Exponential or Linear (on-topic)

[rootbeer23]

Round 2!

I was quite enjoying the discussion.

Where were we?

I think you wanted to make a case for linear economics.
ready ... set ... go!

[Kryo]

well use hotstats and look at your mass rate curve.

if it looks like this:

it is a sign for linear economy


but I am pretty sure, as you are no noob, that it is looking more like this:



which will mean its exponential.

Images were picked randomly via google search

[Kryo]

lol Anaryl, then your mind is neither thinking scientific nor mathematic

[rootbeer23]

Well Kryo - It's true the U.S has grown at an exponential rate of 2% each year (trend on trend). But I don't think people in this thread would be referring to 2% as "exponential economies".

In my mind an exponential economy would be a growth rate of x^x

like for example 1.02^x ?

[Softly]

Obviously if someone is playing sim city, they will have an exponentially increasing supply of mass, provided they don't run into pathfinding issues with engies (by using drones), though this is obviously limited by unit cap.

However, the graph of said mass supply won't be determined by the same function for the whole game, rather there will be a section where you are building t1 mexes, upgrading them, building storage and finally when you reach the mass fab game. At each stage, the mass income vs time graph will be exponential, but the overall graph will look less so because at each stage its gradient increases less because its less efficient a way of getting mass than the stage before. Add to this the fact that you will also be needing to increase the amount you spend on units the further you get in which will depress the curve further. At this stage the chances of it being entirely linear are insignificant, regardless of what the curve actually approximates to. You would effectively be trying to make an exponential curve linear, by taking an exponential curve of it...???

That said, we are assuming that you are a perfectly consistent player (which is not the case, are you telling me that you have never ever built up any kind of mass storage?), and also that mass investment vs extra income is a continuous function (which it isn't, you don't get half a t1 mex if you only put half the mass in...).

Then you have to consider different play styles. If you don't build any mexes then you can have both an exponential and a linear mass curve! Or you can play simcity and get an approximately exponential one over time, or you can play a normal game and have a totally bs curve when all your t2 mexes get tml sniped, and your t1 mexes get periodically raided and destroyed.

So to conclude, and now lets be really technical and on topic. Every single bit of the graph will actually be flat. Your mass income will only go up when you finish a mass upgrade/building at which point it will become a flat curve again. Great lets all go home everyone previous is wrong. Depending on how you play, will depend on what your flat sections will line up and approximate to, although it should always be exponential at each stage of the game.

[Myxir]

as your mass income grows, also your production of unit does (if not you will probably die by enemy units), so in the case you don't play eco only game like x2 thermo or go for turtlewar, your mass income grows linear (because you can't spend ALL on your mexes)

[Softly]

(because you can't spend ALL on your mexes)

No but you don't spend the same on your mexes the entire game. The only way what you say is true would be if you were to invest a constant amount at each stage. Which doesn't happen. Thats like saying I am only going to upgrade one t1 mex at a time until they are all t2, and I will assist none of them ever.

If that is the case I refer back to my previous point of depending on how you play you can make any curve. Doesn't mean you're playing right.

[Kryo]

as your mass income grows, also your production of unit does (if not you will probably die by enemy units), so in the case you don't play eco only game like x2 thermo or go for turtlewar, your mass income grows linear (because you can't spend ALL on your mexes)

lol no! It is definitively not linear

As I pointed out in the other thread, it is exponential, but not in the simple form of mass(t)=m0*exp(A*t). As DilliDalli pointed out, you dont spend all your mass in mexes, and you have a limited amount of mexes. Therefore it would be a formula with a lots of parameters and variables. probably you would never find an analytic formula at all. Therefore this discussion is obsolete.

I can say by 100% that it is NOT linear, and by 99% it is exponential. But its a incredibly complicated case.

[Myxir]

i think you didn't get what i've written

when playing a normal game, you will get more mexes over time and upgrading some of them, but also you'll increase your production of units which also cost mass, therefore you can't spend all your mass into getting more of it (which would cause an exponential growth) but only parts of it

so there are 2 major possiblities:
either you produce less than your income grows, in this case your eco grows exponential
OR you increase your production exactly or even more as your income grows, in this case it's linear

[Softly]

If you put in a constant amount into eco then you will fall behind the guy who puts in more as his eco grows. So exponential > linear

[Edit] Besides Linear is just a special case of exponential.