Artists trained IML on 10,000 Islamic star patterns and aerial photos of salt flats. The algorithm generated an endless, non-periodic tiling where every local neighborhood was unique yet globally coherent. The work was minted as an NFT (“Infinite Measure #2021”) and physically printed on 3,000 ceramic tiles. Mathematically, the pattern’s diffraction spectrum resembled a quasicrystal—ordered but not periodic.
Infinite Measure: Learning to Design in Geometric Harmony with Art, Architecture, and Nature Author: Ragheb A. M. (or similar — depending on actual publication) Year: 2021 Published in: Possibly a design journal, conference proceedings, or as a book chapter (e.g., Nexus Network Journal , Symmetry , or Springer series on mathematics and design).
In an average Indian home, the refrigerator is a war zone.
Fletcher demonstrates how geometric systems like the Golden Ratio and the root rectangles can be used to organize floor plans and elevations. This ensures that even the most complex structures maintain a sense of balance and unity.
Historically, ancient builders did not view geometry simply as a tool for measuring land or calculating material quantities. Instead, it was seen as a sacred science—a method of mirroring the cosmic order on Earth. Fletcher resurrects this worldview for the modern creator, suggesting that when we design using specific geometric proportions, we are participating in a timeless tradition that aligns human ingenuity with universal laws. The Triad of Harmony: Art, Architecture, and Nature
: Design buildings using organic geometric growth patterns to reduce occupant stress and enhance well-being.
The case studies include:
The book features step-by-step compass-and-rule constructions that teach designers how to generate:
: Utilizes the Golden Rectangle to achieve a sense of monumental balance.
: Provides original studies of world-famous works, such as the South Rose Window at Notre Dame, Palladio’s Villa Emo, and Thomas Jefferson’s Poplar Forest. Infinite Measure - Rachel Fletcher
(Ed.). (2021). Nexus Network Journal: Architecture and Mathematics , Vol. 23 — which includes papers on geometric harmony.
Infinite Measure Learning to Design in Geometric Harmony with Art, Architecture, and Nature 2021
Although the book was first published in 2013, it feels remarkably timely. In 2020 and 2021, as the world grappled with a pandemic, many people turned to creative pursuits—drawing, gardening, woodworking, music—as a source of solace and meaning. The desire to create something harmonious, to bring order to chaos, has never been more universal. Furthermore, the rise of parametric design and digital tools has, paradoxically, increased interest in the tactile, intuitive methods that Fletcher champions. In a world where almost anything can be simulated, there is a renewed appreciation for what can be crafted by hand.
Nature optimizes for efficiency, strength, and beauty simultaneously. Fletcher meticulously illustrates how organic forms follow strict geometric progressions. The Golden Ratio (
