= Life blinker
{c}
{title2=$F^2(B)=B$}
= Blinker in Conway's Game of Life
{c}
{synonym}
The <Life blinker> alternates between horizontal and vertical lines of three live cells. Start with $B_0=\{(-1,0),(0,0),(1,0)\}$ and every other cell dead. The two endpoints each have one live neighbor and die; the center has two and survives. The dead cells $(0,-1)$ and $(0,1)$ each have three live neighbors and are born. No other dead cell has three. Therefore
$$
B_1=\{(0,-1),(0,0),(0,1)\},\qquad B_2=B_0.
$$
The same neighbor-count argument with horizontal and vertical exchanged gives the second step. Since $B_1\ne B_0$, the period is exactly two, rather than merely a divisor of two.
\Image[/conway-life-blinker-counts.png]
{title=The <Life blinker>: old neighbor counts produce a period-two <Life oscillator>}
{description=Original computed toy configuration, not measured data. The count panel shows all old neighbor counts in a five-by-five window; the center is excluded. Orange outlines mark the two births. All unshown cells initially are dead, and all panels use the same coordinates with y increasing downward.}
The <Life blinker> is a minimal hands-on check of synchronous updating. Mark both endpoints for death and both births before changing anything. Removing an endpoint early would make a prospective birth see only two neighbors; adding a birth early would alter other counts. A correct implementation reproduces both <sets> above exactly, rather than merely keeping the live population equal to three.
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