A statistical adventure to uncover the game developers system of spawning enemy bases in Factorio.
Whilst playing factorio, I realised that it might be possible to apply the topological data analysis I was currently studying.
Below is a screenshot of the Factorio map, displaying hundreds of enemy bases (in red).
And then by using the programming language Lua, you can extract features from the game server in the in-game console. So using the code below I was able to write all of the enemy base co-ordinates to the user data directory :)
local string = "Index, X, Y"
for k, spawner in pairs (game.surfaces[1].find_entities_filtered{type = "unit-spawner"})
do string = string.."\n"..k..", "..spawner.position.x..", "..spawner.position.y
end
game.write_file("positions.csv", string)
The extracted co-ordinates can be seen in the below figure
And now we can take this data and use the "spatstat" library in R to analyse the data and fit it to a clustering process. Plotting the pair correlation function below demostrates the clear clustering behavior the enemy bases possess, as for a low distance, we can see there is a strong 'attraction' between enemy bases.
Fitting the data to a Matern cluster process, we get approximations of kappa = 0.00001 and scale = 20.3.
We can now generate new clusters of roughly the same distrubition!
Lastly, we can compute the persistence diagram of this dataset:
There is clearly a persistant feature of dimension 1 (denoted by the red triangle), this indicates there is a 'hole' in the data. This makes sense as no enemy bases will be created within a certain distance of the origin, so we get a annulus type structure centered at the origin. You can also see the clusters in the persistence diagram as the black dots (represenenting a persistant feature of dimension 0) climbing up the y-axis (the higher up the cluster on the y-axis, the further away it is from any other cluster).