Pattern Formation

 

Dynamical systems of objects following any set of rules will evolve over time. Studying ways of describing this evolution, especially in order to make meaningful generalizations about what to expect in the long run, is the study of pattern formation.

 

One of the key problems in pattern formation is the role of noise. Noise can be interpreted as random differences in the initial conditions, random fluctuation of parameters and even random system adherence to the rules. Typically, noise can be expected to disrupt an expectedpattern but sometimes (for example, this is the case with Turing systems) noise can actually be necessary or helpful for generating and stabilizing a pattern.

 

In any patterning mechanism, is it important to recognize whether the patterning is directed or self-organized:

 

 

 

 

Directed verses Self-organized Pattern Formation

 

Suppose that 30 students are collected in a room with no distinguishing features on any of the walls. In one case, a teacher located at one wall in the room directs all the students to face the opposite wall. The students will efficiently and spontaneously align in the same direction. In another case, students read instructions from a slip of paper in their hands that they are to all face the same direction. Students will not immediately know which direction they should face and will face the same direction as their neighbors, forming small groups with different alignments. They will need to collect and integrate information about the orientation of their neighbors several times before they are aligned in the same direction. This latter case describes local self-organization in biology, where the slips of paper are the genetic instructions of the cell. Fibroblasts organize exactly this way during wound healing (Edelstein-Keshet and Ermentrout, 1990; Ehrlich and Krummel, 1996; Dallon et al., 1999).

 

 

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Last updated October 5, 2011.