I've had to revise the design once again. Note to self: In the future, do research before drafting! It will save a lot of time LOL. The new specification for the geosphere involves equilateral triangles; see unit
for a more detailed dimensionality. Mettos are now triangular in shape. One of the nice side-effects of this change is that it means an increase in the proportion of walk and overall circulatory system (transportation network) density. There are several advantages to this new arrangement, including that it makes the internal area of the metto a lot more accessible from the outside, and even cross-metto navigation is improved. The effect is really quite dramatic in comparison to the previous geometry, which ended up creating huge areas within each metto that were essentially isolated and remote.
Due to my limited understanding of geometry the geosphere design has been amended. The new configuration is similar to that of a soccer ball. Mettos are hexagonal in shape rather than square, like a honeycomb rather than a grid. There are still however one billion mettos total. Obviously the surface area of each metto will have to be adjusted in order to compensate for the proportional increase in area that comes with adopting a hexagonal rather than square polygon.
The city planet is defined by an artificially created 'world' or 'earth' made entirely out of polytoy. While in reality the planet as a whole is made up of many layers and components that are all bonded at the molecular level, at various strategic junctions (for structural integrity purposes); the primary foundation is a single spherical construct commonly referred to as the geosphere or less commonly the "neosphere".
The geosphere is a spherical, isometric matrix comprised of square sections, like tiles or plates. Each plate constitutes a metto
, and has a unique name. Theoretically there are one billion mettos total that make up the entire geosphere. These plates are both divided and joined by narrow interconnected channels that are called the walk
The following are my personal retrospective notes detailing the evolution of the neotoy geosphere, up to its current level of complexity.
The first phase, my initial outline, was very basic, bordering on total ignorance in terms of what would be physically possible. I had some experience modeling and texturing 3D objects using software called Ray Dream Studio
, this program was the basis for my understanding of applied geometry beyond merely the abstract mathematics.
At the time I wrongly assumed that it would be possible to create a sphere (geosphere) using connected equilateral tiles, i.e. a grid configuration. This was my foundation for the [[metto]], the [[meridians]], and several other key aspects of city infrastructure. If I'd only been a little more observant I would have realized that through my own experimentation with grid based textures (in early attempts to model the city), such a sphere would invariably include a variety of polygons. Since it was critical, for the sake of modularity, that each metto consist of the same surface area, I had to abandon this model.
The second phase was slightly less idiotic, but still ultimately failed to fulfill my criteria. Once again wrongly assuming that sphere geometry was relatively simplistic; I chose a hexagonal configuration, leading to the soccer ball analogy; the hexagon became the new metto, but not for long! It was around this time that I started to seriously examine my basic method of geosphere simulation. I had realized by this time, and correctly so, that if I really wanted to do this right, I would have to put a lot more energy into modeling my simulations at a much higher resolution. This required a lot more research and the use of specialized tools, but ultimately provided invaluable insight into the creative process as a whole.
I started with geodesic spheres and quickly discovered that, once again, due to the inherent complexity of sphere geometry, you cannot make one purely out of hexagons. Geodesic spheres are in fact a combination of hexagons and pentagons in an elastic yet patterned proportion. This discovery lead to more research. At this point I was convinced that I had reached some kind of core "quantum" principle that would play a huge role in determining which direction the project took next. I researched geometric patterns in relation to sphere construction, to see if I could divine a deeper symbolism hidden in the overall design.
For the current phase, I ended up with an elegant yet rather obtuse, er, I mean OBVIOUS solution. The ever-popular and eminently reliable Lowest Common Denominator (LCD). It's pretty clear after looking at even a few real-world geodesic spheres, that while the larger polygons are hexagons and pentagons, the smaller shapes that make up the sub-structure are equilateral triangles. So finally I had arrived at my geometric holy grail. The new metto became an equilateral triangle. Here it's interesting to note that even though I had gone through three significant evolutions of form, I had in the end, still managed to meet all of my original qualifications.