[HN Gopher] Beautiful Abelian Sandpiles
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Beautiful Abelian Sandpiles
Author : eavan0
Score : 131 points
Date : 2025-12-09 20:16 UTC (4 days ago)
(HTM) web link (eavan.blog)
(TXT) w3m dump (eavan.blog)
| skeltoac wrote:
| Now I want to redo a bathroom. Good job, writer!
| ggm wrote:
| Isn't this single frame state of a classic cellular automata?
| Note, not "just" because I mean no disrespect. I don't understand
| how this differs from Conway's life other than nuances of the
| live or die rule.
| gsf_emergency_6 wrote:
| CGL doesn't have the scale invariance ("fractality") of ASM.
| ASM criticality is stable and persistent. "fractal life on
| edge"?
|
| what that looks like
|
| https://youtu.be/rKD51IUNK3A?t=40s
| ggm wrote:
| So that gets to how it differs, but it doesn't say its not a
| cellular automata. It could say "it's a cellular automata
| with different rules"
| gsf_emergency_6 wrote:
| It is a cellular automata distinguished by commutativity.
| You used CGL as the basis for comparison, that's highly
| nonAbelian.
|
| According to Wolfram (& I agree :), everything is a
| cellular automaton, so comparing to CGL made more sense to
| me.
| Sharlin wrote:
| I don't believe that Game of Life is Abelian.
| tripplyons wrote:
| I don't think you could even define an associative binary
| operator on states in the Game of Life because of its
| computational irreducibility.
| recursive wrote:
| It seems the sand only spills up and to the left.
| omoikane wrote:
| It seems like it spills to 4 directions on Chrome, but only up
| and left on Firefox.
|
| The really weird part is that when I fetch
| https://eavan.blog/sandpile.js in Chrome, I see a "toppleAll"
| function near the top, but that same function is not defined
| when the script is fetched with Firefox.
| haritha-j wrote:
| Very related (yet idiotically titled, as always) veritasium video
| https://youtu.be/HBluLfX2F_k?si=6lVPLvJNc2YH_4go
| JimmyBuckets wrote:
| It's like reverse clickbait with him
| SiempreViernes wrote:
| Yeah, I wish he'd do a second channel that is just reposts
| with normal titles.
| lupire wrote:
| https://m.youtube.com/watch?v=S2xHZPH5Sng
|
| "Clickbait is Unreasonably Effective", 2021 - Veritasium's
| apologia for clicbait titles and and thumbnails, and
| statement of principles.
|
| Veritasiuk has at least stuck making soldi educational
| videos, as Mark Rober has let slip away his past effort to
| educate in addition to demonstrate his cool toys.
| FredrikMeyer wrote:
| I implemented this in Rust some years back. It is connected to
| some serious research mathematics (see f.ex
| https://www.ams.org/notices/201008/rtx100800976p.pdf)
|
| https://github.com/FredrikMeyer/abeliansandpile
| seanhunter wrote:
| > "...an abelian group is both associative and commutative..."
|
| If something is not associative it is not a group. An abelian
| group is a group which is commutative.
| MarkusQ wrote:
| So...an abelian group is both associative (because it's a
| group) and commutative (because it's abelian), which is exactly
| what the OP said? It sounds like you're disagreeing about
| something, but I'm not clear what your objection is.
| seanhunter wrote:
| I'm not disagreeing. I'm pointing out that in TFA it sounds
| as associativity is a property of abelian groups specifically
| whereas it as a property of all groups in general. In that
| sense it's not wrong, just the emphasis is a bit misleading.
|
| If you look in an abstract algebra textbook they all
| basically say the same definition for abelian groups (eg in
| Hien)
|
| > "A group G is called abelian if its operation is
| commutative ie for all g, h in G, we have gh = hg".
| mcphage wrote:
| > The rules of abelian groups guarantee that these identity
| sandpiles must exist, but they tell us nothing about how
| beautiful they are.
|
| This has causality backwards--being a group _requires_ an
| identity element. You can 't show something is a group without
| knowing that the identity element exists in the first place.
|
| In fact, a good chunk of how this article talks about the math is
| just... slightly off.
| pmcarlton wrote:
| I found 'xsand.c' (X11) in 1995 by Michael Creutz, that simulated
| these sandpiles; I had fun with the sand but also learned C from
| it.
| OgsyedIE wrote:
| In the case of piling sand exactly in the centre, the
| intermediate states between the initial state and reaching the
| final equilibrium seem to get closer to having a circular
| boundary as the grid size increases, instead of the diamond-
| shaped boundary you might expect for a symmetrical object in a
| planar grid. Take a look at the largest resettable grid doing
| this within a couple seconds of being reset.
| LegionMammal978 wrote:
| It looks like the author has a pretty simple procedure for
| computing the 'identity' sandpile (which they unfortunately don't
| describe at all):
|
| 1. Fill a grid with all 6s, then topple it.
|
| 2. Subtract the result from a fresh grid with all 6s, then topple
| it.
|
| So effectively it's computing 'all 6s' - 'all 6s' to get an
| additive identity. But I'm not entirely sure how to show this
| always leads to a 'recurrent' sandpile.
|
| EDIT: One possible route: The 'all 3s' sandpile is reachable from
| any sandpile via a sequence of 'add 1' operations, including from
| its own successors. Thus (a) it is a 'recurrent' sandpile, (b)
| adding any sandpile to the 'all 3s' sandpile will create another
| 'recurrent' sandpile, and (c) all 'recurrent' sandpiles must be
| reachable in this way. Since by construction, our 'identity'
| sandpile has a value >= 3 in each cell before toppling, it will
| be a 'recurrent' sandpile.
| lupire wrote:
| Wikipedia has a picture/animation of the Identity for rectangular
| and square grids
|
| https://en.wikipedia.org/wiki/Abelian_sandpile_model
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