Jennifer E. Padilla

Bridges Conference and Art Exhibit 2022: Mathematics, Art, Music, Architecture, Culture

Art Exhibit: "Lectio Divina Quasiperiodia"
Penrose tile patterns composed from traditional Islamic geometric motifs fill this hand-bound 72-page, 33 x 33 cm book. It rests on a music stand in front of a floor-to-ceiling, semi-sheer hanging fabric print featuring a Penrose tiling incorporating motifs from the Darb-e Imam shrine. The scale of the fabric and its gentle filtering of ambient light create an immersive experience, inviting the viewer to open the book and explore page upon page of variations on the theme. The images inside express the quasiperiodicity, symmetry, recursive nature, substitution rules, and other elements of the Penrose tiling, generating insight into the fundamental features of its intricate construction and mathematical beauty.

Paper: "Penrose Tiling Arrangements of Traditional Islamic Decagonal Motifs"
Decagonal motifs found in the traditional tile designs of Islamic art and architecture can, with a little refinement, be arranged according to the fundamental quasiperiodic structure of the Penrose tiling. A simple tessellation is applied to six traditional motifs to create analogues to the pentagonal Penrose tiles. Substitution rules guiding hierarchical assembly of these Penrose tiling arrangements are then applied, mediated by the tessellation tiles. I then explore how the artist may include hints to the viewer about the mathematical characteristics of Penrose tilings that these designs represent, including their correct arrangement, substitution rules, quasiperiodicity, and other features.

The Unreasonable Effectiveness of Recursion

Geometric designs rooted in the mathematical concept of recursion shine in works ranging from iridescent acrylic on canvas, to 24K gold leaf on paper, to stark black and white on raw Tyvek sheets. What is recursion? A recurrence is something that is happening again. Recursion is the process of repeatedly applying some action to the outcome from the last time you took that action. More than simple repetition, it remembers the past and keeps building on it, resulting in patterns of unexpected complexity. These bold geometric works invite the senses to participate in contemplation of recursion through images that are precise and true to the technical details of their mathematical content.