Explore x^y=y^x Function: Graphs, MatLab & Oddities

[cronxeh]

I'd like to resurrect the discussion of this interesting function.

Here are a few captivating pictures:

First is a graph of x^y=y^x :
http://www.imag.us/x/cronx/untitledxy.JPG


Second one was achieved in MatLab 6.5:
http://www.imag.us/x/cronx/xyplot2.JPG
EDU>> ezplot('x^y-y^x',[-150,-148])
I rotated the picture 90 degrees

Now this one seemed a bit odd to me.. any thoughts?


Edit:

Ok I'm freaking out here.. is my MatLab out of whack??
Plot of x^y=-y^x :
http://www.imag.us/x/cronx/wtfplot.JPG

 

[NSX]

Maple 10.02 gives funny stuff too:

https://my.ryerson.ca/bbcswebdav/users/m4yip/gt4/xy.gif

Here's the code I used:

restart:
with(plots):
a := implicitplot((x^y=y^x), x=-200..200, y=-200..200);
display({a});

 

[cronxeh]

Can I get a confirmation of this plot? I don't have that many applications that can do multivar plots

 

[Hurkyl]

I would say that your problem is almost entirely due to the fact that you're trying to plot in a region where x^y and y^x are defined almost nowhere.