絵合 Picture Contest

There's a contest going over on flickr to see who has the best photo that fits a theme, and the winner gets a free pro account that's worth $30. One of the themes I'm competing in is "Emergence". "Emergence" is a phenomenon where simple rules, interaction, patterns, etc. create complex systems. There is a group on flickr that is dedicated to photos that show this phenomenon and then explain the underlying principles that lead to the emergent behavior. Anyway, my photo entry into the competition has to do with the complex nature of bubbles and foam that arises from simple interactions. This photo is of a watery foam suspended in the air while a droplet of water forms at the bottom, ready to fall.



This photo is just part one of a set of bubble photos I took. Here are the rest:



Here is the emergent nature of bubbles and foam in a more detailed explanation:

The mysterious nature of bubbles and foam is an example of emergence on both molecular and macroscopic levels.

A typical bubble is formed by simple interactions between soap and water molecules that organize themselves to produce a spherical shape governed by the rules of minimal surfaces (note: a sphere is not actually a mathematically defined minimal surface because it does not have zero mean curvature. What I mean to say is that a sphere provides a maximum volume with a minimum surface area).

A soap molecule has a long structure that is composed of a polar, hydrophillic head and a non-polar, hydrophobic tail. When a soap and water bubble forms, the heads of the soap molecules are attracted to water and stay submerged in it. The tails of the soap molecules are repelled by the water and stick out into the air both inside and outside the bubble providing both structural stability and protection from evaporation. These simple interactions by soap and water on the microscopic level form what we see as a bubble in the macroscopic world. The tendency for nature to maximize the volume to surface area ratio produces a bubble's shape.

Millions of simple water molecules and complex soap molecules interact to form a simple sphere known as a bubble. When multiplied many times over, thousands of simple bubbles interact with each other to form a complex structure known as foam. Understanding how bubbles in foam arrange themselves in the most efficient packing order is a difficult and well documented problem. The concept of minimal surfaces arises again, but even the introduction of just one bubble (to make an interaction of two bubbles) complicates the situation many times over and is a striking example of Plateau's Problem. To put it simply, nature's most efficient packing structure emerges when the walls of the bubbles contact each other at 120 degree angles. To visualize this in two dimensions, imagine just one layer of bubbles side by side, and you will see a hexagonal pattern emerge. This is the same pattern that bees use in their honeycomb designs as it creates the strongest and largest cell using the least amount of wax and energy, stacked together in the most space-efficient design.

See the whole set of bubbly emergent pictures here: www.flickr.com/photos/rentahamster/sets/411459/