These breaks happen after Martian winds deposit sand on the slope, where it gradually accumulates. Eventually, so much sand builds up that the sand underneath can't sustain the weight of the sand on top, and a mini avalanche occurs.
On Earth, this sort of thing usually happens on wind-protected slopes, leading NASA scientists to conclude the side of this dune, called Namib Dune, is also shielded from the wind.
For comparison, the wind-facing side of another nearby dune reveals a very different sand pattern:
(NASA/JPL-Caltech/MSSS)
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