Where Art & Science Intersect
To visualize how Xiang's decomposition algorithm works, he developed computer code that displays the resulting dyadic tree. The input image has been automatically cut into local rectangular pieces in a way carefully designed to achieve a useful global optimality.
For clarity, only a partial decomposition of the input image has been shown, reminding us of the inspirations we receive from nature: that harmony is required between division and unity, Xiang said.
Obtaining such images is an engineering challenge since it requires upright positioning of a tiny embryo, which is shaped like an ellipsis and just a half-millimeter long.
In collaboration with Lu lab at Georgia Tech, Princeton scientists have developed a device to trap and orient a large number of embryos vertically. The technique can be used to study embryos and, eventually, to understand the processes that drive the development of the embryo.
Below left is a simulated view at just (7 centimeters) compared with the original photograph (right). At 18 centimeters a striking phenomenon occurs: if the "eye" or the subject moves slightly, large portions of the field of view seem to flash between all orange and all black. It may be more than coincidence that 18 centimeters is about the typical courtship distance for this species.
Superimposed is a two-dimensional approximation of the field-of-view for each eye of each fish, shown as white rays cast outwards from the eye. Rays are terminated when they collide with another individual or the boundary of the arena.
This rough estimate of what each fish can see from its vantage point in the school is helpful for determining what information an individual has about its neighbors and environment at a given moment. This, in turn, allows scientists to study how information about a stimulus, such as a predator or food, may propagate through a group, changing the configuration of the group itself.