I enjoy giving visual representations to abstract mathematical concepts such as number, form, and process. I often use patterns that convey messages at multiple levels and scales using a wide variety of mathematical elements and media. Some of my work contains fine detail that allows the art to be viewed differently depending on the distance between the viewer and the art. Another prevalent theme in my work is symmetry, where the overall pattern is created by repeated rotation or translation of a smaller very similar units. My overall goal in creating art is to share the beauty and wonder I see in mathematics.
This piece shows the first non-constant approximations to the cosine function using its Taylor series expansion about x=0. The approximation is exact when x=0, but diverges for other values of x. Because the partial sums of the series oscillate between over and under approximations, the regions above the over approximations (yellowish) are disjoint from the regions below the under approximations (reddish). The boundary between these regions is the cosine function.
This work explores a restricted version of the symmetry group 442 (p4) and its some of its normal subgroups. The group contains 128 elements and 256 subgroups. The petals and center of the flowers were generated using 5 of the 14 normal subgroups.