The simplest model of a growing galactic empire is a swelling balloon. Starting at the origin planet the spherical colonization wave will grow at the rate of empire expansion.
The much more messy and difficult to figure model of expansion is via Civilization Clusters. But this model more or less precludes the existence of an empire anyway, so it can be ignored by science fiction writers trying to build an empire.
Imagine a planet inhabited by imperialistic little opportunistic aliens, just like us, whose star is in a galaxy totally uninhabited by any other intelligent creatures (or at least uninhabited by creatures who can defend themselves). Once our imperialists discover interstellar travel, they will spread to the surrounding stars in a manner similar to a watermelon hitting the sidewalk. As previously mentioned, their empire will approximate an expanding sphere, with their homeworld at the center.
It is useful to be able to calculate a bit of geography for your interstellar empires. The control radius between the Imperial (or Sector) Capital and the Rim give you the size of your empire. It would be nice to be able to figure out how many stars are inside the empire, especially if you want to ensure that the Imperial Bureaucracy can actually handle it.
Warning, the galactic plane in the neighborhood of Sol is only about 1,000 light-years thick. If the radius is over 500 light-years the equations will calculate give an incorrect result (too many stars).
Nstars = Rly3 * StarDfactor
NhStars = Rly3 * HStarDfactor
- Nstars = number of stars
- NhStars = number of stars with habitable planets
- StarDfactor = star density factor, use 0.017 or see below
- HStarDfactor = habitable star density factor, use 0.002 or see below
- Rly = empire radius in light-years
- x3 = cube of x, i.e., = x * x * x
Given the number of stars or habitable stars inside the imperial borders, the empire radius is:
Rly = cubeRoot(Nstars * StarRfactor)
Rly = cubeRoot(NhStars * HStarRfactor)
- Rly = empire radius in light-years
- Nstars = number of stars
- NhStars = number of stars with habitable planets
- StarRfactor = star radius factor, use 59.68 or see below
- HStarRfactor = habitable star radius factor, use 464.46 or see below
StarDfactor, HStarDfactor, StarRfactor, HStarRfactor: all depend upon the stellar density, that is, how many stars per cubic light year. Currently the best estimate I could find for stellar density in Sol's neighborhood is Erik Gregersen's 4.0×10-3 stars per cubic light year. The density of stars with human habitable planets I calculated by using Tarter and Turnbull's Habcat dataset. Simplistic math on my part gave a value of 5.14×10-4 habitable stars per cubic light year. But keep in mind that the HabCat dataset came out in 2003.
StarRfactor = StellarDensity / ( (4/3) * π )
StarDfactor = 1 / StarRfactor
HStarRfactor = HStellarDensity / ( (4/3) * π )
HStarDfactor = 1 / HStarRfactor
- StellarDensity = stars per cubic light-year
- HStellarDensity = habitable stars per cubic light-year
You can find how I derived this equation here.
|Erik Gregersen||4.0×10-3 s/ly3||59.68||0.017|
|Globular Cluster||2.02×100 s/ly3||0.118||8.461|
|Galactic Core||2.88×100 s/ly3||0.083||12.064|
|Galactic Center||8.5×101 s/ly3||0.003||356.047|
Once you have decided that your Terran Empire is X number of light years wide or contains Y number of stars, it would help to have a realistic number for the amount of years it will take for the empire to expand to that size. Or from the other side, if you have decided how long the empire has been around, it would help to be able to figure out how many stars and how wide it is. This is a little more difficult.
The SETI scientists are always fretting about the Fermi paradox. As a result, there have been a couple of attempts to model the speed of galactic colonization by a hypothetical alien race. These can be used, keeping in mind that they always assume slower-than-light starships. Such models have inhabited planets colonizing nearby worlds. When the population of the colonies grows large enough, they send out their own colonization missions.
A comprehensive but mathematically intensive model is Burning the Cosmic Commons by Robin Hanson. Another interesting model is Computer Simulation of Cultural Drift: Limitations on Interstellar Colonisation by William Sims Bainbridge. I would like to explain how to use them, but I'm still trying to digest the models myself.
Newman & Sagan (Galactic civilizations; population dynamics and interstellar diffusion. Icarus, 46, 293-327) attempted to apply the gas diffusion equation to interstellar migrations.
∂P/∂t = αP (1 - P/Ps) + γΔ2 ∂/∂x (P/Ps ∂P/∂x)
- P = population of a settlement
- Ps = the carrying capacity of a settlement
- t = time
- x = spatial coordinate
- α = local population growth rate (percentage of current population)
- γ = emigration rate (percentage of current population)
- Δ = mean separation of settlements
- ∂ = partial differential (Yes, I know. Scary Calculus. But don't panic)
The solution to the equation is:
P/Ps = 1 - exp((x - vt) / L)
- L = Δ sqrt(2γ / α) = gradient length scale
- v = sqrt(αγ / 2) = wave speed
However, when Newman and Sagan analyzed the problem, they came to the belated realization that the local growth rate (α) greatly exceeds the emigration rate (γ) so that L <<Δ. Translated into English, this means that the galactic colonization resembled an explosion more than it did a slow gaseous diffusion. Which means the equation is worthless for this purpose. Back to the drawing board.
Eric M. Jones found a more promising approach. In Discrete calculations of interstellar migration and settlement( Icarus Volume 46, Issue 3 , June 1981, Pages 328-336. Costs $15 for the article) he uses a Monte Carlo simulation (i.e., rules are established then a lot of dice are metaphorically thrown). Jones found the following equation will approximate the Monte Carlo results:
v = Δr/ [(Δ/vs) + (1/α) ln(2α/γ)]
- Δr = average radial distance traveled (i.e., distance as meaured from the center of the empire)
- Δ = average distance traveled
- vs = ship speed
- Δx/vs = average travel time (years)
Jones says one can usually assume that Δr = 0.7Δ and neglect the travel time, resulting in:
v = 0.7αΔ / ln(2α/γ)
Assuming the mean separation between settlements (Δ) is 7.2 light years (2.2 parsecs), local population growth rate (α) is 10-3 per year, and the emigration rate (γ) is 10-4 per year, this means the colonization wave will travel at about 2 x 10-3 light-years per year (5 x 10-4 parsecs per year). This would colonize the entire galaxy in a mere 60 million years.
The emigration rate could become much larger. In the 1840's the great Irish emigration reached a whopping 0.01/year. The population of Ireland at the time was about four million, so the emigration was an incredible 40,000 per year or about one hundred per day.
Using the upper equation, with my figure of 8.3 light years for Δ, and a slower-than-light ship speed of 10% c, I figure an expansion wave speed of 1.93 x 10-3 light-years per year. Unfortunately, upping the speed of the ships has little effect. At 50% c it's 1.97 x 10-3 ly/yr, at 100 c it's still 1.97 x 10-3 ly/yr, at ten times the speed of light it's 1.98 x 10-3 ly/yr, and at one thousand times the speed of light it is still 1.97 x 10-3 ly/yr!
At this speed, it would take about 50,000 years to expand to a 100 light year radius empire, which seems like an overly long time to me.
But maybe not. Mr. Jones is talking about a population growth of 10-3 or 0.1% per year. The United States has a growth rate closer to 0.6%, and some nations are crowding 3.0%. If our empire had a growth rate α of 0.6% and a modest emigration rate γ of 10-4 per year, it could reach 100 light years in radius in about 6900 years. And if it had a draconian γ of 10-2, it could reach that size in a mere 260 years.
Starting with two empires: assuming that they have a rough technological parity the two spheres will expand until the borders make contact. Then it will resemble two soap bubbles stuck together, with a flat "neutral zone" populated by spies, smugglers, covert battlefleets intent on causing border incidents, and planets named "Casablanca". The technical term is Buffer Zone.
In the real world such an area is called "No Man's Land" or a "Demilitarized Zone" (DMZ), depending upon whether or not there is ongoing active warfare. No Man's Land is typically located between two hostile armies or battlefleets during a battle, a very unhealthy area to enter. A Demilitarized Zone is typically located between the current national borders separating two hostile nations who are not currently at war. A military incursion into a DMZ is considered an act of war.
A related concept is a Border Zone. These are less about preventing invasion by enemy battle-fleets and more about a nation controlling traffic across the zone. Traffic to be controlled can include:
- Evil people who want to penetrate a protected wildlife area in order to ravage it of valuable minerals or other resources
- Illegal immigrants
- Illegal emigrants (example: East Germany using the Berlin Wall's "death strip" to prevent its citizens from escaping the oppressive regime into the freedom of West Berlin)
In reality, the "neutral zone" will be the less like a plane and more like the intersection of the two spheres. It will be like a lop-sided lens shape. The equation for calculating the volume of the neutral zone can be found here
In his paper Long-term consequences of observing an expanding cosmological civilization S. Jay Olson explores the consequences of colliding empires. One of the assumptions is the growing spheres are domains of expanding civilizations belonging to distinct species who do not wish to share resources; i.e., they are selfish bastards just like us. This results in the formation of hard boundaries between the spheres; i.e., "national" borders which can only be crossed at the expense of sparking interstellar wars and all manner of unpleasantness.
The boundary that forms between two expanding civilizations is a hyperboloid. The exact form depends upon empire expansion speed, separation distance between empires, and starting time of each empire's colonization expansion.
In the diagrams below, Empire Alfa's origin world is located at coordinates -C,0,0 and Empire Bravo's origin world is at coordinates +C,0,0. The distance between the two is 2C. Empire Alfa starts their colonial expansion at time t1 while Empire Bravo starts at time t0. t1 is earlier than t0, meaning that Empire Alfa starts first. It is assumed that Empire Alfa's expanding domain has not yet engulfed Empire Bravo's origin world at time t0, meaning Bravo gets a chance to expand instead of starting out enslaved by Alfa.
The paper assumes that both civilizations will have the same expansion speed, which is as fast as physically possible. Both empires will frantically research how to accelerate their expansion speed until both run up against the theoretical maximum.
At time t1 Empire Alfa starts their colonial expansion. Later at time t0 Empire Bravo starts their expansion (at point C), while Alfa has expanded to a sphere with a radius of 2A (the blue circle). r1(t0) is a fancy way of saying "radius of empire 1 at time zero."
Both spheres will expand, and collide at a point halfway between the edge of the blue circle and point C; that is halfway between boundary of Alfa's sphere at time t0 closest to Bravo's origin world, and the location of Bravo's origin world itself (orange hyperboloid).
When Alfa's sphere has expanded to the violet circle and Bravo's sphere has expanded to the yellow circle, the border between will be the orange hyperboloid.
Mathematically, the hyperboloid will have its foci at -C,0,0 and +C,0,0 (the coordinates of the two empire's origin planets). The semi-major axis will be A (half the radius of Alfa's sphere when Bravo starts expanding). The border will be the x > 0 sheet of the hyperboid.
The "canonical form" of the border hyperboid is:
B2 ≡ C2 - A2
(x2 / A2) - (y2 / B2) - (z2 / B2) = 1
The volumes of two empires can be calculated by hideously complicated equations (2) and (3) found in the paper. No, I'm not going to try and transcribe them here.
The main focus of the paper is what happens when the inhabitants of Origin Planet Bravo become panicked when they observe Origin Planet Alfa start their colonization program. Bravo will instantly start their own colonization drive.
The trouble is, the speed of light means that when Bravo sees Alfa's starting expansion, Bravo is seeing what happened in the past. If Alfa is ten-thousand light-years away from Bravo, it means that when Bravo sees Alfa's start, Alfa actually started ten-thousand years ago. Which is a heck of a head-start.
What this boils down to is that time t0 will occur X years after t1, where X equals the distance between the two empires in light-years.
t0 = t1 + (2 * C)
where t0 and t1 are in years, and C is in light-years.
In FIG 2, the separation distance 2C is an absolutely enormous three billion light years. Graphs (a), (b), (c), and (d) are for expansion speeds of 0.3, 0.6, 0.9, and 0.99 the speed of light respectively. The faster the expansion speed, the smaller the size of Empire Bravo (blue area)
If Origin Planet Bravo observes two empires start their expansion, Bravo is in big trouble.
The graphs in FIG5 shows what happens if Empires Alfa and Charlie are the same distance from Bravo (3 billion light-years, angular separation of 90°), and both start their expansion simultaneously.
At expansion speeds of 0.3 and 0.6 of the speed of light (a and b), Empire Bravo is squeezed (blue area). At the critical expansion speed of 0.75765 of the speed of light (c) Empire Bravo will become "trapped", it will become englobed by Alfa and Charlie with further expansion being impossible. At higher expansion speeds such as 0.9 (d) the size of Bravo's blue area grows smaller.
Obviously the following analysis could also apply to sectors within a single empire.
The following analysis assumes that empires are evenly spaced apart in the galaxy and have equal radius. Which is highly unlikely to be true, but close enough for a first approximation. Meaning you can plot out evenly spaced empires to examine their mutual gross geography, then later randomly move them by hand to make something more believable.
The easiest way to simplify the analysis of galactic empire geography for your science fiction novel is to cheat and make the empires have a diameter of about one thousand light-years, e.g., the average thickness of the galactic disk. This means the empires all lie in a plane, so you can draw a two-dimensional map and not have to worry about three-dimensional overlapping. Assuming all the empires have the same diameter the empires will arranged like hexagons on a hex-grid (assume even spacing, remember?). For what it is worth the latest estimate of the distance between Sol and the galactic plane is 20.8 +/- 0.3 pc (i.e., about 69 light years above the galactic plane). So Sol is close enough for government work to being exactly on the galactic plane.
Looking at the diagram, one can see that Empire Charlie can attack Empire Sol, Empire Bravo, and Empire Delta without trespassing on any other empire. But Empire Charlie cannot attack Empire Echo without sending their battlefleet through either Empire Sol or Empire Delta.
The diagram uses spheres for simplicity, but those concave triangle regions are going to be gobbled up by empires as well. Divide each triangle region into thirds, with slice of the pie going to the nearest empire. In other words the spheres will become vertical hexagonal prisms
Instead of making each empire's diameter the same you can assume that the origin stars of each empire are on average equally spaced, so the centers of the empires will be in a hexagonal array but the diameter of each empire may vary. The galactic disk is only 1K light-years thick, but each empire can spread horizontally until it runs into the current extent of each of the six neighbor empires at the border.
|Empire Sol||(0, 0, 0)|
|Empire Albert||(500, 870, 0)|
|Empire Bravo||(1000, 0, 0)|
|Empire Charlie||(500, -870, 0)|
|Empire Denver||(-500, -870, 0)|
|Empire Echo||(-1000, 0, 0)|
|Empire Foxtrot||(-500, 870, 0)|
The more complicated way is to use as a first approximation something based on the close-packing of equal spheres. This is usually used for stacking oranges or cannon-balls, but it works for interstellar empires as well. This allows one to have empires arranged three-dimensionally without making you pull your hair out by the roots.
This assume even spacing, remember?
The following analysis uses what is known as hexagonal close-packed (HCP), do not use face-centered cubic.
The secret is to harness the awesome power of the Cuboctahedron.
Of all the quasiregular polyhedrons this is the only one where the center-to-vertex radius equals its edge length. In other words, in the diagram to the right, every single line is the same length.
It is sort of a three-dimensional equivalent to a hexagon. Hexagon grids make great two-dimensional flat maps. So cuboctahedron grids make great three-dimensional space-filling maps. You place your galactic empires on the vertexes, and use the line to figure the distance from empire to empire. By the same token square grids make lousy 2D flat maps (see link above), and cube grids make similarly lousy 3D maps.
Buckminster Fuller admired this polyhedron, naming it a "Vector Equilibrium" (which I am telling you because you may encounter the term if you do any research on the topic). The name is because if the edges are considered to be vectors, the outward force of the center vectors is exactly balanced by the confining force of the surface vectors. The polyhedron is in equilibrium. But I digress.
This is called a "one-layer" map, because it has the center sphere surrounded by one layer of additional spheres.
| Empire Albert||0.0, 0.59, 0.81|
| Empire Bravo||0.51, -0.29, 0.81|
| Empire Charlie||-0.51, -0.29, 0.81|
| Empire Sol||0.0, 0.0, 0.0|
| Empire Denver||0.5, 0.87, 0.0|
| Empire Echo||1.0, 0.0, 0.0|
| Empire Foxtrot||0.5, -0.87, 0.0|
| Empire Golf||-0.5, -0.87, 0.0|
| Empire Hotel||-1.0 ,0.0, 0.0|
| Empire India||-0.5, 0.87, 0.0|
| Empire Juliette||0.51, 0.29, -0.81|
| Empire Kilo||0.0, -0.59, -0.81|
| Empire Lima||-0.51, 0.29, -0.81|
To use the Empire Center Coords (3D Geometry) table: choose the desired DIAMETER (not radius), and multiply each coordinate by the diameter. For instance, if you chose an empire diameter of 200 light-years, Empire Charlie would be at coordinates -102, -58, 162.
Empire names are just letters in the NATO Phonetic Alphabet, as place holders. Replace them with your own really cool names that you've invented. In the same way empire numbers (e.g., 4 for Empire Denver) are arbitrary.
Here is a quick example. The above diagram shows the empire of Sol, and the twelve alien empires in the layer that surround it. All of them are one empire-diameter away, and the border between each alien empire and the Solarian Empire is one-half an empire-diameter away. The entire cluster fits inside a sphere with a diameter of three empire-diameters, and a radius of one and one-half empire diameters.
Meanwhile, this simplistic map also shows for each alien empire its closest four other neighbor alien empires. For instance, the five empires closest to the Vorpal Bunnies are: Sol, Berserkers, Space Vikings, Death Robots, and Gray Goo. These are empires that the Vorpal Bunnies might ally with or be at war with.
As mentioned above, you can use this to define the relationship of sectors within a single empire, as well as for relationships between full empires.
Just for fun, a science fiction author can name sectors according to a colorful motif. For example, in Brian Aldiss' collection Starswarm, the sectors are named after colors (vermillion, azure, violet, etc.), though one was named Sector Diamond. That did catch my fancy. So if you have 13 sectors, a gem stone motif would name them something like Sector Aquamarine, Diamond, Emerald, Opal, Ruby, Sapphire, Spinel, Topaz, Amethyst, Citrine, Peridot, Zircon, and Trystine.
In Asimov's novels, sectors are named for the brightest star contained. So Sol is in the "Sirius Sector".
Michael Andre-Driussi decided to take matters into his own hands. Using the Internet Stellar Database, he has compiled a gazetteer of the first thirteen sectors:
| Golf||q Puppis||14||9||8|
| India||Téng Shé jiǔ||15||6||22|
| Juliette||Al Na'ir||11||8||19|
| Kilo||Delta Hydri||14||6||27|
Sector is from my table, Brightest Star is the brightest star in the sector (so sector Charlie would be the "Regulus Sector"), and #G, #F, #K is the number of stars of spectral class G, F, and K respectively (i.e., the spectral classes most like our sun and presumably have the highest chance of hosting human-habitable stars). One can also see that Sector Zubenelgenubi is the richest in class G stars (our sun's spectral class). Nice work Michael!
As near as I can figure, Michael's sectors are 40 light-years in radius, the distance between sector centers is 80 light-years.
Please note that the Internet Stellar Database is slightly obsolete, it lacks star data from the RECONS, DENSE, CTIOPI, and EXTENDED HIPPARCOS star catalogs. The brightest star values are probably good, but the number of stars in each spectral class may be inaccurate.
You can download the AstroSynthesis file here and the readme file here. Warning: you need to purchase the AstroSynthesis software to display the map, it is Windows only, the file is a work in progress and contains mistakes, and the blasted thing is 3.5 megabytes.
If you just want to play around with my empires, load my file into Astrosynthesis and go nuts.
If you want instructions on how I made the file (in case you want to customize it with a different set of stars or different empires or something), read on:
I started with the star dataset compiled by the Evil Dr. Ganymede. I combined RECONS, DENSE, CTIOPI, and EXTENDED HIPPARCOS 22 to 100 light-years. This gives a sphere full of stars with a radius of 100 light-years and a diameter of 200 light-years. Be sure you use the datasets marked "Astrosynthesis XYZ" NOT the ones marked Galactic XYZ.
Since the cluster is three empire-diameters in diameter, this means each empire has a diameter of 200 / 3 = 66.6 light-years and a radius of 33.3 light-years.
Go to my handy-dandy Empire Center Coord Table and multiply each of the coordinates by diameter 66.6. For instance, Empire Albert on the table has coords of 0.0, 0.59, 0.81. Multiply them by 66.6 to get map coords of 0, 39, 54.
I imported Dr. Ganymede's star dataset into AstroSynthesis. Next I went to the menu Sector | Sector Properties and opened the Sector Properties window. On the Sector Setup tab I checked Spherical Sector and set the Sector Radius (R) to 100 light years. On the Grid tab I checked Sphere Grid. Then I clicked the OK button.
The next task is to create "markers" for each of the empires using the map coords just calculated. These would define the centers of each empire. Click the Place New System button and set the type to Marker, and follow the instruction manual.
Then I had to figure out how to draw some lines connecting stars, but limit them to being within a given empire. If you are not interested in the details of AstroSynthesis, just skip over the rest of this.
I selected the marker for Empire Albert, which is at the center of that empire. I opened up the Advanced Search window. In the query I entered within 33.3 where 33.3 is the radius of each empire. Click the Search button and a bunch of stars appear. Click the Select All button then the Close button.
All the stars inside Empire Albert are now selected.
The important step is go to menu Actions | Mass Edit | Political Affiliation and set it to "Empire Albert". This allow you in the future to use the Advance Search to select all the stars in a given empire. You can search on
political="Empire Albert" to select all empire stars. When selecting for purpose of making routes, do search on
root only, political="Empire Albert" because you only need to make routes on root objects.
This next step is not stricly needed, but I use it. You see, by default, routes are not shown on the screen if the screen viewpoint is farther away from a route than 20 light-years. Since the map is 200 light-years diameter, if the viewpoint is far enough so see the entire map, all the routes are invisible. To avoid this unhappy state of affairs, click the menu Actions | Mass Edit | Label Display Distance. In the dialog, I change both numbers to 500 and click OK. While you are at it, you might want to do Actions | Mass Edit | Display Style to set the star and label color to the color you assigned to that empire
Now click the Create Proximity Routes button. A dialog appears. Check the Selected Systems Only radio button. Make the max route length 67 (empire diameter), just to be sure. Set the max routes per system, I use 2 for a sparse map and 3 for a busy map but you can experiment.
THIS IS IMPORTANT!! In Route Type, enter some unique name, e.g., "Albert Route". IF YOU FAIL TO DO THIS, THE ONLY WAY TO DELETE THE ROUTES FOR A GIVEN EMPIRE IS MANUALLY ONE-BY-ONE!!
Set the route color to the empire color. Select line style and line width. Click OK and patiently wait while it adds all the routes.
This would be a good time to save your work. Now go and do the next empire.
In the example above you can see the white routes belonging to Empire Sol and the red routes belonging to Empire Albert. Pollux is a star in-between the empires that is in one of the little voids, see below.
The cute little gridded spheres are AstroSynthesis sub-sectors. Each has the same location and radius as the empire. The utility is that you can temporarily hide each sub sector and all the stars inside, to unclutter the map in order to focus on a section of interest. For fun you can have them display the sphere grid.
I also added markers for "Zenith", "Spinward", "Trailing", etc. for orientation. But you don't have to do this.
AstroSynthesis uses a non-standard attribution for the x, y, and z axes: Dr. Ganymede's star data has already been adjusted to take care of this. Read his notes on Conversion from Galactic XYZ to Astrosynthesis XYZ for details.
Placing the markers for this map, keep in mind that the radius of the entire cluster is 100 light-years. Change this if your cluster has a different radius. Make sure you make the Display Distance of each marker 500 or so, to ensure they will always be visible.
|ZENITH||0, 0, 100||Towards galactic north|
|NADIR||0, 0, -100||Towards galactic south|
|SPINWARD||0, 100, 0||Towards the direction of galactic spin, aka "turnward", "down-spin" or "deosil"|
|TRAILING||0, -100, 0||opposite the direction of galactic spin, aka "anti-spinward", "up-spin" or "widdershins"|
|COREWARD||100, 0, 0||Towards the galactic center, aka "hubward"|
|RIMWARD||-100, 0, 0||Directly away from the galactic center|
The maps below were created in a slightly more complicated manner. The trouble with the method above is that there are quite a few stars that are outside of all the empire spheres. So I wrote a Python program that went through the entire list of stars, and assigned each star to the closest empire center. The empires are no longer spherical, but at least all the stars are included.
The 100 light-year radius sphere contained 2842 stars (counting all stars in binaries and trinaries) with roughly 100 to 200 stars in each of the 13 empires.
I made the stars that are near equidistant from two closest empire centers to be assigned to "Neutral Zone". These will be the hot-spots of intra-Empire hostilities. By experimentation I got good results with my current star data by defining "near equidistant" as "within ±20% of equidistant."
I manually found the sun-like star closest to each empire center, and assign that as the homeworld of each empire.
Once I have all the bugs worked out, I want to try it with a 55 empire map.
The maps below look like a tangles mess, but are surprisingly clear when they are rotated in 3D within AstroSynthesis. I tried making a video but the results were very disappointing.
As with the 2D flat map, the little voids between spheres will also be gobbled up by various empires. If you inflate each empire sphere so it gets its fair share of all the adjacent voids, the sphere will turn into an odd geometric polyhedron called a Rhombic dodecahedron. I didn't mention this at first because you are probably unfamiliar with the shape and they are confusing. But everybody has seen a ball.
Yes, my quick-n-dirty AstroSynthesis technique sadly omits these voids. I figured out a rube-goldberg method to include the voids, but it needs a bit of polish for people who are not comfortable with writing Python programs and AstroSythesis plug-ins.
Rhombic dodecahedron can be stacked with zero voids between them, just like cubes. But they are better than cubes since a given cube's neighbors are at variable distances from the empire center. Since Rhombics are duals of Cuboctahedrons, they too are equidistant from all their neighbors. Which is vital for an empire map.
A rhombic dodecahedron just small enough to contain an empire sphere (that is, the empire sphere is an inscribed sphere within the rhombic dodecahedron where the sphere is tangent to each face of the RD) with have an enclosed volume that is about 1.36 times the volume of the empire sphere. Which makes sense since you are adding the volume of the little voids to the empire. You need to know this since the volume tells you how many stars are inside.
The volume of a rhombic dodecahedron enclosing an empire sphere of a given empire radius is:
RDvol = 1.36 * (4/3) * π * EmpireRadius3
RDvol ≅ 5.6967544 * EmpireRadius3
RDvol = volume of rhombic dodecahedron, in cubic light-years or whatever
EmpireRadius = radius of the empire sphere, in light-years or whatever.
π = pi = 3.14159265...
The same rhombic dodecahedron with have an edge length which is about 1.2247 times the length of the empire sphere radius. You may or may not need to know this, but it may come in handy if you were carving a physical model or something.
I am now going to show my math of how I derived those multiplication factors. If you could care less, skip ahead to the next section.
EmpireVolume = (4/3) * π * EmpireRadius3 (basic formula for volume of a sphere)
EmpireRadius = radius of the empire sphere, in light-years or whatever.
EmpireVolume = volume of empire sphere, in cubic light-years or whatever
π = pi = 3.14159265...
EmpireRadius = (√6 / 3) * RDedge (formula for radius of inscribed sphere in rhombic dodecahedron, where the sphere is the empire sphere)
RDedge = EmpireRadius / (√6 / 3) (use algebra to solve for RDedge)
RDedge ≅ EmpireRadius / 0.8165
RDedge ≅ EmpireRadius * 1.2247 (multiplying by reciprocal is same as dividing)
RDvol = ((16 * √3) / 9) * RDedge3
RDvol = ((16 * √3) / 9) * (EmpireRadius / (√6 / 3))3
RDvol ≅ ((16 * √3) / 9) * (EmpireRadius * 1.2247)3
RDvol ≅ 3.0792 * (EmpireRadius * 1.2247)3
Now to do an in-depth analysis, you need more than the 12 empires in the first layer surrounding Sol, the Sol-shell empires. You should also know the 12 empires surrounding each Sol-shell empire, not just five of them.
To do this you'll need to add a second layer of empires around the original single-layer map.
So if you have just one sphere (Sol Empire) and surround it with a layer of other spheres in the form of a cuboctahedron, you have what Buckminster Full calls a "one-frequency" layer. The number of spheres in a layer is (10*F2) + 2 where F is frequency. So the one-frequency Sol-shell layer has (10*12)+2 = 12 spheres. Add the center sphere and you'll see the basic map has 13 spheres.
Add a layer to that and you'll have a two-frequency layer. (10*22)+2 = 42 spheres. Add the original 13 spheres and you'll see the expanded map has 55 spheres.
With this expanded map, you will have the 12 neighbors of each of the Sol-shell layer empires. Sadly you will only have five neighbors of the outer-layer empires but you have to stop somewhere. The next outer layer will need 92 more spheres, that way lies madness. 55 empires is more than enough to keep you busy.
I used Blender 3d to whip up a couple of charts of 55 in a cuboctahedral array, for your empire plotting convenience. Make notes using your favorite paint program. Alternatively, download the PDF versions and print them on your printer (they are sized to be 8 inches wide) and make notes using a pencil. Go nuts plotting the locations of rival empires in three dimensions.
About thirty years ago I tried to draw such a chart manually on triangular graph paper but the result was not usable. Blender made it a snap. Especially making the twisted version so you could see all the empires, that would have taken me months to do with pen and paper.
This effort comes under the heading of "create custom artwork for diagrams and illustrations of difficult concepts", which I promised to do and have been doing.
Empire Center Coords
(Two Layers around core)
Multiply center coords by chosen empire diameter
(Upper Mid Level)
(Lower Mid Level)
To use the Empire Center Coords (3D Geometry) table: choose the desired DIAMETER (not radius), and multiply each coordinate by the diameter. For instance, if you chose an empire diameter of 100 light-years, Empire Charlie would be at coordinates -51, -29, 81.
If you felt the need to continue the gemstone motif, I made a quick list. The ones after #11 are all in alphabetical order, feel free to scramble them up.
RocketCat was making some notes about the galactic empires existing several centuries in the future, using the two-layer map. He says the empires are as described by some descendant of his named "GalactiCat". All my questions about where he got this information were met with his best "that's for me to know and you to find out" facial expression. Oh well, he always did have sort of a laissez-faire attitude towards causality.
Each empire is approximately 65 light-years in diameter (20 parsecs), 32 light-years in radius (10 parsecs). The entire cluster of 55 empires has a diameter of approximately 325 light-years (100 parsecs). As per my standard directions are: plus X points Coreward, minus X points Rimward, plus y points Spinward and minus y points Trailing. I regret to say that I screwed up: plus Z is Zenith while minus Z is Nadir, the exact opposite of what it should be. Oh well, I'll fix it when I get the time.
(x,y,z in l-y)
|0 Empire Sol||0.00,0.00,0.00||Sirus|
aka Dog Star
|1 Empire Albert||-57.70,5.54,41.08||Iota Ursae Majoris|
|2 Empire Bravo||-53.79,-33.25,-17.60||Beta Eridani|
|3 Empire Charlie||-62.59,44.01,-24.78||Beta Persei|
|4 Empire Denver||-4.90,-29.60,49.20||Delta Leonis|
|5 Empire Echo||-30.32,-22.82,21.19||Delta Velorum|
|6 Empire Foxtrot||-6.00,-39.00,-52.00||Kappa Phoenicis|
|7 Empire Golf||0.92,35.20,-52.20||Sigma Pegasi|
|8 Empire Hotel||3.26,62.92,-0.65||Alpha Cephei|
|9 Empire India||2.43,25.70,55.00||Alcor—Mizar|
|10 Empire Juliette||23.00,-12.00,27.00||Iota Centauri|
|11 Empire Kilo||52.90,-2.82,-46.50||Eta Indi|
|12 Empire Lima||65.90,41.50,16.20||Delta Herculis|
- EMPIRE SPHERE: empire sphere label
- CENTER COORDS: the coordinates of the center of the empire sphere. X, Y, and Z co-ords in light-years
- SECTOR NAME: flashy name for the empire sphere, named after the brightest star in the sphere. So Empire Sol is in the Sirius Sector or Sector Diamond
- EMPIRE CULTURE: code name of the alien civilization ruling the sphere
- THRONE STAR: star hosting the capital planet of the empire. In most cases this is also the home planet that gave birth to the alien race, the cultural origin planet
Empire Culture and Technology Notes
For lack of a better algorithm, I am using the same idea that Piers Anthony used when world-building for his Cluster series. He created his alien species by starting with a unique central organizing principle for each species, and applied it to all facets of their existence. This determined their standard method of solving problems, techniques of debate, method they used to move their bodies across the landscape, sexual organs, and everything else.
Human beings are a "thrust" culture. They solve problems by analysis, that is, cutting away like a scalpel or woodcutting tool. They debate by "getting to the point". They move by thrusting one leg forward in sequence. Their sexual organs thrust in and out.
Meanwhile the Polarians are a "rolling" culture. They solve problems by circling around it and examining it from all sides. They debate by moving around in circles. They move by balancing their bodies atop an organic sphere and roll along. Their sexual organs are used to spin spherical germ cells between the participants. And so on.
Occasionally he would use the same principle for two difference alien species, and use it to highlight how similar they were underneath even though superficially they looked different.
Yes, this is a simplistic and silly way to create an alien culture, but at least it provides good initial brain-storming ideas as a springboard.
- Human-Cetacean Alliance: basically the Terran Empire. By that time cetaceans were recognized as being intelligent, abet weird. The cetaceans forgave humans, eventually, after some eye-watering restitutions were paid.
- Receptor Culture: past masters of the art of energy harvesting. True, the energy sources are low-grade, but waste-not-want-not. They also have a limited ability to harvest the energy from incoming hostile weapons fire. Inspired by Star Trek: The Animated Series episode Beyond the Farthest Star (see image to the right)
- Noise Culture: their combat, tactics, and psychology is based on jamming sensors. Basically sending noise, interference, and false information to an opponents sensors to drown out the signal. Radar jamming, misinformation, disinformation, that sort of thing.
- Transmitter Culture: the entire culture is based around matter transmission. Requires transmitter and receiver (including need to transport receiver via sublight starship). Transmitter recreates what is transmitted, including people (also means original is stays at home and transmitter is also a duplicator. With all that implies).
- Evolver Culture: their combat, tactics, and psychology is based on using genetic algorithms to evolve a solution. Which they are constantly doing all the time.
- Solar-Phoenix Culture: they are the past masters of the art of nuclear fusion. They can fuse any element lighter than Iron-56. Including proton-proton fusion which is real hard to do short of using an entire star. Which means they can use almost half the periodic table as fuel.
- Memory Culture: their culture is based around storage of information. For instance, their warships have memory banks containing detail blueprints. This means that if the ship is damaged, they can recreate the damaged sections perfectly (given energy for the nano-forges and a supply of feedstock). They can practically recreate the ship's armor as fast as enemy weapons fire can blast it away. Buildings and equipment can last for millions of years, or until the power runs out, whichever comes first. Inspiration was from Captain Scarlet and the Mysterons, with the latter's power to "reverse matter". Also inspiration from the computers of Diaspar (see quote) in Arthur C. Clarke's The City and the Stars.
- Sun Parasites: this is less of a culture and more like a disease. Sentient patterns of magnetism and plasma which infect stars. They use the star's energy for food and reproduction, which does not do the star any good. They spread from star to star using microscopic "seeds" attached to astronomically sized magnetic sails. If you make them angry, they can control the star they are infesting enough to make it spit accurately at planets a series of geomagnetic storms powerful enough to make the Carrington Event look like a wet firecracker. Inspired by the Photino Birds from Stephen Baxter's Xeelee Sequence and Out Of The Sun by Arthur C. Clarke (see quote).
- Tunneler Culture: their technology is based around utilization of Einstein–Rosen bridges. They have wormholes small enough to teleport atoms to large enough to transport entire moons. Used for transport, sensors, data transmission, and computation. This also means that some of their machines are composed of components that are physically distant from each other; but exchanging data, fuel, feedstocks, etc through wormholes. Rumor is that some of the aliens can do that with their bodies. Inspired by The Light of Other Days by Stephen Baxter and Arthur C. Clarke.
- Mirage Culture: their combat, tactics, and psychology is based on fooling sensors by refracting electromagnetic radiaion. Generally takes the form of displacing the location of an image by gravitational lensing. Star fleets attacking Mirage Culture ships often feel like they are fighting inside a house of mirrors. They are similar to the Mirror Culture but are more focused on bending light from ambient sources, i.e., they are more concerned with defeating passive sensors instead of active ones.
- Amorphoid Culture: their weapons and technology are inspired by the Protean Weapons of Larry Todd's The Warbots. Weapon complex looks like a puddle of mercury, but can be formed into hundreds of different weapon systems. Weapon circuits are composed of magnetic and gravitic domains, which could not be altered by any amount of twisting and contorting.
- Tensegrity Culture: their philosophy and technology is based around tensegrity. While compression members (like steel girders) have a maximum size, tension members (like cables) can theoretically be of any length. Tensegrity combines compression and tension members for the creation of structures that are infinitely scaleable. The same goes for their philosophy and negotiation style: a combination of push and pull.
- Camouflage Culture: they are so good at camouflage that their genetically engineered worker creatures and equipment can become indistinguishable from asteroid and other natural celestial bodies. By which I mean you could grind one into atoms and it would still look like asteroid dust. Turn your back on it, however, and the asteroid can morph back into the original creature. Inspired by "existing implicate order" from The Ring of Charon by Roger MacBride Allen.
- The Grid:
- Argus Culture: culture is based on the theory that you can never have too many sensors. Ships and installations bristle with sensors and scanners for as many frequencies as is practical, looking in all directions. Sophisticated analytical algorithms ensure that units do not drown in oceans of data. You cannot sneak past an Argus ship, they will spot you.
- Field Culture:
- Mirror Culture: their combat, tactics, and psychology is based on manipulating the vectors of enemy sensors or scanners. They are similar to the Mirage Culture but are more focused on bending light from enemy scanners instead of from ambient sources, i.e., they are more concerned with defeating active sensors instead of passive ones. They also are fond of replacing an image of their spacecraft with an image which is a reflection of their opponent. They do that with debates and negotionations as well.
- Wind Culture: their combat, tactics, and psychology is based on manipulating objects with swarms of particulates or gaseous clouds instead of by solid tools. It is the difference between being knocked down by a hurricane as opposed to being hit with a club. Their warships are more like artificial nebulae composed of billions of microscopic units rather than a single metal spacecraft.
- Cloak Culture: their combat, tactics, and psychology is based on invisibility via reducing their emissions and absorbing or deflecting opponents scanning beams. There ain't no stealth in space, but they do their best.
- Thanatos Culture: no, not "Thanos" but related I suppose. Basically a death-cult civilization in space. Their interaction with other species is hard to distinguish from Beserkers or Morn Cyborgs; but they are religious-nut-job organic beings, not a left-over robot doomsday weapon. Inspired by the Necromonger Empire from the The Chronicles of Riddick.
- Nova Makers aka "Sun Slayers": just what it says on the label. The culture has the technology to create nova bombs. Apparently strangelets are involved. They were spotted in 1968 by Arthur C. Clarke.
- Hive Robots:
- Heisenberg Culture: their combat, tactics, and psychology is based on Heisenberg's uncertainty principle and the observer effect.
- Causality Culture: the culture is based around sophisticated knowledge of cause and effect. They can optimize for the minimum necessary change to create the maximum desired response. Some of their systems resemble byzantine Rube Goldberg machines but they get the job done using the minimum energy.
- Crystal Culture: they use crystal-based technology for everything, especially for data storage, weapons and power sources. Because you should never let a good trope go to waste. Their biochemistry is based on crystals as well.
- Probability Culture: their combat, tactics, and psychology is based on calculating probabilities and probability amplitudes. You don't have to tell them the odds because they already know them to nineteen decimal places.
- Entropy Culture: their combat, tactics, and psychology is based on decreasing or increasing the rate that entropy accumulates in a given system or situation. Generally they try to slow the entropy increase for themselves while speeding it up for their opponents.
- Speed Culture:
- Cyborg Culture:
- Energy Culture: their technology utilizes components made of electromagnetic fields where others would use matter. Directed energy weapons instead of kinetic energy weapons, force fields instead of armor plate. More or less the opposite of the Mass Culture
- Mass Culture: their technology utilizes components made of matter where others would use electromagnetic fields. Warships use armor made of muon-iron instead of defensive force fields, kinetic energy weapons instead of laser beams, technologies utilizing degenerate matter and neutronium, etc. They are more or less the opposite of the Energy Culture.
- Bubble-Cloud Culture:
- Composite Creatures: a colonial siphonophorae, similar to a Portuguese man o' war. That is, while it looks like a single creature it is actually a composite of different types of organisms glued together. Inspired by the "Godspeakers" from The Dragon Never Sleeps by Glen Cook. They look like a group-grope involving giant hydras and starfish atop a heap of exposed intestines.
- Warp Culture:
- Seeder Culture: Directed Panspermia Я Us. They terraform (or "seederform") worlds to make them garden worlds for their species. Along with this the worlds are seeded with microorganisms and nanotechnology to jump-start the evolution of their type of life.
- Seetee Culture: ships and artifacts are composed of equal parts matter and antimatter. Inspired by Seetee Ship by Jack Williamson
- Mutator Culture:
- Precognition Culture:
- Marine Neuron-net: inspiration: Starswarm by Jerry Pournelle, the alien neuron-net super-intelligent plant-like creatures dwelling in the bottom of the planet’s countless shallow lakes and oceans. Secondary inspiration was from The Skeptic alien species from the game Cosmic Encounters.
- Euphoron Culture:
- Living Computer-chip:
- Sculptured Laser Culture:
- Orbital Brains:
- Wave Lattice Culture:
- Aikido Culture: much like the Japanese martial art, the culture's philosophy, psychology, and military arts are based on bending with and redirection the energy of an attack. This does tend to make the culture more defensive than offensive. A member of the Aikido culture surrounded by attackers would calmly walk out of the center of the melee, while the attackers would discover they had grabbed each other. This holds true with a legal debate, hand-to-hand combat, or a starship battle.
- Robot-core Culture:
- Fog Culture:
- Patterns of Chaos: Inspire by Patterns of Chaos by Colin Kapp and Agent of Chaos by Norman Spinrad
- Aura Stars:
- Standing-wave Culture: the culture's psychology and technology is based on the concept of standing waves. In some respects they both move and are stationary simultaneously.
- Plateau-eye Region:
- Star-web Region:
- Bent-space Region:
- Desolid Culture:
- Hyperaging Culture: these creatures evolved on the surface of a neutron star. Ordinary aliens (like humans) are composed of atoms bound by the electromagnetic force. The hyperagers on the other hand have bodies composed of atomic nuclei bound by the strong force. Nuclear reactions are about one million times faster than chemical reactions, so the hyperagers move and live that much faster than humans. A hyperagers 76 hyper-year life space seems like only 40 minutes to a human. This also means the hyperager's rate of technological advance is a million times faster. And you thought "Wink of an Eye" was dangerous. Inspired by the cheela of Dragon's Egg by Robert L. Forward.
Some galactopolitical powers have no fixed address, being more like nomads. They sort of wander through the various empires, wreaking havok along the way.
- Tempath Justice Fleet: an impressively huge star fleet crewed by a species cursed with the power of telempathy. Meaning that if any stellar empire commits a savage act of oppression or genocide, the Justice Fleet will psionically hear the screams of the victims across the galactic spiral arms. And the fleet will come for you. There is a long trail of burnt-off planets marking the tombs of empires that found out the hard way that the Tempath's idea of justice is "an eye for an eye."
- Lungfish: mutated von Neumann probes. Originally meant as a scalable way to explore the galaxy, they have mutated into paperclip maximizers. There are many types, and different types are also at war with each other. Some have become beserkers. Inspired by Lungfish by David Brin.
- The Plunder Fleet: planet looters who strike from some hidden homeworld whose location is being sought after by stellar empires that are sick and tired of being given the "Space Viking" treatment.
- The Ravage Horde: larger swarm of planet looters who have no home planet. Instead, they have mobile space habitats that travel in tandem with the looter fleet, nomad-style.
- Cybervirus: The best description is like a cross between an AI and a rapidly mutating computer virus. It doesn't matter what type of computer or operating system a stellar empire uses. As long as it is Turing Complete the Cybervirus will adapt and find a way in. The model here is The Blight from John Varley's A Fire Upon The Deep
- Living Nebula: intelligent organisms in the form of a living Bok Globule. They like to travel to stars and engulf them for a couple of centuries to suck up solar energy. Pretty much as described in Fred Hoyle's The Black Cloud.
- Electromagnetic Daemons: malevolent organisms composed of patterns of electromagnetic radiation instead of matter
- Stellar Vultures: galactic scavengers who harvest the larger technological resources of dead civilizations
- Stellar Reducers: galactic decomposers and detritivores. Pretty much like Stellar Vultures, except they harvest the stuff the Vultures leave behind as too low grade to be worth it. Since detritivores subsist on waste products, they might be present in civilizations that are not dead yet.
- Morn Cyborgs: pretty much like Fred Saberhagen's Beserkers. Except these are cyborgs instead of robots, which doesn't really make much difference. Both want to destroy all life in the universe, and become a poetic metaphor for Death.
- The Forgotten Empire: basically Forerunners. Their ancient ruins often contain incredibly valuable (and incredibly dangerous) paleotechnology.
- Monolith Culture: basically the star gods from 2001: A Space Odyssey. They have long ago departed for the fourth dimension or something, but their monoliths are lying around everywhere. They are tools designed to foster the birth of new intelligent species. Otherwise they are inert and indestructable.