So I was playing earlier today and decided to apply some of my Calculus I had learned in high school to zombies. I was going to see if I was able to determine how many zombies would spawn at any round. Now if you have no knowledge of calculus this could be confusing, but I will try to explain the best I can.
There is a growth and decay function in Calculus represented by the equation y=Ce^kt
y = number of zombies
C = value when t = 0
e = constant number, similar to pi
k = usually the number you want to find, the growth and decay number that will change the y value
t = time, in this case, round number
Okay, so in attempt to apply this to zombies, I needed some round information. I went to round 61 and recorded rounds 43-61 zombies per round. I took into account nukes that I did and didn't get, the nova rounds (die rise) and everything. I only calculated rounds without nukes to prevent any loss or ambiguity within the formula.
So after a while of calculating various numbers, this is what I came across:
Round 43 gave me k = 0.080355
Round 47 gave me k = 0.076828
Round 48 gave me k = 0.076055
Round 49 gave me k = 0.073966
Round 53 gave me k = 0.072239
Round 61 gave me k = 0.067029
As you go higher and higher in rounds with more zombies, the value of k decreases, making it impossible for k to be a value to calculate. So using more calculus, I decided to plug infinity into a limit function. Using this: limit as t approaches inifinity of y=6e^kt. This will tell us that by plugging in infinity for time, or t, that our final value for zombies will be infinity... I knew this would probably happen, but I wish I could find a constant value for k...
But this does not make any sense with my findings still. If the value of k approaches 0 like it does from my findings, then as k approcahes 0 makes the total zombies that spawn 6... okay, I will work on this later. I may have to use more calculus along with L'Hopital's rule...
Let me know what you calculus buffs think ??
Why not just look at the blops 1 scripts. its all written out in front of you. you can even look at the, not so random, random box code.
yeah right...like this forum is full of calulus buffs. the only calculus I know is integration and differentiation. I thought that's all calulus is
Ugh I got a headache now I need to nap.
Here I am explaining you calculus: you have two variables: T and K. So, as T approaches infinity, K approaches zero. And zero times infinity is an indeterminate form. T grows linearly because is the round, so 1, 2, 3, ... 100000, ... and so on. K decreases but now linearly. It is much slower than T. So, in this particular case, T is faster, so zero times infinity equals infinity. So the more you progress, the more zombies will spawn. Sorry if I made mistakes but english is not my first language.
Why not just play solo and don't get nukes. At the end of each round (starting with round 1) pause the game and see what your kills are.
Example:
Round 1 - 10 kills
Round 2 - 23 kills
A little subtraction tells you that they increased the zombie count by 3.
Yes, I know they increase by more as the game goes up in rounds but still.... this seems a much easier way to do it. I did it one day on TranZit but only up to round 20. I didn't keep the spreadsheet because I forgot on a few rounds to pause and jot down the number but I've intended to do this again.
I dunno..... just seems easier using simple subtraction.
I'll have to try that... If it doesn't work, then I'll probably put the numbers in Excel and drag the box down so it makes the formula for me
Chingpow wrote:
I'll have to try that... If it doesn't work, then I'll probably put the numbers in Excel and drag the box down so it makes the formula for me
That's exactly what I did. 4 colums with forumlas to figure it all out. All I did is plug in the total kills after each round and the formulas did the rest. Here's an example of how I set it up:
My goal was to do this for several games and see if the numbers were consistent... I just slacked off and haven't got back to it yet.
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