# Susan McBurney

Complexity generated with simple rules and elements is a common theme in mathematics. Computer graphics programs extend the reach of the modern artist and the results are often very unexpected. The generating program and/or the algorithm can be either simple or complex. Coming from a math and computer science background, I am especially delighted when the output is intrinsically attractive and mathematically inviting.

Arranged on an Archimedean spiral, these designs all derive from the four-dimensional hypercube. Although a hypercube cannot be physically present in three-dimensional space, a model can be realized, similarly to the process of a 3-D object casting a 2-D shadow. This 3-D model can then be further reduced to a drawing on a 2-dimensional plane. Each of the designs shown is a 2-dimensional drawing of a 3-dimensional model of a four-dimensional object. Each object began with a hypercube which was simply skewed in some manner, usually by dragging a point or edge. The variety of designs simply produced is especially interesting. In each of them, one can vaguely locate the eight cubes that make up the hypercube.