Data visualization is essential to discover patterns and anomalies in large high-dimensional datasets. New dimensionality reduction techniques have thus been developed for visualizing omics data, in particular from single-cell studies. However, jointly showing several types of data, for example, single-cell expression and gene networks, remains a challenge. Here, we present 'U-CIE, a visualization method that encodes arbitrary high-dimensional data as colors using a combination of dimensionality reduction and the CIELAB color space to retain the original structure to the extent possible. U-CIE first uses UMAP to reduce high-dimensional data to three dimensions, partially preserving distances between entities. Next, it embeds the resulting three-dimensional representation within the CIELAB color space. This color model was designed to be perceptually uniform, meaning that the Euclidean distance between any two points should correspond to their relative perceptual difference. Therefore, the combination of UMAP and CIELAB thus results in a color encoding that captures much of the structure of the original high-dimensional data. We illustrate its broad applicability by visualizing single-cell data on a protein network and metagenomic data on a world map and on scatter plots.