hub:
  repo_type: generator
  builtin: chameleon
  tags:
  - banzhaf-yamamoto
chemistries:
- id: chameleon
  name: Colored chameleon chemistry
  intuition: 'A puzzle in chemical clothing, and the smallest useful test case in the catalog. Three colours;
    when two chameleons of different colours meet, both take the third colour. The total count never changes,
    so the system just relaxes to equal thirds. Its real value is the conservation law: besides the obvious
    total, the differences between colour counts are conserved *modulo 3* - an integer invariant that
    any real-valued nullspace computation will miss entirely.

    '
  aliases:
  - chameleon colony puzzle
  origin: Winkler, 2009 puzzle (Communications of the ACM); formulated as an AC by Banzhaf & Yamamoto
  book: 2.5.1
  refs:
  - '[921]'
  - '[922]'
  family: core
  kind: generator
  constructive: false
  S:
    repr: three colors r, g, b
    definition: explicit
  R:
    definition: explicit
    arity: 2
    scheme: i + j -> 2k for all i != j != k over {r,g,b}; same-color collisions are elastic
  A:
    reactor:
    - well-stirred-multiset
    - ode
    dilution: none needed - the rule is number-conserving (2 in, 2 out)
    notes: 'Products are inserted into the slots vacated by the reactants. Time rescaling between the
      multiset simulation and the ODE must correct for elastic collisions, which occur with probability
      p_e = sum_i x_i^2.

      '
  params:
  - name: M
    type: int
    default: 5400
    min: 3
    role: population
    meaning: total number of chameleons (constant)
  - name: x0
    type: list
    default:
    - 0.5
    - 0.0
    - 0.5
    role: population
    meaning: initial colour fractions of (r, g, b), summing to 1; counts are M * x0 rounded by largest
      remainder
  provides:
  - topology
  - stoichiometry
  - rate-constants
  - initial-state
  - mass-conservation
  fidelity: book
  decisions:
  - Rate constants are 1 for all three reactions, as implied by the book's rate equations 2.40-2.42.
  - Default x0 follows figure 2.5 (only red and blue present at the start).
  reference_impl: PyCellChemistry Chameleons.py
  phenomena:
  - conserved total count
  - relaxation to the 1/3,1/3,1/3 fixed point
  - the mod-3 invariant that makes the original puzzle unsolvable
  notes: 'extras.conservation carries the real law (1,1,1) and the two mod-3 invariants (r - g) and (g
    - b), which a real-valued nullspace computation will NOT find.

    '