# LINES BEGINNING WITH HASHTAG ARE 'COMMENTS'


# collatz (n) equals n/2 if n is even, 3n+1 if n is odd

def collatz(n):
    if n%2 == 0:
        return n/2
    else:
        return 3*n+1
        
# compute the inverse as a list (there may be one or two values)        
def collatzInv(n):
    if n%6==4:
        return [2*n, (n-1)/3]
    else:
        return [2*n]
    
# give a list of successive iterations ending at 1        
def collatzEvol(n):
    next = collatz(n)
    evol=[n,next]
    while next <> 1:
        next = collatz(next)
        evol.append(next)
    return evol

# make a list of inverses up to length "level"
def collatzInvEvol(n,level):
    evol = [n]
    while level>0:
        for a in evol:
            evol = union(evol, collatzInv(a))
        level -= 1
    return evol
    
# compute the length of the iteration
def collatzLength(n):
    return len(collatzEvol(n))

#compute the 'max hailstone height'
def collatzMax(n):
    return max(collatzEvol(n))

collatz(99)

#notice the 

list_plot(collatzEvol(27), plotjoined=true)

collatzEvol(27)

maxi = [collatzMax(n) for n in [1..1000]]

list_plot(maxi,ymax= 10000)