Probably a bit early to say, but it could be a VEI-5 compared to the VEI-6 of Pinatubo and Krakatoa.
Probably a bit early to say, but it could be a VEI-5 compared to the VEI-6 of Pinatubo and Krakatoa.
Thanks, people are postulating about a climate impact, so this would likely be less than either of those.Probably a bit early to say, but it could be a VEI-5 compared to the VEI-6 of Pinatubo and Krakatoa.
Great video! Since the patterns emerging are so much more interesting in 3D than in 2D, I wonder what the same rules would look like in 4D projected down to 3D. Even more interesting patterns, or just more chaos?
There seem to be certain patterns that repeat-- in physics, in nonhuman animals, and in humans. I remember reading about this, regarding group theory, comparing the way the cells that detect color in birds' eyes resemble the way bus drivers in Mexico coordinate their schedules. Humans instinctively pick the same patterns that Nature has already created. Also remember reading about how slime molds create structures that resemble human architecture (like the Tokyo subway system)-- or is it the other way around?On a different subject, lately I've gained a fascination for murmurations -- the organized swarming movement of many birds, which can look almost like a single giant organism:
Murmurations are most well known in starlings, but many other birds and animals do it, too, and it's an amazing and beautiful thing to witness. Today I caught an intense murmuration of dunlin from quite close, as a hawk buzzed through them trying to catch a meal: video
Here's a giant one of starlings featured in National Geographic: Flight of the Starlings: Watch This Eerie but Beautiful Phenomenon | Short Film
I, like many others watching these, often wondered, "how do birds orchestrate this?" Who calls out when and where to turn in such perfect unison? The incredible answer: they don't! It is an emergent phenomenon. Each bird is only really paying attention to a few (7 seems to be the magical number) of its nearest neighbors. And every bird has the same status in the flock, no one is in charge. It turns out murmuration behavior can be very well modeled by a simple set of rules ("Boids" algorithm). In no particular order:
Combine that with some interaction with boundaries, obstacles, or a predator, and you can get remarkably murmuration-like behavior on a computer: Youtube -- Coding Adventure: Boids
- Cohesion: each bird tries to fly toward the "center of mass" of other birds within some region. (long-range attraction)
- Separation: each bird tries not to get too close to or collide with neighbors. (short-range repulsion)
- Alignment: each bird tries to fly in the same direction and speed as nearest neighbors. (short-range alignment of velocity vectors)
Nature is awesome.
I love higher dimensional geometry! I have a screensaver that projects higher dimensions down to lower ones and it does create some fantastic effects when viewed from different angles.Great video! Since the patterns emerging are so much more interesting in 3D than in 2D, I wonder what the same rules would look like in 4D projected down to 3D. Even more interesting patterns, or just more chaos?
That would be fascinating to explore and discover. There is so much that is interesting about this algorithm's behavior. I did just finish writing up and testing a flocking code in 2D that I've been working on in my spare time, and in principle there's nothing hard about generalizing it to any number of dimensions. Maybe I'll try it eventually and see if I can learn anything interesting from it. The biggest challenge is probably the computational intensity when you move up a dimension, especially while also having enough boids to allow an interesting structure to exist at all. 3D is very doable but slower, while 4D might be a tedious crawl without optimizations.
Wat, I think you'll find this extremely interestingThat would be fascinating to explore and discover. There is so much that is interesting about this algorithm's behavior. I did just finish writing up and testing a flocking code in 2D that I've been working on in my spare time, and in principle there's nothing hard about generalizing it to any number of dimensions. Maybe I'll try it eventually and see if I can learn anything interesting from it. The biggest challenge is probably the computational intensity when you move up a dimension, especially while also having enough boids to allow an interesting structure to exist at all. 3D is very doable but slower, while 4D might be a tedious crawl without optimizations.
Example with the 2D algorithm and 200 boids. I set a soft boundary (dashed circle), near which boids will feel a force toward the center. (Maybe there is a pond or nesting ground at the center which they do not want to stray too far away from.) I like this a lot more than the usual hard and square or rectangle boundaries in most boid simulations, or even teleporting edges like in the asteroids game.
Yes, universality is a very cool concept. Like how a similar-looking structure appears in the cosmic web due to gravity, or neurons in brains, or above in boids simulations (briefly).Wat, I think you'll find this extremely interesting
https://www.quantamagazine.org/the-univ ... -20180823/
I would love to hear you in that course. You are a wonderful teacher. And I always loved these simple computational models that anyone that knows a little bit of Python can reproduce to convince itself. Share as much as you like because this is endlessly fascinating.
Awesome work! In 2D and 3D the flocks seem to merge, and if splitting, merge again fairly quickly, but it depends on size and shape of the enclosure, likely. In 4D space there appears to be less merging, which might be intuitive since there is more space and therefore less interaction. But is this a permanent feature, or do they eventually merge if you give them more time? The 4D simulation looks pretty similar to a 3D simulation with different kind of boids with an added rule that a boid ignores boids of a different kind. Transferred to flocks of birds it would like thrushes, robins and sparrows flock to their own kind only (but true 4D freedom would also mean that a flock of thrushes could decide to turn more into sparrows and join them). It makes me wonder whether 4D boids could actually exist in nature. Consider a kind of fish or mollusk capable of changing colour. Faced with a predator, they can flee in 3D, but they could also change their colour in order to make them less visible to the predator or to confuse it, and this colour change could also be coordinated in exactly the same way as the movement. There are boundaries of movement, and there are boundaries for how much the colour can change. Would we see more splitting, because the flock could have a hard time keeping the same colour?
Wow, when you mentioned chaotic, it reminded me of our weather patterns. We are currently on the brink of a historic snow storm which has been on and off the models all week and the reason for the inconsistency and vast differences between all the models has been explained with the idea that the pattern is so chaotic right now that minute changes upstream result in vastly different outcomes here. So for example if the ridge out West is off by a few miles we get a 2 inch snow "storm" instead of the 30 inch snowstorm now being predicted. The models were going back and forth between both scenarios all week and now it looks like they're finally locking in for the big snowstorm, now that we're within 24 hours of the event.Yes, universality is a very cool concept. Like how a similar-looking structure appears in the cosmic web due to gravity, or neurons in brains, or above in boids simulations (briefly).Wat, I think you'll find this extremely interesting
https://www.quantamagazine.org/the-univ ... -20180823/
My favorite examples of it are bifurcation diagrams such as the logistic map, which describe the way in which systems enter the chaotic regime. Consider for example a pendulum which experiences some drag while also regularly being pushed. If the drag is too strong then the pendulum barely moves, while if the push is too strong then it just swings around in a full circle endlessly. But for certain combinations of drag and push (and pushing frequency), the behavior is chaotic, in the strict mathematical sense of the term (a tiny change in the initial conditions leads to totally different behavior.) Visually it looks like a mess. It can swing around wildly and then stop, change direction, or seemingly hang still for a while before looping again, and the changes appear totally unpredictable.
If you were to slowly vary the pushing force and watch as the pendulum switches into the chaotic behavior, it's not at all obvious how it happens. If you were to plot its position over time, it would be difficult to tell anything useful. But there is structure there. The trick to seeing it is to look at its motion in phase space: position plotted against velocity, instead of position plotted against time. That could look something like this, where the pendulum's angular position is the horizontal axis and its angular velocity is the vertical axis:
(graphic snatched from Reddit via google search)
The pendulum shown in this plot is swinging chaotically. You can tell because the dots representing positions and velocities are all over the place, never retracing a specific path. The pendulum never repeats the same movement twice. However, the locations of the dots are not random. They tend to follow similar loops and trails in phase space, even if they don't retrace any path exactly. Some combinations of position and velocity also occur more often than others. Some never occur at all. The motion may be chaotic, but that doesn't mean it is random or can do anything.
If we take cross sections of this phase space diagram (that is, plot position at specific repeating time intervals), while varying the pushing force, then we can see how the pendulum swings undergo a series of period-doublings before switching to chaos. It looks a lot like the logistic map, and is also called a bifurcation diagram.
(this graphic is my own, made for a course in computational physics)
What does all of this have to do with universality? The structure in this figure isn't unique to pendulums. Almost any system that transitions from regular behavior to chaos will have something like it, with a series of these bifurcations (actually there are infinitely many, and they form a fractal). Even more crazy is that if you measure the ratio of distances between each bifurcation, you'll approach a number which is the same no matter what bifurcation diagram you apply it to. That number (actually two of them) are fundamental constants of nature. Feigenbaum constants.