This comment was a delight to read. I'm glad its made you see the beauty in mathematics :)

The problem is school and school teachers. School is there to make people into unquestioning factory line workers. Don't expect to learn anything of value there.

Thanks for your comment. I must confess I've never heard of a radon transform before. I'll look into it.

Or maybe an inverse Radon transform, since the image is known and it is the "projections" (string) that is sought?

​​@@virtually_passedYep, the first thing I thought of is that this is a great visualization of how (cone beam) CT works! It would be cool to see with a semi-translucent thread and back light. You could expand to CMYK coloured threads as well :) others have pointed out using the SVD. I'd point you to a classic computer vision paper called EigenFaces, which might be another technique for finding the weights on your basis vectors

@@Bob94390 Yeah, that would be more accurate. Of course, as everyone is saying, the way one does a (inverse) radon transform in practice is through the FT. And even then one rarely does an exact radon transform because it typically creates artifacts. So (my understanding, I am by no means an expert) is that at the end of the day the radon transform is just a model and in reality one is just manipulating FTs.

are we talking about the polar formatting algorithm here? Also, would applying the projection slice theorem help? I suppose projection slice theorem can be problematic since the string here is of uniform density.

That's exactly what I was wondering. Thanks for this comment! Congratulations to the author for this amazing video and all of his brilliant ideas, +1 sub, hoping to see the next video about fft algorithm :)

The machine looks pretty simple actually. One servo motor to rotate the turntable and another one to hold the string inside or outside the nails

@@thewhitefalcon8539 yeah, and then you just code it in such a way that you never have to go over halfway around the circle in one direction on a single sweep so then you don't have to worry about keeping tension on the string while the length is contracting. I didn't realize this when I wrote my original comment, though

@@slightlyenlightenedlayman Even if you did, you'd have the string spool on some kind of springy rotating mechanism like what winds up a clock

I think FFT works here because the matrix is circulant - it's like with polynomials

Awesome. I know so many analyst/programmer-turned-artists! I think once you gain the power to be so creative, some people just can't stop creating!

Thanks!

Always starts from small amount of viewer

We're at 19k!!!

In fact, people tend to choose watching someone shaking their butt rather than watching math.

​​​@@lost.in.maze.official Uh, 3blue1brown is a example of the contrary. Grant gets millions of views on nearly every video they make, even on very obscure topics. Granted, (heh) they're an outlier, but still. Also, it might just be that string art is too obscure of a topic and the mathematics of such a thing are not immediately attention-grabbing. The thumbnail might also be to blame. It's very muted and gray, so it doesn't stand out among other thumbnails.

@@nikkiofthevalley He's not wrong. People'd rather watch others do stupid stuff or entertainment. It's obvious when you look at the most popular people on the platform.

Thanks :)

Glad you liked it!

Glad you think so!

:)

Glad you enjoyed it!

Thank you 🙌

Welcome!

With all due respect, that's honestly a pretty unfair ask. While I know it's not how you intended it (I agree that it would be FUN to recreate this at home), but from an engineer's perspective it feels like you're asking for someone to give away for FREE the product that they worked so hard to conceptualize, design, prototype, code, troubleshoot, refine, and present. If it is someone's intention to do all of this work for it to be freely available, that is a decision that they have made on their own, and have somehow justified, and that's fine; but to REQUEST that they give it away comes off as lazy and entitled, and implies that their expertise and effort has no value. There is more than enough information presented here for someone like yourself who is interested in making such a device to find tutorials and explanations that are already available for individual aspects of the project. By taking this route, you will truly learn by doing, but in the process learn far more and be more capable of creating your own UNIQUE product in the future!

@@jhboulder hmmmm... I also wonder how much of this project has been built on others' open source work? Seems to me that the monetization of that knowledge would be fairly disrespectful to those who believed that knowledge should be openly shared. But that's just my opinion and you by no means have to feel the same. I simply feel like if someone has learned for free, they have a duty to provide their own knowledge to the world the same way. I'm almost done my first project and am excited to share the model freely. I hope you stumble upon it and enjoy!

@@nadimfetaih3841 there's a lot to unpack in that statement. "Open Source" seems to be a more complicated concept than I gave it credit for in the past. Speaking to the comment of 'monetization of knowledge that was gained for free', there are TONS of companies out there that are making money off of products or services that use pieces of Open Source projects, but because their end product is clearly distinguishable from other's finished products, it is generally considered acceptable for them to make money from these products and services. Major software companies are notorious for this, especially Google, Microsoft, Apple, and other similarly large software companies (not to imply that I think that these are the pinnacle of ethical business practices). Quite often, the bulk of the code that is used is just a copy-and-paste of snippets of code from somewhere else that they know already works, so they simply adapt it to their needs. As for the 'they have a duty to provide their own knowledge to the world' again speaks to our current cultural state of entitlement. We have come to expect that if someone else got something free, we should get it for free too. While I can understand where this feeling comes from, I still have trouble completely getting behind the thought that receiving something for free implies that you now have an OBLIGATION to pass it on for free. However, I CAN completely agree with that statement if it's changed ever so slightly to: "if someone has learned for free, they SHOULD CONSIDER PROVIDING their own knowledge to the world the same way." Everyone's situation is different, and there can be very valid reasons to not simply distribute it freely, anything from 'easy access to this could be harmful to society' to 'rent is due, so I need to make money off of my efforts to provide for my family' and a million different reasons. Thanks for respectfully sharing your opinion, and I hope that your maker journey is a successful one!

@@jhboulder Some people actually like to give away their work. Asking costs nothing. It's a binary answer. Being asked doesn't mean you have to say yes. Buying something is lazy and entitled. Making something from someone's designs takes time and effort and is very educational. Sharing enriches everyone. The opposite of sharing is just sad.

@@jhboulder You suggesting that them asking an innocent question is unfair is pretty unfair. I have no respect for the way you answered or your expressed opinions, their question is not freeloading and does not imply that the OP's work has no value. In fact asking for a way to interact further with an authors work does the opposite, it expresses that the work has value.

Glad you enjoyed it!

It's on the list :)

:)

Thank you!

Thank you!! 😁

Personally as a (when I was) teenager 50% homework+ 20% semester exam got me a 70, C-. I had one teacher I liked. Although my math instructor was cool too. I didn't hate math but I never studied. It was only until I was 25 I took an IQ exam that my spacial relations was above 95%. I can see mechanisms in my head, and did study computer aided drafting.No one took the time to find out my strengths. I realize now that I cannot see numbers horizontally but I can see them vertically(in my mind). It weird try it with your kids. Converting maths into visual representations is impactful to comprehend meaning. Reading set theory for myself made the foundations of calculus relatable. I am dyslexic so could be that too. Also, contextual kinetic imagery. Just thinking about what the surface of a material feels like from memory can help with visualizations. Like if you could reach out and grab something and shape it, like a piece of clay. It helps control your concentration. I study math now on and off, but I realize that my imagination is restricted by not understanding certain aspects of mathematics. Hope your kids don't drive you nuts good luck. Thank you for being a teacher for slackers.

More to come!

Oh wow, may I ask what method you used?

@@virtually_passed Instead of looking at all of the pixels that the line intersected or looking at the local neighborhood I just, hmmm actually it's been a while let me look at my code, ok I just looked at the one with the closest center for each in a rough line. So what I did was for slopes less than 1 I used an equation for a line solved for y and rounded, then for slopes greater than 1 I wrote the equation the other way around solved for x and rounded. Then I took the total darkness of all of the pixels along the potential lines and found the one that was darkest, then I subtracted some from the pixels along that line to produce a new image. It may have been a bass ackward way of doing it though, I'm certainly not saying I did it "right" or "well" or "competently" but it did end up working with a little tuning. Also the machine you showed looks super cool.

Glad you like it!

Thanks!

Thanks! I plan to make a lot more of those

Glad you liked it!

Yes you can! Although I'd recommend CMYK instead of RGB

You could even add a white string that could 'cancel out' a line of color at a certain interval, like, at the very end, or in between certain colors. I wonder if this would show up graphically.

Maybe also use the Bayer filter to mosaic the colours and reduce the number of strings used.

Glad it was helpful!

Thanks!

Yay, thank you!

Oh and did you build the machine yourself? Would love to see a video about the machine itself!

Glad you enjoyed it! Next one is almost done

Glad you like it!

Thanks