Can't say I've read the whole excerpt, but there are someinteresting comments in here on x^x and related "towers of powers" and how they relate to limits and...
Various ways of looking at the function z = y^x - x^y to see what's going on. These all take advantage of GC's high-resoluting clipping via "shaders" on the...
This ugly mess is an attempt to see something about the non-real values of the function by using the floor function to sample at rational points so GC doesn't...
There's no coloring for the argument value, and I'm not sure if the smoothness of the graph in all the quadrants is anywhere near accurate, but it does look...
What I did here was create the complex function f(x,y) = (y+i0)^(x+i0) - (x+i0)^(y+i0). Then I graphed the real and imag values of z=f(x,y), and also the...
Work in progress towards illustrating the complex values of x^x, and the weird “spindle” they form, as mentioned in the excerpt from the Robert Kaplan book...
I decided to try to go back to two dimentions using the same technique as my last message... The solution is where the purple and red cross (in Quadrant I, red...
It looks like the the curves Greg used are a reliable way to see where the zeroes are in cases like this. I finally got GC to graph a modulus-surface (improved...
Still struggling with graphing y^x - x^y. Cylindrical coordinates help. The best way to avoid "jaggies" seems to be to avoid taking the absolute value. So...
Nothing too surprising, since if you exchange x and y it's obvious that y^x - x^y changes sign, but below you can see this reflected in the graph with the...
Can't get rid of the jaggies completely, but here's a plot with height representing the modulus and color from red to purple (actually, all the way back to...
Fading out the saturation radially adds a little more depth feeling, it seems. It seems obvious from these graphs that the z = 0 intersection (red contour) has...
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I just realized it makes a lot more sense to look at this upside- down, and also to increase the highlighting via the [h s v] coloring specifier to see more...
Russell, I have been thinking a lot about your equation below. My first attempt contained an error in trying to use GC. However, this attempt may be better....
Chris, It just keeps getting better and better! This has been a personal challenge for you huh? This is one of my favorite views of this equation. I wish the...
As long as you've just got real values for a complex function, you can take advantage of the extra-sharp clipping via the "shader" capability in newer OSs. It...
Many thanks! This is an amazing graph that brings up all kinds of questions. Does anybody know if this is a conformal mapping? (My understanding that...
Here, i've at least got the modulus being plotted correctly, but I need to have something where the cone "duplicates itself" for every new root. Actually, it...
I didn't have the same high resolution in all the sections of the graph before. This takes longer to plot, but you can really see all the details of what's...
A first attempt at visualizing the multiple values you get when you take complex roots. Here is a basic color-coded complex-modulus surface, modified slightly...
An attempt to visualize the successive values of z^x as the complex point z travels along the x -axis. I think that the function of z^x as a whole (i.e.,...
Sorry, there was a mistake in the last graph. I wasn't actually graphing the value of the function at x+N: Below, I think I _am_ graphing the function at x+N,...
... Unfortunately, GC doesn't do recursions yet, except in certain accidental cases:   ...  If I try to do it directly, I can't get anything except...
... By taking out the index I was able to get a few more iterations:   For some reason, it's sometimes possible to get a lot more iterations sometimes,...
Shows the whole range of shapes and colors for a color-coded modulus surface graph of (z-n)^n, where z is a complex-number variable. Only the principle values...
