Drawing inspiration from recent findings including surprisingly decent performance of transformers without positional encoding (NoPE) in the domain of language models and how registers (additional throwaway tokens not tied to input) may improve the performance of large vision transformers (ViTs), we invent and test a variant of ViT called fractal ViT that breaks permutation invariance among the tokens by applying an attention mask between the regular tokens and ``summary tokens'' similar to registers, in isolation or in combination with various positional encodings. These models do not improve upon ViT with registers, highlighting the fact that these findings may be scale, domain, or application-specific.