Grex Reality Conference

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Grex Reality Item 26: Orbits of functions
Entered by hong on Sat Apr 20 00:57:33 UTC 1996:

I was wondering if any startling discoveries have been made
about the orbits of functions (meaning the value an iterated
function will approach).  Has an orbit of any function
been found to be e^1 or pi, for example?

3 responses total.

#1 of 3 by orinoco on Sat Apr 20 01:56:21 1996:

Math I am afraid is not my topic of expertise, but from what little math I
have experience in I have noticed an astounding number of uses, in seemingly
irrelevant applications, for those two numbers; so I would not be surprised
if they did appear in this context too

#2 of 3 by aruba on Wed May 1 06:05:01 1996:

What you describe is the "stable equilibrium point" of a dynamic system,
Bryan.  Let's see; I'm sure you could construct a system with an equilibrium
point at e or pi; I'll have to think about how.

Ah, wait, I found one in a book that converges to pi/2:

f(x) = x + cos(x)

Though that may not be what you're looking for.

#3 of 3 by orinoco on Thu May 2 20:55:10 1996:

wow!  new responses.
aruba--I assume this is a sequence where you get n by putting n-1 into the
function, as graphing it results only in a tilted sine wave

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