The simplest behavior patterns are gaits like walking, or running in uniform speed, and they are defined by fixed relative phase. For example, during walsking, the relative phase between your left and right hip joints is 0.5 cycles:
	And the time series:
	In a jumping kangaroo, or in the gait called “bound” that is common in small rodent moving fast, the relative phase between the hindlegs is 0:
	And the time series:
	During gallop in horses one of the forelegs typically lags slightly behind the other. The relative phase is a small fraction of a cycle, say 0.1:
	And the time series:
	If you have many joints to coordinate (and you do, if you are a vertebrate), then one of the simplest ways would be to have each joint lagging slightly behind its neighbor:
	This creates a traveling wave of phase. If you look for any particular color (= particular phase), red for example, you’ll see it traveling downwards in the animation. A pattern like this can be seen in the legs of a crawling centipede, for example. Here is a traveling wave in the time series of six joints:
	The traveling waves of phase were especially studied in the swimming of undulating fish, especially in the lamprey, which is the most primitive genus of vertebrate in existence today. Swimming in the lamprey is one of the main models for understanding the role of the spinal cord in controlling movement. This animation shows a lamprey fish consisting of six segments (in realty a lamprey has about 100 vertebras) with a the angle between the joints changing in a traveling wave from the left (the “head”) to the right (the “tail”). Note how each phase (say, the red) travel on the body from head to tail. Notice also that the relative phase between the first and the last joints is one whole cycle. A one-cycle traveling wave is typically preserved in fish swimming over a large range of speeds.
	Perhaps you noticed that the last to animations feel “alive” although they were generated by a very simple computer algorithm. I personally suspect (although it might not be easy to prove) that traveling waves is the property that makes us feel some coordination patterns are “alive”.
				To be continuoed...