Thank you for the link! This looks very nice, I hope he will post the code.

I do not think it is that important given the way the controller works (no possibility to graphically edit the output before sending), it could be done in the arduino...

I do prefer the curious machine with a mood and an attitude too (hum, as long as it doesn't start drinking heavily and seeing criters...), since by its mere structure it is more slanted to be a performance artist rather than a drawing technician.
Some scavenged code somewhere to do shading with concentric circles, found in AS220.

void drawCurve(float x, float y, float fx, float fy, float cx, float cy) {
  // Draw a Quadratic Bezier curve from (x, y) to (fx, fy) using control pt
  // (cx, cy)
  float xt=0;
  float yt=0;

  for (float t=0; t<=1; t+=.0025) {
    xt = pow((1-t),2) *x + 2*t*(1-t)*cx+ pow(t,2)*fx;
    yt = pow((1-t),2) *y + 2*t*(1-t)*cy+ pow(t,2)*fy;
    moveTo(xt, yt);
  }  
}
                                                     

void drawCircle(int centerx, int centery, int radius) {
  // Estimate a circle using 20 arc Bezier curve segments
  int segments =20;
  int angle1 = 0;
  int midpoint=0;
   
   moveTo(centerx+radius, centery);

  for (float angle2=360/segments; angle2<=360; angle2+=360/segments) {

    midpoint = angle1+(angle2-angle1)/2;

    float startx=centerx+radius*cos(rads(angle1));
    float starty=centery+radius*sin(rads(angle1));
    float endx=centerx+radius*cos(rads(angle2));
    float endy=centery+radius*sin(rads(angle2));
    
    int t1 = rads(angle1)*1000 ;
    int t2 = rads(angle2)*1000;
    int t3 = angle1;
    int t4 = angle2;

    drawCurve(startx,starty,endx,endy,
              centerx+2*(radius*cos(rads(midpoint))-.25*(radius*cos(rads(angle1)))-.25*(radius*cos(rads(angle2)))),
              centery+2*(radius*sin(rads(midpoint))-.25*(radius*sin(rads(angle1)))-.25*(radius*sin(rads(angle2))))
    );
    
    angle1=angle2;
  }

}


              
void drawCircles(int number, int centerx, int centery, int r) {
   // Draw a certain number of concentric circles at the given center with
   // radius r
   int dr=0;
   if (number > 0) {
     dr = r/number;
     for (int k=0; k<number; k++) {
       drawCircle(centerx, centery, r);
       r=r-dr;
     }
   }
}

Have you tried it? you have some circle stuff commented out in the firmware...

optimizing the polargraph as a mere plotter would require some changes to the comm protocol, maybe a queue...

how many Ks is the accelstepper library eating?

Hah was just too lazy to check (it is late), but yes, it had a familiar look 😉