Figure 15. Our discussion in Sect. 3.4 demonstrates that in two spatial dimensions, the large distance properties of an incompressible active fluid in the ordered phase, e.g., incompressible flock, has the same scale-invariant properties as a two-dimensional smectic liquid crystals and the KPZ surface growth model. The findings thus suggest that instead of the apparent equivalence between an incompressible flock and a two-dimensional lattice depicted by the landscape in Escher’s Day and Nights [top figure (awaiting approval of use from the copyright holder)], the flock should instead be mapped onto a smectics-like layered structure such as sedimentary rocks [66] [Top half of bottom figure: photograph by Tommy Hansen. Public domain. Bottom half of bottom figure: photograph by Ryan McGrady, distributed under a CC-BY 4.0 license.].
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