Mapping Tool Box
Communication Networks Between Center and Outside Limits
Newtools geometry is based in the synergy of the parts of fundamental structures; the interconnectedness of the communication networks that exist between the centers of geometrical systems and the locations-in-common that exist on their outside limits.
​
I have made a separate section of the mapping tool box to explain the mapping of the interiors of the Five Platonic Solids with the VE as an outside boundary for our maps.
Original 146 Fractal Directions
Your Imagination and Simple Design-in-Nature
The 'First Burst' in All-Directions-All-at-Once
How you map the interiors is arbitrary. My first map of what I call the 'first burst' had 146 directions radiating out from the center of this VE (vector equilibrium). The directions without a boundary make it hard to see a pattern. It is when we map the outside limit of this system that the pattern becomes clear; it is a simple fractal pattern you see in Nature. You divide the edge in half, then divide that edge in half, on and on.
​
This building pattern begins with the distance between the VE's center and the midpoint of its outside edge, (B) = √3(3BB) = 10.392304...cm. The end of the pattern is the distance between the center and the center of the square face of the VE, (D) = √2(3BB) = 8.48528...cm. Between these two locations is the symmetric division of these two numbers to define all of the other lines of communication from the center to the outside limits in the fractal pattern.
There are many different kinds of fractal patterns found in Nature. The one we have chosen is the simplest, keep dividing in half. In the center photo it is easy to see the golden ratio, 0.618033988749895... in the construction. The leaves have a 5-sided pentagonal relationship.
My first attempt at mapping the interiors of geometrical systems produced a symmetrical, logical division between the square roots of 3 and 2 relative to 3BB. That a set of square roots of fractions had such an interconnectedness gave me enough encouragement to continue to explore more efficient methods of mapping.