As Keith said, LEDs (non-phosphor color converted like white) work as micro solar cells, generally most sensitive to their emission color. https://www.youtube.com/watch?v=6WGKz2sUa0w
Traditional solar cells... I easily found 17 mm diameter and 22 x 7 mm cells...
I ran a length of a couple hundred LEDs like this. Used a pair of 10 AWG wires for power and ground and tapped the individual strings off that, with the data lines all in series for control. Worked fine.
For how long does the state need to be retained? I'd guess a simple CMOS flipflop driving a non-protected gate MOSFET powered by a lithium coin cell could maintain its state for years.
There was a company that used a technique they called "Mechanically Orbited Carbon" to make analog RAM that was completely passive, random access, and non-volatile.
Here's the manual, it's a hoot.
https://www.makenoisemusic.com/content/manuals/analogmemorymanual.pdf
The G.E.Transistor Manual. I still have my old copy. Good stuff. Even has a section on tunneling diodes. Here's a link with a few for under $10. Cool...
Also, if you're scratch building them, how are you sourcing your cells? If you aren't getting known new, guaranteed in spec cells, you'll want to evaluate them for capacity, internal resistance, & leakage, and then sort them to get roughly the same characteristics per parallel block of cells...
Six in parallel, then put those parallel sections in series.
Be sure to match cell voltages before connecting them in parallel. (You can put them in parallel with each one having a low value resistor (1 ohm or so)and letting the voltages equalize for a while. When the voltages are within a few...
The charger will be putting out a constant current for most of the charge, no danger there at all. In fact it will be a gentler charge for the battery, so that's good (assuming it's from a reputable manufacturer.)
Some chargers have a time out function as an added safeguard, so going to a much...
How critical is the optical timing? I'd forget the Y connection, just make your string 12 neopixels long and duplicate the pattern in the driving software.
If the issue is that the woofer is "dominating the sound", a simple solution might be to add a resistor (an ohm to ten ohms or so) in series with the woofer to reduce the bass. Be sure to use one with a suitable power rating.
Your photo of the original coil looks like it's made of Litz wire, hundreds of separately insulated conductors in parallel to mitigate skin effect at high frequencies, so Q may very well be a factor.
What op amp are you using? This could be zero-crossing distortion (but not around zero if your power supply isn't bipolar). It would typically be somewhere around half the supply voltage (but could be anywhere between 25 ~ 75% or so). Each unit would be a bit different, may drift with...
You'll have to provide a power supply for it (it draws very little current, 100 uA or so, 1.5 uA in shutdown). Since you've got a battery, you could probably power it by 2 or 3 cells closest to ground with no ill effect and put the shunt in series with that and the more positive cells...
Not I2C, but this might be of interest:
http://www.linear.com/product/LTC4150
Generates a level to tell the direction of the current and a pulse with the frequency proportional to magnitude, it does the integration for you.
Designed as a coulomb counter for battery management, has pretty good...
One point I don't see mentioned, if you really do need to generate 13 volts from your LiPO...
Your nominal 14.8 volt battery sounds like it has 4 cells. The typical cell voltage for common lithium batteries is 3.7 volts, times four gives 14.8.
A fully charge cell is usually 4.2 volts (there...
