Use the description and code given in the picture to First find the scaling law for the end to end disrance and radius gyration of 3D random walk polymer as a function of polymer length. What is the code to plot the average end to end distance and end-to-end distance together with the corresponding analytical functions describing their scaling behaviour.

Use plt.savefig() at the end of the code.

End-to-End Distance and Polymer Length We now want to see what happens to the end-to-end distance if we start varying the polymer length. Below, we generate a series of random walk polymers of different length (N_monomers). For each, we calculate the average end to end distance Rce over a number of iterations (N_polymers). [ ] a Generate random polymers with different lengths N_polyners =10 lengths =[10,100,500,1000,5000,10900] if Initialize arpays to store the end-to-end distance and radius of gyration end_to_end_distances = np.zeros((len(lengths), N_polymers)) res = np.zeros((len(lengths), N_polymers )) I Generate the polymers for 1 , length in enumerate(lengths): for j in range ( N_polymers): -. end_to_end_distance, rg= generate_randon_walk_30(1ength) it store end to end distance end_to_end_distances [1,1]= end_to_end_distance res [1,1]=rg II Calculate the average end-to-end distance for each polywer length average_end_to_end_distances =np.mean(end_to_end_distances, axis=1 ) average_rit = np,mean(res,axis=1) I I average_end_to_end distances