> > I think it's a fine method that you've got. I do think that it is > > possible that you could find something new. To me the problem with the > > iterated function is in joining them to physics. I enjoy playing with > > them, but I'm not sure that we have anything more than pretty > > graphics. I do accept the fractal analysis of some natural forms as > > related to accumulation, but that does not get us physical > > principles. > > > > What is the way into a progression here? It is so easy to get lost in > > making graphics, and yet the kernel function comes with no motive. I > > don't mean to be discouraging. I'm just wondering, and this criticism > > extends onto the Mandelbrot function as well. There must be a bridge > > somewhere. Keep going. > > > > - Tim
One way iterated functions are important for physics is in relation to Poincare sections: If a point is moving around an orbit in 3-space, then if we take a plane perpendicular to the motion of this point we can plot the successive positions in the plane that the point cuts it as it moves around the orbit. By looking at the function that describes where these cuts occur we can find out about the stability of the orbit. This can be extended to a point moving around an n-dimensional phase space, in which case the Poincare section will have dimension n-1.