“3D Thinking” Pages 88 to 90 Fu Hsi’s He Tu (River Map): As legend has it Fu Hsi was fishing on the banks of the Yellow River some 5,000 years ago when a supernatural animal, a “Dragon Horse,” rose from the waters carrying on his back the river map within which were hidden the eight primary […]
“3D Thinking” Page 233 Fractals: Named after the mathematician Benoit Mandelbrot. Fractals are defined as mathematical forms that are generated using a defined set of transformations that include a scaling function whereby the set will generate a form and then infinitely break it down into scaled repeats of itself or into, more generally, self-similar patterns of many types. The operational process for generating the Mandelbrot […]
“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 […]
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 […]
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“3D Thinking” Page 32 Neolithic Geometries: Labyrinths are constructed with a single path that winds forwards and backwards, multiple times, before arriving at a central point. The oldest surviving labyrinths appear as Neolithic and Bronze Age rock carvings – a petroglyph labyrinth in Usgalimol, India has been estimated to be 10,000 years old. By the time of the middle ages labyrinths […]
“3D Thinking” Pages 22, 292: Patterns of Perception follow a methodology that has been applied through time from antiquity to the present. The first books to appear that feature “perceptual lattices” are books on designs developed during the early Islamic period – in the middle-east, north Africa, and in Moorish Spain. References are Jules Bourgoin […]
“3D Thinking” Page 74 to 87: The slope ratios, dimensions, construction, and alignment methods, of the Pyramids of Ancient Egypt: THE SLOPES OF THE PYRAMIDS OF EGYPT Given the whole number traditions of ancient Egypt one would expect the slopes of the pyramids to be in whole number proportions too. Whole number grids of square […]
“3D Thinking” Page 190, 191: There are a number of Islamic design methodologies of which the “Nesting Polygon” method is one. The method places an arrangement of polygons within a polygon and continues infinitely placing the same but scaled arrangement within each polygon as it appears. The method was used to generate a lattice from […]
“3D Thinking” Pages 175 to 177 Islamic Geometry: This Seljuk period door dates from 13th-century Anatolia and stands as a possible example of a use of numeric values to communicate a message. The door’s design is based the Islamic “close-packing circle” method of design – in this case an arrangement of close-packing circles within a pentagon. The two primary numbers […]
