(Sierpinski triangle) Write a program that lets the user to enter the order and display the filled Sierpinski triangles as shown in Figure 18.18

/*********************************************************************************
* (Sierpinski triangle) Write a program that lets the user to enter the order    *
* and display the filled Sierpinski triangles as shown in Figure 18.18.          *
*********************************************************************************/
import javafx.application.Application;
import javafx.geometry.Point2D;
import javafx.geometry.Pos;
import javafx.scene.Scene;
import javafx.scene.control.Label;
import javafx.scene.control.TextField;
import javafx.scene.layout.BorderPane;
import javafx.scene.layout.HBox;
import javafx.scene.layout.Pane;
import javafx.scene.paint.Color;
import javafx.scene.shape.Polygon;
import javafx.stage.Stage;

public class Exercise_18_36 extends Application {
	@Override // Override the start method in the Application class
	public void start(Stage primaryStage) {
		SierpinskiTrianglePane trianglePane = new SierpinskiTrianglePane();
		TextField tfOrder = new TextField();
		tfOrder.setOnAction(
			e -> trianglePane.setOrder(Integer.parseInt(tfOrder.getText())));
		tfOrder.setPrefColumnCount(4);
		tfOrder.setAlignment(Pos.BOTTOM_RIGHT);

		// Pane to hold label, text field, and a button
		HBox hBox = new HBox(10);
		hBox.getChildren().addAll(new Label("Enter an order: "), tfOrder);
		hBox.setAlignment(Pos.CENTER);

		BorderPane borderPane = new BorderPane();
		borderPane.setCenter(trianglePane);
		borderPane.setBottom(hBox);

		// Create a scene and place it in the stage
		Scene scene = new Scene(borderPane, 200, 210);
		primaryStage.setTitle("Exercise_18_36"); // Set the stage title
		primaryStage.setScene(scene); // Place the scene in the stage
		primaryStage.show(); // Display the stage

		scene.widthProperty().addListener(ov -> trianglePane.paint());
		scene.heightProperty().addListener(ov -> trianglePane.paint());
	}

	/** Pane for displaying triangles */
	static class SierpinskiTrianglePane extends Pane {
		private int order = 0;

		/** Set a new order */
		public void setOrder(int order) {
			this.order = order;
			paint();
		}

		SierpinskiTrianglePane() {
		}

		protected void paint() {
			// Select three points in proportion to the pane size
			Point2D p1 = new Point2D(getWidth() / 2, 10);
			Point2D p2 = new Point2D(10, getHeight() - 10);
			Point2D p3 = new Point2D(getWidth() - 10, getHeight() - 10);

			this.getChildren().clear(); // Clear the pane before redisplay

			displayTriangles(order, p1, p2, p3);
		}

		private void displayTriangles(int order, Point2D p1,
				Point2D p2, Point2D p3) {
			if (order == 0) {
				// Draw a triangle to connect three points
				Polygon triangle = new Polygon();
				triangle.getPoints().addAll(p1.getX(), p1.getY(), p2.getX(),
					p2.getY(), p3.getX(), p3.getY());
				triangle.setStroke(Color.BLACK);
				triangle.setFill(Color.BLACK);

				this.getChildren().add(triangle);
			}
			else {
				//Get the midpoint on each edge in the triangle
				Point2D p12= p1.midpoint(p2);
				Point2D p23= p2.midpoint(p3);
				Point2D p31= p3.midpoint(p1);

				// Recursively display three triangles
				displayTriangles(order - 1, p1, p12, p31);
				displayTriangles(order - 1, p12, p2, p23);
				displayTriangles(order - 1, p31, p23, p3);
			}
		}
	}
}