  Visual perceptions often come with illusions whose physical origin are not
well understood yet. The encoding of stochastic light intensity $x(t)$ into
spikes with firing rate $r(t)$ at time $t$ is investigated in an experiment
with retinas from bullfrogs to understand the mechanism of anticipation.
Partial information decomposition of the mutual information between $r$ and the
combined state $\{x,\dot x\}$ is found to be consistent with the encoding form:
$r(t) \sim (1-\lambda)x(t) + \lambda \dot x(t) \tau_0$ with $\lambda$ being a
system dependent parameter and $\tau_0$ a constant. This form of $r(t)$
indicates that a retina is capable of anticipation based on the synergistic
information generation between $x$ and $\dot x$. Our results suggest that
illusions such as the anticipation studied here during retinal perception can
originate from the recombination of information extracted in the retinal
network.
