Recognising, describing and explaining Structure is a fundamental part of all branches of the physical and mathematical sciences. We use mathematical models and the laws of physics to gain an understanding of how structure arises. However, we generally do not use mathematical models to objectively define those structures. Structure is a non-local property and is often scale dependent. Visual perception and classification of structure visually is far from objective since our perceptual ability is keyed to seeing particular cues - and it is not particularly consistent. How to achieve this algorithmically, in a way that is independent of tuning parameters, is the general problem that is addressed in this talk. The tools at out disposal for systematically discovering structure in data are mathematical, mainly geometric and topological. Moreover, we can make little progress without strong visualisation techniques. The technique I will describe is based on a simple perceptual model of the visual cortex, its mathematical implementation and its application to various areas, in particular the discovery and quantification of cosmological structure. Application areas are numerous ranging over cosmology, hydrodynamics, magnetic field structures, large database analysis, statistics, and image understanding. The main cosmological results of environmental effects on halo formation in cosmological N-Body simulations will be presented.