Figure 4.

Change in synergy bias across scales. Right: the change in synergy from microscale to macroscale plotted against the starting macroscale synergy for Gaussian systems. There is a clear positive correlation. Indeed, all systems show an increase in synergy at the macroscale and an increase in redundancy at the microscale. The equivalence class structure used to construct the systems holds the mutual information steady across scales, so an increase in synergistic information at the macroscale can only come from a decrease in the redundant information of the microscale. Left: the same plot, although here we display both the Gaussian and deterministic systems. Note that, in contrast to the Gaussian systems, the deterministic systems start at a much lower synergy bias. Typically, these lower synergy systems actually lose synergy bias after coarse-graining, although the linear relationship between how synergistic the macroscale is and how much synergy is lost at the microscale remains. Interestingly, visual examination suggests that for both classes of system, the relationship between the macroscale synergy bias and the change in synergy bias is generally linear and, for both systems, lies along a common line of best fit. This suggests that, while different systems behave differently under coarse-graining, the broader relationship is preserved. (Online version in colour.)