const int ledPin = 9;  // LED connected to digital pin 9
const int period = 5000; // Period of one breathing cycle in milliseconds

void setup() {
  pinMode(ledPin, OUTPUT);
}

void loop() {
  // Get the current time in the cycle
  unsigned long currentTime = millis() % period;

  // Calculate the brightness using a sinusoidal function
  float brightness = (exp(sin(currentTime * M_PI / period)) - 0.36787944) * 108.0;

  // Apply the calculated brightness to the LED
  analogWrite(ledPin, (int)brightness);

  // Small delay to smooth the breathing effect
  delay(10);
}