I remember when I was a kid, Arby's had linear neon lights that would change color in a wave-like pattern. Was I
seeing things? Has anyone else ever seen this?
This is also around the time I really, really started gaining a much higher interest in lighting.

I don't know about a wave pattern, but I've seen those cheap neon clocks that can change the tube from blue to pink with the flip of a switch. and it was only using a single tube..

When I was a kid there was this one small movie theater (long gone now) that had neon lights which at one point were on some sorta dimmer? control... but instead of dimming like a fluorescent would, the 'light' would progressively move along the tube til the whole thing was lit, then shrink back across to the same end it started at. I thought that was awesome! And have always wondered what sorta thing they had in place to make it do that

You might want to send Tuopeek a pm and ask him, he seems so know a fair bit about neon and other vacuum type light sources.. Was this wave like a Crookes dark space effect that sometimes happens in florescent tube where you see a bunch of bright glowing ribbons inside the tube and they slowly move back and forth ? 

The wave like pattern I saw was actually similar to those bright waves I sometimes see in fluorescent lamps. (not swirls, or striations)
I thought it was really awesome... and just to get this out of the way, they definitely were not LED.
@xmaslightsguy, now I'm wondering what kind of lighting was in use in that particular theater

I do wonder if it is frequency driven, I remember my parents had a neon clock in the early 2000s that had the neon in a circle around the numbers. It would turn blue for a minute and then pink for the next minute, then back to blue on a continous loop. I seem to recall the HV circuitry driving the neon tube would make a deep buzzing sound when the tube was blue and it would turn into a higher pitched buzz when it turned pink.

I totally forgot about such neons until you made this thread and now I'm curious too.

Maybe not so much frequency but current ? Something like 2 gases, such that below a current threshold one takes over, above that there is enough current that both take part. If frequency, maybe its made so the gases have differnt ionization/recovery time (i.e. stay ionized for different time after strike), so at one frequency gas A (the faster one) stays ionized, at a lower frequency it suffices to extinguish between the pulses and gas B (the slower one) takes more of the discharge

In high enough power lamps maybe something with Mercury evaporating/condensing ?

I didn't think about current, that is a possibility too. The audible frequency noise change could just be a byproduct of a different current level being fed into the tube. From memory the tube had a phosphor coating on it.

I think I remember the tubes in Arbys had phosphorus coating on them too... but the thing is, with these particular neons, I
do remember seeing waves of light. One minute they would turn to orange, then deep blue, then brighter purple, then red... all smooth
and slow transitions. I remembered this being sooo cool to me, but never thought about just how rare this was. But then again
I didn't know (and still don't) about anything regarding neon lighting.

I know about a Neon discharge tube, where only part of its length is lighted, while the illuminated length is controlled by the current.
In the past these were popular in soviet instruments as an electronic indicator, as it was quite accurate for its simplicity.
The principal construction used two electrodes along the tube with their distance reducing from the connection point till the other end, while the electrodes were made of a resistive material. Otherwise it was just a plain Neon cathode glow discharge.
It worked so:
At low current the discharge struck at the end, where the electrodes were the closest to each other.
There the discharge clamped the voltage, so only that end remained glowing.
But when increasing the current, the resistive electrodes exhibit a voltage drop, so further away from the starting end the available voltage became sufficient to support the discharge, so the illuminated section became longer. As the electroe distance became wider, it requires more current to transfer the discharge there, so only such section glowed, where the voltage drop caused by the current, along the electrodes allowed to reach the voltage required to sustain the discharge.
I don't remember, how it was caled and even if it was (and how much) used elsewhere around the globe.
And I have no idea, what was the lifetime of these indicators...
Even few years ago I've seen someone selling them somewhere on the web...

Medved are you thinking about a linear gas discharge indicator (Also call nixie tubes) like an IN-9 seen here :>  http://www.ebay.com/itm/10-x-IN-9-NIXIE-TUBES-LINEAR-GAS-DISCHARGE-INDICATOR-ARGON-GAS-New-old-stock-/252493013009

If so those really do make awesome looking thermometers..

I always wanted to build a VU meter out of those things, but my motivation to do certain things only goes so far... i do have a few IN-3,IN-9 IV-7 and DM160 indicators though plus a few lightning arrestors lots of little neons in clear,yellow,green,blue and white and also various indicators i've ripped from powerstrips and one i pulled out of a piece of industrial vacuumetube equipment (bayonet base) i also have a lot of flickerflame bulbs.

anyway idk why i said all that but one more worthless fact about my collection of indicator tubes

it is all Soviet!


Actually now that i think of it.... you couldof encountered some sort of VFD... with multiple phosphors

Remember experimenting with neon bulbs years ago at a radio station.Was maintenance day.Had one FM transmitter on the dummy load for test-held the neon bulb by the load while the FM transmitter was on-the lamp glowed purple instead of orange-red as on 60Hz.The bulb also glowed orange when held by one of the AM towers.Remember in a "Ham radio" magazine where they suggested using a small neon lamp as an RF indicator.The neon bulbs glowed purple when exposed to VHF frequencies.

@xmaslightsguy, now I'm wondering what kind of lighting was in use in that particular theater

They looked like regular neon as far as I could tell. Maybe used some form of what Medved mentioned?
It was a long time ago, so I don't remember much of the specifics - other than the light 'growing' along the length of the tube -
They either went vertically floor to ceiling or horizontally along the length of the front windows, so it wasn't just a little short thing either.

One thing I can say that they were definitely not LED or anything, since such didn't exist back then.

...(Also call nixie tubes) ...

Well, the term "nixie tube" seems to mean anything using cathode glow discharge, regardless what it actually does (there is quite significant difference in the applications of just basic neon glow, vs e.g. numeric display, vs this analog indicator, even when all use the same principle of generating light), so it does not specify anything of the use at all...