I wasn't sure how to use two pointers to solve this problem. So I took a different approach. I created a list to store all the sums calculated until a repeating sum was found, in which case is the beginning of a repetitive cycle.

Here's what I did:

class Solution:
  def find(self, num):
    # Initialize the current sums variable and an empty list to keep track of all sums
    ssum = num
    list_ssums = []

    # Repeat this block as long as the sum isn't being repeated (not found in list_ssums)
    while ssum not in list_ssums:
      list_ssums.append(ssum)
      digits = self.num_split(ssum)
      ssum = self.calc_squares(digits)
      if ssum == 1:
        return True   # Base case: return True if 1 is found
    return False      # If any sum repeats itself, break and return False

  # Function that splits the digits
  def num_split(self, num):
    digits = [int(digit) for digit in str(num)]
    return digits

  # Function that calculates the sum of squares
  def calc_squares(self, digits):
    sums = 0
    for digit in digits:
      sums += digit ** 2
    return sums