Wednesday, May 13, 2009

More fun with Traveling Pulse

I started messing around today with the amorphous traveling pulse from yesterday. First thing I did was try creating an asymmetric starting condition by "pipetteing" in both a spot of "standing" as yesterday and also a spot of "tired" adjacent to that so that the pulse could travel only in one direction. As before, the x axis is cyclical space which is why the pulse travels off to the left and then reappears on the right.

Inexplicably, the pulse does not always travel at the same velocity. I have no idea why, maybe its an artifact of the integration but it seems periodic -- like its accelerating and decelerating at some predictable way.

I then start exploring parameter space of the circuit, repeated here for reference.

(Drawing revised 19 May)

I started with 3 vs 5. All things being equal, it should be the case that the concentration of gate 5 needs to be greater than the concentration of gate 3 so that it can overpower "standing" when "tired". As the following phase chart of 3 vs 5 illustrates, this is true. Also, as 3 grows so does the pulse width. This is intuitive because the harder p3 works to pull up "standing", the longer it will take for the discharge circuit to overpower it. Graph of P3 vs P5:

Then I started on P3 vs P4. P4 determines how fast it gets "tired" so more P4 should create a narrower pulse width, which is indeed the case. As you would expect, there's a limit, P4 can make the system tired so quickly that the pulse disappears (it becomes tired the instant it stands). However, there's a relationship between P3, the charging circuit and P4 the "getting tired" drive. As the standing driver is increased, you have to compensate with fast you become "tired". Makes sense. Ratios in the kind of 5-7 ball park seem to work well given the arbitrary other settings I have. Graph of P3 vs P4:

Crazy things happen when you change the two stabilizing gates p1 and p2. When pull down resistors are set to 0.01 and diffusion to 0.3 in this simulation. As p1 increases the pulse travels slower which makes sense as it is harder to charge standing. (Thanks to Xi for pointing out that I had previously stated this backwards.) At some critical value, it the charge circuit can't keep up with the diffusion and pull down sides and the pulse evaporates. Really weird things start happening around p1=0.01 and p2=0.07, looks like it becomes unstable and pattern forming, which is cool.

Some close ups of instability patterns. They look a like Sierpinski triangles which makes some vague sense because the standing and tired are in opposition to each other and can act as some kind of binary counter where diffusion permits the next space over to act as the carry bit. (I say this with while waving my hands furiously :-)

No comments: