Arithmetic representation of symbols according to certain rules

[pbuk]

Is it possible to run your program to find the minimum length of symbols in the same generation that repeats itself?

I think if you are going to make any progress in this subject you should learn to do these things for yourself. If you don't like the look of @jbriggs444's Perl code, try it in Python: you can run it for yourself without installing anything at https://replit.com/@pbuk/StingyInfiniteNlp#main.py, and if you sign up for a repl.it account you can even try some edits.

# See https://www.physicsforums.com/threads/arithmetic-representation-of-symbols-according-to-certain-rules.1016467/

replacements = {
    'A': 'B',
    'B': 'C',
    'C': 'DE',
    'D': 'FC',
    'F': 'GA',
    'G': 'C',
    'E': 'HI',
    'H': 'J',
    'I': 'D',
    'J': 'D',
}

def transform(input):
    ''' Transform the input according to the rules '''
    output = ''
    for char in input:
        output += replacements[char]
    return output

truncateAt = 10

# Set the initial conditions.
current = 'A'
history = []

# This concise loop does all the work!
while not current in reversed(history):
    history.append(current)
    current = transform(current)[:truncateAt]

# Report the results.
cycle = len(history) - history.index(current)
count = len(history)
history.append(current)
print('Cycle length', cycle, 'after', count, 'iterations')

if truncateAt <= 100:
    for index, item in enumerate(history):
        if index == count - cycle or index == count:
            print(index, item, '<<<')
        else:
            print(index, item)