Large-scale neural recordings contain high-dimensional structure that cannot be easily captured by existing data visualization methods. We therefore developed an embedding algorithm called Rastermap, which captures highly nonlinear relationships between neurons, and provides useful visualizations by assigning each neuron to a location in the embedding space. Compared to standard algorithms such as t-SNE and UMAP, Rastermap finds finer and higher dimensional patterns of neural variability, as measured by quantitative benchmarks. We applied Rastermap to a variety of datasets, including spontaneous neural activity, neural activity during a virtual reality task, widefield neural imaging data during a 2AFC task, artificial neural activity from an agent playing atari games, and neural responses to visual textures. We found within these datasets unique subpopulations of neurons encoding abstract properties of the environment.