Pulse the LED with a sine wave.

ledsinewave.c

/* 
  My second sketch: pulse the LED with a sine wave.
  */
  
const float pi =  3.14159;
  
int ledPin = 9;

void sinArc(int analogPin, int duration, float arcStart, float arcStop) {
  int steps = 255;
  int startStep = (int)(arcStart * (float)steps);
  int stopStep = (int)(arcStop * (float)steps);
  int sleep = (int)((float)duration / (float)(stopStep - startStep));
  int maxAmplitude = 256;
  int DCoffSet = 0;
  for(int _step = 0; _step <= steps; _step += 1) {
    int amplitude = DCoffSet + (int)((float)maxAmplitude * sin(pi * (float)_step / (float)steps));
    analogWrite(analogPin, amplitude);
    delay(sleep);
  }
}

void sinOn(int analogPin, int duration) {
  sinArc(analogPin, duration, 0.0, 0.5);
}

void sinOff(int analogPin, int duration) {
  sinArc(analogPin, duration, 0.5, 1.0);
}

void sinWave(int analogPin, int duration) {
  sinArc(analogPin, duration, 0.0, 1.0);
}

void setup() {
  pinMode(13, OUTPUT);
  analogWrite(ledPin, 0);
}

void loop() {
  sinWave(ledPin, 2000);
}