13.5 More complex: π generating π.....

What is a random integer? Is an integer choosen randomly between 1 and 1000000 really representative for all integers choosen randomly? We can see that our experience is only an approximation of an ideal model. Here, we’re going to modify the method for generating random integers... We won’t use the primitive random, we’re going to generate random integers with the π digits sequence.
π digits have always interested mathematicians:

In reality, it seems that the π digit sequence is a really randomly sequence. (Result not demonstrated yet). It’s not possible to predict the following digit after the others, there’s no period.

Here is the method we’re going to use to generate integers randomly choosen:

Let’s create now a new procedure called randompi and let’s modify the procedure test

to gcd :a :b  
if (modulo :a :b)=0 [output :b][output gcd :b modulo :a :b]  
to test :tries  
# We open a flow whose identifier is 1 towards the file  millionpi.txt  
# Here we suppose that millionpi.txt is in the current directory  
# Otherwise, fix it with changedirectory  
openflow 1 "millionpi.txt  
# Set the variable line to the first line of the file millionpi.text  
globalmake "line first readlineflow 1  
# Set the variable counter to  0  
globalmake "counter 0  
repeat :tries [  
  if 1=gcd randompi 7 randompi 7 [globalmake "counter :counter+1]  
# Calculate frequency  
globalmake "f :counter/:tries  
# Display th pi approximation  
print sentence [ pi approximation:] squareroot (6/:f)  
closeflow 1  
to randompi :n  
localmake "number "  
repeat :n [  
# If there’s no char yet on the line  
if 0=count :line [globalmake "line first readlineflow 1]  
# Set the variable char to the first character of the line  
globalmake "char first :line  
# Then remove  first character from the line.  
globalmake "line butfirst :line  
globalmake "number word :number :char  
output :number  
test 10  
approximation de pi: 3.4641016151377544  
test 100  
approximation de pi: 3.1108550841912757  
test 1000  
approximation de pi: 3.081180112566604  
test 10000  
approximation de pi: 3.1403714651066386  
test 70000  
approximation de pi: 3.1361767950325627

We find a correct approximation of π with its own digits!

It’s still possible to imrove the program by indicating the time for the computation. We add on the first line of the procedure test:

globalmake "begin pasttime

Then we append before closeflow:

print sentence [pasttime mis: ] pasttime - :begin