The probability distribution that results from a growing or disintegrating system depends on the constraints imposed by the driving processes on the increments of growth or breakage. Two main families of distributions are prominent in natural systems namely those with small and large variance. The second kind are of most interest in physical/chemical/biological systems and are represented by members of the Generalised Gamma (Amoroso) family. We explore two examples, namely fragmentation of brittle materials and the competitive growth of mineralising systems. In both examples a hierarchy of distributions develops depending on the size and entropy of the system.

Bruce Edward Hobbs was Chief Scientist of Western Australia and Executive Officer of the Office of Science and Innovation at the Department of the Premier and Cabinet between 2002 and 2006. Previously, he held many academic positions including Foundation Professor of Earth Science at Monash University, Visiting Professor at University of California (1980), Visiting Professor at Brown University in Providence, USA (1978), Professor of Structural Geology at the State University of New York (1971) and Geology lecturer at the University of Sydney. Hobbs left academia in 1984 to join CSIRO (Commonwealth Scientific and Industrial Research Organisation) as Chief Research Scientist in the Division of Geomechanics, Melbourne and was promoted several times before becoming Chief of CSIRO Exploration and Mining in 1992. In February 2000, he was appointed Deputy Chief Executive of Minerals and Energy, CSIRO. Hobbs worked on developing computer applications that simulate mechanical behaviour, fluid flow, heat flow and chemical reactions governing ore body formation. The goal is to produce a predictive modelling capability that enhances our ability to discover new ore bodies. In recognition of his great work, he has received numerous prizes and awards including the Jaeger Medal (2001), Senior Fulbright Award (1979), United States Antarctic Research Program Medal (1970), Junior Fulbright Award (1966) and was elected a Fellow of the Australian Academy of Science in 1991.