Thirteen is definitely not the time to try workouts similar to those done in the gym. At thirteen your body is still developing - your focus should be on the overall development of the body. What you need at this age is regular physical activity – the kind you get playing team sports.
Exercise does not stunt growth – it is a myth that gym workouts hamper growth. You will continue to grow as your height is predetermined based on your genes. However, there can be other implications of workouts done at a young age. You are working unsupervised and probably do not know the techniques of exercising right. You can pull a muscle, tear a ligament or damage a tissue or injure your back. You perhaps have no knowledge of supplementing the workout with the right diet. Gym workouts require a diet rich in protein, fibre and calcium. In addition you need to replenish salts that are lost during the exercise.
I would suggest you to take life easy and enjoy being a teen. Go cycling, play team sports. Go for a swim or a run. Leave gym workouts for when you are older. Your focus at this juncture of your life should be to establish good habits that stand by you as you grow older. Learn to eat healthy, keep your self hydrated, focus on all round development of mind, body and personality. Aim at being someone who is admired - physical attributes are superficial - go beyond that. Good luck!
Underestimate me...that'll be fun!