Modeling the Wheat Branching Structure in QS. Al-Baqarah [2]:261: An Inverse Collatz Tree Framework

Inspired by the multiplier effect of charity (sadaqah) as metaphorically described through the wheat plant in QS. Al-Baqarah [2]:261, this study identifies a structural convergence between divine multiplication and mathematical recursion. The developmental sequence of wheat tillers, specifically the emergence of primary tillers (T1, T2, T3) and secondary tillers (T1.1, T1.2), follows a deterministic branching rule dictated by the phyllochron index. This branching morphology provides a biological analog to the Inverse Collatz Tree. Results: The findings indicate that:(1) QS. Al-Baqarah [2]:261 metaphorically describes the expansion of charity through wheat growth, aligning with recursive mathematical structures;(2) The branching of the Collatz Tree during the tillering phase exhibits a Fibonacci branching pattern (1, 2, 3, 5, 8, 13, 21), reflecting the natural efficiency of plant growth;(3) A systematic node labeling system (A-B-C-D-E-F-G) is introduced to map the Collatz tree structure, with complete node distribution provided in Appendix 1. This study offers a novel interdisciplinary framework connecting Qur'anic metaphor, botanical morphogenesis, and Collatz tree structures. The proposed Collatzogin Tree serves as a visual and structural model for understanding recursive branching in number theory, independent of any claim to proving the Collatz conjecture itself.