The distributions of the cluster area, <em>A</em>, and total rain rate, <em>R</em>, for tropical oceanic rain clusters from a cellular automaton (CA) are analysed for their scaling exponent <em>ζ<sub>A</sub></em>, <em>ζ<sub>R</sub></em>, and <em>β</em> where f(s)~s-<em><sup>ζ</sup><sub><sup>S</sup>; </sub>S∈{A,R}</em>; <em>f</em>(<em>s</em>) the probability distribution of <em>S</em>. The CA only includes a few simple rules representing a small set of dynamics thought to be important for convective organization. These rules represent large-scale destabilization of the atmosphere under the moisture static energy framework with a slow driving timescale, as well as convective cells interaction through propagating gravity waves with a fast relaxation timescale. The CA exhibits percolation-like criticality, and the <em>ζ<sub>A</sub></em><sub>­</sub> is estimated to be near the 2-dimensional percolation value of 187/91. This agrees well with the <em>ζ<sub>A</sub></em> estimates over the Indian Ocean warm pool and the tropical Atlantic reported in previous modelling study. Although other critical exponents of the rain cluster distributions from the CA, namely the <em>η<sub>S</sub></em> (scaling exponent of characteristic scale with driving force) and <em>D<sub>S</sub></em> (cluster fractal dimension), <em>S</em><em>∈</em>(<em>A</em>, <em>R</em>}, depend on the adjustable parameter of the CA, the <em>ζ<sub>A</sub></em> is robust to the adjustable parameter. Although the CA cannot account for the observed <em>ζ<sub>A</sub></em> ~ 5/3 reported elsewhere based on observations, further tuning of it such as through the convective cells interaction strength or manner may make it approach the state of self-organized criticality.