as i was saying..

it has been a moment or two..
alright:

news at work

work on the circuit has slowed for the moment, until we build the mechanism which will allow us to couple multiple circuits together. right now, there is a setup which allows the circuits to be coupled "uni-directionally", where one circuit influences the behavior of another, but not vice versa. this generally synchronizes the behaviors of the circuits. in this setup, the primary circuit is called a "master", while the circuit being synchronized by it is called the "slave". this is an awkward yet standard terminology. we will use it here, as you will see.

with this uni-directional synchronizing setup, all behavior is dictated by the master, whether it is periodic or chaotic. all that can be built is a system of circuits that are all controlled by, and thus exhibit, the behavior of the master. this is true except for in the case where they make a loop, so that the master ends up influencing itself through a chain of slaves... in which case the synchronization becomes unstable (more on this later). the point is, i intuit that studying a (loopfree) uni-directionally synchronized system will not be much more interesting (from our perspective) than studying a single circuit. so i will attempt to pursue a "bi-directional" coupling scheme, as i have previously mentioned. i have ordered the remaining necessary electronic components, and they should arrive within a few days.

of course, until then, there are a few things to look into. for instance, my intuition that the master slave setup is not so rich. there are some questions that did strike me about such a system, mostly regarding the degree to which the slave is, well, enslaved by the master. each circuit has parameters that we can change. for different parameter values, the circuits behave differently. what happens if one changes the slave's parameters while it was being driven by a master? can the slave overcome the influence, and revolt? if so, what effect might the revolt have on the master, if any?
-first, i observed which values of the slave's parameters corresponded to its different behaviors when it is not being influenced by a master.
-then, i turned on the master, and allowed the connected the synchronization, and synchronized the slave to the master.
-i then changed the slave's parameters and looked for any indication of a change in its behavior.

there was none.
there was also no change in the master's behavior.
(this second fact turned out to be trivial, since the synchronization circuit has a diode in it. a diode allows current to flow one way, and not the other. so, the setup does not allow any influence to travel backwards from the slave to the master. )

but, i found one thing curious. the place where the master signal comes into the slave is the same place where we were measuring the slave. this is a problem because, in effect, we are just remeasuring the master. the measurements were being taken to close to the source of influence, and they were not a fair representation of the effect of the influence. (it was actually fine, since we were measuring the slave at other points as well). this is just a fairly trivial issue of methodology, and experimental/measurement design... and would normally not be mentionworthy, other than as an account of a sort of "aha! slight/potential folly!"... but it immediately struck me as beautifully analogous to instances of media acquiring bias by measuring at the cause of a situation, as opposed to measuring at the effect.
easy examples are fluttering around us daily... especially vivid are the "scientific" claims released by bp, formerly "brittish petroleum", about the effects of the oil and dispersant in the gulf. in fact, the u.s. federal government and bp (the two conductors of this spill) have demonstrated that they are the least reliable sources of information about the event itself...
sorry.. that may have been a long walk to a not so compelling well... but i find myself trying to forge a general perspective on what a "power system" might just be, in the most general terms, and i keep thinking that systems of governance and perpetuation can generally be systems which contain components that have or produce a resource for the system, and also dynamically allocate that resource to parts of the system. this allocation requires very specific organization in order to be effective and efficient. pathologies vary as the systems do. in power systems, the generator (allocator) is completely devoted to serving its "constituents", although in the event of a constituent component malfunctioning, or becoming damaged, the generator can "shed" that load (disconnect from that component). the system reconfigures, re-routing power around the malfunctioning part. in social governance, the government (allocator) is faced with an everchanging multiscale system to which it supplies (for instance) federal funding. this is quite different from the power system, where the loads do not necessarily change, though their needs change. for social allocators (gov.), there is a vast and fast evolving ecosystems of interdependent entities, all with different motivations, and histories.. all asking for a piece of the federal resource. in the power system, the loads have relationships with each other as well, and they compete at times...but generally it is known before hand which loads have priority (vital loads) over others.
the situation with the social system is interesting, since humans can play multiple roles at different stages of their lives, and are capable of discovering clever indirect ways to create benefit for themselves.
so, for instance, suppose a policy maker (resource allocator) is in a position to influence the benefit of some entity,.. let us say a corporation. if that corporation is able to influence the policy maker's decision (by allocating private resources to say.. an election campaign), then the entity is effectively controlling the allocation it receives, and creating a feedback loop.. whereby one of the components that the allocator is influencing is, itself, influencing the allocator. well... we know that when this happens to coupled chua circuits.. the order (synchronization) throughout the system becomes unstable (in that system, the resource being allocated is really just behavior. that is what is coming from the master to the slave.. information in the form of behavior...being provided and distributed by the master to all the slaves). [addendum: in the chua system, we thought of instability as arising when the master circuit gained an avenue to influence itself through the slaves. in the governance scenario, we speak of it more as the component gaining an avenue to influence itself through the master. it turns out that these are one in the same.] so, what is there to see in the general picture from all of this...well... that is not clear yet.
when a new feedback loop emerges in an evolving dynamical system, the stability should be expected to change.. since the system has essentially gained new influence over an aspect of itself.. for instance, an oven gaining a heat-controlled knob, or workers gaining control over production... or some other such scenario where a system becomes dependent on itself or its environment in a new way. such a thing could be as simple and treacherous as the arrival of a positive/negative feedback loop, sending some aspect of the system off in one direction...

of course, speculations like those above are (hopefully) excusably nebulous, as the nature of such thought is relatively new...
alright.. i will relent for the moment, and leave you with a visual reward for reading so far..

below are two bifurcation diagrams from the circuit here.
essentially, what you are seeing is the over all behavior of the voltage at a point in the circuit as a parameter changes (left to right). in the beginning (far left), the voltage stays constant, and as the parameter increases (moving rightward) the single voltage splits into two which the voltage alternates between. the behavior is periodic (repeating), and as the parameter changes further, the oscillations become larger (alternating between points which are moving away from each other). this is the first pitchfork looking split, opening to the right. then, as the parameter increases further, the oscillations bifurcate (as in the july 7 and the june 22 entry), alternating between four values, as marked by the secondary pitchfork looking openings. further increase leads to more bifurcations, but increasingly quickly, so that we do not actually see them as clearly as the first two.. . leading eventually briefly into chaos (the fuzzy end of the structure in the top left corner of figure 1). as the parameter continues to increase, the dynamics drop back into being periodic, alternating between two values, as seen by the lower pitchfork, to the right of the upper one. more bifurcations are seen..(still going left to right) and another transition into chaos. these dynamics are the same as in the video in the previous entry... this is just a compact way of keeping track of the specific structure of the bifurcation. figure 2 is an visually explained version of what was just stated above. figure 3 is a bifurcation diagram acquired while the parameter was being changed by the pc 104 microcontroller. it turned out that the way that it changes the parameter was very far from "continuously", and so did not make the best bifurcation diagram. on the other hand, figure 1 was made while i adjusted the parameter by hand, as closely as possible to "continuously". i was literally turning the knob with my hand, trying to turn as consistently and continuously as possible. it took quite a few tries to get a good one.. but we got one.

figure 1 (click on these figures to see them larger)


figure 2 (parameter increases from left to right)

figure 3. bifurcation diagram with less control (pc 104)

two videos and some drawings(?)

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!!!!!!!!!!!

oh yea! mike built a sword-bot!

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.

a compendium!

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..

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.

CHAOSaudio by a philadelphia experiment


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

a quick one

today will be visual-

most days, on the train, i am reading steven strogatz' text on nonlinear dynamics and chaos, conspicuously titled as such. it is a thumping good read (a phrase i picked up from saikat biswas).


there are many murals in philadelphia. this might be my favorite so far-

this is a stochastic fractal that jeffsteward and i fumbled out..
i will write more about this later. . but for now.. here is number 4.

here dumped here..
some ramblings for the sake of converging on a useful perspective..
i have found (in a large way) that if i am having trouble grasping something, or if something that i see in nature does not fit with my intuition of nature,
if i just start talking to someone about it... usually my ramblings will come across some perspective that is useful.
it is the same effect that writing has. by talking, i force my implicit ideas to be turned into explicit ideas. through this process, the things which you thought languagelessly about have to be accounted for. when this happens, a lot of structures which may have been overlooked, or misinterpreted (in their vague implicit forms) are forced to become explicit, well-formed, and uttered..

so.. i seem to achieve the same effect when i talk to myself. i ask myself all relevant questions which occur to me in real-time.. and so on.
so, here is some auto-discussion towards resolving my issues in the previous post, pertaining to the seeming information loss when using time delay embedding with the chaotic circuit data.
i think i may have resolved more or less how this might be happening, but i will have to take further data to find out..
the ramble is 12:00 or so.. since i meant it just for myself.
otherwise, i try to keep them kind of short..

scrollPopulation by a philadelphia experiment