[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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       (page generated 2025-04-02 23:00 UTC)