Draw high dimensional tensors as a matrix of matrices (blog.ezyang.com)

A simple, practical way to visualize tensors with four or more dimensions is to draw them as a "matrix of matrices": start from the usual 2D printout and, for each extra dimension, alternately stack the lower-dimensional matrices horizontally then vertically (always horizontal first to preserve row-major order). That alternating stacking produces a fractal-like layout where the first two dims map to x/y positions and higher dims show up as blocks that are skipped over when reading rows. The note walks through 0D–5D examples (including explicit index orders for torch.arange reshaped into 2×2×... tensors) and shows how a 4D (2,2,2,2) layout lets you visually draw the cut lines corresponding to torch.split along each dimension. This representation matters because it makes axis identities and block structure immediately apparent, which helps with debugging reshapes, permutes, stride/memory-layout issues, and teaching tensor indexing. In the special binary-size case the index sequence follows a Morton/Z-order curve (with a generalization when axes have different radices). The author also demonstrates how splitting along dims 0–3 in the 4D example maps to contiguous blocks in the visual grid, clarifying how higher-dimensional slices correspond to simple geometric cuts in the rendered matrix-of-matrices.