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Using techniques of swarm modeling, it is possible to make a somewhat unrealistic model of firefly behavior.

Concretely, the following differential equations that describe the velocity change of firefly

in a swarm of

fireflies are solved in a discrete time-step approximation.

For a swarm of fireflies, the parameters

and

are the interaction strengths,

and

are the correlation lengths, α and β are the interaction power laws,

is the air resistance, and the random variable ξ_i is interpreted as wind turbulence.

Contributed by: Michael Trott with permission of Springer
From: The Mathematica GuideBook for Programming, second edition by Michael Trott (© Springer, 2008).

H. Levine, W.-J. Rappel, and I. Cohen, "Self-Organization in Systems of Self-Propelled Particles," Physical Review E, 63, 017101 2000.

Contributed by: Michael Trott with permission of Springer

From: The Mathematica GuideBook for Programming, second edition by Michael Trott (© Springer, 2008).

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Model of a Firefly Swarm