Example of function plot with animation along plotted function in JavaFX. Uses Canvas to render the plot.

AnimatingPlot.java

import java.util.function.DoubleUnaryOperator;

import javafx.animation.Animation;
import javafx.animation.Transition;
import javafx.application.Application;
import javafx.beans.property.DoubleProperty;
import javafx.geometry.Insets;
import javafx.scene.Scene;
import javafx.scene.canvas.Canvas;
import javafx.scene.canvas.GraphicsContext;
import javafx.scene.control.ComboBox;
import javafx.scene.layout.BorderPane;
import javafx.scene.layout.Pane;
import javafx.scene.shape.Circle;
import javafx.stage.Stage;
import javafx.util.Duration;


public class AnimatingPlot extends Application {
    
    private enum NamedFunction {
        SIN(x -> -Math.sin(2 * Math.PI * x / 100) * 200 + 200, "Sine"),
        COS(x -> -Math.cos(2 * Math.PI * x / 100) * 200 + 200, "Cosine"),
        LOG(x -> -Math.log(x) * 20 + 320, "Log");
        
        private final DoubleUnaryOperator function ;
        private final String displayName ;
        
        NamedFunction(DoubleUnaryOperator function, String displayName) {
            this.function = function ;
            this.displayName = displayName ;
        }
        
        public DoubleUnaryOperator getFunction() {
            return function ;
        }
        
        @Override
        public String toString() {
            return displayName ;
        }
    }
    
    private Transition animation ;

	@Override
	public void start(Stage primaryStage) {
	    	    
		Pane pane = new Pane();
		pane.setMinSize(400, 400);
		pane.setPadding(new Insets(10));
		
		ComboBox<NamedFunction> functionChoice = new ComboBox<>();
		functionChoice.getItems().addAll(NamedFunction.values());
		
		functionChoice.valueProperty().addListener((obs, oldFunction, newFunction) -> {
		    pane.getChildren().clear();
		    if (newFunction != null) {
		        Plot plot = new Plot(newFunction.getFunction(), 400, 400, 0, 400);
		        pane.getChildren().add(plot.getPlot());
		        
		        if (animation != null) {
		            animation.stop();
		        }
		        
		        Circle circle = new Circle(10);
		        pane.getChildren().add(circle);
		        
		        animation = plot.createTransition(
		                Duration.seconds(5), 
		                circle.centerXProperty(), 
		                circle.centerYProperty());
		        
		        animation.setCycleCount(Animation.INDEFINITE);
		        animation.setAutoReverse(true);
		        animation.play();
		    }
		});
		
		BorderPane.setMargin(pane, new Insets(20));
		
		BorderPane root = new BorderPane(pane, functionChoice, null, null, null);
		Scene scene = new Scene(root);
		primaryStage.setScene(scene);
		primaryStage.show();
	}
	
	
	public static class Plot {
	    private final DoubleUnaryOperator function ;
	    private final double startX ;
	    private final double endX ;
	    private final Canvas plot ;
        public Plot(DoubleUnaryOperator function, double width, double height,
                double startX, double endX) {
            this.function = function;
            this.startX = startX;
            this.endX = endX;
            
            this.plot = new Canvas(width, height) ;
            GraphicsContext gc = plot.getGraphicsContext2D();
            gc.moveTo(startX, function.applyAsDouble(startX));
            for (double x = startX; x < endX; x++) {
                gc.lineTo(x, function.applyAsDouble(x));
            }
            gc.stroke();
       }
        
       public Canvas getPlot() {
           return plot ;
       }
       
       public Transition createTransition(Duration cycleDuration, DoubleProperty x, DoubleProperty y) {
           return new Transition() {
               
               {
                   setCycleDuration(cycleDuration);
               }
               
               @Override
               protected void interpolate(double frac) {
                   double xValue = (1 - frac) * startX + frac * endX ;
                   double yValue = function.applyAsDouble(xValue);
                   x.set(xValue);
                   y.set(yValue);
               }
           };
       }
	    
	    
	}

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