The cellular automaton (CA) model exhibits a notable disadvantage of substantial anisotropy, triggered by the square cells, adjacent cell structures, and intrinsic features of the sharp interface model. This disadvantage leads to limitations in simulating dendritic growth with random preferred orientations during the solidification of alloys, particularly in the context of sixfold symmetric alloys. In the present study, drawing inspiration from the processing concept of diffuse interfaces and the gradient energy term in the phase field model, a function concerning the gradient of the field variable associated with the cell state is constructed and the diffusion equation for the field variable is derived. Consequently, a novel field-variable diffusion CA (FCA) model is proposed, which addresses the growth kinetics of the solid-liquid interface in accordance with the lever rule. The proposed model considers constitutional supercooling and the Gibbs-Thomson effect, employing the concentration potential method to manage solute diffusion and redistribution. The growth rate of interface cells is modulated by introducing a field-variable diffusion term. The analysis reveals that within the square-grid discretization mode, the model demonstrates validation under various conditions, focusing on the steady-state characteristics of the dendritic tip and growth kinetics of the sixfold symmetric Mg-6%Al (mass fraction) alloy. The findings are consistent with the predictions of the LGK model, suggesting that the FCA model can effectively emulate dendritic morphology with multifold symmetry and random preferred orientations, and elucidate critical dendritic arm behaviors, such as competitive dendritic growth and coarsening.