And that’s because it’s technically a fractal in formation; an infinitely similar pattern. Withal, one of Sierpiński’s well-known fractals (along with the Sierpiński gasket/recursive triangle and curve).
I'd say sirpensky carpet is a good wave proetction, since it blocks most of the wave for a long time and whatever gets out, does so from the borders which is generally safer
I thought it was interesting that the bottom-most border was where the wave snuck through, but the open channel just above it, which should be topologically identical in a continuous carpet was totally different. It looks like the wave reflections off the corners of the larger blocks interfere with propagation along the open channels.
I live on the gulf coast on a man made beach. To protect the coastline, a lot of places have “riprap” which is usually just discarded scrap concrete from demolition projects. I understand that’s pretty much what you’ve done, but it would be cool to simulate with randomly shaped geometric objects rather than a regular pattern or random pattern of similarly shaped ones
Gave me a way to look at wavebreak placement and rules for formal automata. When you take rules for particle combinations and state that there is a span of possible configurations or tilings, then you can think of an aggregate formation process as a wave transfer of energy. My cousin told me about something like this in French Nuc. Chemistry, inter-Z numbered atomic elements in mineralization processes, but that the findings were in the bin with Kevran's work. The simulation here could probably explain some of Kevran's results as De Broglie wave condensation.
Hi Nils, beautiful video as always. I recently learned that photosystems in plant chloroplasts are circular and rely on properties like a quantum walk for an incident photon to reach the reaction center at the center. Would you be able to model distributions of antenna complexes (which function as obstacles for the photon to reach the center), comparing distributions such as triangular/ golden mean/ poisson disc? I'd be fascinated to learn what simulations predict the optimum distribution would be (my guess is triangular), and whether biology follows that distribution.
Although there's an interesting trade-off between maximizing light collecting area (and thus distribution of antenna) and minimizing obstacles for an incident photon). Not sure how that could be modeled, but fascinating all the same!
That sounds interesting. Do you have any idea of what boundary conditions to put on the discs? Maybe some simulations in the playlist th-cam.com/play/PLAZp3rbgWLo2VvXUsaiRbw33x2qMKASdF.html already provide some information. Most of them use perfectly reflecting boundary conditions, but other use refracting obstacles, that let the wave go through, but at a lower speed.
could you add a very slight absorption to the baffles, that way the energy can be divided into 3 buckets - left, right, and 'absorbed' at the moment, things with a very long, but extremely reliable path would eventually leak all the energy through
I could try something like that. I have made simulations with refracting and dissipating obstacles for other geometries, see for instance th-cam.com/video/TUYFUbMwPWg/w-d-xo.html
Neat/surprising-to-me how the graphed energy appears to move on the graph outside of main region. I guess it makes sense that if the amount coming out was varying/oscillating over time, that the amount at each horizontal position outside of it would largely just move, assuming that the waves are approximately moving just outwards in those regions?
The energy should mainly just be transported outside the obstacles, yes. There is some effect of the boundaries, which reflect part of the energy (an unwanted effect due to the difficulty of coding absorbing boundary conditions). Round-off errors and discretization errors have an effect too.
Niles, I love your content! It is inspiring me to play with programming and math again. If you don't mind me asking, what is your education/profession? I assume the videos you share are related to your work?
Thanks! I have a degree in physics, then obtained a PhD on mathematical physics problems, and have not a faculty position in mathematics. My first research work was on mathematical billiards (the particle equivalent of the wave simulations). My current work has more to do with stochastic processes, and is not directly related to these simulations, though there are some common themes. There are some links with further info in my channel "about" page.
Would a waves be able to penetrate a true Sierpinski carpet with infinite depth? Obviously you couldn’t calculate an infinite carpet but its an interesting thought
I expect an infinite depth carpet would not let any waves through. The simulations are limited by the grid size, though, so it would be nice to have a mathematical analysis of that.
Is there a mechanism by which the total amount of energy in the system decreases? I mean, in a scenario with perfectly reflecting walls, the energy would only get sparce with time but not decrease. However, here it seems that it does decrease. Edit: reading the info, it seems that the left and right boundaries absorb some amount of energy.
They do, though it's rather an undesired effect of the numerical implementation. It is notoriously difficult to implement perfectly absorbing boundary conditions.
I haven't tried in with the energy plot yet, but there are several simulations with periodically arriving waves on this channel, the last one being th-cam.com/video/eIwX5Z6jf2s/w-d-xo.html
It shows a wave (sound or water) hitting a fractal, that could be sound insulation or a wave protection. The top plot shows the energy as a function of the x coordinate.
Hello. Nice work. Great absorption with the sierpinski pattern. Do you think to try somerhing like this with 3, 4, 5, 6 edge could also give good results?
The result seems to depend mainly on the width and straightness of open channels of water. So other obstacle shapes should work as well, as long as no large open channels are created. I may try that at some point.
It seems that one of the most important factors is how small the channels are. So moving obstacles around should not decrease the effectiveness, as long as no wide channels are opened.
Looks almost fractal in design. Super cool.
And that’s because it’s technically a fractal in formation; an infinitely similar pattern. Withal, one of Sierpiński’s well-known fractals (along with the Sierpiński gasket/recursive triangle and curve).
@@PhamThanhLoan311 well, it's part of a series of things that approach a fractal...
I'd say sirpensky carpet is a good wave proetction, since it blocks most of the wave for a long time and whatever gets out, does so from the borders which is generally safer
I thought it was interesting that the bottom-most border was where the wave snuck through, but the open channel just above it, which should be topologically identical in a continuous carpet was totally different. It looks like the wave reflections off the corners of the larger blocks interfere with propagation along the open channels.
It's called a mangrove forest.
This looks more efficient than the other
Definitely. All the energy hovers around -40 dB while the others are around -30 db or more.
I live on the gulf coast on a man made beach. To protect the coastline, a lot of places have “riprap” which is usually just discarded scrap concrete from demolition projects. I understand that’s pretty much what you’ve done, but it would be cool to simulate with randomly shaped geometric objects rather than a regular pattern or random pattern of similarly shaped ones
Random patterns indeed seem to be quite good at slowing down waves. See for instance here: th-cam.com/video/omXj8vH1WSo/w-d-xo.html
Gave me a way to look at wavebreak placement and rules for formal automata. When you take rules for particle combinations and state that there is a span of possible configurations or tilings, then you can think of an aggregate formation process as a wave transfer of energy. My cousin told me about something like this in French Nuc. Chemistry, inter-Z numbered atomic elements in mineralization processes, but that the findings were in the bin with Kevran's work. The simulation here could probably explain some of Kevran's results as De Broglie wave condensation.
Your videos are amazing 👍🏻
Thank you so much 😀
I love that you put the log scale as well, it really makes a diference
Thanks! It's more informative that way, indeed.
Hi Nils, beautiful video as always. I recently learned that photosystems in plant chloroplasts are circular and rely on properties like a quantum walk for an incident photon to reach the reaction center at the center. Would you be able to model distributions of antenna complexes (which function as obstacles for the photon to reach the center), comparing distributions such as triangular/ golden mean/ poisson disc? I'd be fascinated to learn what simulations predict the optimum distribution would be (my guess is triangular), and whether biology follows that distribution.
Although there's an interesting trade-off between maximizing light collecting area (and thus distribution of antenna) and minimizing obstacles for an incident photon). Not sure how that could be modeled, but fascinating all the same!
That sounds interesting. Do you have any idea of what boundary conditions to put on the discs? Maybe some simulations in the playlist th-cam.com/play/PLAZp3rbgWLo2VvXUsaiRbw33x2qMKASdF.html already provide some information. Most of them use perfectly reflecting boundary conditions, but other use refracting obstacles, that let the wave go through, but at a lower speed.
Fab !
That looks very effective. Probably because it works across many wavelengths?
Yes, the multi-scale properties of fractals seem to be important here.
could you add a very slight absorption to the baffles, that way the energy can be divided into 3 buckets - left, right, and 'absorbed' at the moment, things with a very long, but extremely reliable path would eventually leak all the energy through
I could try something like that. I have made simulations with refracting and dissipating obstacles for other geometries, see for instance th-cam.com/video/TUYFUbMwPWg/w-d-xo.html
i don’t know what any of this mean but give my brain some bright colours and nice sounds and it’ll be happy
Glad if that's what this video does... Sometimes math can be art!
i was sad the DONG at the beginning of the song didn't syncronize with hitting the carpet, but otherwise cool video!
Neat/surprising-to-me how the graphed energy appears to move on the graph outside of main region. I guess it makes sense that if the amount coming out was varying/oscillating over time, that the amount at each horizontal position outside of it would largely just move, assuming that the waves are approximately moving just outwards in those regions?
The energy should mainly just be transported outside the obstacles, yes. There is some effect of the boundaries, which reflect part of the energy (an unwanted effect due to the difficulty of coding absorbing boundary conditions). Round-off errors and discretization errors have an effect too.
Niles, I love your content! It is inspiring me to play with programming and math again. If you don't mind me asking, what is your education/profession? I assume the videos you share are related to your work?
Thanks! I have a degree in physics, then obtained a PhD on mathematical physics problems, and have not a faculty position in mathematics. My first research work was on mathematical billiards (the particle equivalent of the wave simulations). My current work has more to do with stochastic processes, and is not directly related to these simulations, though there are some common themes. There are some links with further info in my channel "about" page.
Would a waves be able to penetrate a true Sierpinski carpet with infinite depth? Obviously you couldn’t calculate an infinite carpet but its an interesting thought
I expect an infinite depth carpet would not let any waves through. The simulations are limited by the grid size, though, so it would be nice to have a mathematical analysis of that.
Is there a mechanism by which the total amount of energy in the system decreases? I mean, in a scenario with perfectly reflecting walls, the energy would only get sparce with time but not decrease. However, here it seems that it does decrease.
Edit: reading the info, it seems that the left and right boundaries absorb some amount of energy.
Yes, the energy can escape on the left and right boundaries.
@@NilsBerglund thanks for your answer. Do these boundaries reflect some percentage of the energy?
They do, though it's rather an undesired effect of the numerical implementation. It is notoriously difficult to implement perfectly absorbing boundary conditions.
What if you pump it periodically? That's a bit more like real waves on the ocean shore.
I haven't tried in with the energy plot yet, but there are several simulations with periodically arriving waves on this channel, the last one being th-cam.com/video/eIwX5Z6jf2s/w-d-xo.html
Wath is happening? I dont understand but seems amazing, please explian me if you can
It shows a wave (sound or water) hitting a fractal, that could be sound insulation or a wave protection. The top plot shows the energy as a function of the x coordinate.
Hello. Nice work. Great absorption with the sierpinski pattern. Do you think to try somerhing like this with 3, 4, 5, 6 edge could also give good results?
The result seems to depend mainly on the width and straightness of open channels of water. So other obstacle shapes should work as well, as long as no large open channels are created. I may try that at some point.
Why don't you test different tree braching wave protections?
I wonder about wave propagation in/across a labyrinth made of a Peano, Hilbert or Moore curve.
How does the overall positioning affect the result? Does moving the large square around change anything?
It seems that one of the most important factors is how small the channels are. So moving obstacles around should not decrease the effectiveness, as long as no wide channels are opened.