"While the circuit in post #5 can be expanded to 15 stages (barely), neither the timing between stages not the LED brightness will be a constant across one complete cycle. "
Ground rules: Diode Vf = Vbe = 0.6 V. Vcesat = 0.1 V. LED Vf = 2.0 V
Rightmost transistor = Q1. Leftmost transistor = Q5. The leftmost transistor in a 15 stage circuit = Q15.
Q1 comes on first. 0.6+0.1+(2x2.0) = 4.7 V, so the voltage across the 390 ohm resistor is 7.3 V and the current through the LEDs is 18.7 mA.
Q5 comes on last. 0.6+(0.6x4)+0.1+(2x2.0) = 7.1 V. Voltage across 330 ohm resistor is 4.9 V. Current through LEDs is 14.8 mA, a decrease of over 20%. That is visible.
The voltage ramp driving the transistor bases comes from an exponential R-C ramp. While the turn on voltage for each successive stage increases linearly, the driving ramp is exponential. Therefore the time delay between each stage coming on increases at a modified exponential rate. According to the datasheet for a standard 555 with a low load current, Vout-low = 0.01 V and Vout-high = 10.7 V, so the output ramp 100 uF capacitor starts at 0 V and is charged by a 10.7 V source through a 4.7 K resistor. The first LED comes on 55.9 ms after the 555 output goes high. The 2nd LED comes on at 86.6 ms, so the first LED is on by itself for 30.7 ms.
At the other end of the ramp, the 4th LED comes on at 154.6 ms and the 5th LED comes on at 192.8 ms, a difference of 38.2 ms, an increase of almost 25%.
At 5 stages the irregularities in brightness and timing are visible, but not terrible. But the question you were responding to was about 15 stages, and my reply was about whether or not your circuit could work for this problem. It can not.
The details regarding the first stage (Q1) are as above. But for Q15 things are much worse. The voltage across the LED current limiting resistor is only 12 - (0.6+(0.6x14)+0.1+(2x2.0)) = 0.9V. Given the possible variations in 16 diodes plus 2 LEDs in series, 0.9 V is not enough headroom to set accurately the LED current.
WORSE than that is the timing variation. The on time of the first LED by itself is the time between stages 1 and 2, and still is 30.7 ms. BUT, the time between stages 14 and 15 (the on time of the next-to-last stage) is (1069.2-864.6) = 204.6 seconds, or over 3 minutes. This does not include the increase in time caused by the capacitor leakage current, which becomes significant as the cap's charging current decreases. With your circuit expanded to 15 LED stages with a first stage time of 30 ms, the 15th LED will come on after 17.8 minutes.
Clearly the oscillator timing components do not support this long of an output period, and even if they did I don't think a 17 minute blink time is what the OP wants for a turn signal, so I don't understand why you proposed this circuit as a solution to this problem.
You obviously have absolutely no understanding of electronics and you should keep your ideas to yourself and not make a fool of yourself.
Your circuit is not a workable response to this thread, and your response to my reply is inappropriate for several reasons. You obviously have no understanding of the problem posed by this thread, and should follow your own advice.
ak
Time constant calculator used for this analysis:
http://ladyada.net/library/rccalc.html