Wolfram (2,3) Machine

Wolfram's (2,3) machine, number 596440, as a true Turing machine. Its two states A and B over symbols { 0, 1, 2 } never halt. The distinctive feature is the tape itself: rather than a blank background it runs over an infinite alternating 0 1 0 1 … pattern. Each cell remembers the background digit it was born holding and hands the opposite digit to any neighbour it grows, so the revealed tape always alternates correctly in both directions — even behind the head, where the background is preserved separately from the symbol the head has overwritten.

A demonstration of weak universality — a machine that is universal only over a structured, non-blank background. It motivates the self-growing-tape pattern's one real variation: each cell stores an immutable background digit alongside its current symbol, so an infinite periodic environment can be revealed on demand without ever being pre-populated. The Concepts guide's Turing Machines page covers the background trick and the limits of the universality claim in full.

# wolfram-23.osi.yaml — emitted automatically
semantic_model:
  name: "wolfram-23"
  source: "duckdb://wolfram-23.db"
  entities:
    - name: cell
      primary_key: id
  dimensions:
    - name: state
      type: categorical
    - name: t
      type: time
  measures:
    - name: row_count
      agg: count
    - name: active
      agg: sum
      filter: "state = 'ACTIVE'"