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#Processing, 197 bytes

void setup(){size(255,255);float r=255,a=r,g=0,b=0,i,j,k;background(a);for(i=0;i<a;k=i<43?g+=6:i<85?r-=6:i<a/2?b+=6:i<170?g-=6:i<213?r+=6:a>1?b-=6:0,i++)for(j=0;j<a;point(i,j++))stroke(r,g,b,a-j);}

This outputs the image in a 255x255 sized window

###Ungolfed

void setup(){
  size(255,255);
  float r=255,a=r,g=0,b=0,i,j,k;
  background(a);
  for(i=0;i<a;k=i<43?g+=6:i<85?r-=6:i<a/2?b+=6:i<170?g-=6:i<213?r+=6:a>1?b-=6:0,i++)
    for(j=0;j<a;point(i,j++))
      stroke(r,g,b,a-j);
}