http://www.mapleprimes.com/posts/39897-Repeating-Powers en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Wed, 10 Jun 2026 16:17:20 GMT Wed, 10 Jun 2026 16:17:20 GMT The latest comments added to the Post, Repeating Powers http://www.mapleprimes.com/images/mapleprimeswhite.jpg http://www.mapleprimes.com/posts/39897-Repeating-Powers http://www.mapleprimes.com/posts/39897-Repeating-Powers?ref=Feed:MaplePrimes:Repeating Powers:Comments#comment73144 <p>What you are observing is one branch of a bifurcation.&nbsp; Try the following,</p> <pre> f := proc(x,n) local y,z; z := 1./x; y := z; to n do y := z^y end do end proc: plt1 := plot(rcurry(f,100),10..16): plt2 := plot(rcurry(f,101),10..16): plots[display](plt1,plt2); </pre> <div>A nice exercise is computing where the bifurcation should occur as n goes to infinity.&nbsp; I got (x,y) = (e^e, 1/e) = (15.15, 0.37). Actually, it isn't clear whether it is a bifurcation with n at infinity, or the point where the iteration diverges.</div> The latest comments added to the Post, Repeating Powers 73144 Sun, 02 Mar 2008 21:23:24 Z Joe Riel Joe Riel http://www.mapleprimes.com/posts/39897-Repeating-Powers?ref=Feed:MaplePrimes:Repeating Powers:Comments#comment72977 <p>Joe Riel, I used your program to make another one that shows the bifurcation going to (e^e, 1/e) .</p> <p>restart; with(plots): f := proc (x, n) local y, z; z := 1./x; y := z; to n do y := z^y end do end proc:</p> <p>plt1 := animate(plot, [rcurry(f, 100*a), 10.0 .. 15.2], a = 1 .. 8):</p> <p>plt2 := animate(plot, [rcurry(f, 100*a+1), 10.0 .. 15.2], a = 1 .. 8):</p> <p>plt3 := plot([1/exp(1)], 10.0 .. 15.2, gridlines = true, linestyle = dash, color = blue):</p> <p>print(display(plt1, plt2, plt3, view = [9.9 .. 15.3, .35 .. .40])):</p> <p><a href="http://beta.mapleprimes.com/files/565_tetrations4.mw">Download 565_tetrations4.mw</a><br /> <a href="http://beta.mapleprimes.com/viewfile/2351">View file details</a></p> <p>&nbsp;</p> <p>My program takes a couple of minutes to compute.<a href="http:// marvinrayburns.com/begining.gif"><br /> </a></p> <p><img width="500" height="500" align="left" alt="http://marvinrayburns.com/begining.gif" src="http://marvinrayburns.com/begining.gif" /></p> <p>&nbsp;</p> <p><maple></maple></p> The latest comments added to the Post, Repeating Powers 72977 Sun, 09 Mar 2008 01:01:05 Z Marvin Ray Burns Marvin Ray Burns