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In this thesis, the author develops numerical techniques for tracking and characterising the convoluted nodal lines in three-dimensional space, analysing their geometry on the small scale, as well as their global fractality and topological complexity---including knotting---on the large scale.

Alexander von Humboldt (1769 1859) was one of the most respected scientists of his time; Darwin called him 'the greatest scientific traveller who ever lived'. From 1799 Humboldt spent five years exploring the Americas, reporting his findings in thirty volumes, published over a period of more than twenty years from 1805. His Essai Politique, describing northern New Spain, particularly Mexico, was one of the first studies of a single country written to take account of both its history, its society and its political development. In 1824, the English mining engineer John Taylor published this...