As part of an inter-disciplinary effort, we are visually exploring a current problem in philosophical logic related to information processing. Given a set of inconsistent sentences or inputs, a processor cannot unambiguously infer any specific consequence. Traces represent subsets of possible consequences which can be inferred classically from partitions of the set of inputs. We are interested in the relationship between a given set of Boolean inputs and its respective trace(s). We have developed a visualization paradigm which allows us to view and explore this relationship effectively.

The illustration of the iterative process of this boolean function produces a fractal image. Fractals are mathematical objects in which patterns emerge across many orders of magnitude as a reoccurring feature. For example, the branching feature in a tree is a fractal pattern that is observed throughout the structure, from the roots to the veins in leaves.

Fractals are complex systems. The main characteristic of a complex system is its chaotic non predictable nature, that is, a cause-and-effect scheme represented by a differential equation cannot provide an adequate description. Another important aspect of complex systems is the emergent features in which patterns of behavior are observable in the overall system but cannot be inferred by the study of smaller parts. H2O molecules do not give hints to the possible configuration of ice.

To resolve intractable problems encountered with complex systems we use a method called synthetic micro analysis. To understand complex systems is to understand behavior and interaction in multi-bodied systems. Synthetic micro analysis combines the top down observation of features at the macro level of a system and a bottom up modeling of individual constituents at the micro level. The challenge is to identify features in constituents that are consistent in behavior with top down observations. An example is to model the behavior of H2O molecules. The micro level observes the tranference of energy between molecules under the influence of a state parameter such as the local temperature of the system. At the macro level, we observe how H2O combines into different structures such as solid, liquid then gas as the temperature is elevated.

This approach is systematic, however, successful modeling often requires a sound intuition and a profound understanding of what constitutes complexity. My study of complex systems has demonstrated that most of life is complex and intractable from the view of conventional methods.