A couple LEDs between an op amp output, and opposite supply voltage of the other one, will have a brightness determined by how much different the op amp output voltage is in relation to the supply voltage on the other end of that particular LED.
While one LED is getting brighter, the other LED is getting dimmer in the circuit shown.
The op amp output voltage follows the voltage of the partially charging and discharging capacitor.
While the 555 timer timing capacitor is charging up to 2/3 of the supply voltage, the op amp output voltage is rising. At that time, the LED to the positive supply gets more dim, while the LED headed towards the negative supply (ground), gets brighter. The op amp output voltage is always the same as what the timing capacitor voltage is.
Whereas, while the 555 timing capacitor is discharging down to 1/3 of the supply voltage, the op amp output voltage is also going down. The LED headed to the negative supply (ground) gets more dim, while the LED headed towards the positive supply gets brighter. Again, the op amp output voltage is the same as the timing capacitor voltage.
The more voltage difference between the output and the supply voltage that is connected to the particular LED, the brighter the LED will be. The less voltage difference, the more dim the LED will be.
Each LED’s series resistor value also influences the brightness, but not near as much as the voltage difference. It mostly just needs to limit current enough to protect the LED and not overheat when there is the maximum voltage difference across the protective resistor and LED.
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