# -*- coding: utf-8 -*-
"""
Created on Thu Oct 17 14:22:59 2019

@author: gullholm
"""
# Q1
import random
import numpy as np
import matplotlib.pyplot as plt
# First makes vector with the resolution and size of the grid
N = 10
size = [0]*N
res = [0]*N
ress = [0]*N

for n in range(N):
    size[n] = 2**(n+1)
    res[n] = 2**-(n+1)

# makes brownian motion for finest grid 2^-10
Z = np.zeros(size[9])
sigma = res[9]
Z = sigma*np.random.randn(1024)
Z[0] = 0
B_10 = np.cumsum(Z)
for i in range(N):
    ress[i] = np.arange(0,1, res[i])



def BM(B):      # function that's makes the bigger grids
    lgd = int(len(B)/2)
    B_new = [0]*lgd
    for i in range(1,lgd):
            B_new[i] = (1/2)*(B[i]+B[i+1]-B[i-1]) # each coarser grid is the mean of two finer
    return(B_new)


B_9 = BM(B_10)
B_8 = BM(B_9)
B_7 = BM(B_8)
B_6 = BM(B_7)
B_5 = BM(B_6)
B_4 = BM(B_5)
B_3 = BM(B_4)
B_2 = BM(B_3)
B_1 = BM(B_2)


plt.plot(ress[9], B_10)
plt.plot(ress[8], B_9)
plt.plot(ress[7], B_8)
plt.plot(ress[6], B_7)
plt.plot(ress[5], B_6)
plt.plot(ress[4], B_5)
plt.plot(ress[3], B_4)
plt.plot(ress[2], B_3)
plt.plot(ress[1], B_2)
plt.plot(ress[0], B_1)