I did another rendition because the wavelength I chose earlier was too small to really see the geometry of the pattern.  As you can see, it's argyle.

What really confuses me - both in my made-up Array World and in real-world examples - is what is actually meant by "cancelling out"?  Experimentally, it signifies that the probability of a photon appearing at that point is 0, but how does this happen?

What it boils down to is that I'm really baffled by the notion of electrons emitting photons when they change state.  Experiments show that the amount of potential energy the electron lost in the drop in orbital is proportional to the frequency of the light emitted when it does so (Freqency = Energy / Planck's constant).  This same frequency is what determines the diffraction pattern you see - a single photon interfering with itself.

So, due to quantum mechanics, the state change of an electron is instantaneous - there is no inbetween state.  But frequency seems only to come into being over time - that's why it's called, ahem, *frequency*.  Originally, I'd thought that wave must represent a message of "I'm in the higher energy state" followed some period later by the "I'm in the lower energy state", but this would require multiple state changes to form an actual wave, also leads me to be really confused as to why "higher energy" and "lower energy" would interfere to make "no energy".

Then I remembered something from Physics II, about the oscillating electric and magnetic fields of a light wave,  and lo, there's a nice animation of it on Wikipedia: http://en.wikipedia.org/wiki/Electromagnetic_radiation.  Since as far as I know, electrons are a constant negative charge, not an oscilating one, and changing state doesn't change the charge, so I don't think this is some kind of notification of charge change.  But I do recall that a moving charge results in a current, and that current generate magnetic fields, and magnetic fields generate electric fields, so if a change in potential energy as a current, maybe there is something there.  Maybe the electron movies, and generates this magnetic field (which could be the one pictured), and the electric field perpendicular to it (in the axis not shown).

But does this emitted field come into being at that particular wavelength?  Is it like a full cycle of the wave is instantaneously stamped in place somewhere around the electron?  If so, where?  Next to it?  Around it, in perfect conformation of its shape? Does the electron block its own emitted light?  Does this stamped light cause problems becuase sine the wavefront of the stamp will be a full wavelength distant from where it started, it's actually exceeded the speed of light?  Or is it possible to just have one pixel of the wavelength somehow be encoded with the information it needs to change over time - like a counter for how many frames the field can advance before changing from positive to negative?

Another thought I had is that perhaps during the state change, the electron's position changes by an amount equal to the wavelength, such that the space left behind becomes part of the advancing ligth wave - but this would mean that smaller changes resulted in higher frequency waves, which is against what we've measured.

My last idea was kind of vague, but basically, I read that in higher orbitals, the frequency of the electron itself is roughly equivalent to the frequency of the light emitted.  And then on good ole' Wikipedia, I read that the probability distribution for an electron is a big like a standing wave on the head of a drum.  For the lowest orbital, it looked like a concentric circle expanding and contracting, which gave me the idea that perhaps on the state change, this wave is sort of "bleeding" out into space in the form of light.  I couldn't tell you the mechanism; I suppose I imagined that some border for the wave drops or recedes and lets a bit of it out.  (Incidentally, I tried looking up the equation for this wave at higher n, but it was rather intimidating, being long and featuring polar coordinates and other things that I haven't thought about since 10th grade, and which I'd have a hard time converting to the Array World form, as it doesn't have circles or spheres. )

And of course we have the same problem when the light is re-absorbed by another electron (which, I presume, is how we are able to see the diffraction pattern in the first place).  What is actually happening at a fundamental level?

Consider my mind to be officially boggled.