbol). The WRITE code has no 'same as read symbol', so one-step copying needs two rules (24 bits), longer than the 19-bit string; the report's 'self-replicating' is taken as this plus/minus-strand replication. The parasite 0000000100100010111 has its only 111 at the end, encodes no rule, and is copied by the replicator the same way (report: replicated without replicating themselves).
• Consequence of that framing (open doubt): the initiator 111 supplies READ = 11 (both) and the first bit of WRITE, so every rule reads both symbols and writes 1 or the opposite of the read symbol; the READ codes 0, 1, blank and the WRITE codes 0, blank are never used. The report says the initiator 'may be taken to be a particular triplet such as 111', so its C program may have used another marker; nothing else in the report pins it, and the framing is kept because it is the only literal one that makes the published replicator work.
• Report section 4 says about 2^17 strings must be sampled to find a replicator 'i.e. ca 10^8' (inconsistent: 2^17 is about 1.3 x 10^5). With the reconstructed decoding, 10133 of the 2^19 strings of length 19 replicate through their complement (about 2^-5.7) and one copies itself directly; the published estimate is not reproduced, which suggests further unpublished details of the C implementation.
• Recognizons: the report fixes the doublet code and the initiator/terminator 111 but not the reading frame. Chemart reads them like rules: from every 111, doublets until a later 111 starting on a doublet boundary, the end of the string, or R symbols. The parasite and the replicator then share the recognizon '#' of their common tail ...0111, as the report requires. Two molecules collide when recognizons of equal length agree wherever neither has #, which is the same as sharing a specific pattern once each # is resolved at random (the report's nondeterministic accept). No reading frame tried (forward/reversed; at, after or before the initiator; three terminator rules) lets the replicator collide with its complement, so under recognition patterns the plus/minus cycle does not close; recognition none shows the full cycle. Open doubt.
• Consequence for the soup (not reproduced): with recognition patterns the replicator can collide with itself (making its complement) but never with its complement, so nothing ever writes a new replicator and the inoculated replicator declines (seed 0, 20000 steps: from 20 of 200 to 0). The report's run, in which the replicating rule survives and the parasite master sequence goes extinct, is therefore not reproduced. With recognition none the plus/minus reaction does fire (e.g. seed 1), but in both modes (seeds 0-2, population 200, up to 20000 steps) the replicator dies out: random background processors keep writing the one-symbol string '1', and every product displaces a random molecule, so short junk strings take over the population.
• Reaction scheme: the report makes processing purely catalytic (the processed string is not removed; new strings are written on a blank tape), so reactions are s1 + s2 -> s1 + s2 + s3; the book's s1 + s2 -> s1 + s3 is followed only in the report's optional crossed-tape variant (two tapes, no finite-state machine), which is not implemented. No rates are published, so rates are None.
• Soup: the report's algorithm with a pattern space, earlier-placed molecule as processor, removal of both references and of overwritten molecules' references. The linear domain of 2^M symbol positions with partial overwriting is replaced by a population of whole molecules in which each product replaces a random molecule (Moran displacement, outflow constant-total). The report's exponential random cutoff is the fixed max_steps. Errors act on written symbols only (a write flips with probability error_rate); the report says all elementary steps are error-prone without specifying how.
• v1 params dropped: n_wildcards (the number of # is encoded in each string, not a global knob) and grid (no spatial domain; 'space' removed from provides, lattice-2d from A.reactor). The v1 l (polymer length) is kept as the soup's random-string length: strings are otherwise of any length.
• Book references: [247] (Ehricht, Ellinger & McCaskill 1997, CATCH) is a wet-lab cross-hybridization amplification paper, and [136] (Breyer et al., Artificial Life 4(1), 1998, not 1999) simulates DNA/RNA 3SR chemistries in NGEN; neither describes the pattern processing chemistry. [843] (POLYP) describes hardware. The book's 'length l' and the review's 'l was typically 20' do not appear in the report, whose M = 20 sizes the domain (2^M positions) and whose runs use length 19 (section 4) or about 30 (section 3).

Sources

• McCaskill, J. S. (1988). Polymer chemistry on tape: a computational model for emergent genetics. Internal report, Max-Planck-Institut fuer biophysikalische Chemie, Goettingen (book ref [566]); scanned, 19 pages: section 2 (pattern space, Holland conditions, recognizons, processors, crossed-tape variant), section 3 items 1-5 (doublet codes), section 4 (replicator, parasite, run). https://homepage.ruhr-uni-bochum.de/john.mccaskill/publications/publications/283.pdf
• Dittrich, P., Ziegler, J. & Banzhaf, W. (2001). Artificial chemistries - a review. Artificial Life 7(3):225-275, section 3.5.1 (the source of the book's text). https://www.cs.mun.ca/~banzhaf/papers/alchemistry_review_MIT.pdf
• McCaskill, J. S., Maeke, T., Gemm, U., Schulte, L. & Tangen, U. (1997). NGEN: a massively parallel reconfigurable computer for biological simulation. LNCS 1259:260-276 (first pages only: 'networks of interacting molecular Turing machines', pairwise recognition plus unary processing). https://doi.org/10.1007/3-540-63173-9_52
• Breyer, J., Ackermann, J. & McCaskill, J. S. (1998). Evolving reaction-diffusion ecosystems with self-assembling structures in thin films. Artificial Life 4(1):25-40 (book [136]; abstract only). https://doi.org/10.1162/106454698568422

Banzhaf & Yamamoto, Artificial Chemistries (2015), §10.5.3

Preview at default parameters

7 species · 12 reactions · status complete · seed 1

2 p0001111100111010111 -> 2 p0001111100111010111 + p1110000011000101000
p0001111100111010111 + p0000000100100010111 -> p0001111100111010111 + p0000000100100010111 + p1111111011011101000
2 p1110000011000101000 -> 2 p1110000011000101000 + p1111111111111111111
p1111111011011101000 + p0001111100111010111 -> p1111111011011101000 + p0001111100111010111 + p1
2 p1111111011011101000 -> 2 p1111111011011101000 + p1
p0001111100111010111 + p1111111011011101000 -> p0001111100111010111 + p1111111011011101000 + p0000000100100010111
p1111111111111111111 + p0001111100111010111 -> p1111111111111111111 + p0001111100111010111 + p1110000011000101000
p1111111111111111111 + p0000000100100010111 -> p1111111111111111111 + p0000000100100010111 + p1111111011011101000
p1111111111111111111 + p1111111011011101000 -> p1111111111111111111 + p1111111011011101000 + p0000000100100010111
2 p1111111111111111111 -> 2 p1111111111111111111 + p0000000000000000000
p0001111100111010111 + p1111111111111111111 -> p0001111100111010111 + p1111111111111111111 + p0000000000000000000
p1111111011011101000 + p1111111111111111111 -> p1111111011011101000 + p1111111111111111111 + p1

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