Smooooooth...

import java.awt.image.*;
import javax.imageio.*;
import java.io.*;
import java.awt.*;
import java.lang.Math;

class Main {

  static int w = 1920;
  static int h = 1200;
  static int iterations = 10;

  public static void main(String[] args) {
    BufferedImage bi = new BufferedImage(w, h, BufferedImage.TYPE_INT_ARGB);

    for (int y = 0; y < h; y++) {
      for (int x = 0; x < w; x++) {
        bi.setRGB(x, y, (int)(Math.random()*-16777217));
      }
    }

    try {
      ImageIO.write(bi, "png", new File("C:\\Users\\Connor\\Desktop\\pic_0.png"));
    } catch(IOException e) {
    }

    for (int n = 0; n < 10; n++) {
      System.out.println();
      for (int i = 0; i < iterations; i++) {
        bi = smooth(bi);
      }

      try {
        ImageIO.write(bi, "png", new File("C:\\Users\\Connor\\Desktop\\pic_" + (100*(n+1)) + ".png"));
      } catch(IOException e) {
      }
    }

  }

  public static BufferedImage smooth(BufferedImage bi) {
    BufferedImage img = new BufferedImage(bi.getWidth(), bi.getHeight(), bi.getType());
    for (int y = 0; y < h; y++) {
      for (int x = 0; x < w; x++) {
        img.setRGB(x, y, getAverageColor(x, y, bi));
      }
    }
    return img;
  }

  public static int getAverageColor(int x, int y, BufferedImage template) {
    int n = 0;
    int d = 0;
    if (x > 0) {
      n+=template.getRGB(x-1, y);
      d++;
    }
    if (y > 0) {
      n+=template.getRGB(x, y-1);
      d++;
    }
    if (x < template.getWidth()-1) {
      n+=template.getRGB(x+1, y);
      d++;
    }
    if (y < template.getHeight()-1) {
      n+=template.getRGB(x, y+1);
      d++;
    }
    return (int)(n*1f/d+.5f);
  }

}