08/22/2007, 11:00 PM
Daniel Wrote:I spoke with Stephen Wolfram in 1986 who assured me that no solution for a continuously iterated function that displayed chaotic behavior was known at the time.What do you mean by "chaotic behaviour"? In our case the functions to be iterated are \( b^x \), which are a rather behaving function afaik.
Quote:Requiring a fixed point is not much of a requirement. Sure the fixed points may be complex and lead to odd looking solutions, but so what?Not exactly odd looking but simply complex for real arguments.
Thats simply not what we want
All the basic functions you learn in analysis yield real values for real arguments.Quote: Cris Moore asked about the compatability of solutions from different fixed points. By using a fractal with low entropy I was able to experimentally show the correct logrithmic spiral of a neighboring fixed point ...So does that mean the solutions are equal? Id rather guessed that they are different for different fixed points. Did you compute the fixed points and their derivative of \( e^x \)? Are they all attracting?
