In [1]:

    

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


    

In [2]:

    

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 i in range(len(data)):
        for k, v in variables.items():
            v.append(data[str(i)][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)


    

In [3]:

    

raw = read_results("results/results-3colors-run2.json")


    

In [4]:

    

raw.head(10)


    

    
Out[4]:






  

    

      

      
File-bytes
      
Monte-Carlo-Pi
      
Rule
      
Serial-Correlation
      
Entropy
      
Chi-square
      
Mean
    
  
  

    

      
0
      
100000.0
      
4.000000
      
4.113183e+11
      
-0.000010
      
0.000181
      
2.549949e+07
      
108.000130
    
    

      
1
      
100000.0
      
3.885755
      
6.605369e+12
      
0.250278
      
3.914079
      
1.780723e+06
      
110.799190
    
    

      
2
      
100000.0
      
2.892116
      
6.633363e+11
      
-0.164928
      
4.578474
      
1.195098e+06
      
134.035750
    
    

      
3
      
100000.0
      
3.195248
      
1.980947e+12
      
0.001541
      
7.256266
      
1.017603e+05
      
117.142440
    
    

      
4
      
100000.0
      
3.374295
      
1.558258e+12
      
0.098804
      
4.189589
      
1.554628e+06
      
149.702550
    
    

      
5
      
13739.0
      
3.349934
      
5.405423e+12
      
0.091629
      
6.790931
      
3.612954e+04
      
120.242812
    
    

      
6
      
54452.0
      
3.223361
      
4.294112e+12
      
0.013476
      
7.487716
      
4.737094e+04
      
124.792588
    
    

      
7
      
251.0
      
1.658537
      
1.974610e+12
      
0.116582
      
5.142711
      
2.516044e+03
      
184.549801
    
    

      
8
      
1.0
      
NaN
      
6.945126e+11
      
-100000.000000
      
0.000000
      
2.550000e+02
      
161.000000
    
    

      
9
      
100000.0
      
2.893796
      
5.312357e+12
      
-0.114630
      
4.418390
      
1.539882e+06
      
116.494340
    
  

In [5]:

    

sample = raw[raw['File-bytes'] == float(1E5)]
print(len(raw))
print(len(sample))


    

    




500
338

In [6]:

    

sample.info()


    

    




<class 'pandas.core.frame.DataFrame'>
Int64Index: 338 entries, 0 to 498
Data columns (total 7 columns):
File-bytes            338 non-null float64
Monte-Carlo-Pi        338 non-null float64
Rule                  338 non-null float64
Serial-Correlation    338 non-null float64
Entropy               338 non-null float64
Chi-square            338 non-null float64
Mean                  338 non-null float64
dtypes: float64(7)
memory usage: 21.1 KB

In [7]:

    

sample["pi_deviation"] = np.abs(sample["Monte-Carlo-Pi"] - np.pi)
sample["mean_deviation"] = np.abs(sample["Mean"] - 255 / 2)
sample["p-value"] = chisqprob(sample["Chi-square"], 255)
sample["langton"] = [(27 - digits(r, 3).zfill(27).count("0"))/27 for r in list(map(int,sample["Rule"]))]

sample['Entropy_norm'] = sample['Entropy'] / 8
sample['Entropy'] = sample['Entropy_norm']
sample = sample.drop('Entropy_norm', axis=1)


    

    




/home/martijn/.virtualenvs/complex-systems/lib/python3.4/site-packages/ipykernel/__main__.py:1: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame.
Try using .loc[row_indexer,col_indexer] = value instead

See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy
  if __name__ == '__main__':
/home/martijn/.virtualenvs/complex-systems/lib/python3.4/site-packages/ipykernel/__main__.py:2: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame.
Try using .loc[row_indexer,col_indexer] = value instead

See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy
  from ipykernel import kernelapp as app
/home/martijn/.virtualenvs/complex-systems/lib/python3.4/site-packages/ipykernel/__main__.py:3: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame.
Try using .loc[row_indexer,col_indexer] = value instead

See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy
  app.launch_new_instance()
/home/martijn/.virtualenvs/complex-systems/lib/python3.4/site-packages/ipykernel/__main__.py:4: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame.
Try using .loc[row_indexer,col_indexer] = value instead

See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy
/home/martijn/.virtualenvs/complex-systems/lib/python3.4/site-packages/ipykernel/__main__.py:6: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame.
Try using .loc[row_indexer,col_indexer] = value instead

See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy
/home/martijn/.virtualenvs/complex-systems/lib/python3.4/site-packages/ipykernel/__main__.py:7: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame.
Try using .loc[row_indexer,col_indexer] = value instead

See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy

In [8]:

    

sample.describe()


    

    
Out[8]:






  

    

      

      
File-bytes
      
Monte-Carlo-Pi
      
Rule
      
Serial-Correlation
      
Entropy
      
Chi-square
      
Mean
      
pi_deviation
      
mean_deviation
      
p-value
      
langton
    
  
  

    

      
count
      
338.0
      
338.000000
      
3.380000e+02
      
338.000000
      
338.000000
      
3.380000e+02
      
338.000000
      
338.000000
      
338.000000
      
338.0
      
338.000000
    
    

      
mean
      
100000.0
      
3.222844
      
3.739090e+12
      
-7396.448195
      
0.502197
      
6.603855e+06
      
114.104770
      
0.592599
      
30.574848
      
0.0
      
0.656038
    
    

      
std
      
0.0
      
0.860926
      
2.178847e+12
      
26210.112173
      
0.316821
      
9.507254e+06
      
43.017466
      
0.628967
      
33.058610
      
0.0
      
0.095427
    
    

      
min
      
100000.0
      
0.000000
      
2.133775e+10
      
-100000.000000
      
0.000000
      
4.427120e+04
      
0.000000
      
0.002773
      
0.007560
      
0.0
      
0.370370
    
    

      
25%
      
100000.0
      
2.997900
      
1.712792e+12
      
-0.086712
      
0.283449
      
2.976926e+05
      
100.591710
      
0.175800
      
8.862285
      
0.0
      
0.592593
    
    

      
50%
      
100000.0
      
3.355454
      
3.717093e+12
      
-0.000486
      
0.525635
      
1.722141e+06
      
120.224965
      
0.461058
      
19.383025
      
0.0
      
0.666667
    
    

      
75%
      
100000.0
      
3.858934
      
5.596833e+12
      
0.051101
      
0.820136
      
6.551231e+06
      
137.145382
      
0.858407
      
39.445090
      
0.0
      
0.703704
    
    

      
max
      
100000.0
      
4.000000
      
7.604736e+12
      
0.783507
      
0.961217
      
2.550000e+07
      
242.443550
      
3.141593
      
127.500000
      
0.0
      
0.888889
    
  

In [9]:

    

sample[sample.mean_deviation < 1]


    

    
Out[9]:






  

    

      

      
File-bytes
      
Monte-Carlo-Pi
      
Rule
      
Serial-Correlation
      
Entropy
      
Chi-square
      
Mean
      
pi_deviation
      
mean_deviation
      
p-value
      
langton
    
  
  

    

      
36
      
100000.0
      
3.127325
      
9.381791e+11
      
-0.041062
      
0.601161
      
1.097448e+06
      
126.96237
      
0.014268
      
0.53763
      
0.0
      
0.629630
    
    

      
50
      
100000.0
      
2.981399
      
2.007083e+12
      
-0.026640
      
0.573680
      
1.306385e+06
      
127.07470
      
0.160194
      
0.42530
      
0.0
      
0.666667
    
    

      
86
      
100000.0
      
2.997240
      
4.072651e+12
      
-0.007934
      
0.913943
      
1.015266e+05
      
126.55526
      
0.144353
      
0.94474
      
0.0
      
0.518519
    
    

      
140
      
100000.0
      
3.241330
      
2.453827e+12
      
-0.057470
      
0.828608
      
3.410276e+05
      
127.75273
      
0.099737
      
0.25273
      
0.0
      
0.703704
    
    

      
156
      
100000.0
      
2.995320
      
2.566393e+12
      
0.007654
      
0.904705
      
1.145263e+05
      
128.37223
      
0.146273
      
0.87223
      
0.0
      
0.592593
    
    

      
162
      
100000.0
      
3.237730
      
3.162927e+12
      
0.003802
      
0.841759
      
2.981401e+05
      
127.31256
      
0.096137
      
0.18744
      
0.0
      
0.703704
    
    

      
220
      
100000.0
      
3.090844
      
4.876568e+12
      
0.009873
      
0.927911
      
9.445427e+04
      
127.31454
      
0.050749
      
0.18546
      
0.0
      
0.666667
    
    

      
279
      
100000.0
      
3.364455
      
6.630534e+12
      
0.051399
      
0.833139
      
2.453993e+05
      
127.62971
      
0.222862
      
0.12971
      
0.0
      
0.851852
    
    

      
309
      
100000.0
      
3.095884
      
6.695664e+12
      
-0.008912
      
0.912255
      
1.040294e+05
      
127.46819
      
0.045709
      
0.03181
      
0.0
      
0.592593
    
    

      
329
      
100000.0
      
3.235089
      
4.781620e+12
      
-0.058853
      
0.815225
      
3.324369e+05
      
127.90400
      
0.093496
      
0.40400
      
0.0
      
0.629630
    
    

      
356
      
100000.0
      
3.130205
      
3.036424e+12
      
-0.011411
      
0.940659
      
7.160753e+04
      
127.49244
      
0.011388
      
0.00756
      
0.0
      
0.740741
    
    

      
415
      
100000.0
      
3.175327
      
6.444096e+12
      
0.001555
      
0.942212
      
8.368959e+04
      
128.39780
      
0.033734
      
0.89780
      
0.0
      
0.740741
    
    

      
432
      
100000.0
      
3.131405
      
3.062631e+12
      
-0.051513
      
0.803990
      
3.820025e+05
      
127.35581
      
0.010188
      
0.14419
      
0.0
      
0.703704
    
    

      
433
      
100000.0
      
3.025081
      
1.858608e+12
      
-0.030206
      
0.748324
      
4.694376e+05
      
126.79656
      
0.116512
      
0.70344
      
0.0
      
0.518519
    
    

      
466
      
100000.0
      
2.675387
      
1.810948e+12
      
0.039682
      
0.558679
      
1.265171e+06
      
128.08895
      
0.466206
      
0.58895
      
0.0
      
0.444444
    
  

In [15]:

    

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

ax1 = plt.gca()
sample.plot("langton", "Entropy", ax=ax1, kind="scatter", marker='o', alpha=.5, s=40)
plt.savefig('plots/3c-entropy-langton.png', format='png', dpi=400)

ax1 = plt.gca()
sample.plot("langton", "Entropy", ax=ax1, kind="scatter", marker='o', alpha=.5, s=40)
plt.savefig('plots/3c-entropy-langton.svg', format='svg', dpi=400)


    

In [10]:

    

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

ax2 = plt.gca()
sample.plot("langton", "Chi-square", ax=ax2, logy=True, kind="scatter", marker='o', alpha=.5, s=40)
plt.savefig('plots/3c-chisquare-langton.png', format='png', dpi=400)

ax2 = plt.gca()
sample.plot("langton", "Chi-square", ax=ax2, logy=True, kind="scatter", marker='o', alpha=.5, s=40)
plt.savefig('plots/3c-chisquare-langton.svg', format='svg', dpi=400)


    

In [ ]:

    




    

In [ ]:

    




    

In [ ]: