• Since it's just 1 static immutable drawing, there's no need to put that in draw(). You can do everything within setup(), plus noLoop().  Or even in Processing's static mode.
• if all drawings use noStroke(), you can move that at the top of the for loop.
• Any function which accepts a float or a double as its parameter(s), also accepts any other primitive data-types (except boolean). No need to convert an int into float for fill() for example!
• You can use function map() to convert a source value range into a desired value range.

size(600, 600);
smooth();
noLoop();
noStroke();
ellipseMode(CENTER);
background(-1);

final int w = width, h = height;
final int cx = w >> 1, cy = h >> 1;
final int step = 030;

for (int i = 0; i <= w; i += step) {
  fill( map(i, 0, w, 0, 0400) );
  ellipse(cx, cy, w - i, h - i);
}

2. //import processing.pdf.*;
3. size(600, 600); //PDF, "gradient_B&W.pdf");
4. smooth();
5. noLoop();
6. noStroke();
7. ellipseMode(CENTER);
8. background(-1);
9. 
   
10. final int w = width, h = height;
11. final int cx = w >> 1, cy = h >> 1;
12. final int step = 010;
13. 
    
14. for (int i = 0; i <= w; i += step) {
15.   fill( map(i, 0, w, 0, 0400) );
16.   ellipse(cx, cy, w - i, h - i);
17. }
18.   // Exit the program 
19.   println("Finished.");
20.   //saveFrame("output-####.png");
21.   exit();

  fill( map(i, 0, w, 0400, 0) );

2. void setup(){
3.   
4.   size(800, 800);
5.   background(200);
6.   smooth();
7. 
   
8.   int radius = width/2;
9.   // create some gradients
10.   for (int i=radius; i< width; i+=width){
11.     for (int j =radius; j< height; j+=width){
12.       createGradient(i, j, radius, 
13.       color(int(255), int(255), int(255)), 
14.       color(int(0), int(0), int(0)));
15.     }
16.   }
17. }
18. 
    
19. void createGradient (float x, float y, float radius, color c1, color c2){
20.   float px = 0, py = 0, angle = 0;
21. 
    
22.   // calculate differences between color components 
23.   float deltaR = red(c2)-red(c1);
24.   float deltaG = green(c2)-green(c1);
25.   float deltaB = blue(c2)-blue(c1);
26.   // hack to ensure there are no holes in gradient
27.   // needs to be increased, as radius increases
28.   float gapFiller = 32.0;
29. 
    
30.   for (int i=0; i< radius; i++){
31.     for (float j=0; j<360; j+=1.0/gapFiller){
32.       px = x+cos(radians(angle))*i;
33.       py = y+sin(radians(angle))*i;
34.       angle+=1.0/gapFiller;
35.       color c = color(
36.       (red(c1)+(i)*(deltaR/radius)),
37.       (green(c1)+(i)*(deltaG/radius)),
38.       (blue(c1)+(i)*(deltaB/radius)) 
39.         );
40.       set(int(px), int(py), c);      
41.     }
42.   }
43.   // adds smooth edge 
44.   // hack anti-aliasing
45.   noFill();
46.   stroke(150);
47.   strokeWeight(2);
48.   ellipse(x, y, width, width);
49. }