Chapter 18 Exercise 36, Introduction to Java Programming, Tenth Edition Y. Daniel LiangY.

18.36 (Sierpinski triangle)
Write a program that lets the user to enter the order
and display the filled Sierpinski triangles

import javafx.geometry.Insets;
import javafx.geometry.Point2D;
import javafx.geometry.Pos;
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.shape.Polyline;

public class SierpinskiTrianglePane extends BorderPane {

    TextField tfOrder = new TextField();
    Label lblOrder = new Label("Enter an order:");
    Pane pane = new Pane();

    int order;

    public SierpinskiTrianglePane() {

        tfOrder.setOnAction(e -> {
            order = Integer.parseInt(tfOrder.getText());
            paint();
        });

        HBox hBox = new HBox(20, lblOrder, tfOrder);
        hBox.setPadding(new Insets(10));
        hBox.setAlignment(Pos.BASELINE_RIGHT);

        tfOrder.setPrefColumnCount(8);

        setCenter(pane);
        setBottom(hBox);
        setPrefWidth(400);
        setPrefHeight(400);

    }

    public void paint() {

        pane.getChildren().clear();

        Point2D p0 = new Point2D(getWidth() * 0.5, getHeight() * 0.1); // top
        Point2D p1 = new Point2D(getWidth() * 0.10, getHeight() * 0.75); // left
        Point2D p2 = new Point2D(getWidth() * 0.90, getHeight() * 0.75); // right

        drawTriangles(order, p0, p1, p2);
    }

    private void drawTriangles(int order, Point2D p0, Point2D p1, Point2D p2) {

        if (order == 0) {
            Polyline poly = new Polyline(
                    p0.getX(), p0.getY(),
                    p1.getX(), p1.getY(),
                    p2.getX(), p2.getY(),
                    p0.getX(), p0.getY()
            );
            pane.getChildren().add(poly);
        } else {
            Point2D p01 = p0.midpoint(p1); // top left
            Point2D p11 = p1.midpoint(p2); // bottom
            Point2D p21 = p2.midpoint(p0); // top right

            drawTriangles(order - 1, p1, p11, p01);
            drawTriangles(order - 1, p2, p11, p21);
            drawTriangles(order - 1, p0, p01, p21);

        }
    }

}

import javafx.application.Application;
import javafx.geometry.Insets;
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.Polyline;
import javafx.stage.Stage;

public class Exercise_36  extends Application {

    @Override
    public void start(Stage primaryStage) throws Exception {

        SierpinskiTrianglePane pane = new SierpinskiTrianglePane();

        primaryStage.setScene(new Scene(pane));
        primaryStage.setTitle("Sierpinski triangle");
        primaryStage.show();
    }

    public class SierpinskiTrianglePane extends BorderPane {

        TextField tfOrder = new TextField();
        Label lblOrder = new Label("Enter an order:");
        Pane pane = new Pane();

        int order;

        public SierpinskiTrianglePane() {

            tfOrder.setOnAction(e -> {
                try {
                    order = Integer.parseInt(tfOrder.getText());
                } catch (NumberFormatException ex) {
                    order = 0;
                    tfOrder.setText("0");
                }
                paint();
            });

            HBox hBox = new HBox(20, lblOrder, tfOrder);
            hBox.setPadding(new Insets(10));
            hBox.setAlignment(Pos.BASELINE_CENTER);
            tfOrder.setAlignment(Pos.BASELINE_RIGHT);
            tfOrder.setPrefColumnCount(4);
            tfOrder.setText("0");
            setCenter(pane);
            setBottom(hBox);
            setPrefWidth(400);
            setPrefHeight(400);

        }

        public void paint() {

            pane.getChildren().clear();

            Point2D p0 = new Point2D(getWidth() * 0.5, getHeight() * 0.1); // top
            Point2D p1 = new Point2D(getWidth() * 0.10, getHeight() * 0.75); // left
            Point2D p2 = new Point2D(getWidth() * 0.90, getHeight() * 0.75); // right

            drawTriangles(order, p0, p1, p2);
        }

        private void drawTriangles(int order, Point2D p0, Point2D p1, Point2D p2) {

            if (order == 0) {
                Polyline poly = new Polyline(
                        p0.getX(), p0.getY(),
                        p1.getX(), p1.getY(),
                        p2.getX(), p2.getY(),
                        p0.getX(), p0.getY()
                );
                poly.setFill(Color.BLUE);
                pane.getChildren().add(poly);
            } else {
                Point2D p01 = p0.midpoint(p1); // top left
                Point2D p11 = p1.midpoint(p2); // bottom
                Point2D p21 = p2.midpoint(p0); // top right

                drawTriangles(order - 1, p1, p11, p01);
                drawTriangles(order - 1, p2, p11, p21);
                drawTriangles(order - 1, p0, p01, p21);


            }
        }

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