ABSTRACT
This chapter applies different theoretical elements and tools of the Mathematics of Complexity in order to better understand what kind of heterogeneity is expected in soils and granular media, how to measure it, and how heterogeneity may be characterized and simulated. It uses it for giving a precise meaning to the term heterogeneity commonly used in an ambiguous way. The chapter demonstrates that Predictive algorithms, empiric facts, and models shed light on different reasons yielding emergent heterogeneity structures. It illustrates using a simple model "the intermittent pluri-sink model", how simple linear actions mixed with a random component lead to the emergence of complex heterogeneity patterns. The chapter emphasizes how complexity may appear under quite simple and natural actions evolving in time. It presents an entropy based approach which in some way reinforces the PSD self-similar model proposed in Martín and Taguas.
