I have been fascinated with geometric tessellations as long as I can remember. Since 2014, I have been publishing interactive computer graphics works on shadertoy.com, with multiple Truchet tilings and several examples of Wythoff's kaleidoscopic construction on the sphere and hyperbolic plane.
Like many people, I took up sewing during the pandemic for home mask-making, and in January 2021 embarked on a journey to combine my love of tiling with the art of quilting. Although in hindsight, the projects I took on were a little ambitious, I am encouraged by the results, and by the ability to hold in my hands the type of compositions that were previously just collections of pixels on a screen.
The central pentagons in this pillowcase form the classical Cairo pentagonal tiling, which dates back to at least 18th-century India. It is the dual of the snub-square tessellation of the plane. Each central pentagon has two right angles and three 120$^{\circ}$ angles. Moving out to the left and right, the composition smoothly transitions to feature pentagons with three right angles and two 135$^{\circ}$ angles.
The central panel is assembled using English paper piecing. The pattern was created using a custom computer program which output 1:1 templates for cutting and basting to the fabric. Fabrics were chosen to match matplotlib's "viridis" colormap. The quilting stitches reveal a regular square lattice that underlies the tiling.
The sewing pattern for this quilt was created using a custom computer program written to establish the composition, and then recursively decompose it into modules to be machine-sewn along straight seams. The base modules, seen in the design as the four distinct half-dart and half-kite shapes with half-outlines, were assembled using foundation paper piecing.
Fabrics were chosen to match matplotlib's "plasma" colormap, and were hand-dyed and bleached to better complement each other.
Other Penrose quilts exist; what makes this one unique are the modular assembly technique and the outlines between shapes. The piece is quilted along the centers of the outlines, so that the familiar Penrose kite and dart shapes are visible on the back.
