Six yolks in a bowl: Why not optimal circle packing? Making soufflé tonight, I wondered if the six yolks took on the
optimal circle packing configuration.
They do not. It is only with seven congruent circles that the optimal
packing places one in the center.

Q.
  Why don't the yolks in a bowl follow the optimal packing of congruent
  circles in a circle?


          


          

Six yolks in a bowl.


          


          

Image from Wikipedia.
Optimal packings for $5,6,7$ circles.


 A: The system doesn't try to minimise the radius of the enclosing circle, but its potential energy. We can idealise this as non-overlapping disks in a convex rotationally symmetric potential $V$ with $V(0) = 0$. The configuration that was physically realised then has potential energy $5 V(d)$ (with $d$ the diameter of the yolks) while the configuration from Wikipedia would have potential energy $6 V(d)$.
A: In addition to the excellent answers already added, it is important to note that in addition to Martin Hairer's description, this problem is distinct from circle packing in another way: the system tries to minimize the potential function at every point in time, subject to the physical laws governing the movement of egg yolks in a bowl. This is not generally equivalent to minimizing the potential function, and might lead to a local but not global minimum.
One example of this is a pencil balancing on its tip. This is an equilibrium state, but clearly the potential energy is suboptimal. This example is admittedly rather far from the egg yolk problem though, so an edit from someone with a more similar example would probably be appropriate.
A: Those packing rules only apply for rigid circles. Anyone who's ever cracked an egg knows that yolks are not rigid. As a result of that, you can clearly see that the sides of yolks are flattened as they touch another yolk.
So those packing rules simply don't apply.
A: What do you mean, "the yolks don't follow optimal packing"? Sure they do. The configuration with one yolk in the center has the exact same radius as the one with six yolks distributed along the edge.
It also has lower potential energy, thus the 6-circle solution you cited is a non-global optimum at best. In fact it's probably metastable, given egg yolks' general tendency to be squishy blobs instead of perfect circles.
A: In addition to the non-rigid quality of egg yolks and the noted third dimension, it would take precision to align six yolks in a circle.  By random placement, they most often find a closer packing, i. e. one without a big honking space in the middle.
