From Sunflowers to God’s Divine Architecture of Life.

In response to questions from readers of the “Visual Thinking, Seeing Through Time” book series (ebook and print formats) I’ve added a SUPPLEMENTS page to this website. This is the first! “From Sunflowers to God’s Divine Architecture of Life.” This supplement relates to Book 1, Chapter 5, Ancient Egypt. It also covers Book 2, Chapter […]

Explore Visual Thinking Through Time

Overview Visual Thinking, Seeing Through Time is a five-book series. It explores the development of visual logic from archaic humans through early civilizations. It continues into the age of artificial intelligence. The series examines how visual‑cognitive structures shape human reasoning across the arts. These structures affect architecture and geometry. This reveals deep connections between perception, culture, […]

Launch of ‘Visual Thinking’: Five Books on Art and Geometry

“Visual Thinking, Seeing Through Time” is a five-book odyssey through the human experience in Architecture, the Arts, and Geometry from the dawn of consciousness to the frontiers of artificial intelligence.

Altair Designs and Jules Bourgoin. Bridges MathArt 2025.

Jules Bourgoin was a master of Early Islamic visual logic.

The Story of Visual Thinking—Geometry, Architecture, and the Arts. AI Audio Review.

An AI-generated 30 minute audio review of my latest book.

Nazca Lines: Spirals and Labyrinths

This will be my only post for 2021 as I’ve been working on my new book all to do with visualization and imagination in the arts and architecture; through time (almost complete). This post is from my 2020 paper given at Bridges Math/Art 2020. Two animations and one illustration sequence. The Nazca giant-geoglyph spirals that […]

THE QUEST FOR BEAUTY – IN DESIGN & ARCHITECTURE

The animation is of a storyboard – the actual presentation will be feature movie-clips, photographs, illustrations and animations. The “Quest…” will be a keynote lecture given at the Goods Shed Arts Center in Tetbury, Gloucestershire, England Feb 13th 2019 followed by a Workshop Feb 14th. follows mankind’s striving to create designs and architectural structures that […]

DYNAMIC SPHERES: GOLDEN RATIO ARCHITECTURE

“3D Thinking” Page 288: A “Golden Ratio” structure extracted from a 3D lattice generated by the sphere cluster, HP1.3. See Page 271, “3D THINKING ANIMATIONS.” The lattice is created by connecting the centers of the “Golden Ratio” spheres. The illustration shows how the lattice is generated and then how the  structure is extracted from the space-filling […]

SHAPE CHANGING POLYHEDRA

“3D Thinking” Page 238: Shape Changing Polyhedra The original idea for shape changing polyhedra came from studying muqarnas and playing with children’s building blocks. The featured image is of the Nasir al-Mulk Mosque Muqarnas in Shiraz, Iran. The building blocks were as in the photo:  An introduction to the logic of this geometry can be seen in […]

DYNAMIC SPHERE GEOMETRY

The concept originated studying the geometry of a particular window in old Cairo.   “3D Thinking” Page 264: The Dynamic Sphere Geometry is a type of 2D and 3D logic that, in the first place, generates “close-packing” tessellating arrangements of circles and spheres that infinitely fill space. Connecting circle and sphere centers or adding clipped […]