Some pointers to take note of:
1. The variable/controllable blink rate should range from about 0.5Hz to no more than 8Hz - anything faster will appear as a flicker, which you do not want.
2. As the LED goes from full OFF to full ON and back to full OFF, its brightness has to be varied using some kind pulse modulation such as PWM or MIBAM. The frequency of this modulation has to be high enough that there is no flickering as the LEDs pulsate. Refer to the video and especially the drawing posted previously.
In essence, each of the LEDs is being driven by 2 modulated signals at the same time. A low frequency one from 0.5-8Hz which is the blink rate and a higher frequency one that controls the 0-100-0% percent brightness ramp which gives the LEDs a pulsating effect - instead of just going OFF-ON-OFF.
Hint: Think FM.
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