Abstract: Layout enrichment methods for multidimensional projections aim to enhance 2D scatterplots with additional information. We address the representation of categorical attributes with respect to a numerical feature, like the importance of a data point or its frequency, by colouring the scatterplots' background. However, applying existing space-filling methods has limitations: Voronoi partitionings, including weighted variants, do not correctly account for the relative weight of data points, resulting in disproportionately small or large areas, depending on the data point density. Neighbourhood Treemaps (Nmap) preserve the relative size of areas given data point weights but are restricted to rectangular shapes, often positioned far from the associated data points. To address these issues, we propose FluidMap, a space-filling layout enrichment inspired by fluid dynamics. Our algorithm simulates the behaviour of coloured fluids spreading under pressure, with projected data points serving as sources and weights determining the amount of fluid to be distributed. FluidMap generates flexibly shaped areas that maintain sizes proportional to data point weights and include their assigned data points. We compare our method to Voronoi-based techniques and Nmap by quantifying their visual properties. Additionally, through an expert study, we assess task-specific differences. Our method outperforms existing techniques in preserving proportional representation and spatial consistency simultaneously.