Sketch to draw the Superformula and save it to a PDF.

superformula.pde

import controlP5.*;
import processing.pdf.*;

float scaler = 50;
int m = 2;
float n1 = 1;
float n2 = 1;
float n3 = 1;


boolean save = false;

ControlP5 controlP5;
ControlGroup group;

void setup() {
  size(500, 500);
  smooth();
  controlP5 = new ControlP5(this);
  group = controlP5.addGroup("myGroup",0,0);
  
  controlP5.addSlider("scaler",   0, 250, scaler, 10, 420, width - 50, 10).setGroup(group);
  controlP5.addSlider("m",         0.001, 20, m, 10, 432, width - 50, 10).setGroup(group);
  controlP5.addSlider("n1",        0.001, 20, n1, 10, 444, width - 50, 10).setGroup(group);
  controlP5.addSlider("n2",        0.001, 20, n2, 10, 456, width - 50, 10).setGroup(group);
  controlP5.addSlider("n3",        0.001, 20, n3, 10, 468, width - 50, 10).setGroup(group);

  controlP5.addButton("save", 1, 10, 480, 100, 10).setGroup(group);
}

void draw() {
  noFill();  
  if (save) {
    beginRecord(PDF, "superformula_"+m+"_"+n1+"_"+n2+"_"+n3+".pdf"); 
    PFont f = createFont("", 10);
    textFont(f);
    fill(0);
    text("m: "+m, 10, 420);
    text("n1: "+n1, 10, 432);
    text("n2: "+n2, 10, 444);
    text("n3: "+n3, 10, 456);
    
    
    noFill();
  } else {
    stroke(255);
    background(0);
  }

  pushMatrix();
  translate(width/2, height/2 - 50);
  beginShape();
  PVector[] points = superformula(m, n1, n2, n3);
  for (int i=0;i<points.length;i++) {
    vertex(points[i].x * scaler, points[i].y * scaler);
  }
  endShape();
  popMatrix();

  if (save) {
    endRecord(); 
    save = false;
  }

}


PVector[] superformula(float m,float n1,float n2,float n3) {
  int NP = 360;
  float phi = TWO_PI / NP;
  PVector[] points = new PVector[NP+1];
  for (int i=0;i<=NP;i++) {
    points[i] = superformulaPoint(m,n1,n2,n3,phi * i);
  }
  return points;
}

PVector superformulaPoint(float m,float n1,float n2,float n3,float phi) {
  float r;
  float t1,t2;
  float a=1,b=1;

  float x = 0;
  float y = 0;

  t1 = cos(m * phi / 4) / a;
  t1 = abs(t1);
  t1 = pow(t1,n2);

  t2 = sin(m * phi / 4) / b;
  t2 = abs(t2);
  t2 = pow(t2,n3);

  r = pow(t1+t2,1/n1);
  if (abs(r) == 0) {
    x = 0;
    y = 0;
  }  else {
    r = 1 / r;
    x = r * cos(phi);
    y = r * sin(phi);
  }

  return new PVector(x, y);
}

void keyPressed() {
  if (group.isVisible()) {
    group.hide();
  } else {
    group.show();
  }
}