+- MKLab (https://mklab.gr)
+-- Forum: [INDEX] (https://mklab.gr/forumdisplay.php?fid=1)
+--- Forum: MATHEMATICS (https://mklab.gr/forumdisplay.php?fid=3)
+---- Forum: ARTICLES (https://mklab.gr/forumdisplay.php?fid=13)
+----- Forum: ARTS AND VISUALIZATION (https://mklab.gr/forumdisplay.php?fid=155)
+----- Thread: Mathematics as seen by an artist (/showthread.php?tid=1981)
Mathematics as seen by an artist - mklabgr - 09-15-2026
The article “Mathematics as seen by an artist: Inspiring mathematical objects” by Stéphane Vinatier and Reg Alcorn explores how mathematical structures can become sources of artistic inspiration. It focuses on two objects: Truchet tiles, introduced by Sébastien Truchet in 1704, and the Ulam spiral, famously created by Stanisław Ulam in 1963. Truchet tiles arise from dividing squares diagonally into two colors and studying their possible arrangements, connecting combinatorics with tilings and ornamental design.
The Ulam spiral arranges integers in a square spiral and reveals striking diagonal patterns of prime numbers. The authors explain that these alignments are connected to quadratic polynomials—particularly Euler's polynomial $n^2+n+41$—that produce unusually many prime values. They also discuss the Hardy–Littlewood conjecture and the fact that, beyond linear polynomials, much of our understanding of the frequency of prime values remains conjectural.
The mathematical ideas ultimately become the foundation for Alcorn's Transitions series of paintings. He expands the Truchet-tile vocabulary to six tiles, chooses a sequence of tiles, and repeatedly winds that sequence into a spiral across the canvas. Although the underlying rule is extremely simple, different sequence lengths and orders generate remarkably complex and sometimes unpredictable geometric patterns. The resulting black-and-white structure is then transformed through carefully chosen colors, mixtures, pigments, and optical effects, with the artist combining mathematical calculation with intuition.
Alcorn also experiments with multiple spiral centers, Pythagorean $3$-$4$-$5$ triangular tiles, and combinations of different tiling systems. The central message is that simple mathematical rules can generate enormous artistic complexity, illustrating a broader principle shared by mathematics, art, music, and even biological evolution: from a simple beginning can emerge an astonishing richness of forms.
ARTICLE [PDF]