In [2]:

    

import json
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
from scipy import integrate
from scipy.stats import chisqprob
from gmpy2 import digits

import recipe


    

In [3]:

    

s_rands_paper = recipe.rands_paper
d_five = recipe.five
d_five['Entropy_norm'] = d_five['Entropy'] / 8
d_five['Entropy'] = d_five['Entropy_norm']
d_five = d_five.drop('Entropy_norm', axis=1)

d_five['p_value_deviation'] = np.abs(d_five['p-value'] - 0.5)


    

In [4]:

    

d_five_p10_90 = d_five[(d_five['p-value'] > 0.1) & (d_five['p-value'] < 0.9)]
d_five_p05_95 = d_five[(d_five['p-value'] > 0.05) & (d_five['p-value'] < 0.95)]
d_rands_paper = d_five[d_five.rule.isin(s_rands_paper)]

len_five_p10_90 = len(d_five_p10_90)
len_five_p05_95 = len(d_five_p05_95)
len_rands_paper = len(d_rands_paper)

print("Random according to paper: #%d " % len_rands_paper, end="")
print(list(d_rands_paper.rule.sort_values()))
print("Between  5 - 95%%: #%d " % len_five_p05_95, end="")
print(list(d_five_p05_95.rule.sort_values()))
print("Between 10 - 90%%: #%d " % len_five_p10_90, end="")
print(list(d_five_p10_90.rule.sort_values()))


    

    




Random according to paper: #28 [15, 30, 45, 60, 75, 85, 86, 89, 90, 101, 102, 105, 106, 120, 135, 149, 150, 153, 154, 165, 166, 169, 170, 180, 195, 210, 225, 240]
Between  5 - 95%: #21 [30, 45, 60, 75, 86, 90, 101, 102, 105, 106, 120, 122, 135, 149, 150, 153, 161, 165, 169, 195, 225]
Between 10 - 90%: #19 [30, 45, 60, 75, 86, 90, 102, 105, 106, 122, 135, 149, 150, 153, 161, 165, 169, 195, 225]

In [5]:

    

s_five_p05_p95 = set(d_five_p05_95.rule)
s_five_p10_p90 = set(d_five_p10_90.rule)

print("Random from paper but not according to us: ", end="") 
print(set(d_rands_paper.rule) - set(d_five_p10_90.rule))

print()

print("Random from paper but not according to us: ", end="") 
print(set(d_five_p10_90.rule) - set(d_rands_paper.rule))


    

    




Random from paper but not according to us: {101, 166, 170, 15, 240, 210, 180, 85, 120, 89, 154}

Random from paper but not according to us: {161, 122}

In [6]:

    

d_five[d_five.rule.isin(set(d_rands_paper.rule) - set(d_five_p10_90.rule))][['Entropy', 'mean_deviation', 'p-value']]


    

    
Out[6]:






  

    

      

      
Entropy
      
mean_deviation
      
p-value
    
  
  

    

      
15
      
0.903346
      
4.724540
      
0.000000
    
    

      
85
      
0.872812
      
0.162692
      
0.000000
    
    

      
89
      
0.999961
      
0.089662
      
0.950925
    
    

      
101
      
0.999960
      
0.053356
      
0.943729
    
    

      
120
      
0.999947
      
0.171428
      
0.050093
    
    

      
154
      
0.905389
      
0.104222
      
0.000000
    
    

      
166
      
0.908783
      
6.754538
      
0.000000
    
    

      
170
      
0.880623
      
3.419920
      
0.000000
    
    

      
180
      
0.888805
      
1.506982
      
0.000000
    
    

      
210
      
0.891130
      
12.487088
      
0.000000
    
    

      
240
      
0.902752
      
11.236362
      
0.000000
    
  

In [7]:

    

# Plot Entropy of all rules against the langton parameter
ax1 = plt.gca()
d_five.plot("langton", "Entropy", ax=ax1, kind="scatter", marker='o', alpha=.5, s=40)
d_five_p10_90.plot("langton", "Entropy", ax=ax1, kind="scatter", color="r", marker='o', alpha=.5, s=40)
plt.show()

ax1 = plt.gca()
d_five.plot("langton", "Entropy", ax=ax1, kind="scatter", marker='o', alpha=.5, s=40)
d_five_p10_90.plot("langton", "Entropy", ax=ax1, kind="scatter", color="r", marker='o', alpha=.5, s=40)
plt.savefig('plots/entropy-langton.png', format='png', dpi=400)

ax1 = plt.gca()
d_five.plot("langton", "Entropy", ax=ax1, kind="scatter", marker='o', alpha=.5, s=40)
d_five_p10_90.plot("langton", "Entropy", ax=ax1, kind="scatter", color="r", marker='o', alpha=.5, s=40)
plt.savefig('plots/entropy-langton.svg', format='svg', dpi=400)


    

In [11]:

    

# Plot Chi-Square of all rules against the langton parameter
ax2 = plt.gca()
d_five.plot("langton", "Chi-square", ax=ax2, logy=True, kind="scatter", marker='o', alpha=.5, s=40)
d_five_p10_90.plot("langton", "Chi-square", ax=ax2, logy=True, kind="scatter", color="r", marker='o', alpha=.5, s=40)
plt.show()

ax2 = plt.gca()
d_five.plot("langton", "Chi-square", ax=ax2, logy=True, kind="scatter", marker='o', alpha=.5, s=40)
d_five_p10_90.plot("langton", "Chi-square", ax=ax2, logy=True, kind="scatter", color="r", marker='o', alpha=.5, s=40)
plt.savefig('plots/chisquare-langton.png', format='png', dpi=400)

ax2 = plt.gca()
d_five.plot("langton", "Chi-square", ax=ax2, logy=True, kind="scatter", marker='o', alpha=.5, s=40)
d_five_p10_90.plot("langton", "Chi-square", ax=ax2, logy=True, kind="scatter", color="r", marker='o', alpha=.5, s=40)
plt.savefig('plots/chisquare-langton.svg', format='svg', dpi=400)


    

In [10]:

    

# Plot Mean of all rules against the langton parameter
ax3 = plt.gca()
d_five.plot("langton", "Mean", ax=ax3, kind="scatter", marker='o', alpha=.5, s=40)
d_five_p10_90.plot("langton", "Mean", ax=ax3, kind="scatter", color="r", marker='o', alpha=.5, s=40)
plt.show()

ax3 = plt.gca()
d_five.plot("langton", "Mean", ax=ax3, kind="scatter", marker='o', alpha=.5, s=40)
d_five_p10_90.plot("langton", "Mean", ax=ax3, kind="scatter", color="r", marker='o', alpha=.5, s=40)
plt.savefig('plots/mean-langton.png', format='png', dpi=400)

ax3 = plt.gca()
d_five.plot("langton", "Mean", ax=ax3, kind="scatter", marker='o', alpha=.5, s=40)
d_five_p10_90.plot("langton", "Mean", ax=ax3, kind="scatter", color="r", marker='o', alpha=.5, s=40)
plt.savefig('plots/mean-langton.svg', format='svg', dpi=400)


    

In [30]:

    

# Plot Monte Carlo of all rules against the langton parameter
ax4 = plt.gca()
d_five.plot("langton", "Monte-Carlo-Pi", ax=ax4, kind="scatter", marker='o', alpha=.5, s=40)
d_five_p10_90.plot("langton", "Monte-Carlo-Pi", ax=ax4, kind="scatter", color="r", marker='o', alpha=.5, s=40)
plt.show()

ax4 = plt.gca()
d_five.plot("langton", "Monte-Carlo-Pi", ax=ax4, kind="scatter", marker='o', alpha=.5, s=40)
d_five_p10_90.plot("langton", "Monte-Carlo-Pi", ax=ax4, kind="scatter", color="r", marker='o', alpha=.5, s=40)
plt.savefig('plots/monte-carlo-langton.png', format='png', dpi=400)

ax4 = plt.gca()
d_five.plot("langton", "Monte-Carlo-Pi", ax=ax4, kind="scatter", marker='o', alpha=.5, s=40)
d_five_p10_90.plot("langton", "Monte-Carlo-Pi", ax=ax4, kind="scatter", color="r", marker='o', alpha=.5, s=40)
plt.savefig('plots/monte-carlo-langton.svg', format='svg', dpi=400)


    

In [37]:

    

# Plot Serial Correlation of all rules against the langton parameter
ax5 = plt.gca()
d_five.plot("langton", "Serial-Correlation", ax=ax5, kind="scatter", marker='o', alpha=.5, s=40)
d_five_p10_90.plot("langton", "Serial-Correlation", ax=ax5, kind="scatter", color="r", marker='o', alpha=.5, s=40)
plt.show()

ax5 = plt.gca()
d_five.plot("langton", "Serial-Correlation", ax=ax5, kind="scatter", marker='o', alpha=.5, s=40)
d_five_p10_90.plot("langton", "Serial-Correlation", ax=ax5, kind="scatter", color="r", marker='o', alpha=.5, s=40)
plt.savefig('plots/serial-correlation-langton.png', format='png', dpi=400)

ax5 = plt.gca()
d_five.plot("langton", "Serial-Correlation", ax=ax5, kind="scatter", marker='o', alpha=.5, s=40)
d_five_p10_90.plot("langton", "Serial-Correlation", ax=ax5, kind="scatter", color="r", marker='o', alpha=.5, s=40)
plt.savefig('plots/serial-correlation-langton.svg', format='svg', dpi=400)


    

In [41]:

    

# Plot p-value of all rules against the langton parameter
ax6 = plt.gca()
d_five.plot("langton", "p-value", ax=ax6, kind="scatter", marker='o', alpha=.5, s=40)
d_five_p10_90.plot("langton", "p-value", ax=ax6, kind="scatter", color="r", marker='o', alpha=.5, s=40)
plt.show()

ax6 = plt.gca()
d_five.plot("langton", "p-value", ax=ax6, kind="scatter", marker='o', alpha=.5, s=40)
d_five_p10_90.plot("langton", "p-value", ax=ax6, kind="scatter", color="r", marker='o', alpha=.5, s=40)
plt.savefig('plots/p-value-langton.png', format='png', dpi=400)

ax6 = plt.gca()
d_five.plot("langton", "p-value", ax=ax6, kind="scatter", marker='o', alpha=.5, s=40)
d_five_p10_90.plot("langton", "p-value", ax=ax6, kind="scatter", color="r", marker='o', alpha=.5, s=40)
plt.savefig('plots/p-value-langton.svg', format='svg', dpi=400)


    

In [ ]:

    




    

In [ ]:

    




    

In [ ]:

    




    

In [11]:

    

# Cutoff rules with high Chi-Square (not random)
d_rands_paper_chi = d_rands_paper[(d_rands_paper["Chi-square"] < 300)] # 300 or 1E5 is same cutoff

print("Number of random rules according to paper: %d" % len(d_rands_paper))
print("Number of paper rules with high Chi-Square: %d " % (len(d_rands_paper) - len(d_rands_paper_chi)), end="")
print(set(d_rands_paper.rule) - set(d_rands_paper_chi.rule))


    

    




Number of random rules according to paper: 28
Number of paper rules with high Chi-Square: 8 {166, 170, 15, 240, 210, 180, 85, 154}

In [14]:

    

selection = d_five_p10_90[['rule', 'pi_deviation', 'mean_deviation', 'p_value_deviation', 'Serial-Correlation']]


    

In [15]:

    

selection


    

    
Out[15]:






  

    

      

      
rule
      
pi_deviation
      
mean_deviation
      
p_value_deviation
      
Serial-Correlation
    
  
  

    

      
30
      
30
      
0.007324
      
0.009032
      
0.270481
      
-0.002542
    
    

      
45
      
45
      
0.000836
      
0.026764
      
0.290890
      
0.000934
    
    

      
60
      
60
      
0.003140
      
0.049358
      
0.215533
      
0.001424
    
    

      
75
      
75
      
0.004052
      
0.026974
      
0.224544
      
-0.001767
    
    

      
86
      
86
      
0.008420
      
0.109408
      
0.045251
      
-0.001377
    
    

      
90
      
90
      
0.000116
      
0.064950
      
0.347723
      
-0.000760
    
    

      
102
      
102
      
0.002716
      
0.014618
      
0.367914
      
0.001276
    
    

      
105
      
105
      
0.002140
      
0.012444
      
0.395692
      
0.000286
    
    

      
106
      
106
      
0.003284
      
0.033468
      
0.388576
      
0.000740
    
    

      
122
      
122
      
0.004828
      
0.114394
      
0.227844
      
-0.000534
    
    

      
135
      
135
      
0.017645
      
0.111598
      
0.165868
      
-0.001099
    
    

      
149
      
149
      
0.010588
      
0.205130
      
0.052170
      
0.001348
    
    

      
150
      
150
      
0.009388
      
0.132046
      
0.073749
      
-0.000408
    
    

      
153
      
153
      
0.002660
      
0.085626
      
0.295055
      
-0.000457
    
    

      
161
      
161
      
0.008564
      
0.321102
      
0.387520
      
-0.000821
    
    

      
165
      
165
      
0.002428
      
0.085176
      
0.333809
      
-0.000892
    
    

      
169
      
169
      
0.002708
      
0.025158
      
0.312015
      
-0.000215
    
    

      
195
      
195
      
0.001276
      
0.082446
      
0.013847
      
-0.001481
    
    

      
225
      
225
      
0.000460
      
0.028304
      
0.054775
      
-0.001858
    
  

In [ ]:

    

p_value_top_10 = selection.sort_values(by='p_value_deviation').head(10)
mean_top_10 = selection.sort_values(by='mean_deviation').head(10)
pi_top_10 = selection.sort_values(by='pi_deviation').head(10)


    

In [ ]:

    

print("Top 10 p-value: \t", end="")
print(p_value_top_10.rule.values)
print("Top 10 Mean: \t\t", end="")
print(mean_top_10.rule.values)
print("Top 10 Monte-Carlo-Pi: \t", end="")
print(pi_top_10.rule.values)

print()

print("Both in top 10 p-value and Mean: ", end="")
print(set(p_value_top_10.rule.values) & set(mean_top_10.rule.values))
print("In all three top 10s: ", end="")
print(set(p_value_top_10.rule.values) & set(mean_top_10.rule.values) & set(pi_top_10.rule.values))


    

In [ ]:

    

selection[selection.rule.isin(set(p_value_top_10.rule.values) & set(mean_top_10.rule.values) & set(pi_top_10.rule.values))]


    

In [ ]:

    

p_value_top_10


    

In [ ]:

    

mean_top_10


    

In [ ]:

    

pi_top_10


    

In [ ]:

    

def read_results(filename):
    results = (File_bytes, Monte_Carlo_Pi, Rule, Serial_Correlation, Entropy, Chi_square, Mean) = [[] for _ in range(7)]
    with open(filename) as f:
        data = json.load(f)
    variables = {"File-bytes": File_bytes, "Monte-Carlo-Pi": Monte_Carlo_Pi, "Rule": Rule, "Serial-Correlation": Serial_Correlation,
                 "Entropy": Entropy, "Chi-square": Chi_square, "Mean": Mean}
    for k, v in variables.items():
        v.append(data[k])
    results = np.array([np.array(r) for r in results]).T
    headers = ["File-bytes", "Monte-Carlo-Pi", "Rule", "Serial-Correlation", "Entropy", "Chi-square", "Mean"]
    return pd.DataFrame(results, columns=headers)

python = read_results('python_1466717839.json')
urandom = read_results('urandom_1466717941.json')


    

In [ ]:

    

for d in (python, urandom):
    d["pi_deviation"] = np.abs(d["Monte-Carlo-Pi"] - np.pi)
    d["mean_deviation"] = np.abs(d["Mean"] - 255 / 2)
    d["p-value"] = chisqprob(d["Chi-square"], 255)
    d['Entropy_norm'] = d['Entropy'] / 8
    d['Entropy'] = d['Entropy_norm']
    d['p_value_deviation'] = np.abs(d['p-value'] - 0.5)


    

In [ ]:

    

python[['pi_deviation', 'mean_deviation', 'p_value_deviation']]


    

In [ ]:

    

urandom[['pi_deviation', 'mean_deviation', 'p_value_deviation']]


    

In [ ]:

    

selection


    

In [ ]: