Life blinker 2026-10-13
The Life blinker alternates between horizontal and vertical lines of three live cells. Start with and every other cell dead. The two endpoints each have one live neighbor and die; the center has two and survives. The dead cells and each have three live neighbors and are born. No other dead cell has three. Therefore
The same neighbor-count argument with horizontal and vertical exchanged gives the second step. Since , the period is exactly two, rather than merely a divisor of two.
Figure 1.
The Life blinker: old neighbor counts produce a period-two Life oscillator
. 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. Details.
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.
Life oscillator 2026-10-13
A Life oscillator is a nonconstant periodic orbit of the Conway's Game of Life update function . Its period is the least positive integer for which , comparing the entire live-cell set at the same coordinates. A configuration that never changes is instead a fixed point; a Life glider is not a Life oscillator on the infinite board because it returns at displaced coordinates. The Life blinker has period two.[ref]