An Arduino sketch which fades an LED in and out.

fade.ino

int led_pin = 13;

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

void loop() {

  int on_time;
  int off_time;
  int period = 1000;
  
  for(int i = 1; i <= period; i = i+1) {
      on_time = i;
      digitalWrite(led_pin, HIGH);
      delayMicroseconds(on_time);
      
      off_time = period - on_time;
      digitalWrite(led_pin, LOW);
      delayMicroseconds(off_time);
  }

  for(int i = period; i > 0; i = i-1) {
      on_time = i;
      digitalWrite(led_pin, HIGH);
      delayMicroseconds(on_time);
      
      off_time = period - on_time;
      digitalWrite(led_pin, LOW);
      delayMicroseconds(off_time);
  }

}