some threshold i'll say if it kind of goes inside the zone uh we'll color our particle a different color and we'll say boom this has hit the corner at some point so what we have so far is a very simple simulation you know you have a particle a direction it bounces and if it hits a corner any four of them um it turns green which means let's now just generalize this thing let's spawn in a bunch of points and run the simulation and uh you know now we can see you know which ones turn green and we can launch this at uh randomly distributed points uh sparse points dense points it doesn't really matter but uh the key takeaway is you know we know which particles are eventually going to hit the corner so let's take that information and actually color our particles to begin with so we know which ones are going to hit before we even launch the simulation well what you're going to notice is that they kind of follow this geometric pattern no matter what direction we pick they they kind of come in these bands of lines um and if you think about it that makes sense because if a particle is going to collide right with the corner the one right before it that's going in the same direction that's trailing it of course is also gonna hit it so of course you get these geometric lines and that's gonna change depending on the direction even more interestingly again if we're running a simulation with only five or six collisions which is a big preface for this right i'm only doing five or six collisions right this might be different if it's infinite you're gonna notice that the denser our grid is like the more points that we're sampling you're gonna see in proportion uh this thing kind of like shrinks to zero in terms of what points actually end up hitting the corner so like the probability of picking a random point and it's gonna hit the corner under our conditions and five to six collisions uh it's approaching zero uh which i thought was also interesting but now since we set up the simulation why have one direction that we launched this and what if we have multiple directions like the ones on the left are going one direction the ones on the right uh well then our kind of grid of you know the ones we know that are gonna hit eventually within five or six things is gonna start looking more interesting and if we were to take our like direction and randomize the out of it right every point goes in a different direction based off some noise thing well one we get a very cool looking simulation but we also get this kind of band map in some sense so this is you can think of this as our solution map these are the points that are gonna eventually hit the corner within again five to six collisions and i don't know i just thought that was interesting that that's it hey everybody thank you for watching my exploration on the dvd corner thing i i got tired of the idea a day in to simulating it but whatever it's done now um and this exploration is sponsored by squarespace no not that one you doofus squarespace the service that lets you make websites if you're in the market for making a website and you don't want to code everything and you just want to basically use very good looking presets to begin with drag and drop my website URL_TOKEN was
START_SPONSOR_TOKEN um and this exploration is sponsored by squarespace no not that one you doofus squarespace the service that lets you make websites if you're in the market for making a website and you don't want to code everything and you just want to basically use very good looking presets to begin with drag and drop my website URL_TOKEN was END_SPONSOR_TOKEN