The Algorithmic Art of Silk
The creation of patterned silk for a traditional Korean hanbok is an exercise in applied mathematics. Weaving is fundamentally a binary process—at any point, a vertical warp thread is either raised or lowered to allow the horizontal weft thread to pass. The complex patterns seen in historical textiles are the physical result of a complex algorithm, executed line by line. For the most elaborate designs, weavers used a type of drawloom, a precursor to modern programmable machines. This technology allowed for individual control over groups of warp threads, enabling non-repeating and complex imagery.
The mathematics are embedded in the structure of the weave itself. Geometric patterns are among the most ancient, found in Korean textiles dating back to prehistoric times. During the Joseon Dynasty (1392–1910), these patterns became codified with specific rules of construction and repetition. A pattern like the "water wheel" is built from the tessellation of circles, hexagons, and triangles. Another, the endless mahn (卍) pattern, uses a repeating unit based on a right triangle, which is reflected and rotated with 90-degree symmetry to create an interlocking field that symbolizes eternity. This process of generating a large, complex pattern from a simple geometric unit through transformation—rotation, reflection, translation—is a core mathematical concept. The loom itself acts as the device that executes these geometric transformations thread by thread.