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Ex_4_1.py

+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Wed May 10 07:53:17 2023
+
+@author: delvigne
+"""
+
+'''
+Exercice 4.1 Simulating Brownian motion based on a random walk process
+'''
+
+import numpy as np 
+import pylab 
+import random 
+n = 100000 #n is the number of steps(increase in the value of n increses the compelxity of graph) 
+x = np.zeros(n) # x and y are arrays which store the coordinates of the position 
+y = np.zeros(n) 
+direction=["NORTH","SOUTH","EAST","WEST"] # Assuming the four directions of movement.
+for i in range(1, n): 
+    step = random.choice(direction) #Randomly choosing the direction of movement. 
+    if step == "EAST": #updating the direction with respect to the direction of motion choosen.
+        x[i] = x[i - 1] + 1
+        y[i] = y[i - 1] 
+    elif step == "WEST": 
+        x[i] = x[i - 1] - 1
+        y[i] = y[i - 1] 
+    elif step == "NORTH": 
+        x[i] = x[i - 1] 
+        y[i] = y[i - 1] + 1
+    else: 
+        x[i] = x[i - 1] 
+        y[i] = y[i - 1] - 1
+pylab.title("Random Walk 2-D")
+pylab.plot(x, y) #plotting the walk.
+pylab.show()