Landmine alignment
Landmines are one of the few entities that don't align to the 1x1 meter grid (the others being locomotives and cargo/fluid/artillery wagons).This can be a pain if you're trying to create a complex defensive pattern with landmines and dragon's teeth. Here's a post I found that provides a centered grid-aligned mine blueprint.
Landmine Size
Just centering landmines isn't really in the spirit of optimization. So how close can we lay landmines? I found through experimentation that the diameter D of a landmine is .80078125 (factorio-generated train/landmine blueprints have 8 fractional decimal places). Factorio will accept blueprints with closer landmines but once the first landmine is laid down your construction bot won't be able to place the second. This blueprint demonstrates two pair of landmines .80078125 and .80078124 meters apart - only 3 landmines will place because two of them are too closely spaced.Spidertrons and landmines
Spidertrons can't cross tightly-laid landmines, similar to fully-packed walls/pipes/rails (reference). Here's an 11x11 landmine (9x9 meter) blueprint. If you tile it, spidertrons can't cross.- spidertron_stretch_lol.png (1.97 MiB) Viewed 3150 times
Landmine/circle packing
We should be able to lay landmines even tighter - in an infinite 2d space the tightest circle packing method is to alternate rows offset by sin(30°)*D==.5*D and separated from the previous row by cos(30°)*D~=.86602540*D. Sadly, this doesn't work - when we offset rows by .5*D we still have to separate rows by D. In other words, landmines occupy a square not a circle and D is the width not the diameter.Landmine implementation details
As I was experimenting with circle packing I realized I could find the landmine dimensions using the easier but less fun method - look at the game's lua code. entities.lua lists a land-mine collision box as [-.4,-.4] to [.4,.4]. Of course that doesn't square with my experimental data - my best guess is that the collision detection disallows edges that equal each other and factorio only resolves to 1/128 decimeter (1/1280==0.00078125). I didn't find a way for this to relate to an IEEE 754 float or double resolution.Perfectly packed Landmines
If you want to pack landmines perfectly and be grid-aligned, lay a landmine field of size 256x256 landmines, 205x205 meters (.80078125==205/256). I do not recommend you do this, that's 2^16==65536 landmines. I couldn't upload this blueprint to factorioprints and I didn't even try here.
