# Hartmut F. W. Höft

I have long been fascinated by the human urge to attempt to recognize patterns even among apparent randomness. The urge exists in finding constellations among the stars, in human artistic constructs such as poetry, and in abstract objects such as number sequences and geometric figures. In my current work I take circles and spheres, sometimes distort them, and paint the resulting 2D and 3D surfaces in colors based on the digits of π. I create patterns using functions such as shifts, polynomials or modular arithmetic that I apply to the digit sequences. Frequently, the resulting patterns are incomplete on the visible portion of a surface keeping the tension between pattern and randomness unresolved for the viewer.

This 2-dimensional figure is a grid of concentric semicircles growing logarithmically and their horizontal tangents. The quadrilaterals defined by this grid I color with subsequences of π, row by row. The logarithmic growth of the radii together with the white central triangles and the increasing closeness between the linear sides of the quadrilaterals and the circular arcs produces the illusion of an elliptical dome rising vertically. The sequence of colors in the bottom row represents 3 1 4 1 5 9 2 6 5 3 5 8 9 7 9 .... symmetrically from the center, and each subsequent row is shifted by 3, 4, 5, 6, ... digits from the previous row. This translational pattern by triangular numbers is quickly lost, leaving symmetry confined to the rows.

I draw a two-dimensional mesh on the surface f(s, t) = e^(sin(s)*cos(t)) * (cos(s)*sin(t), sin(s)*sin(t), cos(s)*cos(t)) and project the mesh curves onto the y-z-plane. This top-down view of the surface creates the fourfold symmetry of the image. Since the levels of the mesh are defined by trigonometric functions, fewer curves appear at the corners giving the illusion that the underlying surface contains four symmetric notches. I introduce a hint of randomness by coloring the sequence of the mesh curves with the digits of π. These colors also demonstrate that the surface self-intersects along the central vertical axis where the color of mesh curves abruptly changes, the sides of the central square being painted in four different colors.