here is a quick overview of our experimental set up as of today. we are taking some particular data in order to create a bifurcation diagram of the circuit (more later). experimental bifurcation diagrams are tricky.. but i think that i have a scheme in the works...
this is a video of our circuit bifurcating! wait for about 13 seconds.. then the system will begin its migration from periodic through a bunch of bifurcations into chaos (whenever it looks less like a couple of loops, and more "smeary", that is the chaotic regime. it happens a few times..)
hopefully, this will all be worked out soon, and we may move on to making a network of bi-directionally coupled circuits, that is to say, a group of circuits, each of which are capable of chaos, where some are connected in such a way that they influence each other.. odd stuff happens.. as one might imagine.
UNRELATEDLY, or not.. here are a series of tiny drawings that i have done.. unconsciously. that is to say.. my movements which create the drawings are unpremeditated, and no thought goes into the drawings. simply, each movement is a thoughtless reaction to the last motion... here is an older video of the movements, just to give you an idea.. i work much smaller now.. as you will see in the photos below
drawrings! two legged creature with organs(?) i, blind, sculpt with sword a room with one wall and floor they are small.. unexpectant dancer i am not sure why this blog does this, but it often insists on loading my photos 90 degrees off from how i have them as files.. however. i originally drew the directly above and directly below drawing oriented 90 degrees counterclockwise..
i have meant to draw one page every day.... but i have only drawn three pages so far...
-HEAT WAVE!! apparently, there is a heat wave here in philly.. and yes, it is hot, but .. as far as i knew.. that is what happens in summer. but fret not.. GOLDEN WATERMELON TO THE RESCUE!!! thanks mom!!!!!!!!!!!
i nearly forgot! a grad student that works in our lab (his name is mike) built this robot last week, and has been putting variations on it since. here is a video from its early days
here is its samurai phase
i notice now that i look back at this video (especially the first one), that it tends to pull to the right.. that might be fixed now, though.
they have these trees here that shed bark pieces which are rather have smooth boundaries and non trivial fundamental groups, er.. i mean, they have holes in them. and as you can tell by looking at the surface of the piece that peeled off.. this happens in layers, iteratively, as more exterior tree turns to bark, and peels..
there are some that are similar, but they shred like paper, instead of peeling so neatly.. i will try to get a photo of those kids too..
-soul veg.
a brief excursion to DC led us looking around the place for the Soul Vegetarian restaurant, which is the world's largest vegan restaurant chain. the restaurants are run by the african hebrew isrealites. they are vegan not because of their spiritual values, but simply because it is the simple honest way to treat your body well. their motto in tallahassee is-
"your health is your wealth!".
they are an interesting 'culture' (their phrase), who essentially emerged following the torah (the old testament), or perhaps the follow the full tanakh (hebrew bible).. i am not sure now that i think of it. but anyway, they follow it in a fairly broad manner, and claim a heritage as follows:
"As a direct result of their disobedience to the laws and commandments of God, the ancient Hebrew Israelites were held captive by various nations including the Egyptians, Assyrians and Babylonians. In 70 C.E. the remnants of The African Hebrew Israelites were driven from Jerusalem by the Romans into different parts of the world, including Africa. Many Hebrew Israelites migrated to West Africa where they, once again, were carried away captive - this time by Europeans on slave ships - to the Americas along with other African tribes people."
In 1966 our spiritual leader, Ben Ammi, had a vision that it was time for the Children of Israel who remained in America (the land of their captivity) to return to the Holy Land (the land of their origin).
there is a soul veg restaruant in tallahassee where juliet used to work (she is one of the few nonafrican hebrew isrealites to work there, if not the only). juliet and i have been to the one in atlanta (one of them, anyway..). we went looking for this one in DC, and when we finally found it, it was long closed up.. so, we stopped at an organic grocer a block or two north of there. they boasted vegan foods on their advertising window painting.. so, intriguedly, we walked over to it. when we looked inside, the place was large, and completely empty.. . and then though i expected it to be locked, the front door was open. after walking in, we could see all the way to the back, there was a room, with lights on, and what looked like food laid out in a case. sure enough, it was soul veg, in guerrilla restaurant mode. they had a wonderful selection, and were super-generous.. even giving us the gift of some free vegan steak (bbq sauce and seitan), which i was not very enthusiastic about eating (i am trying to keep away from highly processed foodlike objects), though i was enthusiastic about their graciousness..! thanks DC soul veg!
right so.. as we were driving away.. i snapped this photo of the side of a building where someone had drawn this:
-more DC the photo below was my view in DC, waiting for my bus.. bothering the shit out of some people working the fancy restaurant inside. the place was pretty empty, and i came in, asking if it would be possible to get some coffee, and sit outside. the hostess personess acted as though i had asked her to co-sign a loan. then she asked a guy who was SUPER-watching the world cup game at the time if it would be alright... he answered, perhaps one word per second. he then commenced to apologize, asking me to wait for a bit (which i was of course very glad to), while he (i think) tried to pause the game on a tivo like contraption. this failed, and so he hurriedly made me a little pot of coffee.. and resumed his game watching. i sat outside and worked a little (trying to figure out what a variant of the chaos game was doing (more on this later)). it was lovely. then, upon reentering to pay.. they just told me it was alright.. that i could just go. it felt just like this time when i was young. it was after dinner, and i was taking my plate into the kitchen, when i dropped it, and it broke. i immediately felt horrible.. and fully expected to be punished. my parents were quick to say that it was fine, do not feel bad, that i could just go on, and play in my room.. that they would take care of it. it was such an awkward instance of feeling unjustly like i was going unpunished for a burdensome trespass against another.. this is how much the kids in fancy hotels in DC love this soccer game.. (different hotel). i seem to be scowling.. but i think the facial expression is incidental..
Friday, July 2, 2010
there is a lot that is getting going in the lab..
-earlier issues about not being able to recreate the attractor from the time delay embedding;RESOLVED: the issue was that the system was being under sampled. so for instance, the data that i showed in a previous post (post 4) was under sampled.
here is one second of the data from the system measured on august 16 with a resolution of 1khz (1000 measurements per second)
figure 1
here is one second of the same system measured later, at 10khz (10,000 measurements per second).
figure 2
there is clearly a large difference. let us look closer at the later(high resolution) data-
figure 3
this is the chaotic behavior of the system. with this data, i am able to reconstruct the attractor of the system (via time delay embedding) using only one measurement (x) , instead of two (x and y). FINALLY! not only that, but, since i can create as many time delay variables as i want, i can embed the data in arbitrarily high dimensions. for instance, if someone wanted to plot the attractor in three dimesions without time delay embedding (or some other equivalent trick), they would have to setup a whole new measurement on the system. with time delay embedding i just have to construct a new time delay variable. for instance, from the two-dimensional embedding x(n), x(n+t), i could go further into three-dimensions by introducing x(n+2t). so, here is a successful three-dimensional reconstruction from time delay embedding.
figure 4
i wish i could post it such that you could rotate the thing in 3-D.. it would be nice.. but that (though possible) would likely take a while. i can rotate it in 3-D.. and it is really cool..
[what is funny is that, if you plot under-sampled points from output x and y (as seen in post 4, figure 6) you can still recreate the attractor. this is because the two variables x and y stay correlated over time, and so, no matter when you sample them, the pair of their values will lie on the attractor. however, if you take the variable x, and plot it against a time delayed copy of itself (see post 4), then the sampling has an enormous impact on the relationship between the variables (since they are time dependent constructs). so, the absence of structure in post 4, fig. 8 results from the system being under sampled, and the measurements being so far apart is equivalent to improperly choosing the time delay really really big.. this causes the variable x(n) and x(n+t) to become uncorrelated, so that the time delay reconstruction gives no information..
the fact that the attractor was still being recovered even though the dynamics were not being sampled well was initially how i convinced myself that there was not a sampling problem. ]
the photo below is alex tozzo, a colleague here. he is awesome. he sort of makes sure that everything that we need is in place and working. though he is a mechanical engineer, he is one of the resident chaotic circuit caretakers... here he is, toiling in the gumption trap that is a nonlinear thing which is not doing what you want it to do.. (the lens cover of my camera does not open by itself all the way.. and it has to be opened with the fingers. i sometimes forget.. )
figure 5
a week or so ago, we received two high school interns in the lab. gabe and chirag. chirag has become interested in the chaos work that we are doing, and so he will be jumping into the project with us. he is quite virtuosic with computers.. below is a photo of a few labpersons (left to right: chin, frank, chirag, alex). chin bet frank lunch that chirag could not get the data acquisition scheme working...
figure 6
here he is below, having just worked out the data acquisition scheme .. now we can take data from multiple sources, at more than sufficient resolutions, for very long durations. CHOICE!
figure 7
this following audio is from the chaotic circuit itself. alex and company rigged the audio output last year sometime while using synchronized chaotic circuits to mask (kind of encrypt) an audio signal.. enjoy.. i think that alex's phone rang (silently) right at second 15 or so.. .which is when the frequency moves a little higher.. and maintains consistently higher.
this is just the first audio interpretation of chaos (hopefully). chirag has written some code that takes text musical notation and converts them to midi outputs.. so now, all i have to do is alter some of my code so that i can take chaotic sequences, and convert them to text denoting musical notes with duration, and then together, we will make chaotic music.. more to come
