Entropy Experiment

cat /dev/input/mouse1 > test1 && ent -bc test1
-----------------------------------------------------------------------------------------------
Value Char Occurrences Fraction
  0             2648   0.711828
  1             1072   0.288172

Total:          3720   1.000000

Entropy = 0.866348 bits per bit.

Optimum compression would reduce the size
of this 3720 bit file by 13 percent.

Chi square distribution for 3720 samples is 667.68, and randomly
would exceed this value less than 0.01 percent of the times.

Arithmetic mean value of data bits is 0.2882 (0.5 = random).
Monte Carlo value for Pi is 4.000000000 (error 27.32 percent).
Serial correlation coefficient is 0.397180 (totally uncorrelated = 0.0).


cat /dev/urandom > test2 && ent -bc test2
-----------------------------------------------------------------------------------------------
Value Char Occurrences Fraction
  0        319292565   0.499976
  1        319322987   0.500024

Total:     638615552   1.000000

Entropy = 1.000000 bits per bit.

Optimum compression would reduce the size
of this 638615552 bit file by 0 percent.

Chi square distribution for 638615552 samples is 1.45, and randomly
would exceed this value 22.87 percent of the times.

Arithmetic mean value of data bits is 0.5000 (0.5 = random).
Monte Carlo value for Pi is 3.141439619 (error 0.00 percent).
Serial correlation coefficient is -0.000006 (totally uncorrelated = 0.0).


cat /dev/null > test3 && ent -bc test3
-----------------------------------------------------------------------------------------------
Value Char Occurrences Fraction
  0         74178560   1.000000

Total:      74178560   1.000000

Entropy = 0.000000 bits per bit.

Optimum compression would reduce the size
of this 74178560 bit file by 100 percent.

Chi square distribution for 74178560 samples is 74178560.00, and randomly
would exceed this value less than 0.01 percent of the times.

Arithmetic mean value of data bits is 0.0000 (0.5 = random).
Monte Carlo value for Pi is 4.000000000 (error 27.32 percent).
Serial correlation coefficient is undefined (all values equal!).