$1\mathrm{/}x$ Probability Distribution in a Close Proximity of the Bak-Tang-Wiesenfeld Sandpile

The mechanism of self-organized criticality is based on a steady slow loading and a quick huge stress-release. We add the clustering of the events in space and time to the Bak-Tang-Wiesenfeld cellular automaton and obtain the truncated $1\mathrm{/}x$ probability distribution of the events over their sizes.