Abstract
Pointwise partial information decomposition provides a means to quantify information modification in discrete systems exhibiting intrinsic distributed computation. In his seminal “Computation at the Edge of Chaos”, Chris Langton investigated how intrinsic computation emerges in cellular automata which support the three primitive functions of computation—information storage, transfer, and modification. Despite the appealing description, Langton gave no precise information-theoretic definition of the three primitive functions. In the decades since, information storage and transfer have been defined; however, a satisfactory definition of information modification has proven to be more elusive. This paper uses the recently introduced pointwise partial information decomposition to provide a quantitative measure of information modification. Moreover, this approach provides a hierarchy of different types of modifications, which each combine or synthesis different combinations of stored or transferred information. This ability to identify different types of information modification events in both space and time is exemplified with an application to cellular automata.