On Wed, Sep 30, 2009 at 3:04 AM, Brian Blais <bbl...@bryant.edu> wrote: > On Sep 28, 2009, at 16:30 , Gregor Lingl wrote: > > Brian Blais schrieb: > > However, as I think > about it, I can not think of a single problem where I *needed* the > graphic calculator, or where it gave me more insight than I could do > by hand. > > I think I have a counterexample. > Run the script, that you can find here: > http://svn.python.org/view/*checkout*/python/branches/release26-maint/Demo/turtle/tdemo_chaos.py?revision=73559&content-type=text%2Fplain > What do you think?
The Logistic Map x-->rx(1-x) for varying values of r is easy to examine on a calculator, but excessive by hand. Feigenbaum discovered its periodicities on a calculator without any graphing capability, but having graphs makes insight much easier, in the same way that the Mandelbrot set was discovered mathematically in the 1920s, but became of major interest only after computers permitted it to be visualized. Of course, with a computer, you can visualize the entire bifurcation diagram in a few seconds. http://en.wikipedia.org/wiki/Logistic_map http://en.wikipedia.org/wiki/Bifurcation_diagram The bifurcation diagram of the logistic map is related to the Mandelbrot set, http://www.math.lsa.umich.edu/mmss/coursesONLINE/chaos/chaos6/index.html and has applications in physics, such as a dripping faucet. -- Edward Mokurai (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) Cherlin Silent Thunder is my name, and Children are my nation. The Cosmos is my dwelling place, the Truth my destination. http://earthtreasury.org/ _______________________________________________ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
