We produce the first low to mid frequency radio simulation that incorporates both traditional extragalactic radio sources as well as synchrotron cosmic web emission. The FIlaments & GAlactic RadiO (FIGARO) simulation includes ten unique SI{4x4}{degree} fields, incorporating active galactic nucleii (AGNs), star forming galaxies (SFGs) and synchrotron cosmic web emission out to a redshift of $z = 0.8$ and over the frequency range 100-1400 MHz. To do this, the simulation brings together a recent $100^3$ Mpc$^3$ magneto-hydrodynamic simulation (Vazza et al., 2019), calibrated to match observed radio relic population statistics, alongside updated `T-RECS code for simulating extragalactic radio sources (Bonaldi et al., 2019). Uniquely, the AGNs and SFGs are populated and positioned in accordance with the underlying matter density of the cosmological simulation. In this way, the simulation provides an accurate understanding of the apparent morphology, angular scales, and brightness of the cosmic web as well as -- crucially -- the clustering properties of the cosmic web with respect to the embedded extragalactic radio population. We find that the synchrotron cosmic web does not closely trace the underlying mass distribution of the cosmic web, but is instead dominated by shocked shells of emission surrounding dark matter halos and resembles a large, undetected population of radio relics. We also show that, with accurate kernels, the cosmic web radio emission is clearly detectable by cross-correlation techniques and this signal is separable from the embedded extragalactic radio population. We offer the simulation as a public resource towards the development of techniques for detecting and measuring the synchrotron cosmic web.
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