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blockspins's profile
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@blockspins

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bgc

@blockspins

readin and writin

Joined January 2010

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    1. D ␣ a ␣ n ␣ P ␣ i ␣ p ␣ o ␣ n ␣ i‏ @sigfpe 12 Jun 2019
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      Abelian sandpiles are completely amazing. No low quality youtube video can do justice to all the intricate things that happen during the process. Here's an example partway through the firing process after 16000000 grains were dropped in the centre.pic.twitter.com/3WKzdcfaoM

      8 replies 30 retweets 145 likes
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    2. D ␣ a ␣ n ␣ P ␣ i ␣ p ␣ o ␣ n ␣ i‏ @sigfpe 12 Jun 2019
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      The "playing field" here is even so there isn't really an exact centre. You can see some subtle asymmetry as a result. I really need a decent GPU for this.

      2 replies 0 retweets 3 likes
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    3. D ␣ a ␣ n ␣ P ␣ i ␣ p ␣ o ␣ n ␣ i‏ @sigfpe 12 Jun 2019
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      Here's an example on YouTube. Butbthe compression really ruins ithttps://youtu.be/GViAq_IWOg4 

      2 replies 1 retweet 8 likes
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    4. D ␣ a ␣ n ␣ P ␣ i ␣ p ␣ o ␣ n ␣ i‏ @sigfpe 13 Jun 2019
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      1D sandpiles are a polynomial algebra with rewrite rule 2X → X² + 1 If you remember 7 Trees in 1, that was about X → X² + 1 I wonder what relationship there is. https://arxiv.org/abs/math/9405205 … In fact, I considered a version of 7-in-1 with piles: http://blog.sigfpe.com/2007/09/arboreal-isomorphisms-from-nuclear.html …

      7 replies 1 retweet 13 likes
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    5. D ␣ a ␣ n ␣ P ␣ i ␣ p ␣ o ␣ n ␣ i‏ @sigfpe 13 Jun 2019
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      Some code for rendering sandpiles using TF for acceleration. Sadly, on OSX you'll only get multicore, not GPU acceleration.https://github.com/dpiponi/pile 

      2 replies 1 retweet 11 likes
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    6. D ␣ a ␣ n ␣ P ␣ i ␣ p ␣ o ␣ n ␣ i‏ @sigfpe 14 Jun 2019
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      "Abelian sandpile" is a weird name. Of course they're abelian. The surprising property is associativity. They should be called "associative sandpiles".

      3 replies 0 retweets 8 likes
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    7. D ␣ a ␣ n ␣ P ␣ i ␣ p ␣ o ␣ n ␣ i‏ @sigfpe 16 Jun 2019
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      Rewrote the code in Swift/Metal. Got this 2^24 grain, 1536x1536 result on my 2015 Macbook Pro in the time it takes to make a batch of cookie dough - 30-45 minutes. 3,000,000 iterations, each over about 2,000,000 pixels.pic.twitter.com/FNy4DcqWVG

      1 reply 0 retweets 24 likes
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    8. D ␣ a ␣ n ␣ P ␣ i ␣ p ␣ o ␣ n ␣ i‏ @sigfpe 16 Jun 2019
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      (I'd release the code but it uses a fixed size "threadgroup" and I've no idea if that's portable to other Macs. Busy week ahead but I'll try to rewrite the code to use a dynamic size based on querying the hardware.)

      1 reply 0 retweets 4 likes
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    9. D ␣ a ␣ n ␣ P ␣ i ␣ p ␣ o ␣ n ␣ i‏ @sigfpe 17 Jun 2019
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      On left: 2^25 grains at 2048x2048 On right: 2^18 grains at 256x256 So many similar details. I don't know if this scale invariance is well understood yetpic.twitter.com/rboEnZDrDn

      3 replies 0 retweets 13 likes
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      bgc‏ @blockspins 17 Jun 2019
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      Replying to @sigfpe

      A lot has been proved in the last few years! Here's a recent review by Levine and Peres in the Bulletin of the AMS:http://www.ams.org/journals/bull/2017-54-03/S0273-0979-2017-01573-X/ …

      9:30 AM - 17 Jun 2019
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      • Bullfrog D ␣ a ␣ n ␣ P ␣ i ␣ p ␣ o ␣ n ␣ i
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        1. New conversation
        2. bgc‏ @blockspins 17 Jun 2019
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          Replying to @blockspins @sigfpe

          More details on the scaling limit in the pair of articles by Levine, Pegden and Smart, "Apollonian structure in the Abelian sandpile" https://arxiv.org/abs/1208.4839  and "The Apollonian structure of integer superharmonic matrices" https://arxiv.org/abs/1309.3267 

          1 reply 0 retweets 2 likes
        3. D ␣ a ␣ n ␣ P ␣ i ␣ p ␣ o ␣ n ␣ i‏ @sigfpe 17 Jun 2019
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          Replying to @blockspins

          Oh wow, the circle packing connection looks incredible!

          0 replies 0 retweets 1 like
        4. End of conversation

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