  A freely walking fly visits roughly 100 stereotyped states in a strongly
non-Markovian sequence. To explore these dynamics, we develop a generalization
of the information bottleneck method, compressing the large number of
behavioral states into a more compact description that maximally preserves the
correlations between successive states. Surprisingly, preserving these short
time correlations with a compression into just two states captures the long
ranged correlations seen in the raw data. Having reduced the behavior to a
binary sequence, we describe the distribution of these sequences by an Ising
model with pairwise interactions, which is the maximum entropy model that
matches the two-point correlations. Matching the correlation function at longer
and longer times drives the resulting model toward the Ising model with inverse
square interactions and near zero magnetic field. The emergence of this
statistical physics problem from the analysis real data on animal behavior is
unexpected.

Neurons and Cognition;Statistical Mechanics