Select maturation length before hitting flag. Each mature cell splits off a baby. Each baby matures after either 1 time step or 2. 1 yields repeated doubling (geometric sequence). 2 yields a Fibonacci sequence: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233... With the Fibonacci sequence, the count / previous count approximates golden ratio, 1.61803....
Shows that the maturation delay generates the Fibonacci sequence. Immature (baby) cells must mature after they are born and before they can split off themselves, when set to 2. By contrast, a maturation time of 1, really no delay, leads to the simplest geometric sequence, doubling at each time step. Baby cells shown as smaller. Mature cells shown as larger and has a visible split developing. With the maturation length of 2, the result is 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233... each number is the total cell count. Ratio of each count to the previous count gets ever closer to the golden ratio 1.61803.... Boman, B.M.; Dinh, T.N.; Decker, K.; Emerick, B.; Raymond, C.; Schleiniger, G. Why do Fibonacci numbers appear in patterns of growth in nature? A model for tissue renewal based on asymmetric cell division. Fibonacci Q. 2017, 55, 30–41. C. P. Spears and M. Bicknell-Johnson, Asymmetric cell division: Binomial identities for age analysis of mortal vs. immortal trees, In G. E. Bergum, A. N. Philippou, and A. F. Horadam, editors, Applications of Fibonacci Numbers 7, pages 377–391. Springer Netherlands, 1998. C. P. Spears, M. Bicknell-Johnson, and J. Yan, Fibonacci phyllotaxis by asymmetric cell division: Zeckendorf and wythoff trees, In F. Luca and P. Stanica, editors, Congressus Numerantium 201, pages 257–272, Winnepeg, Canada, 2009. Utilitas Mathematica Publishing.
