Professor Tudor Griffith was one of the founding members of the European Study Group on Cardiovascular Oscillations, and hosted the 1st ESGCO Conference in Cardiff, Wales in 2000. Tudor was a passionate scientist, who managed to combine his enthusiasm for vascular biology with his background in physics, to make key and insightful advances to our knowledge and understanding of the integrated vascular control mechanisms that co-ordinate blood flow in tissue perfusion. He had a particular interest in the endothelium, the monolayer of cells that lines the entire cardiovascular system and which is in prime position to sense a wide variety of modulatory stimuli, both chemical and mechanical. Over the last 20 years Tudor produced a series of research papers in which he used chaos theory to analyse the behaviour of arteries that underpins vasomotion. The research led to the development of mathematical models that were able to predict calcium oscillations in vascular smooth muscle with a view to predicting events in a complete virtual artery. This article will review the field in which he worked, with an obvious emphasis on his contribution.