qts as CON WAYS game of life

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Below is a self-contained rule-set that (i) remains faithful to the three pillars and variational functional of Quantum-Teleodynamic Synthesis (QTS), yet (ii) collapses—when you implement it literally—to the ordinary B3/S23 update of Conway’s Game of Life. I first show how each QTS pillar is re-expressed on a two-state lattice and then give a ready-to-code rule list and reference pseudocode.

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1. Translating QTS into a Minimal Cellular-Automaton Grammar

Pillar I (quantum-coherent substrate)
Interpretation on a grid: every live cell embodies a local “coherent excitation.” The eight-neighbour stencil is the cell’s interaction light-cone. A birth or survival event is allowed only when the neighbourhood size keeps decoherence costs minimal (≤3 simultaneous couplings). LF Yadda – A Blog About Life

Pillar II (information-thermodynamic ratchet)
The neighbourhood count n encodes environmental regularities. Allowing growth at exactly n = 3 and maintenance at n = 2 or 3 maximises entropy export per bit of stored information: three couplings create the lowest Kolmogorov-complex pattern able to copy itself (glider), while two couplings preserve existing information with no extra coherence cost. LF Yadda – A Blog About Life

Pillar III (emergent teleodynamics)
Iterating the two rules above minimises the discrete analogue of F=⟨S˙env⟩−α I+β C\mathcal F = \langle\dot S_{\text{env}}\rangle-\alpha\,\mathcal I+\beta\,\mathcal CF=⟨S˙env​⟩−αI+βC

because (a) over-crowded sites (n > 3) sacrifice information and coherence for little extra dissipation, so they are deleted; (b) under-crowded sites (n < 2) cannot export enough entropy, so they vanish; (c) the attractors that remain (blinkers, gliders, Gosper gun) are the teleodynamic “agents” of the lattice. LF Yadda – A Blog About Life

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2. Explicit Rule-Set (QTS-Life → Conway Life)

For every cell s(t) ∈ {0,1} and its Moore-neighbour sum n(t):

1. Quantum-Coherence Gate
   If n(t) ∈ {0,1,4,5,6,7,8}
    ⇒ coherence cost > benefit → set s(t + 1) ← 0 (death).
2. Information-Ratchet Birth
   If s(t)=0 and n(t)=3
    ⇒ minimal 3-body resonance → set s(t + 1) ← 1 (birth).
3. Information-Ratchet Survival
   If s(t)=1 and n(t) ∈ {2,3}
    ⇒ entropy export optimal → keep s(t + 1) ← 1 (survival).
4. Teleodynamic Pruning
   All other combinations default to s(t + 1) ← 0.

Note: Rules 2–4 condense to Conway’s classic B3/S23 scheme; Rule 1 simply states its complementary set in QTS language.

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3. Reference Pseudocode (Python-style)

pythonCopyEditdef qts_life_step(grid):
    # grid : 2-D numpy array of 0/1
    nbrs = sum(np.roll(np.roll(grid,i,0),j,1)
               for i in (-1,0,1) for j in (-1,0,1) if (i,j)!=(0,0))
    birth  = (grid==0) & (nbrs==3)
    survive= (grid==1) & ((nbrs==2)|(nbrs==3))
    return (birth | survive).astype(int)

Drop this into any Life viewer and you recover gliders, blinkers, etc. The names of the conditionals correspond exactly to Pillar II’s “birth” and “survival” ratchets; the masking operations implement Pillar I’s coherence gate, and the function as a whole realises Pillar III’s teleodynamic update by repeating qts_life_step each tick.

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4. Why the Mapping Works

• Energy flow vs. neighbour count Neighbour number is the CA’s proxy for entropy export rate ⟨Ṡₑₙᵥ⟩. Births at 3 add just enough new channels to dissipate without raising coherence costs beyond β.
• Information storage A 2- or 3-neighbour live cell sits at an information optimum: it is neither random nor frozen, hence maximises I per cell.
• Coherence cost More than three entangled neighbours raises C faster than the gain in ⟨Ṡₑₙᵥ⟩, so the functional F increases; the automaton deletes those states exactly as Life does.

Thus the familiar elegance of Conway’s Game emerges as the discrete, low-dimensional limit of the QTS variational principle.