This is doing my head in, every time I think I'm just starting to grasp the reasons, it slips through my fingers.
Right, so this video from BigClive about some cool led filament. You can see, and it's mentioned, that the ends are brighter than the middle.
The diagram that Clive made is this, I've changed the colours and removed the double connections for clarity, the blue in this image is the leds, the yellow is the copper (and the green is the PCB)
Ok, so each LED has one leg on the bottom "bus" and one on the top "bus", progressing from left to right the first led has a short bottom trace and a long top trace, and the last led has a short top trace and a long bottom trace. The knee-jerk is "yeah, they balance out so all the leds have the same total resistance in series, should be equal brightness assuming matched leds right". But the big brightness drop off towards the middle says otherwise.
So we introduce here a simulation
Falstad LinkAnd so far so good, each diode equal current, but this is treating wires as ideal, so let's fix that with a sledgehammer...
and there we go, reducing LED current towards the middle, high current at the ends.
So looking at this for a while and musing, I came to the partial realisations
* The resistor current of course is not the same for all resistors, that's obvious from the get go, the bottom left and top right resistors each carry "4 leds worth" of current, while the top right and bottom left resistors each carry "1 leds worth" of current, and the midde two are between that.
* So let us attribute "an led worth" as a unit of current
* The resistors in the rightmost led's current path carry, from left to right, 4 units, 3 units, 2 units and 1 unit of current
* The resistors in 2nd from the right (next to the rightmost) path carry 4 units, 3 units, 2 units and another 4 units for the top most resistor
* Since the resistors here are 1 ohm, we can say then that the voltage dropped by each resistor equal it's units of current, so we can total those units to get the total voltage dropped by the resistors in the current path
* The resistors in the rightmost led therefore drop 10 units of voltage, and the resistors in the led next to it drop 13 units of voltage
And this is about the point where I introduce the forward voltages of diodes and my brain short-circuits. I feel like I'm so close to an intuitive understanding of this effect, but not quite there, maybe I'm looking at it in the wrong way.
NB: I know it can be
"fixed" with this and it, very nearly clicks for me, the higher current paths need more conductivity, the lower current paths need less.