Fireflies are insects who get their name from their ability to light up.

Different species of fireflies produce different flashing light patterns.

These blinking patterns are a sort of signal to help fireflies find potential mates.

Some species of fireflies are able to synchronize their flashing patterns.

At first, different fireflies will flash their own lights at different times and different frequencies (shown in the first animation), but then gradually begin to pick up on each others behavior until eventually all the fireflies begin to flash their lights together at the same time (shown in the second animation).

This phenomenon can be explained by something called phase synchronization.

Mathematica code:

R[n_] := (SeedRandom[n]; RandomReal[])G[g_, f_, t_] := Graphics[  Table[   {If[f*Round[R[n*t]] == 0, Yellow, Black],    Opacity[If[g == 0, 1, .5 (1 + Sin[2 Pi ((2/3)*.05*t + R[n]*.4)])]],     Disk[     {Cos[19 (.05*t + n)*2 Pi/75],        Cos[3 (.05*t + n)*2 Pi/75]},       .005*Cos[(.05*t + n)*2 Pi/75] + .01]}, {n, 1, 75}],PlotRange -> 1.3, ImageSize -> 500, Background -> Black]Manipulate[ G[0, 1, t],{t, 1, 20, 1}]Manipulate[ G[1, 0, t],{t, 1, 60, 1}]
Filed under: #GIF  #Mathematica  #biology  #phase  #circles

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I miss the summers where there were a million different fireflies :(
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Fireflies are insects who get their name from their ability to light up. Different species of fireflies produce...