AFTERLIFE

Verification

What was actually proven by simulating the engine — still lifes, oscillators, spaceships, the four authored scenes, determinism, the default lens, rule presets, theming, colour/B3-S23 invariance, the production build, mobile touch, and the 24-specimen catalogue — plus the honest limitations.

Every claim on this page was checked by actually simulating the rule — with standalone, dependency-free reimplementations of the same B3/S23 step the app itself runs — not recalled from memory. The full logs, generation-by-generation population tables and ASCII renders live in the app's repository under docs/verification/; this page summarises what they show.

The engine itself

  • All seven standard still lifes (block, beehive, loaf, boat, tub, ship, pond) hold their exact bitmap after a step.
  • Four period-2 oscillators, the period-3 pulsar, and the period-15 pentadecathlon all return to their exact starting shape after their expected period.
  • The four common spaceships translate by their known displacement every period — a glider moves (1, 1) every 4 generations.
  • The Gosper glider gun emits a glider (a net +5 population) every 30 generations, checked over generations 120–300 on an unbounded grid.
  • The R-pentomino, acorn and diehard, run on an unbounded grid, match the published literature exactly: the R-pentomino stabilises at generation 1103 with population 116; the acorn at generation 5206 with population 633; diehard dies out completely at generation 130.

The same R-pentomino run again on the actual 256×160 torus behaves differently: its escaping gliders wrap around the world and re-collide with their own debris, so instead of freezing at population 116, it keeps evolving and only settles — into a period-2 cycle at population 109 — at generation 2189. The torus and an unbounded plane are genuinely different environments; only the torus is what you'll see in the app.

Determinism

Rewinding and replaying the same recorded history through the engine's goto(), in a scrambled, out-of-order sequence of target generations, produces bit-identical state every time, matching an independently-run reference simulation. This is what makes scrubbing the history ribbon trustworthy rather than approximate.

The authored scenes

Each was verified by offline simulation before shipping:

  • The default scene's opening encounter between two travelling gliders happens at generation 123.
  • In One Cell, flipping a single cell sterilises the collision entirely — that future is dead by generation 54, while the untouched original reaches a population of 221.
  • In First Contact, a glider and a lightweight spaceship collide at generation 116 and settle into a traffic light.
  • In Keep Something Alive, the baseline activity dies at generation 85; the shipped one-edit solution keeps something moving all the way to the target generation, 150.

The 24 specimens

Every specimen in the catalogue was independently verified for its period, displacement, or (for seeds) stabilisation behaviour.

There is deliberately no puffer. Over 2,600 candidate LWSS/b-heptomino arrangements were generated and searched; the 73 that showed sustained population growth were long-run looking for a clean, periodic puffer signature. None qualified — population either flattened to a constant value or grew irregularly without ever settling into a repeating pattern. Two remembered block-laying-switch-engine constructions were also tried and both failed the same way. Rather than ship an unverified "puffer," the specimen was cut entirely.

Colour never touches the rule

The 5 newer lenses (lineage, immigration, quadlife, velocity, neighbors — see Features for what each means) add colour state that rides along with every cell. A dedicated test seeds that colour state, actively poisons it, and confirms the resulting live/dead bits come out byte-identical to a run with no colour reasoning applied at all — including a glider's exact shape and period, and two identically seeded engines matching bit-for-bit after 40 steps. Colour also survives rewind, branching and reload bit-exactly, because it's captured directly in history keyframes rather than replayed forward from a default (the fix for a real bug where colour used to be lost on reload, traced to replay skipping edits recorded at the generation-0 baseline).

The production build itself is checked

A dedicated Playwright project builds the app for real — vite build, not the dev server — and asserts against actual rendered canvas pixels: every lens (including the 5 multi-hue ones) produces real, richly differentiated, never-white colour, and switching between all 8 in the built bundle produces zero new console errors. This exists because of a real shipped bug: Tailwind v4 + Lightning CSS downlevel design tokens to lab(...) in the production build (the dev server serves oklch(...) verbatim), which broke the old regex-only colour parser and made it silently fall back to solid white for every lens — in production only, which is exactly why it shipped once before this check existed.

The default lens is measurably colourful

The default lens changed from Life to Lineage (see Features). This was checked, not just argued for by design intent: with zero interaction, the opening scene at generation 0 shows several genuinely distinct, significantly-represented hue buckets — measured at 12 in an actual run, using the same colour-bucketing method the production-build lens tests use for the other 7 lenses. The committed regression test asserts a robust ≥3 as its threshold rather than an exact count, so it doesn't become flaky as the opening scene's own content changes over time.

Rule presets: verified, not assumed from reputation

Beyond Conway's own B3/S23, 10 curated Life-like rule presets ship in the Rules panel. Every preset's headline claim was actually run against the real engine and is re-checked by the app's own test suite on every commit — a claim that can't be reproduced there doesn't belong in the preset list:

  • HighLife — a seeded 5-cell pentomino produces 4 exact copies of itself by generation 5 (population 5 → 20), genuine self-replication, before the copies collide and collapse to extinction by generation 10.
  • Day & Night — a solid 3×3 block becomes a stable oscillator, its population cycling 9, 9, 5, 5 indefinitely, rather than freezing (as under Conway) or dying.
  • Seeds — a single 2×2 block explodes to a population of 128 within 12 generations on a 64×64 torus.
  • Maze — a 96×96 random soup at density 0.4 locks to an exactly static 5072-cell structure by around generation 40.
  • Mazectric — the identical starting soup instead settles into a perfect period-6 population cycle, visibly thinner than Maze's frozen result.
  • Replicator — a single live cell dies, but every one of its 8 neighbours is born, turning one cell into an exact 8-cell ring after one generation — the parity mechanism behind the whole "Replicator" rule family.
  • Life without Death — seeded with 15% random noise, population never once decreases across 60 generations, checked every step.
  • 2×2 — a 96×96 soup at density 0.3, run 400 generations, stays bounded (roughly 1700–2200 cells) without collapsing to zero or exploding to the board's full capacity.
  • Coral — a solid 16×16 block grows briefly then freezes into an exactly static 612-cell structure; a sparse random soup instead dies back hard first, then steadily re-accretes rather than either freezing or collapsing.

Diamoeba was tried and dropped. It's reputed to organise a dense random soup into stable diamond-shaped blobs, but that behaviour is reportedly sensitive to a narrow initial-density band. Uniform soups were tried at four densities on a 128×128 torus: the two lower densities went fully extinct, one decayed to extinction more slowly, and the highest exploded to fill literally every cell on the board — no stable diamond blobs at any density tried. Rather than ship an unverified headline claim, it was left out.

The generalised rule kernel (a lookup table indexed once per cell, rather than a hardcoded B3/S23 branch) costs essentially nothing when the active rule is still Conway's own: measured on a 512×512 board, 200 steps after a 20-step warmup, the same test harness before and after generalising the engine measured 3.2598 ms/step → 3.2856 ms/step — a 0.8% difference, within normal run-to-run noise. Conway's own hand-unrolled fast path is kept and dispatched to whenever the active rule canonicalises to exactly B3/S23.

Every theme clears the same bar the default does

The app's 5 built-in themes, and any custom theme a user builds, are held to a programmatic check: the 8 lenses' semantic accent colours (life, age, activity, time, branch A/B, diff, warn) must stay at least a minimum distance apart in OKLab colour space, pairwise. That minimum isn't an arbitrary number — it's calibrated to the shipped default theme's own closest real pair (age vs. warn), measured at a distance of 0.0491. A custom theme that would make two different concepts read as visually the same colour fails this check and can't be saved.

Mobile touch actually commits

A real bug, now fixed and covered: the touch-input handler used to unconditionally clear the active drag mode on every single-finger release, which meant 100% of one-finger draw/erase/select touches silently failed to commit on a real touch device — no error, the mark just never appeared. Dedicated mobile end-to-end coverage now asserts a single-finger draw commits on release, a plain tap with no movement also commits, two fingers pan/zoom without drawing, and a second finger landing mid-stroke ends the draw cleanly instead of corrupting it.

Known limitations

Honest gaps, not hidden ones:

  • The Time Sculpture's slice colours render dark under software WebGL (SwiftShader) — the renderer used by headless/CI browsers and some sandboxes. This is an artifact of that renderer, not the colour ramp; the same math produces correct values headlessly, and a real GPU renders it correctly.
  • Specimen recognition reliably auto-names gap-heavy shapes (the pulsar, the pentadecathlon, both glider guns) only when the shape is the sole occupant of the scanned region — their internal gaps fragment the connected-components fallback into several unnamed pieces if anything else shares the region.
  • On narrow screens, the drawer and inspector become slide-over sheets rather than docked columns; unlike the app's dialogs, these sheets are not focus-trapped.
  • One hairline colour token (used for the active branch row and similar decorative accents) falls below the 3:1 ratio WCAG's non-text-contrast guidance recommends — a deliberate choice for a purely decorative edge, not an oversight.
  • Web MIDI output and system/mic audio reactivity depend on real browser and hardware support and degrade to an honest disabled state, never a silent no-op, when unavailable.
  • A Time Sculpture turntable export was designed (orbit the existing 3D camera, reuse the PNG-export path per frame) but cut — untested against real WebGL, and inherently realtime-paced rather than a clean offline replay like the rest of export. Animated GIF export and audio export were also cut for a time over a verification gap (no reference decoder / no OfflineAudioContext in the unit-test environment) but have since shipped, verified against real Chromium decoders — see Features. Exported WebM video is not silent when an audio track is supplied.
  • Site theming (this guide/wiki) was scoped and deliberately not built — the app's 5 runtime themes are an app-only feature today.

895 unit tests across 91 files, plus 126 Playwright end-to-end tests across 27 spec files (96 desktop, 24 mobile-touch, 6 against a real production build), back all of the above; typecheck and build both run clean. A separate, more expensive Art-mode performance/ resource-safety suite (6 specs) runs on its own schedule against its own dev server rather than as part of that count. One flake is currently known: a mobile-only touch test that scrubs, edits, compares and opens the Time Sculpture in one continuous journey intermittently hits a real, reproducible race in the history-scrub path under full-suite load, rather than a click-timing flake.