Describe how the albums have aged with time using mathematical functions!

[perfectchaos180]

perfectchaos, you should give the reasoning for your given functions in relation to the respective albums (lolpun that probably few will get there).

But hey:

WDADU: y = 1 ---(very meh)
IaW: y = (n!)^2 ---(it's awesome, it "contains" higher values of awesome)
Awake: y = (n+1)! ---(also very awesome, factorial grows fast)
FII: y'' + y = 0 ---(second derivative plus the original function...they took a new spin on their sound, but =0 because I'm not digging the whole album)
SFAM: y = e + x ---(kind of meh, so linear)
SDOIT: y = (n!)^3 ---(Yes, the album is amazing, tremendous growth here)
ToT: (x-5)^2 = 12(y-19) ---(a shifted, skinny parabola? but yeah, very good, even if they narrowed down their style a lot to straight up metal with some progressiveness)
8VM: x^2 + y^2 = 58 ---(double references FTW...one is obvious, the other one isn't, can you guess it?)
SC: x = 2 + t, y = t ---(really hit or miss, thus the parameter t)
BC&SL: y = e^(10x) ---(big growth here as well)

Done nerding out here.

Woo! one or two people got into it!

And as far as the Octavarium references, one is the 5 and the 8, the other is it is a circle.... A FULL CIRCLE

[jsem]

Images and Words: x^kevin moore

[ddtonfire]

Octavarium: y = cos(x)

Mine is more like y= 2sin(x-4)+1

Oh yeah? Well mine is y = sin(x-𝛑/2)

[ScioPath]

WDADU:  y = ^{x^2}√(x) , x > 1   [Didn't know or care about it in the first small portion of my DT fanhood. Discovered it and my excitement reached a small peak, before a gradual decrease.]








Aw screw it, I'm not doing math on holiday.

[Global Laziness]

This thread could stand more graphs and fewer functions for those of us who aren't mathematically-inclined.

[kartmaze2]

BCSL: y(x) = δ(x)
(dirac delta function)

[cthrubuoy]

This thread could stand more graphs and fewer functions for those of us who aren't mathematically-inclined.

https://www.wolframalpha.com/

otherwise, WUT.

[Metabog]

BCSL: y(x) = δ(x)
(dirac delta function)

O rly? Is that the normalized delta function or does it go to ∞? Is it centered on the BCSL release time?

[kartmaze2]

BCSL: y(x) = δ(x)
(dirac delta function)

O rly? Is that the normalized delta function or does it go to ∞? Is it centered on the BCSL release time?

It's the "regular" one that goes to infinity, and it's centered around the time when I just had heard it for the first time. A more exact formula would maybe be y(t) = δ(t) + c, where c is some constant representing an average DT-album.   

[Metabog]

To me, the albums represent the Fourier Transform or frequency response of the DT awesomeness in the time domain. A 4th Order Lowpass filter has been applied, with the corner frequency at w0 = Octavarium (5858hz). This would mean that the awesomeness of the albums after Octavarium decays at 24db per octave. This of course doesn't tell us much about the change in popularity over time for each album.

[wolfking]

WTF is going on in here!?

[kartmaze2]

To me, the albums represent the Fourier Transform or frequency response of the DT awesomeness in the time domain. A 4th Order Lowpass filter has been applied, with the corner frequency at w0 = Octavarium (5858hz). This would mean that the awesomeness of the albums after Octavarium decays at 24db per octave. This of course doesn't tell us much about the change in popularity over time for each album.

This doesn't make any sense. The only thing you will get out of a Fourier Transform of DT's awesomeness over time is maybe a peak around F = 1.585×10^-8 Hz (which is about 2 years) and maybe some other high values in that area. Higher frequencies will in comparison be neglectible, and thus a lowpass filter will be useless.

[Metabog]

To me, the albums represent the Fourier Transform or frequency response of the DT awesomeness in the time domain. A 4th Order Lowpass filter has been applied, with the corner frequency at w0 = Octavarium (5858hz). This would mean that the awesomeness of the albums after Octavarium decays at 24db per octave. This of course doesn't tell us much about the change in popularity over time for each album.

This doesn't make any sense. The only thing you will get out of a Fourier Transform of DT's awesomeness over time is maybe a peak around F = 1.585×10^-8 Hz (which is about 2 years) and maybe some other high values in that area. Higher frequencies will in comparison be neglectible, and thus a lowpass filter will be useless.

You're right, of course, I was just being poetic. DT isn't even a a periodic fuction to take a DFT of. What I was trying to envision is the albums spread across the spectrum at frequencies relevant to their release times. Then if you put a window function with the shape of a lowpass filter's frequency response to that, the newer albums would be attenuated. 

Then again, it's a perfect sphere colliding with our fate... and the signal ends where it began. Hey maybe DT hid something in it's own popularity spectrogram. NUGGETZ.

[kartmaze2]

They have been quite periodic for many years now, actually... 

[SixDegrees]

.

[Global Laziness]

This thread could stand more graphs and fewer functions for those of us who aren't mathematically-inclined.

https://www.wolframalpha.com/

otherwise, WUT.

Wow, that is really cool.

[Jamesman42]

I use wolfram a lot, especially when I help calculus students visualize graphs that are hard to see clearly on a graphing calculator, or 3-d graphs.

[ddtonfire]

I  Mathematica soooooo much! 

[Jamesman42]

I  Mathematica soooooo much! 

YES. Sometimes I'll just browse through all the different "articles" they have on different topics in math. Number theory really interests me.

[perfectchaos180]

Ok guys the holiday is over time to do some math

THIS TOPIC WILL NOT DIE (it may asymptotically approach 0 replies, but it will never quite get there!)

[Kosmo]

Maths is easily my most hated thing ever, but i also can't live without it.

[Jamesman42]

Ok guys the holiday is over time to do some math

THIS TOPIC WILL NOT DIE (it may asymptotically approach 0 new replies, but it will never quite get there!)

FTFY

[ddtonfire]

dreplies/dtime is negative 

[Jamesman42]

Take its inverse!