Because progressions based on Phi are not only beautiful, they are not to quick and not to slow. Human mind use Phi to judge if "it's a lot" or "it's not much". Phi makes this "just enough".

Approximation of Phi are used in game design in many games (Shadowrun (66%), Vampire oWod (60%), Eve Online (exact phi), Mare nostrum (66%) for those that just comes to my mind) :)

You're right for your maths, but:

<Modifier       TargetProperty="SystemInfluenceRadius"  Operation="Addition"        Value="$(SystemInfluenceStock)"/>
<Modifier       TargetProperty="SystemInfluenceRadius"  Operation="Division"        Value="3.14115926" />
<Modifier       TargetProperty="SystemInfluenceRadius"  Operation="Power"           Value="0.5"/>
<Modifier       TargetProperty="SystemInfluenceRadius"  Operation="Multiplication"  Value="0.75" Priority="1"/>

For me, this means:

R = R + SIS

then

R = R / Pi

then

R = R ^ 0.5

then

R = R * 0.75

So:

R = R + SIS, this means, in physics, that SIS is a length. You don't add carrots to lions. You add lenght with lenght. => we already stated that  should be a surface, not a length.

Because Empire is a territory, not a distance. If  tries to emulate political power, then you have much much power in a 10km radius circle than in a 5km radius. It's not 2x, it's 4x.

So, if  counted areas instead of lenght, then from a certain score of , to increase a radius by 2x, then you would need 4x more .

If  were volumes, then to increase a radius by 2x, you need 8x more .

But since it's lenghts, then to increase your radius by 2x, you need 2x more . And the area you control will increase by 4x.

This is wrong.

...

Anyway, this leads to, about as you said, R = (((R+SiS)/Pi)^0.5)*0.75

Where it should be:

R = R+(((SiS)/Pi)^0.5)*0.75

Now, maybe R = 0. But no.

line 10,

<Property Name="SystemInfluenceRadius"  BaseValue="10"/>

Is +10 the fow natural growth or something ? Why it should be accounted as Empire points ? This means a 0 Empire point output would grow, this is not normal.

That's for the formula. But as I said, the formula is not the main point.

I present, and this needs to be confirmed, that Homesystems use global Empire point output, not the system's.

With actual numbers Empire generation from ingame system vs homesystems, use the numbers and compare.

There is no reason for those jumbo circles, all centered on homesystems.

If that formula works, so be it. I don't like it but I'm happy to be wrong :)

But there's an obvious problem with homesystems, just have a look at the screenshots ;)

every system use their own influence, only difference is that homesystem has a flat bonus of 7 and IA gets huge multipliers everywhere in higher difficulties.

I can confirm this for sure since i already had systems with bigger borders than my home system ( 1 st colonized system had huge Bilgeli on it, and was 5 planet so i built my unique wonders there and its border was much bigger than my home system). The thing is it's the unique improvements (mostly denarque institute and the super light content stuff) that gives this huge boost to influence.

also 

R = R + SIS, this means, in physics, that SIS is a length. You don't add carrots to lions.

I think you have trouble with the formula really, maybe because it's a sequential mode where operations are done step by step.

if you look closely you will notice that R is square rooted (^0.5), so at the top of the lines it's an area and at the end it's a radius ^^ that makes the influence used to fill an area

Also it's very important that you understand that this isn't the border GROWTH but the borer as a whole, meaning if between 2 turns your SIS decrease, your border decrease

what you call SIS is the total net worth of influence produced by your system, the border radius is then calculated in function of this value.

anyway i invite you to look at my updated 1st post, i modified the formula to make it based of volume instead of area and it looks pretty good i must admit

Could you find and give your systems  output ?

Also, why do you try to tell about borders, when a circle's circumferance is 2.pi.r ? I'm talking from a physics point of vue. You can't do thing like "say X is carrots, add it to Y lion and tada you've got Z mashmallows".

You also can't say "I'll add this lenght to this thing whatever it is, take the square root and tada result's still a length". This is just physics' Hello World.

No wonder radiuses are all fucked up.

If it's for the game where i had a system with bigger borders than the home system it was an old save, but you can just try and make a colony in a big system and put all your influence building there and you will see that it's border will grow much more than your home system (though you shouldn't wait too much as the home system will keep accumulating systeminfluencestock)

i guess it is best tested as lumeris

Anyway i looked closely at how it works and there is actually no problems with the current system except the fact that it underestimated the potential growth in influence gain (14 at the start of the game to more than 1000 in less than 100 turns)

Pejman wrote:

I think you have trouble with the formula really, maybe because it's a sequential mode where operations are done step by step.

if you look closely you will notice that R is square rooted (^0.5), so at the top of the lines it's an area and at the end it's a radius ^^ that makes the influence used to fill an area

We can already agree on that :

Kweel_Nakashyn wrote:

Anyway, this leads to, about as you said, R = (((R+SiS)/Pi)^0.5)*0.75

Where it should be:

R = R+(((SiS)/Pi)^0.5)*0.75

R = (((R+SiS)/Pi)^0.5)*0.75 is still wrong. This states R is either a lenght or an area but the formula states it's kind of both. The second formula is right.

If R is just a variable placeholder then why it's not initialized to 0 ?

Pejman wrote:

we are not dealing with physical units but mathematical  variables

Yeah sure, Pi & square roots is just there for lulz effect.

Mathematically it's wrong too. I don't know how you compute radius increases, but it's not like that.

((R+X)/Pi)^0.5 is not equal to R + (X/Pi)^0.5. The difference is (((R+X)^0.5 - X^0.5) / (Pi^0.5)) - R.

If R = 10 and X is say 200, then the difference is +/- 10 when you are dealing with values like +/- 8.

So in one case you've got 8, in the other one 18. Now, 100%+ difference and you're still wondering that this formula diverges.

This is because they did like "yeah, in informatics, physics who cares" and used strange lenght units based on area, like "my square is area 1, and the lenght of it is 1 so HEY guys let's invent some math stuff about 1 area = 1 lenght. If 1 area = 1 lenght then 10 area = 10 lenght..." AKA congrats, with this kind of work you makes pizzas shaped probes crashing on Mars, or transforms Ariane 5 into a reversal rocket AKA EPIC FAIL AKA free ticket for the informatician who made this to sun atmosphere.

OK now if someone gave me 1€ each time I solve a bug from an informatician with a math formation aka "physics is for math noobs LOL", in my work, that does stupid things that provokes bugs because they are dealing with world meaning values and they have no idea what they are doing like adding time values differences to money and so on, I'll be fracking millionaire.

Also each time I correct some bugs from informaticians that ignore electronics too.

App. math is not ignoring the science for what it is used because it is used there as a tool. When math is a used as a science, you're free to invent worlds where you can add pandas to bananas so it creates chewing-gums. But since you want your numbers to have an euclidian geometry meaning, you're not here.

Pejman wrote:

so you should stop worrying about the corectness opf the formulas and focus more on how the game plays out ^^.

The games play not very well today. This is what worries me much. I said at least 2 times "if the formula works, so be it", but it doesn't.