𝌎:Adjacent Possible

The adjacent possible of a system is the set of all possible states that could potentially exist (i.e. are reachable) in the next step of computation, given the current state of the system. It's useful to consider the adjacent possible whenever the phase space of a system is too large to enumerate (as is the case with complex adaptive systems). Time evolution operators are realizing the adjacent possible as they compute.

┌───────────── ADJACENT.POSSIBLE.WIKI ─────────────────┐
│ Adjacent Possible: Branching Evolution               │
│━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━│
│                                                      │
│ Adjacent Possible Tree Structure:                    │
│ ┌────────────────────────────────────────────────┐   │
│ │                     ┌─C─┐                      │   │
│ │                  ╱╲ │   │ ╱╲                   │   │
│ │                 ╱  ╲│   │╱  ╲                  │   │
│ │              ┌─S₁┐ ┌S₂┐ ┌S₃┐ ┌S₄┐             │   │
│ │             ╱│  │╱│  │╲│  │╲│  │              │   │
│ │          ┌─P₁┐┌P₂┐┌P₃┐┌P₄┐┌P₅┐┌P₆┐            │   │
│ │         ╱│  ││  ││  ││  ││  ││  │╲           │   │
│ │      ┌─F₁┐┌F₂┐└──┘└──┘└──┘└──┘┌F₃┐           │   │
│ │      │  ││  │                  │  │           │   │
│ │      └──┘└──┘                  └──┘           │   │
│ │                                                │   │
│ │ Key:                                          │   │
│ │ C = Current State                             │   │
│ │ S₁-S₄ = First-Order Adjacent States           │   │
│ │ P₁-P₆ = Second-Order Possibilities            │   │
│ │ F₁-F₃ = Third-Order Future States             │   │
│ │ ╱╲ = Branching Transitions                    │   │
│ └────────────────────────────────────────────────┘   │
│                                                      │
│ Temporal Evolution Layers:                           │
│ ┌────────────────────────────────────────────────┐   │
│ │ t₀    ●      Current Moment                    │   │
│ │                                                │   │
│ │ t₁   ● ● ● ●  Adjacent Possible               │   │
│ │                                                │   │
│ │ t₂  ● ● ● ● ● ● Second-Order                  │   │
│ │                                                │   │
│ │ t₃ ● ● ●     ● ● ● Third-Order   │   │
│ │                                                │   │
│ │ Accessibility:  High ● → ○ → ⊙ → ◯ Low         │   │
│ └────────────────────────────────────────────────┘   │
│                                                      │
│ Phase Space Properties:                              │
│ • Branching factor increases with complexity         │
│ • Path-dependent accessibility                       │
│ • Combinatorial explosion at deeper levels           │
│ • Local constraints shape possible branches          │
│                                                      │
│ Evolution Operator T(n):                             │
│ T(n): S(t) → {S₁(t+n), S₂(t+n), ..., Sₖ(t+n)}      │
│                                                      │
│ Where:                                              │
│ n = Temporal depth                                  │
│ k = Number of possible states at depth n            │
│ S(t) = State at time t                             │
│                                                      │
│ [Explore Branches] [Calculate Futures]               │
│ [View Time Evolution] [Export Tree]                  │
└──────────────────────────────────────────────────────┘