chemart / bondable-ca

hub:
  repo_type: generator
  builtin: bondable-ca
  tags:
  - banzhaf-yamamoto
chemistries:
- id: bondable-ca
  name: Bondable Cellular Automata (BCA)
  intuition: 'Reactivity that is not declared but *measured*. Each atom is a small one-dimensional cellular
    automaton, and its type is the Wolfram rule that runs it. To decide whether two atoms bond, you let
    their dynamics settle and read an emergent property - the mean polarity - then compare. Bonded atoms
    also influence each other''s neighbourhoods, so a bond can strengthen or weaken itself. Ordering all
    256 rules by settled polarity even produces something like a periodic table. This is the sub-symbolic
    idea: chemistry emerging from an internal dynamical system rather than from a table.

    '
  aliases:
  - BCA
  - sub-symbolic cellular automata chemistry
  origin: Hatcher, Banzhaf & Yu, 2011
  book: 10.7.3
  refs:
  - '[372]'
  - '[373]'
  - '[264]'
  - doi:10.7551/978-0-262-29714-1-ch051
  - http://www.cs.mun.ca/~banzhaf/papers/bondable2011.pdf
  family: automata
  kind: generator
  constructive: true
  S:
    repr: 'An atom is a 1-d binary CA of width w with periodic (closed) boundaries; its type is the Wolfram
      rule number 0..255 that runs it. A molecule is a chain of bonded atoms, identified by its atom types,
      its cell states and the alignment offset of each bond, minimised over the chain and its reverse.

      '
    definition: implicit
    notes: 'Species are the molecules reached by the closure; the structure string r<rule>:<cells>~+<offset>~r<rule>:<cells>
      carries the whole molecule, so two molecules with the same skeleton but different cell states are
      different species (r165-r90, r165-r90#2).

      '
  R:
    definition: implicit
    arity:
    - 1
    - 2
    scheme: 'Association A + B -> AB and dissociation AB -> A + B, both driven by OBSERVABLES of the atoms''
      dynamics rather than declared. Two molecules bond end to end when their settled mean polarities
      satisfy the polarity criterion and the strongest cyclic alignment of the two facing atoms has a
      contiguous complementary run of at least bond_threshold cells. Once bonded, each CA''s neighbourhood
      is influenced by the other inside that run, which can strengthen or weaken the bond; a bond that
      has fallen below the threshold breaks and each fragment settles again.

      '
    notes: 'No rate constants: the book gives no kinetics, so every reaction carries rate None. Molecules
      are chains, so each atom bonds at most two partners.

      '
  A:
    reactor: well-stirred-multiset
    dilution: none
    notes: 'The model''s reactor is collisions in a well-stirred mixture. Chemart returns the reaction
      closure of the seed atom types (chemart.expand.expand over arities 1 and 2) instead of one sampled
      collision sequence, so the network is reproducible without a population; status becomes truncated
      when max_species binds.

      '
  params:
  - name: w
    type: int
    default: 12
    min: 3
    max: 16
    range: book fig. 10.16 is drawn for w = 12
    role: structural
    meaning: CA width in cells on a periodic ring; an atom has 2^w configurations, so wide rings settle
      slowly
  - name: atom_types
    type: list
    default:
    - 0
    - 18
    - 90
    - 110
    - 165
    - 184
    - 204
    - 255
    range: the full periodic table is all 256 rules; its closure is far larger than the default species
      budget
    role: structural
    meaning: Wolfram rule numbers 0..255 seeded into the reactor; each becomes one atom species, settled
      from the standard start
  - name: bond_threshold
    type: int
    default: 10
    min: 1
    max: 16
    range: must be <= w; 6-8 make almost everything bond and the closure runs into max_species
    role: structural
    meaning: smallest bonding strength (longest contiguous complementary run) at which a bond forms and
      survives
  - name: polarity_rule
    type: enum
    default: opposite-sign
    choices:
    - opposite-sign
    - sum-zero
    - any
    role: structural
    meaning: 'the polarity condition two colliding molecules must meet: settled mean polarities of opposite
      sign, summing to zero within 0.5, or no condition'
  - name: coupling
    type: enum
    default: replace
    choices:
    - replace
    - xor
    - none
    role: structural
    meaning: 'how a bonded cell''s neighbourhood is influenced by the partner: the facing neighbour is
      taken from the partner''s aligned cell, exclusive-ored with it, or (none) not coupled at all, which
      is the control that switches the book''s interaction off'
  - name: settle_iterations
    type: int
    default: 256
    min: 2
    max: 65536
    range: the shading of fig. 10.16 tops out at 2048; free atoms at w = 12 all settle by iteration 28
    role: structural
    meaning: iterations allowed for the dynamics to reach an attractor before the observable is read;
      a trajectory that has not closed is reported unsettled and averaged over its second half
  - name: max_atoms
    type: int
    default: 3
    min: 2
    max: 12
    role: structural
    meaning: largest molecule the closure will build, in atoms per chain
  - name: max_species
    type: int
    default: 200
    min: 1
    role: structural
    meaning: species budget of the closure; the status becomes truncated if it binds (the default closure
      completes at 23 species)
  provides:
  - topology
  - stoichiometry
  - mass-conservation
  - sequence-structure-function
  fidelity: book+decisions
  sources:
  - 'Banzhaf & Yamamoto (2015), section 10.7.3 and figures 10.15-10.16: atoms as 1-d binary CAs with closed
    boundaries, mean polarity as the observable, bonding strength as the largest contiguous sequence of
    complementary binary numbers, the coupled neighbourhood once bonded, and the ''periodic table'' of
    the 256 rules by settled mean polarity.'
  - Hatcher, M., Banzhaf, W. & Yu, T. (2011). Bondable cellular automata. In Proc. 11th European Conference
    on Artificial Life (ECAL 2011), pages 326-333, MIT Press. doi:10.7551/978-0-262-29714-1-ch051 (book
    ref [373]). Open copy on Banzhaf's page, http://www.cs.mun.ca/~banzhaf/papers/bondable2011.pdf, found
    after the implementation was written (the implementation decisions were made without it). Its model
    differs from Chemart's in the start state (a single live cell), the running mean polarity, the bond
    site (longest run of 1s against longest run of 0s, no threshold), the coupling (a linked cell sees
    its partner's whole neighbourhood), unbonding (when the bonded atoms no longer have opposite polarity)
    and molecule shape (binary trees, up to two atom pairs per bond). Its Table 3 (75 positive, 115 negative,
    66 neutral rules) is reproduced by Chemart's CA step from its start state.
  - 'Faulconbridge, Stepney, Miller & Caves (2011). RBN-World: a sub-symbolic artificial chemistry (book
    ref [264]), the system in which the sub-symbolic idea was first discussed; implemented separately
    as the rbn-world model of catalog id rbn.'
  decisions:
  - 'Authorship corrected: the v1 entry said ''Gross, Banzhaf et al., 2011''. The book''s bibliography
    [373] is M. Hatcher, W. Banzhaf and T. Yu, ''Bondable cellular automata'', ECAL 2011, 326-333, and
    the book''s own text credits [373] and [372] (Hatcher, unpublished, 2013) for figures 10.15 and 10.16.
    The book prints the ECAL-2011 entry with ''2001'', a typo; Crossref and OpenAlex both give 2011 for
    doi:10.7551/978-0-262-29714-1-ch051.'
  - 'Neither [373] nor [372] was accessible, so fidelity is book+decisions: the model comes from book
    10.7.3 and its two figures, and every gap below was filled under the constraint that the result must
    reproduce figure 10.16, which it does.'
  - The settling procedure is nowhere in the book's text; it was recovered from figure 10.16 itself. The
    figure places 202 of the 256 rules in columns -12..+12 and lists the remaining 54 in a wide block
    below the table. Column 0 of the table is empty and the block holds exactly the density-preserving
    rules (204 identity, 170 and 240 shift, 184 traffic, 232 majority, 51 inversion), so the block is
    the polarity-0 column, drawn separately because 54 boxes do not fit in one column.
  - 'Recovered procedure: every atom starts from floor(w / 2) contiguous ones on the ring (a balanced
    start, which is why the density-preserving rules sit at 0); the settled mean polarity is the mean
    of (ones - zeros) over the attractor cycle, and the settling iteration is the transient before it
    (''the transition time of the dynamical system made up of that CA'', fig. 10.16 caption). This reproduces
    the figure for all 256 rules within +-0.5 and exactly for 226. A search over all 4096 initial conditions
    of width 12 found none better: the contiguous half-block, and only it up to rotation, attains that
    score (alternating cells score 16/256, a single seed cell 92/256).'
  - 'The alternative reading of ''settles'', that the polarity becomes constant and non-settling rules
    are the 54 unplaced ones, was tested and rejected: it scores 144/256, and it would leave the identity
    rule 204 (polarity constant at 0 from the start) unplaced.'
  - 30 rules have a fractional cycle mean and are drawn at the nearest integer column. The 8 whose mean
    is exactly +-2.5 (26, 82, 167, 181 drawn toward zero; 154, 166, 180, 210 drawn away from it) are split
    4/4, so the figure's own tie-breaking is inconsistent; the test therefore accepts +-0.5 and additionally
    pins the 226 exact values.
  - 'Mean polarity is reported on the figure''s scale: ones - zeros in -w..+w, i.e. w times the per-cell
    mean of +-1. For a molecule it is averaged over its atoms, keeping the same scale.'
  - Bonding strength (fig. 10.15, 'largest contiguous sequence of complementary binary numbers') is maximised
    over the w cyclic alignments of one ring against the other, ties going to the smallest offset. The
    book does not say whether the rings may be rotated against each other; allowing every alignment is
    what makes the quantity symmetric, which the figure's single green bar per pair implies.
  - 'Coupling law: the book says only that ''each cell in an atom is influenced by the neighborhood cells
    of the other (bonded) atom''. Chemart implements it as, inside the bonded run, the neighbour that
    faces the partner being taken from the partner''s aligned cell, which keeps the neighbourhood three
    cells wide and so keeps Wolfram''s 256 rules meaningful. coupling=xor is offered as the other natural
    reading and coupling=none as the control that switches the interaction off. The bonded run is recomputed
    from the current cells at every step, so a bond can grow or shrink, which is the book''s ''might lead
    to an increase in bonding or a decrease''.'
  - 'Association criterion: the book says reactions are ''observed under the right polarity conditions''
    without giving them. opposite-sign (the default) makes bonding the polarity analogue of the complementary-cell
    bond; sum-zero and any are offered as alternatives. Molecules bond end to end, in whichever of the
    four orientations of the two chains gives the strongest bond.'
  - 'Dissociation: after the coupled molecule settles, it splits at the first bond whose run has fallen
    below bond_threshold, and each fragment settles again on its own. The book only says molecules ''can
    collide to form larger molecules or, alternatively, decay''.'
  - 'Molecules are chains: figure 10.15 shows two atoms bonded side by side, and each atom is given at
    most two partners. Branched molecules and rings are not built. Species identity is the canonical chain
    code minimised over the chain and its reverse, so it is invariant under the molecule''s symmetry.'
  - settle_iterations caps the search for an attractor. A free atom of width w has only 2^w configurations,
    but a coupled molecule's joint state space is 2^(n*w), so its transient need not be short; without
    the cap a single association can run for millions of steps. A trajectory that has not closed within
    the cap is reported unsettled in extras.analysis.unsettled_molecules and its observable averaged over
    the second half. At w = 12 every free atom settles by iteration 28, so the cap never binds for the
    periodic table.
  - 'v1 parameters: rule_set (type matrix, default ''0..255'') becomes atom_types, a list of rule numbers;
    settle_iterations, whose v1 default was the figure''s shading legend ''2, 8, 32, 128, 512, 2048''
    rather than a value, becomes an integer cap; bond_threshold gains a default. max_atoms and max_species
    are added to bound the closure.'
  - 'energies dropped from provides: the v1 note called mean polarity ''an energy-like state variable'',
    but it is an observable of the dynamics, not a per-species energy, and the book gives no energy scale
    or thermodynamics. Bond strengths and molecule polarities are reported in extras.analysis instead.'
  - 'No rate constants or rate laws: the book gives no kinetics for BCA, so every reaction carries rate
    None rather than an invented number.'
  phenomena:
  - 'a ''periodic table'' of the 256 rules ordered by settled mean polarity (book fig. 10.16): 20 rules
    settle at -12 (the ring dies to all zeros), 20 at +12 (all ones) and 54 at 0'
  - density-preserving rules (204 identity, 170 and 240 shift, 184 traffic, 232 majority) hold the balanced
    start's polarity and so settle at 0
  - every rule at w = 12 settles within 28 iterations, well inside the largest shading bucket (2048) of
    fig. 10.16
  - 'reactivity is read off an observable of an internal dynamical system rather than declared: a sub-symbolic
    artificial chemistry'
  - bonding strength is symmetric and bounded by w, and two rings that are equal up to a half-ring rotation
    are fully complementary
  - once bonded, the coupled neighbourhoods change each atom's trajectory, so a bond can strengthen or
    weaken and molecules decay
  notes: 'Called a *sub-symbolic* AC: reactivity is not declared but read off an emergent property of
    an internal dynamical system, an idea first discussed for RBNs in [264] (catalog id rbn, model rbn-world).
    Figure 10.16 is the published result this entry reproduces: it is recoverable in full from the book''s
    own page, and pinning the settling procedure against it is what fixes the parts of the model the text
    leaves open.

    '