  We present a new approach to exoplanet characterisation using techniques from
complexity science, with potential applications to biosignature detection. This
agnostic method makes use of the temporal variability of light reflected or
emitted from a planet. We use a technique known as epsilon machine
reconstruction to compute the statistical complexity, a measure of the minimal
model size for time series data. We demonstrate that statistical complexity is
an effective measure of the complexity of planetary features. Increasing levels
of qualitative planetary complexity correlate with increases in statistical
complexity and Shannon entropy, demonstrating that our approach can identify
planets with the richest dynamics. We also compare Earth time series with
Jupiter data, and find that for the three wavelengths considered, Earth's
average complexity and entropy rate are approximately 50% and 43% higher than
Jupiter's, respectively. The majority of schemes for the detection of
extraterrestrial life rely upon biochemical signatures and planetary context.
However, it is increasingly recognised that extraterrestrial life could be very
different to life on Earth. Under the hypothesis that there is a correlation
between the presence of a biosphere and observable planetary complexity, our
technique offers an agnostic and quantitative method for the measurement
thereof.
