Bianchi type-I solutions to Einstein’s field equations (EFE) are well-known and are characterized with homogeneity and anisotropy. These spacetimes specify a generalization of the Friedmann-Lemaître-Robertson-Walker (FLRW) where the universe could not keep spatial-invariance in its dynamics of cosmological expansion or contraction posing an anisotropic expansion which tends to decay as the universe evolves resulting into the present-day nearly an isotropic cosmic structure. In the present study we explore the character of anisotropy in the framework of \(f\left( R \right)\) gravity in shaping cosmological evolution. We envisage geometrically the anisotropy mimicking the role as an independent metric degree of freedom apart from the average scale factor contrary to the approach followed in the general relativity where the scale factor due to time-dependence leverages the anisotropy to be uniquely determined. In order to investigate how the anisotropy evolution takes place in an anisotropic spacetime within \(f\left( R \right)\) context, we analyze it through Ricci scalar R which could lead to computing the scale factor alongside the anisotropy contribution throughout the time cosmologically. Additionally, We find out the critical role of anisotropy in the analysis of models under consideration where it gets suppressed in the large-scale structure of the cosmic evolution of the universe. By applying the certain construction method specifically two possibly viable phases are explored-quasi-de Sitter as implied by exponential expansion during inflationary dynamics and contraction phase as required by bounce models resulting from power laws in the purview of ekpyrotic frameworks. Furthermore, We work out a connection in relation to nonlinear behavior and the interplay between R as spawned in anisotropic spacetime and the expression pertaining to the anisotropy in \(f\left( R \right)\) gravity. The occurence of possible singularities in explored anisotropic scenarios with the growth of scale factors has also been discussed briefly. Finally, by indicating an anisotropic solution in \(f\left( R \right)\) models we urge the need of designating both the average scale factor and the total anisotropy as functions of time.
