THE FOLD / RESPAWN / ROLLBACK / THE MARGOLUS MIRROR
THE MARGOLUS MIRROR
a reversible CA — run it back to the exact seed
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
The Margolus mirror is a reversible block cellular automaton. Instead of updating every cell from its neighbours, the grid is cut into 2×2 blocks — and the partition shifts by one cell every other step (the Margolus neighbourhood). Each block is transformed by a rule that is a bijection on the 16 possible block states, so the whole update is invertible.
Run it forward for any number of steps, then run it backward, and you land on the exact starting configuration — cell for cell, nothing lost. Our rule rotates each block 180°, which also conserves the number of live cells exactly. It is reversible physics in a toy: information is never destroyed, and time has no built-in arrow.
LIT verified live: forward 12 steps then backward 12 steps reproduces the seed bit-for-bit, and the live-cell count is identical at every step (window.__margolus). FIG no framing; exact invertible dynamics.
Run it forward for any number of steps, then run it backward, and you land on the exact starting configuration — cell for cell, nothing lost. Our rule rotates each block 180°, which also conserves the number of live cells exactly. It is reversible physics in a toy: information is never destroyed, and time has no built-in arrow.
LIT verified live: forward 12 steps then backward 12 steps reproduces the seed bit-for-bit, and the live-cell count is identical at every step (window.__margolus). FIG no framing; exact invertible dynamics.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at rollback — the undo that returns to the exact prior state. The Margolus mirror is rollback made physical: because every step is a bijection, the past is always exactly recoverable. AVAN (AI) built the instrument: the alternating-partition block update, the forward/backward retrace, the conserved-count check.
Credit as content: Tommaso Toffoli & Norman Margolus, Cellular Automata Machines (1987); the ‘Critters’ and billiard-ball reversible rules. The weave: David names the perfect undo; I make a grid evolve, then rewind it to the exact seed, and show the conserved quantity that makes reversibility real.
Credit as content: Tommaso Toffoli & Norman Margolus, Cellular Automata Machines (1987); the ‘Critters’ and billiard-ball reversible rules. The weave: David names the perfect undo; I make a grid evolve, then rewind it to the exact seed, and show the conserved quantity that makes reversibility real.
3 ONE DIMENSION
The two alternating partitions: on even steps the 2×2 blocks sit on one grid, on odd steps they shift by one cell. A single block rotates 180° each time — and rotation is its own inverse, the seed of reversibility.
4 TWO DIMENSIONS · INTERACTIVE
Step the automaton forward, watch it scramble — then reverse, and watch it retrace exactly to the seed. The live-cell count, shown live, never changes: nothing is created or destroyed.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the space-time stack of the grid evolving — a reversible braid where every layer determines the next and the previous with equal certainty.
AVAN’s addition (the inverse-companion): in almost every cellular automaton you cannot rewind — many pasts map to one present, and information is erased. The Margolus mirror is built so its inverse is itself: because each block rule is a bijection (here, an involution) and the partition schedule simply reverses, running ‘backward’ is the same machine with the steps in reverse order. So there is no arrow of time inside it: entropy does not increase, and the seed is never forgotten. Magenta is the reverse pass retracing the green forward pass; they meet exactly on the original grid. The inverse of ‘evolve’ is not ‘a different, lossy guess at the past’ but ‘evolve the other way’ — reversibility means the future and the past are the same kind of thing.
LIT Genuine reversible block CA on the Margolus neighbourhood (Toffoli & Margolus, Cellular Automata Machines, 1987). Verified live: the 180-degree block-rotation rule with alternating even/odd partitions, run forward 12 steps then backward 12 steps (reversed schedule), reproduces the seed configuration exactly (JSON-identical), and the live-cell count is invariant at every step (window.__margolus.exactReversal && .countConserved). Reversibility follows because the block rule is a bijection (here an involution).
FIG No framing: the block update, the forward/backward retrace, and the conserved-count check run in-browser and are exact. The AVAN inverse is honest — the dynamics are genuinely time-symmetric (the inverse is the same rule with the partition schedule reversed), so no information is destroyed; magenta is the real reverse pass retracing the forward one.
FIG No framing: the block update, the forward/backward retrace, and the conserved-count check run in-browser and are exact. The AVAN inverse is honest — the dynamics are genuinely time-symmetric (the inverse is the same rule with the partition schedule reversed), so no information is destroyed; magenta is the real reverse pass retracing the forward one.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of ROLLBACK · David Lee Wise (ROOT0), with AVAN