## RIVER CULTURES: I-CHING

“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 primaryContinue reading RIVER CULTURES: I-CHING

## FRACTALS: THE MANDELBROT SET

“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 MandelbrotContinue reading FRACTALS: THE MANDELBROT SET

## SHAPE CHANGING POLYHEDRA

“3D Thinking” Page 238: Shape Changing Polyhedra An introduction the logic of this geometry can be seen in a paper I delivered to the Bridges Conference this August, 2016: http://archive.bridgesmathart.org/2016/bridges2016-225.pdf. Shape-Changing Polyhedra are three-dimensional forms composed of polygons that are flexibly connected. Of most interest are shape-changing polyhedra ‘shells’ that connect in a modular fashionContinue reading SHAPE CHANGING POLYHEDRA

## DYNAMIC SPHERE GEOMETRY

“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 tangents or tangent planes, creates two- and three-dimensional lattices from which two- and three-dimensionalContinue reading DYNAMIC SPHERE GEOMETRY

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## LABRYNTHS MYSTERIES and METHODS

“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 labyrinthsContinue reading LABRYNTHS MYSTERIES and METHODS