"Dimmer" noob question

Thanks.
Using Mega 2560

Arduino code:

const int ledPin = 9;      // the pin that the LED is attached to

void setup()
{
  // initialize the serial communication:
  Serial.begin(9600);
  // initialize the ledPin as an output:
  pinMode(ledPin, OUTPUT);
}

void loop() {
  byte brightness;

  // check if data has been sent from the computer:
  if (Serial.available()) {
    // read the most recent byte (which will be from 0 to 255):
    brightness = Serial.read();
    // set the brightness of the LED:
    analogWrite(ledPin, brightness);
  }
}

Processing code:

 import processing.serial.*;
 Serial port;
 
 void setup() {
 size(256, 150);
 
 println("Available serial ports:");
 println(Serial.list());
 
 // Uses the first port in this list (number 0).  Change this to
 // select the port corresponding to your Arduino board.  The last
 // parameter (e.g. 9600) is the speed of the communication.  It
 // has to correspond to the value passed to Serial.begin() in your
 // Arduino sketch.
 port = new Serial(this, Serial.list()[1], 9600);  
 
 // If you know the name of the port used by the Arduino board, you
 // can specify it directly like this.
 //port = new Serial(this, "COM1", 9600);
 }
 
 void draw() {
 // draw a gradient from black to white
 for (int i = 0; i < 256; i++) {
 stroke(i);
 line(i, 0, i, 150);
 }
 
 // write the current X-position of the mouse to the serial port as
 // a single byte
 port.write(mouseX);
 }