User:Tropylium/Mediums

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Each stable medium has a dual counterpart (obtainable by on/off reversal) and a strobe counterpart (p2 oscillating, obtainable by A/B and S/D reversal of both the medium and its dual).

Any medium may exist only in certain CA rules, which may be speficied with BADS notation. In addition to the immediate stability, of interest is in which areas of CA rulespace the medium may be stable or instable against perturbations. A global lability condition (GLC) causes any imperfection in the medium to expand; a global stability condition causes any imperfection in the medium to remain in place. More than one of each may exist. In more complex mediums, directed versions may exist, that force expansion or stability only in some direction(s) from certain kinds of sites. In any stable medium, lability conditions are of the type B/D, while in a strobe medium they are of the type A/S.

The rank of a medium is the number of BADS conditions it requires for overall stability. In addition to the rank, another useful measure of the complexity of a regular medium is the number of distinct phases.

Conway's Game of Life supports at least the following mediums:

  • Vacuum
  • Zebra stripes
  • Chickenwire
  • Venetian blinds (strobe large zebra stripes)
  • The A4/S3 mediums

Vacuum

Vacuum is the most widely seen medium (indeed the only medium explicitly supported by most CA programs), and together with its inverse (which we may call the antivacuum) the only rank 1 medium: its stability requires only A0.

  • GLC: B1 (diagonally at c)
  • B2 domino engine
  • GSC: A123 (octogonally)

Rank 2 mediums

Oscillating vacuum

B0/D8, single phase

Checkerboard

Checkerboard is a self-dual medium with two two phases. The stable form requires A4/S4, the oscillating form B4/D4.

  • GLC: B5, D3 (diagonally at c, from on vs. off perturbations)
  • GSC: S3456, A2345 (diagonally, on vs. off)

Zebra stripes

Zebra stripes is a self-dual medium with four phases. It is the simplest anisotropic medium. The stable form requires A6/S2, the oscillating form B6/D2.

  • DLC: B7, D1 (both along-the-grain at c; stabilizable)
  • DSC: S2345, A3456 (both against-the-grain)

Chicken wire

Chicken wire, or more exactly 2-chicken wire, is self-dual medium with eight phases. The stable form requires A5/S3.

Large checkerboard

A self-dual medium with eight phases. It requires, like the smaller version, A4/S4.

Large zebra stripes

A self-dual medium with eight phases. A3/S5. The strobe version is known as venetian blinds.

3x3 mediums

In a unit cell of size 3x3, every individual cell has all the other cells as neighbors. From this follows that all agars of this size are of rank 2, and all agars with equally many living cells per unit cell have the same stability conditions.

  • A1/S0 dot agar: 9 phases
  • A2/S1 mediums (duals: A7S6)
    • Duplets agar: 18 phases
    • Dominos agar: 18 phases
  • A3/S2 mediums (duals: A6S5)
    • Diagonal agar: 6 phases
    • Pinstripes agar: 6 phases
    • Skew agar: 36 phases
    • Preblock agar: 36 phases
  • A4/S3 mediums (duals: A5S4)
    • Marshland agar: 9 phases
    • Block agar: 9 phases
    • Prepond agar: 36 phases
    • Siamese table agar: 36 phases
    • Siamese snake agar: 36 phases
    • GLCs: B5 (at c/1, stoppable by tables in one direction), D2 (at c/1, stoppable by blocks; by tables/snakes in one direction)

Within each class, the unit cells may be mixed and matched to yield a variety of irregular or larger regular mediums.

Rank 3 mediums

Mesh

Mesh is an A8/S46 medium with four phases.

  • GLC: D5 (at c/1 diagonally and orthogonally, from off perturbations)
  • GSC: S34567 (orthogonally), A7/S4567 (diagonally)

Skew mesh

Skew mesh is an A8/S56 medium with 16 phases.

  • GLC: D4 (from off perturbations)

Workable stable (skew) mesh rules do not exist, as adding S5 (S4) allows mixing and matching between the two mediums for irregular results (any live area is highly likely to leave a huge mess in its wake).