This paper explores the implications of the vanishing complexity condition in $ f(\mathbf{R}) $ gravity theory for static spherical spacetimes. The concept of complexity is introduced as a measure of the anisotropy and inhomogeneity in the interior of a self-gravitating structure. The complexity factor $ Y_{TF} $ is defined based on the anisotropic fluid distribution and is used to analyze the physical properties of compact objects. The field equations for $ f(\mathbf{R}) $ gravity are derived, and the spherical mass function is defined in both geometric and matter terms. The complexity-free condition is introduced to simplify the system of field equations, allowing for the development of different models. The paper also discusses the physical conditions required for a realistic model, including the behavior of energy density, pressure, and anisotropy. Three distinct models are presented, each with its own set of parameters and graphical representations. The results show that these models exhibit the necessary properties for the existence of physically viable and stable structures for certain values of the model parameter. The analysis also includes the study of gravitational redshift and stability criteria, demonstrating that the models are stable and meet the required physical conditions. The findings highlight the importance of the complexity factor in understanding the behavior of compact objects in $ f(\mathbf{R}) $ gravity.This paper explores the implications of the vanishing complexity condition in $ f(\mathbf{R}) $ gravity theory for static spherical spacetimes. The concept of complexity is introduced as a measure of the anisotropy and inhomogeneity in the interior of a self-gravitating structure. The complexity factor $ Y_{TF} $ is defined based on the anisotropic fluid distribution and is used to analyze the physical properties of compact objects. The field equations for $ f(\mathbf{R}) $ gravity are derived, and the spherical mass function is defined in both geometric and matter terms. The complexity-free condition is introduced to simplify the system of field equations, allowing for the development of different models. The paper also discusses the physical conditions required for a realistic model, including the behavior of energy density, pressure, and anisotropy. Three distinct models are presented, each with its own set of parameters and graphical representations. The results show that these models exhibit the necessary properties for the existence of physically viable and stable structures for certain values of the model parameter. The analysis also includes the study of gravitational redshift and stability criteria, demonstrating that the models are stable and meet the required physical conditions. The findings highlight the importance of the complexity factor in understanding the behavior of compact objects in $ f(\mathbf{R}) $ gravity.