These are actually bugs in HEXPIC, not Axe. But, being as they're both part of the same package, I figured this would warrant:

There are several lines in HEXPIC that bring up various errors and prevent the program from running in the 0.4.3 version. The first bug I noticed was the line pxl-Test(58-Z, X+1->P below the label conditionals. The line appears to reference a pixel outside of the screen and it brings up an error when I try to run it. Changing it to pxl-Test(58-Z, X->P fixes the problem for me.

The second error occurs in Lbl F at the line coded not(pxl-Test(50-Z/7,70+X/7->P70+X/7 is a decimal, so testing the pixel is impossible. This is also easily fixed with the simply addition of a round() command like
not(pxl-Test(50-Z/7,round(70+X/7,0->P
The third problem is the same as the second one and occurs just below it. Change the 70+X/7 to a round(70+X/7,0 and the problem is fixed.

Fixing those causes the program to run for me, although the cursor is a bit off. It's still usable though.

No decimals? I suppose that I'd have to approximate with 10, then. That works, although it appears that I'll have to modify my formulae to get a more realistic "bounce." This simulation would be a lot more suited to a mathematically inclined language like TI-BASIC. Oh well, what's a challenge if not a chance to learn [and clear your RAM in the process]?

The Axe language in general has very high similarity to both Assembly and Basic, so a strong background in either one will definitely help with programming.  An assembly tutorial will have some very useful information for you about how some things actually work and a Basic tutorial would help with program flow since the syntax is similar, however the optimizations are completely different and hardly any basic "tricks" can actually be carried over.  What programming languages do you have a background in?

I have a background in some Python, and TI-BASIC with a little bit of experience in other languages. The language I'm most familiar with would definitely be TI-BASIC though. However, I wouldn't say I'm anything more than passable in any computer languages.

Just [another] quick question: How do you do grayscale in Axe?

I noticed the >Dec in the Documentation after I posted that, but thanks. Does anyone happen to know of a good tutorial on Axe with things like user interaction, such as an Axe equivalent of the Input() command in BASIC? Even getting the Pxl-On command to work would be great. Just Pxl-On(x, y) doesn't appear to draw anything on the screen, although that's likely because I'm confused by the whole buffers concept.

I'm extremely new to Axe, so this is probably just User error, but for me, Axe doesn't appear to want to compile programs. I copied an extremely simple sprite control from the documentation PDF to get a feel for how the language worked without accidentally destroying my RAM. When I tried to compile it in Axe 0.4.3, it gave me a File name error. Looking at the list of errors, supposedly I designated the compiled program as the source. However, I was never given the opportunity to designate any program names for the compiled code.

And just for reference, here's the code:

:.Steel A Parser
:[3C7EDBFFBDDB663C]→Pic1
:For(A,0,19)
:rand^88→{A+L1}
:rand^54→{A+L2}
:End
:For(A,0,19)
:Pt-On({A+L1},{A+L2},Pic1)
:End
:DispGraph

In all likelihood, any help will be a "duh" moment. But thanks.

Ps: I did search the forum for similar topics, but I didn't see any.