"LED that I'm soldering to a protoshield to start off, fade up to full brightness for a period of about 45 seconds, begin fading to dark again and as it dims, to strobe."

MFA.ino

const byte ledPin = 11; // pwm pin

boolean bIsGoingUp = true;

long fadeUpTime = 15000;   // 45 * 1000 milliseconds
long fadeDownTime = 15000; // 
long nextTransition = -1;

long strobeOnTime = 200; // the time the strobe effect will be on
long strobeOffTime = 1000; // the time the normal fade out will be on
boolean bIsStrobeOn = false;
long nextStrobeTransition = -1;

void setup() {
  // nothing b/c we are using pwm out
  Serial.begin(9600);
}

void loop() {
  long now = millis();
  
  if(now > nextTransition) {
    Serial.println("Transitioning.");
    if(bIsGoingUp) {
      nextTransition = now + fadeDownTime;
      bIsGoingUp = false;
      Serial.println("Going down!");
    } else {
      nextTransition = now + fadeUpTime;
      bIsGoingUp = true;
      Serial.println("Going up!");
    }   
  }
  
  long remainingTime = nextTransition - now;
  
  Serial.println(remainingTime);
  
  byte pwmValue = 0;
  
  if(bIsGoingUp) {
    pwmValue = map(remainingTime,fadeUpTime,0,0,255);
  } else {
    if(bIsStrobeOn) {
      pwmValue = 255; // max
    } else {
      pwmValue = map(remainingTime,fadeUpTime,0,255,0);
    }
    
    if(now > nextStrobeTransition) {
     if(bIsStrobeOn) {
       nextStrobeTransition = now + strobeOffTime;
       bIsStrobeOn = false;
     } else {
       nextStrobeTransition = now + strobeOnTime;
       bIsStrobeOn = true;
     }
      
    }
  }
  
  analogWrite(ledPin,pwmValue);
  
  delay(10);
  
}