COMPUTATIONAL WORLDS / EXPERIMENT 02
A Single Difference.
Change one cell.
Watch two futures diverge.
Same rule. Same start. One intervention.
Active experiment: Rule 90 · 129 cells · Fixed-zero (outside cells are zero)
Rule 90 is additive: the difference obeys the same XOR rule on its own, ignoring the background. It grows into the single-cell triangle pattern, with both fronts moving one cell per generation until they reach the edges.
Checked for this run: every row of the difference panel equals a lone cell evolved under Rule 90 from the flip.
Generation
192 / 192
Different cells
8 / 129
Fraction different
6.20%
Fronts from the flip
−42 to +42 cells
01 / Baseline
Original worldSPACE → 0–128 · TIME ↓ 0–192
02 / Perturbed
Exactly one cell flippedSPACE → 0–128 · TIME ↓ 0–192
03 / Difference
Exact XOR of the two worldsSPACE → 0–128 · TIME ↓ 0–192
Bright cells are 1. Orange marks a difference, not a third cell state. The dashed line marks generation 24, where cell 64 is flipped only in the perturbed world. Space and time use identical scales in every panel.
Difference over time
Fraction of all 129 cells · 0 to 100%At generation 192, the difference survives in 100% of 128 runs, with a mean of 5.86% of cells different. The runs keep this rule, width, boundary and flip generation, and vary the seed (37 onward) and the flip position across the row. One run is an anecdote; the mean is the damage-spreading measurement.
What changed at this moment?
Differences occupy 8 cells. After 168 generations the outermost sit −42 and +42 cells from the flip: average front speeds of 0.25 leftward and 0.25 rightward, in cells per generation. A radius-one rule cannot exceed 1.
At generation 192, cell 64: baseline 0, perturbed 0, XOR 0.
Computed preview. All three panels show the same generations.
A finite, deterministic damage-spreading experiment. It does not by itself prove chaos, universality, or computational irreducibility. The preview starts paused; playback pauses when the page is hidden or this experiment leaves the screen.
A small intervention, measured.
The baseline evolves without intervention. The second world starts identically, then one bit is inverted at the chosen generation before its next update. The orange panel marks only cells where the two worlds disagree. Rewinding the shared timeline reveals the same computed experiment, not a new random run.
Background: damage spreading and Lyapunov exponents in cellular automata ↗