Quanta Magazine is a gem. Science for the rest of us, particularly physics, warms the cockles of yours truly's heart, especially when it comes to the mysterious connect between order and disorder, a subject that never ceases to amaze given just how profound the connect truly is. With this in mind, the eyes of birds have an interesting tale to tell with it's indirect link to random walks, chaos and close packing, commonplace phenomena that show the inner workings of reality in subtle and interesting ways.
Chaos - Lorenz attractor aka The butterfly effect
Close packing of cannon balls
Seven years ago, Joe Corbo stared into the eye of a chicken and saw something astonishing. The color-sensitive cone cells that carpeted the retina (detached from the fowl, and mounted under a microscope) appeared as polka dots of five different colors and sizes. But Corbo observed that, unlike the randomly dispersed cones in human eyes, or the neat rows of cones in the eyes of many fish, the chicken’s cones had a haphazard and yet remarkably uniform distribution. The dots’ locations followed no discernible rule, and yet dots never appeared too close together or too far apart. Each of the five interspersed sets of cones, and all of them together, exhibited this same arresting mix of randomness and regularity. Corbo, who runs a biology lab at Washington University in St. Louis, was hooked.
When this notion of unordered yet uniform distribution is connected to the universality of phase transitions and the permutations of randomness, a more comprehensive view of reality emerges.
Beyond the one-dimensional random walk, there are many other kinds of random shapes. There are varieties of random paths, random two-dimensional surfaces, random growth models that approximate, for example, the way a lichen spreads on a rock. All of these shapes emerge naturally in the physical world, yet until recently they’ve existed beyond the boundaries of rigorous mathematical thought. Given a large collection of random paths or random two-dimensional shapes, mathematicians would have been at a loss to say much about what these random objects shared in common.
“You take the most natural objects — trees, paths, surfaces — and you show they’re all related to each other,” Sheffield said. “And once you have these relationships, you can prove all sorts of new theorems you couldn’t prove before.”
Mandelbrot would get this research without question.