Land expansion calculations

[Eagleeye]

Did a little playing around with land expansion. Here is what I found out.

LV Game Dev stated in another thread that the maximum number of tiles to purchase is 131,072.

However, if you are not yet at that limit, you can make 1 final land purchase that brings you over that total. So the goal is to get as close to 131,072 without going over.

The FIRST time you expand east or west, you can buy a strip that is 38 wide and however tall your current map is.

The SECOND time you expand east or west, and every time after that, the strip is only 32 wide.

This means if you start on the largest map in sandbox mode... it's 250 wide, 200 tall. Here are the dimensions with each land expansion...

Added	Width	Height	Tiles
	250	200	50000
38	288	200	57600
32	320	200	64000
32	352	200	70400
32	384	200	76800
32	416	200	83200
32	448	200	89600
32	480	200	96000
32	512	200	102400
32	544	200	108800
32	576	200	115200
32	608	200	121600
32	640	200	128000
32	672	200	134400

So as you can see, if you get to 134,400, you have expanded as much as you can by doing nothing but east/west expansion. You can expand 13 times this way.

The first time you expand north/south, you are given 56 tiles. This means your first expansion from 250x200 yields 250x256. Subsequent expansions give you 32 more tiles each time once again.

Doing the same process for north/south purchases... doing nothing but expanding south until we exceed the tile limit, we find that we can expand only 10 times before we hit 136,000 tiles even.

Added	Width	Height	Tiles
	250	200	50000
56	250	256	64000
32	250	288	72000
32	250	320	80000
32	250	352	88000
32	250	384	96000
32	250	416	104000
32	250	448	112000
32	250	480	120000
32	250	512	128000
32	250	544	136000

This seems to indicate that if you want the most total possible space, you should expand east 12 times, then expand ONCE south...

128,000 tiles on a 640x200 map (12th east expansion)... then add a 640x56 area south... for a total of 640x256=163840 tiles. This seems to be the largest possible map you can get, the final purchase giving you 35840 more tiles after starting with 97.66% of the total possible area allowed.

If we expand south instead, and do so 11 times, we start out once again with 128,000 tiles (250x512)... but this time we are only adding 38 to the side instead of 56 to the bottom. This gives us a final parcel of land that is 288x512, which is 147,456 tiles total. That's 16,384 LESS than doing it the first way.

What about a hybrid?

Let's try expanding east, then south, and alternating.

Width	Height	Tiles
250	200	50000
288	200	57600
288	256	73728
320	256	81920
320	288	92160
352	288	101376
352	320	112640
384	320	122880
384	352	135168

As you can see, this is the fastest way to get as much possible expansion PER STEP YOU TAKE... you get to your maximum in 8 purchases.

Now let's try the OTHER way... going south first, then east, and alternating.

Width	Height	Tiles
250	200	50000
250	256	64000
288	256	73728
288	288	82944
320	288	92160
320	320	102400
352	320	112640
352	352	123904
384	352	135168

As you can see you actually end up with the exact same result.... you just take a little different path to it. Same number of steps, too.

The question I asked myself at this point is... what if that final step, we doubled up on going one direction?

First I went WHWHWHWH... then I went HWHWHWHW... what if we go WHWHWHWW? And what if we go HWHWHWHH? (H = height expansion, W = width expansion)

Doubling up on the final Width expansion gives us FEWER tiles: 133120
Doubling up on the final HEIGHT expansion gives us the same! 135168

Anyway... some food for thought. :)

[Scifiwriterguy]

That was extremely well thought-out, with strong experimental methodology. I'm thinking you do mathematical analysis for a living...or a very serious hobby. All you're missing is a conclusion. :)

(Or people could...you know...*gasp* read the whole thing.)

[Eagleeye]

The conclusion depends on what your goal is. :) Since I don't know what YOUR goal is, I can't make any conclusion.

[Dark Phantom]

Some interesting thoughts there. So to max an extra large airport it says to go east 12 times and south once.It gives you a wide airport but not real deep.Sounds interesting and may have to try it. Thanks for the tips :)