Consider cellular automata in which a cell's next state depends on both its local neighborhood and a few possible distant interactions. Inspired by chess (future post). The distant interactions could be with the first nonempty cell for each of the directions a chess queen can move (or no interaction if there is nothing along a ray).
"Mostly local but with a few distant interactions" tells a story that people can relate to (to be elaborated on in a future post).
The distance between galaxies seems not that much greater than the size of galaxies. Milky Way diameter 100,000 ly. Distance to Andromeda 2.5 million ly, so scale factor of 25. This means (maybe) that after becoming a galactic civilization, it's not that much more difficult to then become an intergalactic civilization. Star Trek (and others) are unrealistic in limiting themselves to just one galaxy.
Compare this with other cosmic distances:
Half-circumference of earth (farthest possible distance between any two points on earth): 20,000 km. Minimum distance to Mars: 55 million km. Scale factor 2750. Going from being a planetary civilization to being an interplanetary civilization is difficult.
Size of solar system, defined by semimajor axis of Neptune's orbit: 4.5e9 km. Distance to Alpha Centauri: 4e13 km. Scale factor 9000. Going from being a solar-system spanning civilization to being an interstellar civilization is difficult.
These distance ratios don't take into account the difficulty of escaping gravity wells. Don't know if it matters.
We consider a city street layout of concentric circles and radial spokes. Far from the center, city blocks are roughly shaped like rectangles. When the aspect ratio of a block exceeds the square root of 2, add a new radial street bisecting the block (and all blocks further out). Blocks will be roughly square-shaped.
This is similar to the principle of A series paper sizes, e.g., A4, in which cutting a sheet in half results in a similar shape.
First, in the center, is a circle of unit diameter. It's a traffic rotary. We choose starting with this circle, and not a circle of unit radius, because it looks prettier. Second is annulus of thickness 1 divided into 4 because sqrt 0.5 < pi/4 < sqrt 2. Third is annulus divided into 8 because sqrt 0.5 < 3*pi/8 < sqrt 2. Fourth and fifth are divided into 16: sqrt 0.5 < 5*pi/16 < 7*pi/16 < sqrt 2.
Counting the center circle as 1, the circles at which new radial rays start are circles 1 2 3 5 8 15 30 59 116 231 462 923...
nextodd(x)=if(x%2,x,x+1)
nn(x)=(nextodd(ceil(sqrt(2)/Pi*2^x))+1)/2
for(i=1,12,print(nn(i)))
Maybe useful as a template for a 2D barcode, though better, as already done in QR, is a square grid of squares.
Maybe for an artistic pixelation. Or go 囲碁.
It's of course possible to 4-color it, and pretty easily: alternating regions of checkerboards. Can it be 3-colored? It cannot be 2-colored.
In 3D, start by projecting a cube onto a sphere. There is and will always be distortion near the vertices. Repeatedly subdivide squares into quarters as necessary. Slabs of aspect ratio 1.4x1.4x1 become divided into 4 columns of aspect ratio 0.7x0.7x1. Far from the center or vertices, blocks will be roughly cube-shaped.
