A Processing Sketch

circles.pde

import gifAnimation.*;
GifMaker gifExport;
// total_frames determine how many frames will be in the gif
int frames = 0, total_frames = 10,
    randx, randy, radius;
  
public void setup(){
size(1200,900);
background(255);

//outputting the gif
   smooth();
frameRate(12);
// 5 is the quality factor, 
  gifExport = new GifMaker(this, "circles.gif",5);
  gifExport.setRepeat(0); // make it an "endless" animation

}

// function to vary the color with coordinates
color var_color(int x, int y,float alp){
  
// find the center of the image
  int center_x = int(width/2);
  int center_y = int(height/2);
// find the distance from the origin
  int dis_y = abs(y - center_y);
  int dis_x = abs(x - center_x);
// determine the red and blue color depending
// on the coordinates
  int red_value   =  int(255 * dis_y / height);
  int blue_value  =  int(255 * dis_x / width);
  return color(red_value,0,blue_value,alp);
}

// function that draws a set of circles with 
// exponential growth and a changing 
// alpha value in the color
void circles(){ 
  
 float alpha = 100; 
 randx = int(random(width));
 randy = int(random(height));
 
for(int k = 0; k<12;k++){
  radius *=3;
  alpha *=0.8;
  
color color_use = var_color(randx,randy,alpha);
  stroke(color_use);
  noFill();
  ellipse(randx,randy,radius,radius);
    }
}

// function to export the gif, called 
// every 20 times circles() is called
// each frame of gif has 20 set of circles
void export(){

if(frames < total_frames) {

    gifExport.setDelay(20);
    gifExport.addFrame();
    frames++;
  } else {
    gifExport.finish();
    frames++;
    println("gif saved");
    exit();
  }
}

void draw(){
    
  int j = 0;
    
 while (j<20){
   radius=1;
    circles();
    j++;
   
  }
  export();
}