ButterFlyFX

package funWithParametricEquations;

import javafx.animation.AnimationTimer;
import javafx.application.Application;
import javafx.geometry.Point2D;
import javafx.scene.Parent;
import javafx.scene.Scene;
import javafx.scene.canvas.Canvas;
import javafx.scene.canvas.GraphicsContext;
import javafx.scene.layout.Pane;
import javafx.scene.paint.Color;
import javafx.stage.Stage;
import static java.lang.Math.*;

/**
 *
 * @author Aamir khan
 */
public class Butterfly extends Application {

    private GraphicsContext g;
    double t = 0.0;
    final int WIDTH = 800;
    final int HEIGHT = 600;

    @Override
    public void start(Stage win) throws Exception {
        Scene scene = new Scene(createContent(), WIDTH, HEIGHT);
        win.setScene(scene);
        win.setTitle("ButterFly - aamir-4u.blogspot.in");
        win.show();
    }

    public static void main(String[] args) {
        launch(args);
    }

    private Parent createContent() {
        Pane root = new Pane();
        Canvas canvas = new Canvas(WIDTH, HEIGHT);
        g = canvas.getGraphicsContext2D();

        AnimationTimer timer;
        timer = new AnimationTimer() {
            @Override
            public void handle(long now) {
                t += 0.010;
                draw();
            }

            private void draw() {
                Point2D p = curve();
                g.setStroke(Color.RED);
                double newX = p.getX() + 400;
                double newY = p.getY() + 300;
                final int STROKE_SIZE = 1;
                g.strokeOval(newX, newY, STROKE_SIZE, STROKE_SIZE);
            }

            private Point2D curve() {
                double x = sin(t) * (pow(E,cos(t)) - 2 * cos(4*t) - pow(sin(t/12),5));
                double y = cos(t) * (pow(E,cos(t)) - 2 * cos(4*t) - pow(sin(t/12),5));
                final double PREF_RADIUS = 85;
                return new Point2D(x, y).multiply(PREF_RADIUS);
            }

        };
        timer.start();
        root.getChildren().add(canvas);
        return root;
    }

}