A central objective in computer vision is to design models with appropriate 2-D inductive bias. Desiderata for 2-D inductive bias include two-dimensional position awareness, dynamic spatial locality, and translation and permutation invariance. To address these goals, we leverage an expressive variation of the multidimensional State Space Model (SSM). Our approach introduces efficient parameterization, accelerated computation, and a suitable normalization scheme. Empirically, we observe that incorporating our layer at the beginning of each transformer block of Vision Transformers (ViT), as well as when replacing the Conv2D filters of ConvNeXT with our proposed layers significantly enhances performance for multiple backbones and across multiple datasets. The new layer is effective even with a negligible amount of additional parameters and inference time. Ablation studies and visualizations demonstrate that the layer has a strong 2-D inductive bias. For example, vision transformers equipped with our layer exhibit effective performance even without positional encoding. Our code is attached as supplementary.