Below are the screenshots of code and a few snapshots of race simulated:
https://media.cheggcdn.com/coop/640/6408d87d-69be-41fb-aca9-b31804cc41b1/1594544593066_Screenshot1950.png
https://media.cheggcdn.com/coop/35b/35bcc142-8735-4851-9a1f-d9ab112d4159/1594544658555_Screenshot1951.png
Race:
https://media.cheggcdn.com/coop/35d/35dfe747-4336-4d90-a718-1914c5091dd5/1594544714150_Screenshot1952.png
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https://media.cheggcdn.com/coop/35d/35dad45e-97bc-46d1-9203-af9e013f790b/1594544765606_Screenshot1953.png
Below is the java code for Snail.java. The 4 functions are implemented as mentioned in the question.

Snail.java

import java.util.LinkedList;
import java.util.Queue;
public class Snail {
public static char icon = '@';
private int position;
private int raceLength = 50;/**for storing raceLength**/
private Queue<Integer> movePattern;
/**implementing snail constructor**/
   public Snail(int[] pattern) {
       position = 0;
   movePattern = (Queue<Integer>) new LinkedList<Integer>();
       for (int pt: pattern)
           movePattern.add(pt);
   }
   /**implementing move method**/
public void move(){
   int move=movePattern.peek();
   movePattern.remove();
   position = Math.min(position+move, raceLength);
   movePattern.add(move);
}
/**implementing getPosition method**/
public int getPosition(){
   return position;
}
/**implementing display method**/
public void display(){
   int dashesBefore = position;
   int dashesAfter = raceLength - position;
   for(int i = 0 ; i < dashesBefore ; i++)
       System.out.print("-");
   System.out.print(icon);
   for(int i = 0 ; i < dashesAfter ; i++)
       System.out.print("-");
   System.out.println();
}
}

Below is the SnailRace.java. It is used unmodified to test & simulate the above Snails class.

SnailRace.java

public class SnailRace {
  
   private Snail[] participants;
   public static int raceLength = 50;
   public SnailRace() {
       participants = new Snail[3];
       participants[0] = new Snail(new int[]{1,0,1,2,1,0});
       participants[1] = new Snail(new int[]{2,1,1,0});
       participants[2] = new Snail(new int[]{0,0,3});
      
       try{
           startRace();
       } catch(Exception e){
           System.out.println("An error occurred");
       }
   }
public void startRace() throws InterruptedException{
   boolean racing = true;
   while(racing){
       for(int i = 0; i < participants.length; i++){
           participants[i].move();
       }
       for(int i = 0; i < participants.length; i++){
           if(participants[i].getPosition() == raceLength){
               racing = false;
           }
       }
       display();
       Thread.sleep(500);
   }
}
public void display(){
   for(int i = 0; i < participants.length; i++){
           participants[i].display();
       }
   System.out.println("\n\n\n\n");
}
   public static void main(String[] args) {
       new SnailRace();

   }

}