In the video below is a simulation of a packing process on a growing surface. As an analogy, imagine a picnic blanket that you are randomly placing plates on. All the plates are the same size, they are not allowed to overlap, you must place as many as you possibly can at any one moment, and once you put one down you cannot move it. Now do this while the blanket grows. The video below plays a rescaled version of what you would see (by rescaled it is meant the video is constantly mapped back to the unit square, which makes visualisation easier).

If you look closely, can you see ordered regions surrounded by disordered regions? Do you notice how these ordered regions 'pulsate' as the system grows? The state of matter the disks are in is technically referred to as 'super-Poissonian', and is typically associated with critical points (for any physicist reading the size distribution of the ordered islands follows a scale-free power law). Why is the system super-Poissonian? An incomplete answer is the following: short-range correlations are being established by the packing process, which are then exported to larger and larger distances by growth. These long-range correlations gives rise to the critical-like behaviour. More information regarding this can be found here.

What if the plates grow too?

We now repeat the experiment but with magical plates, whereby the plates also grow too. This results in the plates forming a different state of matter from before! This state of matter is be referred to as either hyperuniform or super-homogenous. The video is again a rescaled version of what you would see.

Is there a real-world example?

This work was motivated by (and applied to) chromatophores in the oval squid (image below). The black cells on its body are called chromatophores. Chromatophores do not move, and as the squid grows new ones appear on the surface in the same manner as our plate and picnic blanket analogy. These chromatophores also appear to be super-Poissonian! More information regarding the work described on this page be found here.