Fig. 4: Stripe fracturing and reproduction probabilities.

a Probability of a stripe to stay intact and hence not to fracture (1 − P_fracture). Error bars indicate 95% CI. Due to the constant rate of extension of individual stripes, the stripe length is proportional to time and stripe length can be interpreted as stripe’s effective age. As shown, short (/young) stripes do not fracture and only once their length exceeds  ≈ 200h the fracturing probability becomes nonzero. b An example of a stripe’s length evolution (\({\rm{Re}}=710\)) during its journey through the channel. At each fracturing event the original stripe is shortened and hence has a lower probability to fracture (see (a)). c Growth and fracturing sequences of a stripe. Since stripes grow linearly in time, the stripe’s size is proportional to its effective age. In turn the probability to fracture increases with stripe length, and once fractured, the original stripe is shortened, which can be interpreted as the return to a younger effective age. As shown by the grey curves, localized stripes are subject to this cyclic growth-fracturing process as they move downstream. The diagonal line corresponds to the growth of a stripe in the absence of fracturing, while the colour gradient illustrates the increasing probability for it to fracture. The horizontal and vertical arrows indicate fracturing events which reset a stripe’s length and effective age. The black curve highlights the evolution of one stripe, for which numbers have been added to clarify the sequence of fracturing/reset events - see the main text for details. Note that here only fracturing of stripe segments larger than 20h are shown for clarity. To compare the dynamics of stripes in our experiment to those in earlier computational studies we analysed the data from Shimizu and Manneville⁴⁵ (supplemental movie at \({\rm{Re}}=725\)) and the stripe length evolution for a representative time interval (≈5000 advective units), shown in red. d Reproduction probability, i.e., the fracturing probability, only counting events at which daughter stripes grow and survive. Error bars indicate 95% CI. The corresponding survival curve (red) is of type 1, aging, whereas the puff splitting curve shown for comparison³⁰ is of type 2, memoryless.