Exa-scale simulations are on the horizon but almost no new design for the output has been proposed in recent years. In simulations using individual time steps, the traditional snapshots are over resolving particles/cells with large time steps and are under resolving the particles/cells with short time steps. Therefore, they are unable to follow fast events and use efficiently the storage space. The Continuous Simulation Data Stream (CSDS) is designed to decrease this space while providing an accurate state of the simulation at any time. It takes advantage of the individual time step to ensure the same relative accuracy for all the particles. The outputs consist of a single file representing the full evolution of the simulation. Within this file, the particles are written independently and at their own frequency. Through the interpolation of the records, the state of the simulation can be recovered at any point in time. In this paper, we show that the CSDS can reduce the storage space by 2.76x for the same accuracy than snapshots or increase the accuracy by 67.8x for the same storage space whilst retaining an acceptable reading speed for analysis. By using interpolation between records, the CSDS provides the state of the simulation, with a high accuracy, at any time. This should largely improve the analysis of fast events such as supernovae and simplify the construction of light-cone outputs. (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).