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The Fourth Dimension Unveiled: A Preliminary Reconnaissance of
Four-Dimensional Objects from Mathematics and Physics

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Joshua Fagans

This thesis introduces IC4D,
a means of visualizing 4 dimensions, and a tool for
interactively exploring 4-dimensional data. IC4D is a computer program that
allows a user to freely rotate a virtual 4-dimensional object, in 4-dimensional space,
while observing its continuously transforming 2-dimensional shadow. In this way, the user
readily develops an intuitive grasp of the 4-dimensional structure. The 4-dimensional
objects explored in this paper are examples taken from mathematics and physics:
The Klein bottle embedded in 4-dimensional space; the Complex Gamma Function;
full phase space flows of the famous Henon-Heiles Hamiltonian; and sections of the
phase space orbits of a ball bouncing between a flat wall and a rippled wall.
IC4D is being developed on NeXT workstations for computers running the
NEXTSTEP operating system.