I burnt milk while boiling it. I noticed that the burnt milk on the bottom of the pan, formed a pattern that vaguely resembled the pattern of cork-cells . Why is this pattern being formed?
Milk comprises sugars and fats, with the sugars being prone to caramelization upon exposure to heat from stovetop. You can see the developing brown color and if you scrape further, you will see burnt organic material (black). The observed markings result from bubbles that were unable to ascend to the surface and consequently became entrapped and collapsed at the base of the pan during the boiling process.
The pattern has everything to do with the interacting of opposing forces such as in convection, combined with mass transport, precipitation, and agglomeration of particles in the fluid. The same pattern can be formed regardless of the chemistry involved and is certainly not a crystal.
See Turing patterns, which exemplify "how patterns in nature, such as stripes and spots, can arise naturally and autonomously from a homogeneous, uniform state." https://en.wikipedia.org/wiki/Turing_pattern
Also check out a convection specific instance of pattern formation, Bénard cells, but similar: https://en.wikipedia.org/wiki/Rayleigh%E2%80%93B%C3%A9nard_convection
In this case, the bubbles form hundred/thousands of times, from the same locations called nucleation sites. Each time pushing a little more flocculated milk protein to the edge of the nucleation site. The patterns of the nucleation sites themselves are random at first and then become evenly spread by a process of symmetry breaking, where the nearby sites make it harder to form a site so they become an average distance apart, making the pattern. The physical remnants of the pattern are what you see.
If you watch carefully boiling of milk or water at lower level of pan , bubble form due to the high heat at bottom rapidly ,the shape you see there is just the result of that the cavity is result of complete evaporation of water and fats get stick to the corner of bubble shape.