4 ms·

Everything is a fractal, even socially

by buyingarmor 7y ago

coldtea 7y ago
Well, a sine wave is not a fractal, for one...
- nickthemagicman 7y ago
  On a quantum enough level it may be. (I have no idea what that means)
- Scene_Cast2 7y ago
  Random interesting (to me) tangent - couldn't you find a recursive function that, at its limit, was a sine? Could any function be generated this way? And throw some variant of Kolmogorov complexity metric on this class of function-generating fractals and this becomes a neat mathematical area.
  - excessive 7y ago
    Here is one in Python. Uncomment the if statement if you want it to terminate. def sin(x): def recur(x, n, s, p, f): #if n > 9: return s; return recur(x, n + 2, s + p/f, -p*x*x, f*(n + 1)*(n + 2)) return recur(x, 1, 0, x, 1) Of course maybe it's cheating from your intent because it's really just implementing the Taylor series, and it has too many arguments. I believe any analytic function could be defined this way if you can figure out the pattern for its derivatives.
  - perl4ever 7y ago
    Function sine(x As Double, Optional term, Optional p = 1#) As Double If IsMissing(term) Then term = x End If If term <> 0 Then sine = term + sine(x, -term * x / (p + 1) * x / (p + 2), p + 2) End If End Function Edit: This is my interpretation of the Taylor series approximation, but it's probably a bad idea to use this for anything that matters. One reason is that it doesn't reduce large angles, and another is that people who know what they're doing prefer to use some other formula, from a cursory Googling...though I'm not sure why.
pbhjpbhj 7y ago
Define fractal?
- drdeca 7y ago
  Something with non-integer fractal dimension? Actually, idk if that is exactly the right definition, because I think some fractals have integer dimension? Idk
golergka 7y ago
We live in a society.
- nickthemagicman 7y ago
  Or does society live in US?
- knolax 7y ago
  BOTTOM TEXT

Everything is a fractal, even socially

coldtea 7y ago

Well, a sine wave is not a fractal, for one...

nickthemagicman 7y ago
On a quantum enough level it may be. (I have no idea what that means)
Scene_Cast2 7y ago
Random interesting (to me) tangent - couldn't you find a recursive function that, at its limit, was a sine? Could any function be generated this way? And throw some variant of Kolmogorov complexity metric on this class of function-generating fractals and this becomes a neat mathematical area.
- excessive 7y ago
  Here is one in Python. Uncomment the if statement if you want it to terminate. def sin(x): def recur(x, n, s, p, f): #if n > 9: return s; return recur(x, n + 2, s + p/f, -p*x*x, f*(n + 1)*(n + 2)) return recur(x, 1, 0, x, 1) Of course maybe it's cheating from your intent because it's really just implementing the Taylor series, and it has too many arguments. I believe any analytic function could be defined this way if you can figure out the pattern for its derivatives.
- perl4ever 7y ago
  Function sine(x As Double, Optional term, Optional p = 1#) As Double If IsMissing(term) Then term = x End If If term <> 0 Then sine = term + sine(x, -term * x / (p + 1) * x / (p + 2), p + 2) End If End Function Edit: This is my interpretation of the Taylor series approximation, but it's probably a bad idea to use this for anything that matters. One reason is that it doesn't reduce large angles, and another is that people who know what they're doing prefer to use some other formula, from a cursory Googling...though I'm not sure why.

pbhjpbhj 7y ago

Define fractal?

drdeca 7y ago
Something with non-integer fractal dimension? Actually, idk if that is exactly the right definition, because I think some fractals have integer dimension? Idk

golergka 7y ago

We live in a society.

nickthemagicman 7y ago
Or does society live in US?
knolax 7y ago
BOTTOM TEXT