Objective. This study presents a universal phantom for positron emission tomography (PET) that allows arbitrary static and dynamic activity distributions of various complexities to be generated using a single PET acquisition.Approach. We collected a high-statistics dataset (with a total of 22.4 × 10⁹prompt coincidences and an event density of 2.75 × 10⁶events mm^-3) by raster-scanning a single plane with a²²Na point source mounted on a robotic arm in the field-of-view of the uEXPLORER PET/CT scanner. The source position was determined from the reconstructed dynamic frames. Uniquely, true coincidences were separated from scattered and random events based on the distance between their line-of-response and the known source location. Finally, we randomly sampled the dataset to generate the desired activity distributions modeling several different phantoms.Main results. Overall, the target and the reconstructed phantom images had good agreement. The analysis of a simple geometric distribution showed high quantitative accuracy of the phantom, with mean error of <-3.0% relative to the ground truth for activity concentrations ranging from 5.3 to 47.7 kBq ml^-1. The model of a high-resolution¹⁸F-fluorodeoxyglucose distribution in the brain illustrates the usefulness of the technique in simulating realistic static neuroimaging studies. A dynamic¹⁸F-florbetaben study was modeled based on the time-activity curves of a human study and a segmented brain phantom with no coincidences repeating between frames. For all time points, the mean voxel-wise errors ranged from -4.4% to -0.7% in grey matter and from -3.9% to +2.8% in white matter.Significance. The proposed phantom technique is highly flexible and allows modeling of static and dynamic brain PET studies with high quantitative accuracy. It overcomes several key limitations of the existing phantoms and has many promising applications for the purposes of image reconstruction, data correction methods, and system performance evaluation, particularly for new high-performance dedicated brain PET scanners.