Mathematics and visual art converge in their mutual preoccupation with patterns and structures. In mathematics, patterns and structures are usually approached cognitively and symbolically; in visual art, they are experienced perceptually and palpably. The former approach is largely quantitative in nature, the latter largely qualitative. My work investigates the combination of these approaches; often, I begin with the quantitative with the intention of eliciting qualitative experiences. Current work includes combinations and permutations of points, lines, and planes. My processes are to derive complete families of forms within a given set of parameters, reduce the family to unique forms that do not repeat other forms by rotation or reflection, and then to select subfamilies of forms for use in compositions.
The 26 forms in this composition are the complete set of unique forms that result from connecting the 8 vertexes of an octagon into 2 triangles and 1 line segment. This group of forms is a subset of a much larger superset of forms that includes all combinations of points, lines, and shapes derived from the vertexes of an octagon. In this composition, those forms of the same color and in the same vertical alignment utilize the same combination of triangles, yet each form in each column (and throughout the composition) is a unique organization of triangles and line. Those forms that are on/near the apex of the each semi-circle utilize 1 triangle from each of the forms at the ends of the semi-circle.
The 22 individual "5-strutforms" in this composition are the complete set of continuous lines (with changes of direction but without branching or crossing) made from 6 adjacent points in a grid array. These forms are a subset of a much larger complete set of 5-strutforms. Composition and color reveal additional orders. The 5-strutforms fit into a rectangular envelope of varying proportions; those rectangles and their strutforms are arranged in a gradation from most extended at left to most compact at right. Colors indicate symmetries: red rectangles contain forms with reflective symmetry; yellow rectangles contain forms with rotational symmetry; blue rectangles contain asymmetrical forms.