Thunderstorms emit fluxes of gamma rays known as gamma-ray glows^1,2, sporadically observed by aircraft^1,3,4,5,6,7, balloons^8,9,10,11 and from the ground^{12,13,14,15,16,17,18}. Observations report increased gamma-ray emissions by tens of percent up to two orders of magnitude above the background, sometimes abruptly terminated by lightning discharges^1,3,4,5. Glows are produced by the acceleration of energetic electrons in high-electric-field regions within thunderclouds⁸ and contribute to charge dissipation³. Glows had been considered as quasi-stationary phenomena^3,5,12, with durations up to a few tens of seconds and spatial scales up to 10–20 km. However, no measurements of the full extension in space and time of a gamma-ray-glow region and their occurring frequency have been reported so far. Here we show that tropical thunderclouds over ocean and coastal regions commonly emit gamma rays for hours over areas up to a few thousand square kilometres. Emission is associated with deep convective cores; it is not uniform and continuous but shows characteristic timescales of 1–10 s and even subsecond for individual glows. The dynamics of gamma-glowing thunderclouds strongly contradicts the quasi-stationary picture of glows and instead resembles that of a huge gamma-glowing ‘boiling pot’ in both pattern and behaviour.