Recursive function in a physics equation

1. May 15, 2004

noize11

Hoping someone can point out an example of a recursive function in a physics equation. If this is not a valid step that would be great to hear about too. Also if anyone has even tried to introduce such an equation in the past or how it might be represented. [I'm not the best student of maths].

I have a form in mind that I can only express with recursion.

2. May 15, 2004

baffledMatt

What do you mean by recursion? Is it of the form:
$x_{n+1} = f(x_n)$
or is it something like
$y = f(y)$
where f(y) is some nasty integral or something which you can't solve?

In either case, yes, recursion occurs a lot in physics and is the basis for things like perturbation theory.

Matt

3. May 15, 2004

noize11

Something more along these lines:

$$v(t) = 3 * v(t)$$

Obviously this equation cannot be solved as there is no terminating condition specified. Trying to solve this when t=1 for instance gives:

$$v(1) = 3* (3* (3 * (3 * (3* ...))))$$

I have a structure that relies on this form of recursion, but how do I go about specifying the terminating value? For instance, suppose I simply wanted a value > 8 * PI. How is it that I would express this?

4. May 15, 2004

baffledMatt

Hmm, either something fishy is going on or you need help from a mathematician (which sadly I'm not).

By my reconing the only 'physical' solution to your equation is zero. My argument would run as follows:

Assume $v(t)$ has a solution $v(t)>0$.

$v(t) = 3 v(t) \Rightarrow 1 = 3$
This is a contradiction hence $v(t)=0$.

Unless I am wrong in thinking your symbol $*$ means multiply?

Ok, as I said before I am not a mathematician so if I've done something stupid please don't hurt me :)

Matt

5. May 16, 2004

BreAkeR

Would you like to explain better what you are trying to do. It is interesting your topic and please give us details. I really don't know what to say about your recursive physics, but I ran into similar ideas, too. Maybe I can help :)

6. May 16, 2004

mee

fractals

Aren't fractals recursive?

7. May 16, 2004

baffledMatt

If by that you mean a great many of them are generated by recursive algorithms, then yes they definitely are.

Matt