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blockspins's profile
bgc
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@blockspins

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bgc

@blockspins

readin and writin

Joined January 2010

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    bgc‏ @blockspins 27 Jan 2019
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    bgc Retweeted Michael Fogleman

    These beautiful images are related to a famous number theory problem that goes back to Gauss: the question of counting the number of lattice points inside a circle of a given radius r. Let's start the thread 👇 with an acoustic reinterpretation: 1/nhttps://twitter.com/FogleBird/status/1089322537236996097 …

    bgc added,

    Michael Fogleman @FogleBird
    Each pattern is similar to the one before it. pic.twitter.com/4Fqa5X6nVY
    Show this thread
    1:16 AM - 27 Jan 2019
    • 1 Retweet
    • 7 Likes
    • Eliot Gro-Tsen AthanasiosAnastasiou Andé Jon E. Amit Patel Michael Fogleman
    1 reply 1 retweet 7 likes
      1. New conversation
      2. bgc‏ @blockspins 27 Jan 2019
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        Suppose there's a firecracker at every grid point and they all go off at time t = 0. The 💥 noise propagates out from each grid point in a circle moving at the speed of sound, so the white (resp. black) regions consist of all points that have heard an odd (resp. even) # of 💥 2/n

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      3. bgc‏ @blockspins 27 Jan 2019
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        If we change our perspective a bit, we can see that at time t, the number of 💥 that an observer at a point p has heard is equal to the number of grid points within distance v*t (where v is the speed of sound). (image from http://mathworld.wolfram.com/GausssCircleProblem.html …) 3/npic.twitter.com/dJNDGp3Arf

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      4. bgc‏ @blockspins 27 Jan 2019
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        Translating back to the black & white images, we see that we can determine the number of times a given point has switched colors by counting grid points inside a circle, and for large circle radii, this is approximately π*r^2. 4/5

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      5. bgc‏ @blockspins 27 Jan 2019
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        (The Gauss circle problem https://en.wikipedia.org/wiki/Gauss_circle_problem … asks for a bound on that error.) Now let's turn to the question of whether the fraction of black and white pixels goes to 1/2 for large radius r. 5/6

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      6. bgc‏ @blockspins 27 Jan 2019
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        I can translate this into questions about the even/odd parity of the number of grid points within distance r of each point of the square, but I don't know enough number theory to be able to tell whether this follows from known results... 🤷‍♂️ Anyone wanna take it from here? 6/6

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      7. bgc‏ @blockspins 23 Apr 2019
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        bgc Retweeted Gro-Tsen

        Here's a thread with some similar movies and a link to some more discussion (in French) by @gro_tsen:https://twitter.com/gro_tsen/status/1120692989846872064 …

        bgc added,

        Gro-Tsen @gro_tsen
        Another video which MIGHT have been nice if YouTube's video compression hadn't completely smudged it: https://www.youtube.com/watch?v=7sd_z_1gmes …
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        0 replies 0 retweets 1 like
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