Can We Test if Cats are Chaotic?

In lieu of pictures, please tell me about your cat in great enough detail that I can visualize them in my head thank you (or dog or other pet, or if you don't have one (like me) I accept house plants) edit: I've been keeping up with all of these and love them all, if I happen to not respond to your comment please know I've read it and probably went 'awwweee' to it. Thank you :)

EDIT: I just realized I never stayed the delay I used for Helga's caterfly - it was about 35 time steps. Audacity says the recording is sampled at 44.1 kHz, so 1 time step is about 22 microseconds. However, A viewer made their own caterfly (!!) and it does look quite a bit different to the one shown in the video. For example, their caterfly does not have two clear lobes and the delay they used was very different as well (still looks awesome though imo). It very could be that it depends on the recording method and probably even the cat.

You Tube doesn't let me speak straightforwardly of certain parts of a cat's body when suggesting why purring might be chaotic, but besides breathing there might be circulation through arteries and veins, and swallowing of multiple liquids produced in the mouth and movement of various other things in the head and chest, and the occasional mew.

I learned a lot! Thanks!

Does one of those background cats have a Drawfee Bobby Hill face drawn on it? Because that's incredible. As is the whole video. As someone who finds Chaos Theory super interesting and found it through Biology and Environmental Science, and who also really likes cats, this really feels like it was made for me.

chaos theory is the study of things at the "human level" ???
Well I certainly was never taught it that way, or ever heard it descibed that way

Awesome video. You and physics for the birds are masters of this genre of videos. (im not sure what you would call the genre; intro to some physics or math concept with some relatable application?)

On a serious note, you have an incredible ability to take complex concepts and show their core in an almost painfully simple yet respectful way. Truly wonderful.

The only addition I would have considered would be showing how a non-chaotic signal performed on the same test

CHAOS CONTROL

This video is a nice way to start 2024.

So this is just how I made the data make sense to myself, but I think it's useful to remember how our data was obtained.

In physics, we think of the starting conditions in a system and see how small changes in the starting conditions are reflected in the outcome. Going back to the weather example, we interpret the chaos as meaning that small changes in starting horiztonal/vertical temperature and convection lead to big changes in the ending temperatures and convection.

We can also isolate these variables by only changing one factor at a time. From this, we might find that the system is not chaotic with respect to vertical temepraure, but is chaotic with respect to convection (just a hypothetical).

So, now taking that and going back to the purring example, what is being compared? Well, we are comparing the waveform of a cat pur to the waveform of a cat pur. So what do the starting conditions represent? They represent different starting amplitudes along the pur wave forns. Thus, the small changes in the starting conditions correspond to starting with slightly different amplitudes across the 4 waveforms (as represented by slightly different coordinates).

Finally, the big question, what does it mean for cat purring to be chaotic? It means that if you have a slightly different set of starting amplitudes between two coordinates, then you will have very different final amplitudes between the two coordinates. In other (more sensible) words, the amplitude pattern of each "pur cycle" (an in and out breath) differs somewhat from one cycle to the next. This means that the amplitude pattern for each consective "pur cycle" drifts significantly from the previous pur cycle to the next.

From this, what I think you have shown is that cat purs are irregular and, thus, unpredictable in their variations. I'm not sure whether this is an interesting result or not, mostly because we don't even know why cats pur in the first place, but i still find it intriguing regardless

P.s. amazing video by the way, your content is always top-notch and amazing

I wonder if there are examples where the stretch factor itself oscillates? Meaning the ball of points would stretch out and become chaotic as the system evolves but then re-converge into a tightly packed ball at some point in the future.

I am very grateful for the opportunity to watch your neat excellent work! It's disheartening how most of what's consumed nowadays is mediocre views-oriented garbage... your work, on the other hand, along with other great and resilient creators, is worthy of our time, attention and appreciation! So thank you very much. It's always inspiring to see someone putting in the hard work! 🎉❤

All detailed measurements are chaotic to a certain degree, it's a logical consequence of having multiple resulting states (frequencies) that can be produced. On the scale of a cat's purr, saying it's chaotic would mean that, if given the initial conditions and a function of the cat's purr, the results would differ more as time progresses for different initial conditions. In short, a chaotic system is a deterministic system (we can tell what it's possible states are) that is sensitive to changes in initial conditions. A good entry example would be what we call the logistic map

Thank you for the immense quality of this video's production!

Hi David, first of all great video! I would love if you or someone would help me solve a doubt. I knew this chaos theory approach was for deterministic systems (is it?). Can we otherwise consider the cat purr as the result of a stochastic process with big dispertion? If so, is there a way for us to understand if the deterministic part of the problem is chaotic or if the stretch is caused by the random part?
Loved those cat video breaks

oh no, is that a sonic reference?

We have a English Lab. However in lieu of time (i'm sitting at a stoplight while typing this) here is quick description: Undercooked corn dog with legs.

I just wanna say I really appreciate you mentioning the importance of interdisciplinary work. I'm kind of a generalist although I'm mostly focused on art/graphics and programming and it's just nice having someone else appreciate this kind of work where most employers only see that I do both and automatically assume I'm worse at both than most others. Even though understanding the whole process of how graphics are made to how they are ultimately displayed and animated on your screen has helped me both to figure out graphical errors when programming as well as helping me understand my tools to create graphics way better than I would've otherwise

Human breathing patterns at night are also chaotic..

I wanna gatekeep this channel

My quest log has been updated: Create an app that gives you a visual of how chaotic a sound is.

I've dedicated a part of my life to chaos as how it relates to sound, and the reason I am dedicated is because I believe chaotic sounds are objectively more pleasing than non-chaotic sounds... for certain genres of music anyway. Synthwave is an example of using very little to no chaotic sounds. I don't know of a music genre that focuses on chaotic sounds but Dubstep gets close. Objectively bad vs good dubstep may come down to majority non-chaotic vs chaotic sounds. Edit: And the reason for this is because our ears like organic sounds... which are usually chaotic. Hence why car enthusiasts like a good roaring car engine (which I hypothesize is a chaotic sound). Edit2: One of my goals in life is to invent a music genre that focuses on chaotic sounds. I'm in the process of programming the synthesizer for that.

Using my knowledge of sound synthesis, I assume that most organic sounds are chaotic because we cannot move our vocal chords like we move our arm, precise and intentional. Vocal chords require to be vibrated and the system is self-stimulating as well in order to create vibration patterns. It is a complex resonance systems where stimulation feeds back into itself. Edit: I'm going to also guess that a car engine is an example of a mechanical chaotic sound because of the self-interacting systems involved. If I'm right, I would also guess that you can hear chaos if you are familiar with its qualities. Edit2: I will also guess that most involuntary movements caused by brain disease such as hand tremors, the movement is also chaotic instead of random.

To try to answer your question, if the cats purr is indeed chaotic then it probably could be interpreted that when cats purr their respiratory rate varies in a mostly unpredictable way as well as any other variable affecting it (purr pitch frequency, maybe even blood pressure)

The difference between cats that can purr and cats that can roar is the hyoid bone: if the bone is rigid then it can vibrate, aka purr, but if the bone is more flexible then it cannot reach an optimal resonance for a "true" purr... but research is still being done on specifics

so the butterfly effect was just a proverb in some sense. like a drawn picture in a stretch? amazing

is it fair to think about chaotic-ness in terms of crystaline vs. amorphous? as in, cat purrs being temporally non-crystalline, not quite temporally (instead of spatially) regular and repeating, so to speak. in that sense though, wouldn’t most natural processes be chaotic/amorphous, when viewed from a large enough spatial or temporal frame of reference?

> The reason I've analyzed only one cat is because it is really hard to get long, clean recordings of cat purring.

Can attest! I made many attempts to record my cat over the years, and she always finds time to move, to sniff the phone with which I record, to breathe into the mic and so on. It’s really hard to find where to hold the phone relative to the cat and if maybe I should just place the phone right on the cat’s body. This would filter out higher partials in the sound but maybe would capture the overal shape more faithfully, IDK. Cats are alive.

I am going to be conducting some in-depth research on whether or not breasts are chaotic...

I don’t know what I’m talking about but it seems to me that if the two lobes are inhale and exhale purrs then the crossed up area in the middle is the silence at the top of an inhale or the bottom of an exhale. If you sample the audio at this point you would have no way of knowing if you were moving from inhale to exhale or vice versa without knowing where you were before.

2 things, a few minutes into the video we've seen a few ways to visualize a cat's purr, but we haven't heard any cat purr in the video yet.
Also you're good at explaining things to yourself that you already understand, not going in-depth for those who don't learn by "this is what it looks like, now let's move on"

This video is so effective at explaining chaos theory that I'm gonna go learn how to read sheet music for guitar instead of tablature.

The only things I truly understood from this video were the “Shadow Clone Manifold” and “Shadow the Manifold”. Quite the man of culture you are.

Isn’t it 5D? Given that the 4D is time?

Yo where'd you make this? Great video!

Great video again!

Amazingly animated, well done! :)

For what it is worth, its been said that purring strengthens the cats bones... 💀

How long did it take you to find the research paper on finding the 'stretch factor'? I've always wondered how people find research papers and how long it takes.

As someone who is studying Data Science with Computer Science this is a really great video, it just shows how science and math can be really fun. Sometimes the best experiment/study are the ones where you expect a certain outcome and then get the complete opposite. Please keep making videos!

House 420 had a green roof

Honestly time delay coordinates makes sense, it finds the chaos by showing that the variance in frequencies across time also has variance