[HN Gopher] Animals Made from 13 Circles (2016)
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Animals Made from 13 Circles (2016)
Author : jihadjihad
Score : 387 points
Date : 2025-04-02 15:35 UTC (7 hours ago)
(HTM) web link (www.dorithegiant.com)
(TXT) w3m dump (www.dorithegiant.com)
| ajross wrote:
| I tend to wonder if stuff like this is an informative boundary on
| AI capabilities. I mean, you can't ask a LLM today to do that
| (AFAICT). "Here's a simply-specified but extremely broad search
| space, solve this problem in it" isn't something that fits the
| model. But it's a relatively common (if not "easy") task human
| beings like to show off.
|
| What needs to change to enable this kind of exploration?
| JohnKemeny wrote:
| Is it impossible, in this day and age, to enjoy a post without
| thinking about LLMs? It's like an obsession.
| generationP wrote:
| Nope, but this post is such a neat illustration of the
| richness of "life" that fits into 39 real parameters (each
| circle can be coordinatized as 3 real numbers: one for its
| radius and two for its center) that my first thought on
| seeing it was also "no surprise then that a matrix with a
| million entries can talk like an erudite person".
| floxy wrote:
| Wouldn't you also need a two parameters for the arc
| starting position and stopping position for each circle,
| and then a few more to identify the areas that need to be
| filled, along with the color?
| laurentlb wrote:
| Once you've drawn the circles, I think you just need to
| specify which regions are filled.
|
| Arcs are just intersection of circles, so they are
| implicit, as far as I can tell.
| jstanley wrote:
| And all of those are simply translation and scaling of 36
| parameters with an implicit unit circle at the origin.
|
| Then if you want to factor out rotations, drop another
| parameter and say the 1st explicit circle lies on the x
| axis.
| y1n0 wrote:
| It should be obvious that this is entirely up to the reader.
| Take some responsibility for your own happiness. Nobody else
| is responsible for your enjoyment of anything.
| elpocko wrote:
| Yes, it is impossible. People will think about things they
| find interesting regardless of your (dis-)approval. Who are
| you even calling "obsessive?" The collective of people who
| dare to mention algorithms you don't like? I mean, what the
| fuck?
| albedoa wrote:
| Calm down dude, for fuck's sake. Read yourself back.
| ajross wrote:
| Well, sort of? I mean, I've seen plenty of clever art in my
| life. I'm still figuring out AI. I posted that in the hope
| that someone in the community here would show up with
| something insightful to say.
| abeppu wrote:
| Actually, the (in)famous "sparks of general intelligence paper"
| about GPT-4 included tasks such as "Draw a unicorn in TikZ"
| which really is not that far off from this task. There were
| also examples for drawing cars/trucks/cats etc with SVG.
|
| But I do think that evolutionary algorithms or MCMC variants
| could do a better job of this, especially if paired with an
| auxiliary model for scoring their intermediate results.
| gwern wrote:
| Yes, this has been done in many forms with other algorithms.
| You score each generation with a model like CLIP, for
| example, and then you can evolve 'Mona Lisa made of
| triangles', say. A constraint like 'exactly 13 circles' will
| work fine. (And you might experiment with loosening it, like
| generating a lot of candidates with 5-30 circles each, as a
| 'library' or 'seeds', before shrinking them all towards 13,
| to see if you get novel animal designs which are find to find
| if you simply start the obvious way with 13 circles
| initialized to random points & sizes.)
| iamwil wrote:
| I was thinking it could, actually, given a feedback loop. The
| tool use would a json that takes 13 circles, each with x, y
| position, radius, and whether it's filled in or empty, and
| output an image. It could look at the image and iterate.
| abeppu wrote:
| See also work from Schmidhuber in the mid/late 1990s
| https://people.idsia.ch/~juergen/locoart/node12.html
| moconnor wrote:
| I thought this was a joke, but he actually _did_ do this first.
| Impressive!
| seanhunter wrote:
| I'm not sure whether or not he did this first, but it's very
| similar to an extremely impressive, but old and well-known
| illustration of the power of Fourier analysis in which you
| construct a "Fourier epicycle" (think: machine made of
| circular gears of different ratios) that can sketch any
| image. 3blue1brown has a great video on Fourier Epicycles but
| you can also get the idea here https://mathematica.stackexcha
| nge.com/questions/171755/how-c...
| iamwil wrote:
| Or check out drawing Homer Simpson with the same technique
| https://www.youtube.com/watch?v=QVuU2YCwHjw
| floxy wrote:
| Also of potential interest is Kempe's Universailty Theroem
| which states you can draw any (polynomial) shape with a set
| of mechanical linkages. Like one that will sign your name.
|
| https://academic.oup.com/plms/article/s1-7/1/213/1570315?lo
| g...
|
| http://www.koutschan.de/data/link/
| dekhn wrote:
| damn, I got nerdsniped again
| ehaveman wrote:
| wow, that's beautiful - the whole site
| https://people.idsia.ch/~juergen/ is an amazing rabbit hole im
| gonna lose myself in.
| Etheryte wrote:
| The red button is an absolute delight, be sure not to press
| it.
| srean wrote:
| He was done a great deal of injustice when he was passed over
| for the Turing award that was given to Hinton, Bengio, LeCun.
|
| Then there is this from his blog --
|
| Dec 2024: Sadly, the Nobel Prize in Physics 2024 for Hopfield &
| Hinton is a Nobel Prize for plagiarism. They republished
| methodologies developed in Ukraine and Japan by Ivakhnenko and
| Amari in the 1960s & 1970s, as well as other techniques,
| without citing the original papers. Even in later surveys, they
| didn't credit the original inventors (thus turning what may
| have been unintentional plagiarism into a deliberate form).
| None of the important algorithms for modern Artificial
| Intelligence were created by Hopfield & Hinton. Details in the
| recent technical report, with lots of references, links, and
| facts.
|
| https://people.idsia.ch/~juergen/physics-nobel-2024-plagiari...
| moralestapia wrote:
| Agree.
|
| Also, AlphaFold is great but hardly an innovation. David
| Baker deserved it 100%.
| iamwil wrote:
| I remember some post that I can find now, that demonstrated the
| twitter bird logo is also made from circles. All I can find is
| this reddit post now.
|
| https://www.reddit.com/r/interestingasfuck/comments/txdimd/t...
| neallindsay wrote:
| That was referenced in the post as the impetus for making
| these. Unfortunately it just links to a Google search.
| wwarren wrote:
| It's mentioned in the article under the images as the
| inspiration for this work
| tylershuster wrote:
| https://designshack.net/articles/graphics/twitters-new-logo-...
| curiousObject wrote:
| Interesting.
|
| What animals _cannot_ be accurately depicted with 13 circles?
| nonethewiser wrote:
| minecraft sheep
| dylan604 wrote:
| An owl?
| ccozan wrote:
| Could be this https://chatgpt.com/canvas/shared/67ed7147fc708
| 191be5b81ed4e...
|
| But not that artsy as the OG.
| dylan604 wrote:
| It was much less of an actual example as it was a reference
| to the draw the rest of the owl meme
| trieloff wrote:
| Pelican on a bicycle
| addaon wrote:
| More generally, any animal that cannot be drawn in 12 circles
| cannot be drawn in 13 circles when riding a bicycle. By
| recursion, no animal can be drawn when riding a stack of
| seven bicycles.
| mixedbit wrote:
| centipede
| curiousObject wrote:
| I think so. With 13 circles, I can't figure out how you could
| represent more than 26 legs (and other features would be
| lost).
| InitialLastName wrote:
| You can use perspective tricks to only show half the legs
|
| A mature house centipede has 15 pairs of legs. You can
| probably get the point across with a portion of that, and
| use two parts of a circle for 2 legs.
| bsza wrote:
| You can depict any animal swallowed by a pufferfish with 1
| circle.
| jessekv wrote:
| What is essential is invisible to the eye.
| tzury wrote:
| 2016...
|
| This type of content is becoming rarer on the internet nowadays.
| KiranRao0 wrote:
| I don't think less of this type of content exists. Its just
| harder to find when inundated with all other slop on the
| internet.
| netghost wrote:
| Or we just don't look past twitter and such.
| ryandrake wrote:
| Just doing a Google search for "animals made from circles",
| you get the usual header full of "Images" and "Videos" crap,
| then in the actual results links, you have the usual
| Pinterest linkslop, Facebook linkslop, Reddit linkslop, a
| bunch of articles written by the designer (now we're getting
| somewhere). OP's link is finally on page 4 of the search
| results.
| dwringer wrote:
| For me, searching "animals made from circles", your comment
| put this HN thread as the #1 result while the #2 result was
| a syndicated article about the linked post. When I get more
| specific and search "animals drawn only from circles" it
| turns up the linked post as the first result. But my
| results may be more specific partly because I don't use ad
| blockers.
| paulirish wrote:
| Vaguely related and also fun: https://www.koalastothemax.com/
| (2011)
| nonethewiser wrote:
| Im curious what the process looks like to implement this. It
| seems like it would be easiest to _start_ with the animal using
| only perfectly(?) curved lines and then complete them into
| circles after the fact. Although that seems kind of pointless and
| I imagine they start with circles. And I guess it would hard to
| have a curve from a perfect circle without the circle?
|
| I just have a hard time imagining you start with circles, lay
| them down (resize as needed) and continue. I mean I guess that
| doesnt sound so crazy after I say it... it just seems like it
| would add a lot of extra noise to the image that would make it
| much harder to draw.
| tarentel wrote:
| I can't speak to this but I took a drawing class a long time
| ago. I'm not very good but it was a lot of drawing circles.
| When you see people freehand stuff it's kind of wild but that's
| not how people learn how to draw they're just very good at it
| from practice. Most of learning is drawing very basic shapes,
| usually circles, and erasing parts that don't make sense and
| continuing.
| tmountain wrote:
| I have been practicing art a lot lately. You can draw just
| about anything using spheres, cubes, cylinders, and cones.
| You start off with the 2d versions.
| tarentel wrote:
| I stopped after a few classes but I was amazed at how good
| I got in a short amount of time after learning how to break
| stuff down which isn't something I really thought about
| before. By all metrics I'm still a pretty terrible drawer
| but prior to that stick figures would have been
| challenging.
| kunzhi wrote:
| Drawing from circles, squares, triangles, etc. in art is
| called "construction" and is definitely a foundational
| technique. It really is amazing how much easier drawing
| becomes once it's understood (and practiced).
| floxy wrote:
| Another good resource for learning how to draw
| realistically is the book: "Drawing on the Right Side of
| the Brain". The premise is that your brain wants to take
| shortcuts and group/chunk things together on what they
| should look like, instead of what things actually look
| like. But even a rectangle in real life has non-right-
| angles because of perspective, etc.. And if you draw what
| you actually see, then the drawings come out correct.
| Some of the exercises are copying other drawings placed
| upside-down, so that you brain doesn't try to over-
| interpret things. I can't recommend this enough if you
| want to go from a beginner to something respectable in
| drawing abilities.
|
| https://www.amazon.com/Drawing-Right-Side-Brain-
| Definitive/d...
|
| https://kk.org/cooltools/drawing-on-the-right-side-of-
| the-br...
| tmountain wrote:
| I read the book and loved it (about 15 years ago).
| There's no royal road to becoming an artist but lots of
| joy along the way. Whatever the path, enjoy it!
| jihadjihad wrote:
| > drawing very basic shapes, usually circles, and erasing
| parts that don't make sense
|
| There's a hilarious Spongebob bit [0] where Squidward is
| teaching an art class, and he starts off in that exact manner
| of trying to draw a perfect circle, only to have Spongebob
| subvert the entire idea. The whole episode is artistic gold
| IMO.
|
| 0: https://www.youtube.com/watch?v=vTlpFEvmxdM
| tarentel wrote:
| I do remember that. Sorry I can't find a better website but
| this is a similar joke.
|
| https://www.reddit.com/r/restofthefuckingowl/comments/6f71j
| m...
| adamanonymous wrote:
| There are some photos of sketches at the bottom of the page.
| Looks like they started with curves and turned them into
| circles later
| nonethewiser wrote:
| I suppose the thing the circle is really informing is the
| "perfectness" of the curve. You cant just draw in curves and
| extend it to a circle (wont be perfect). I guess Im not sure
| how you get "perfect" curves.
|
| I suspect its a stencil or something. So in some sense the
| circle does exist first, even if they only draw the curve
| from it initially (before marking it up with the full circle
| after the fact).
| PebblesRox wrote:
| If I were trying to do something like this I would sketch
| it out first with imperfect curves and then worry about
| making it perfect once I was at the computer. It would look
| slightly different but I don't think it would make that
| much of an impact in the initial design process.
| laurentlb wrote:
| There's some information on:
| https://www.smashingmagazine.com/2017/01/illustrating-animal...
|
| "While sketching, I kept track of the number of circles I was
| using, counting one for every curve." After sketching an
| animal, it should be easier to adjust the image by
| inserting/removing/moving circles.
| nonethewiser wrote:
| Awesome, thank you!
| DrNosferatu wrote:
| Not exactly circles, but famously:
|
| With four parameters I can fit an elephant, and with five I can
| make him wiggle his trunk.
|
| https://en.m.wikipedia.org/wiki/Von_Neumann%27s_elephant
| WorkerBee28474 wrote:
| Related: 'A meeting with Enrico Fermi'
| https://www.nature.com/articles/427297a
| kbelder wrote:
| "and with 20 billion I can make it hold a conversation."
| deadbabe wrote:
| Could an AI generate art like this and actually utilize perfect
| circles, to create whatever you ask?
| dukeofdoom wrote:
| This guy is doing something similar for his game:
|
| The Procedural Animation
| https://www.youtube.com/watch?v=qlfh_rv6khY
|
| Gibbon: Beyond the Trees - Wolfire Games
| https://www.youtube.com/watch?v=KCKdGlpsdlo
| glxxyz wrote:
| I never really liked Twitter but I feel oddly nostalgic for the
| logo now.
| ksajh wrote:
| class Animal {
|
| Circle circles_[13];
|
| }
| gnramires wrote:
| You also need to encode the painted areas somehow. They are not
| only intersections on K shapes, but sometimes exclusions as
| well (like (A^B)/C). Two ways come to mind:
|
| (1) Listing closed curves by vertices. Each vertex of a painted
| area is an intersection of two or more circles, and delimits a
| section of a circle. So the section of circles that enclose a
| circle can be encoded each by the union of:
|
| (1.1) A circle (index); (1.2) A 2nd circle (index) that
| intersects the 1st on a first point; (1.3) A bit identifying
| the (first) intersection (because there may be 2 possible);
| (1.4) A 3rd circle (index) that intersects the 1st on a second
| point; (1.5) A bit identifying the (second) intersection.
|
| Note the base circle would be the first intersection of a
| subsequent section of this closed curve, and the 3rd circle
| would be the subsequent base circle. So 1/2/3 won't be
| necessary for subsequent curves. So only (K+2) indices + (K+1)
| bits are necessary for this encoding.
|
| Total ~K log2(K)+K bits. I hypothesize (left to the reader :))
| a closed curve should contain at most 2x13 points. There can be
| at most 2^13 distinct regions however, so each figure (Animal)
| can be encoded with less than that many curves per figure. So
| each figure (Animal) can be encoded with less than 2^13 x
| 26x(5+1) bits =~ 1.3Mbit.
|
| But that's mostly pathological cases, if each Animal must be a
| fully connected area, then that might reduce (hypothesis above)
| to at most only 26x(5+1) bits = 156 bits, or 20 bytes!
|
| I left out a problem which area shapes encoded within each
| other (like eyes). In that case you need at most another 156
| bits per inner cutout shape.
|
| (2) Alternatively, you could use boolean operations to encode
| each shape. Also left as a fun problem :)
| mondobe wrote:
| interface Animal { Circle[13] circles();
| // Leftover from Intro to CS, remember to remove void
| make_sound(); }
| barbazoo wrote:
| Could this be the next captcha challenge? "Draw an animal out of
| 13 circles to prove you are human".
| CamperBob2 wrote:
| I was thinking that this would be low-hanging fruit for a
| model. The parameter space is so tiny compared to what a
| diffusion model already has to deal with...
| apankrat wrote:
| I did something similar 15+ years ago to use as an avatar in
| forums, twitters and some such - https://swapped.ch/#!/personal-
| mark
| __s wrote:
| Curious how well transforms on circles could be composed to
| animate these animals
| agys wrote:
| My aunt grifted me "Animali Compassati" when I was a kid... A
| small book with instructions for animals that you could draw with
| a compass. The site is unclear somehow... but the instructions
| were pretty great in the book.
|
| https://www.danielenannini.it/en/portfolio/animali-compassat...
|
| https://www.compasses-zoo.net/compasses-zoo/index.php
| sverhagen wrote:
| It feels like I'm looking at the next so many Ubuntu backgrounds!
| ge96 wrote:
| I miss being creative, before I knew how to make front end UIs I
| had crazy ideas but then became grounded. This one isn't super
| crazy but I like those vertical buildings.
|
| Tangent, with a dark/colorful theme in an editor the minimap
| looks like a city scape
| ezekg wrote:
| It's really satisfying to create logomarks solely out of circles,
| idk why. A challenge, I guess.
|
| I did a few back in my day as a designer:
|
| 1. https://dribbble.com/shots/1909369-Liberty-Eagle-Arms
|
| 2. https://dribbble.com/shots/1553151-Flint-mark-icons
|
| That first one is some of my best work.
| fracus wrote:
| Art with restrictions can be more interesting than without.
| PlunderBunny wrote:
| Architecture too. The worst building come from architects given
| a blank page to start with. Constraints, and sympathy for the
| surrounding built environment produce great work.
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