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Animals Made from 13 Circles (2016)

618 points - yesterday at 3:35 PM

Source
  • DrNosferatu

    yesterday at 4:58 PM

    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

      • KolibriFly

        today at 5:26 AM

        Feels like the mathematical version of "just because you can doesn't mean you should."

        • kbelder

          yesterday at 9:33 PM

          "and with 20 billion I can make it hold a conversation."

            • NitpickLawyer

              today at 5:45 AM

              To paraphrase that quote about hydrogen: Give gradient descent a few billion parameters, and it starts wondering where it came from and what does it all mean.

              • kazinator

                today at 1:18 AM

                Bravo! HN Gold.

            • WorkerBee28474

              yesterday at 9:14 PM

              Related: 'A meeting with Enrico Fermi' https://www.nature.com/articles/427297a

              • rob74

                today at 8:33 AM

                Looks more like an amoeba to me...

            • ezekg

              yesterday at 8:52 PM

              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.

                • tuyiown

                  today at 7:38 AM

                  Constraints forces creativity. Some well chosen constraints are aesthetics rules that helps you land pleasing results. Poetry has a long history on that matter.

                  Another example of constrained creativity is early to mid nineties electronic music.

                  • KolibriFly

                    today at 5:42 AM

                    There's something oddly meditative about designing within strict constraints like circles

                    • jaredhallen

                      today at 12:13 AM

                      Yeah, those are all really nice. Good work.

                  • rob74

                    today at 8:27 AM

                    > Inspired by the Twitter logo, which is made from 13 perfect circles

                    Compared to that, the new logo doesn't have a circle (segment) anywhere to be seen (unless you consider straight lines as circle segments with the center located at infinity of course), and is simply the "mathematical double-struck capital X" from an unknown but probably pre-existing font (apparently Monotype's "Special Alphabets 4" comes close, but isn't identical, according to https://tweethunter.io/blog/how-to-write-twitter-x-iphone-ma...).

                    • sverhagen

                      yesterday at 6:46 PM

                      It feels like I'm looking at the next so many Ubuntu backgrounds!

                      • nonethewiser

                        yesterday at 4:47 PM

                        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

                            yesterday at 4:59 PM

                            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.

                              • jihadjihad

                                yesterday at 7:25 PM

                                > 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

                              • tmountain

                                yesterday at 6:32 PM

                                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

                                    yesterday at 7:36 PM

                                    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.

                                      • floxy

                                        yesterday at 8:44 PM

                                        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

                                            yesterday at 9:56 PM

                                            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!

                                        • kunzhi

                                          yesterday at 7:58 PM

                                          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).

                                  • barrenko

                                    today at 6:14 AM

                                    True, I did some amateur vector art (in Illustrator) and you basically have to compose objects out of basic shapes. It is truly highly meditative.

                                • laurentlb

                                  yesterday at 5:08 PM

                                  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

                                      yesterday at 5:35 PM

                                      Awesome, thank you!

                                  • adamanonymous

                                    yesterday at 4:59 PM

                                    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

                                        yesterday at 5:29 PM

                                        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

                                            yesterday at 5:49 PM

                                            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.

                                    • KolibriFly

                                      today at 6:14 AM

                                      What's wild is how much clarity and personality you can get from that process. Instead of adding noise, it forces simplification, which actually helps with visual clarity

                                  • iamwil

                                    yesterday at 4:23 PM

                                    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

                                        yesterday at 4:31 PM

                                        That was referenced in the post as the impetus for making these. Unfortunately it just links to a Google search.

                                        • KolibriFly

                                          today at 6:16 AM

                                          Not sure how precise it really is, but it looks convincing enough to feel intentional

                                          • wwarren

                                            yesterday at 4:31 PM

                                            It’s mentioned in the article under the images as the inspiration for this work

                                        • apankrat

                                          yesterday at 5:49 PM

                                          I did something similar 15+ years ago to use as an avatar in forums, twitters and some such - https://swapped.ch/#!/personal-mark

                                          • thesz

                                            today at 7:42 AM

                                            Because circles there also need operations over them (union, intersection or subtraction), it is a good example of low complexity art [1].

                                            [1] https://en.wikipedia.org/wiki/Low-complexity_art

                                            My son is a big fan of bytebeat [2], which is also a low complexity art, but music.

                                            [2] https://dollchan.net/bytebeat/#4AAAA+kUryC/X0CixswNhQyM1Q01N...

                                            • abeppu

                                              yesterday at 3:56 PM

                                              See also work from Schmidhuber in the mid/late 1990s https://people.idsia.ch/~juergen/locoart/node12.html

                                                • ehaveman

                                                  yesterday at 4:21 PM

                                                  wow, that's beautiful - the whole site https://people.idsia.ch/~juergen/ is an amazing rabbit hole im gonna lose myself in.

                                                    • Etheryte

                                                      yesterday at 4:28 PM

                                                      The red button is an absolute delight, be sure not to press it.

                                                  • srean

                                                    yesterday at 6:21 PM

                                                    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

                                                        yesterday at 8:15 PM

                                                        Agree.

                                                        Also, AlphaFold is great but hardly an innovation. David Baker deserved it 100%.

                                                    • moconnor

                                                      yesterday at 4:06 PM

                                                      I thought this was a joke, but he actually did do this first. Impressive!

                                                • enqk

                                                  today at 2:00 PM

                                                  Japanese family crests (Mon: ç´‹) are almost entirely made of circles (and lines, but that's rarer)

                                                  Often depicting slices of vegetables, animals..

                                                  From few circles to hundreds

                                                  • fracus

                                                    yesterday at 9:06 PM

                                                    Art with restrictions can be more interesting than without.

                                                      • yesthisiswes

                                                        today at 12:34 AM

                                                        This is so true. I took a figure drawing class in college and we were instructed to draw with a cloth and charcoal dust. Easily some of the best work I made came out of that restriction.

                                                        • PlunderBunny

                                                          yesterday at 9:32 PM

                                                          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.

                                                      • vismit2000

                                                        today at 8:09 AM

                                                        Reminds of 'Drawing with circles' in 3b1b classic on Fourier series: https://www.youtube.com/watch?v=r6sGWTCMz2k

                                                        So if we remove the condition of 13, everything is in fact made of circles only!

                                                        • saunved_42

                                                          today at 5:42 AM

                                                          I really love the way these look. I'm imagining a short film with these characters, and it'd be a nice experiment to see how it turns out.

                                                          • ge96

                                                            yesterday at 8:09 PM

                                                            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

                                                            • gcanyon

                                                              today at 3:51 AM

                                                              It bugs me than e.g. the owl's ears benefit from a dramatic change in color that isn't related to anything outlined by the circles.

                                                              • agys

                                                                yesterday at 5:56 PM

                                                                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

                                                                • noduerme

                                                                  today at 8:51 AM

                                                                  This page feels like an AI traveled back in time and (faked) the date.

                                                                  [edit] Nevermind. I'm being too harsh. The creator was obviously having fun and being creative. That's cool. I think if nothing else this just proves how jaded and skeptical about clever artwork I've become in the past few years.

                                                                    • today at 10:28 AM

                                                                  • kleiba

                                                                    today at 10:34 AM

                                                                    Not circles, but arcs.

                                                                      • hmwhy

                                                                        today at 10:52 AM

                                                                        If you pay closer attention, you can see that some of the designs rely on very deliberate placements of circles; for example, eyes of the monkey and owl, and the nose of the whale.

                                                                        Those are just the obvious ones that I can immediately spot — there was probably a lot of careful consideration into the placement of circles in order to facilitate good looking arcs and circles that bring the animals to "life".

                                                                          • kleiba

                                                                            today at 12:10 PM

                                                                            Sure, you're not wrong. But a circle is just an arc of length 2pi * radius.

                                                                    • KolibriFly

                                                                      today at 5:24 AM

                                                                      Reminds me of how some of the best ideas come out of working within restrictions, not in spite of them

                                                                      • __s

                                                                        yesterday at 5:52 PM

                                                                        Curious how well transforms on circles could be composed to animate these animals

                                                                        • today at 9:46 AM

                                                                          • glxxyz

                                                                            yesterday at 5:27 PM

                                                                            I never really liked Twitter but I feel oddly nostalgic for the logo now.

                                                                            • paulirish

                                                                              yesterday at 4:41 PM

                                                                              Vaguely related and also fun: https://www.koalastothemax.com/ (2011)

                                                                              • tzury

                                                                                yesterday at 4:29 PM

                                                                                2016…

                                                                                This type of content is becoming rarer on the internet nowadays.

                                                                                  • KiranRao0

                                                                                    yesterday at 4:48 PM

                                                                                    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.

                                                                                      • ryandrake

                                                                                        yesterday at 4:57 PM

                                                                                        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

                                                                                            yesterday at 5:20 PM

                                                                                            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.

                                                                                        • netghost

                                                                                          yesterday at 4:56 PM

                                                                                          Or we just don't look past twitter and such.

                                                                                  • barbazoo

                                                                                    yesterday at 5:29 PM

                                                                                    Could this be the next captcha challenge? "Draw an animal out of 13 circles to prove you are human".

                                                                                      • CamperBob2

                                                                                        yesterday at 5:34 PM

                                                                                        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...

                                                                                    • I_Nidhi

                                                                                      today at 10:31 AM

                                                                                      Reminds me of the time we made geometric art using a compass. https://homeschoolmath.blogspot.com/2013/02/geometric-art-pr...

                                                                                      • curiousObject

                                                                                        yesterday at 4:26 PM

                                                                                        Interesting.

                                                                                        What animals cannot be accurately depicted with 13 circles?

                                                                                          • bsza

                                                                                            yesterday at 5:06 PM

                                                                                            You can depict any animal swallowed by a pufferfish with 1 circle.

                                                                                              • jessekv

                                                                                                yesterday at 7:46 PM

                                                                                                What is essential is invisible to the eye.

                                                                                            • trieloff

                                                                                              yesterday at 4:45 PM

                                                                                              Pelican on a bicycle

                                                                                                • addaon

                                                                                                  yesterday at 6:47 PM

                                                                                                  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.

                                                                                              • Y_Y

                                                                                                today at 1:39 PM

                                                                                                Corals?

                                                                                                • nonethewiser

                                                                                                  yesterday at 4:44 PM

                                                                                                  minecraft sheep

                                                                                                  • mixedbit

                                                                                                    yesterday at 5:05 PM

                                                                                                    centipede

                                                                                                      • globnomulous

                                                                                                        today at 1:00 PM

                                                                                                        I was going to suggest "octopus" but your answer is better.

                                                                                                        • curiousObject

                                                                                                          yesterday at 6:10 PM

                                                                                                          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

                                                                                                              yesterday at 6:36 PM

                                                                                                              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.

                                                                                                      • dylan604

                                                                                                        yesterday at 4:45 PM

                                                                                                        An owl?

                                                                                                  • ksajh

                                                                                                    yesterday at 5:29 PM

                                                                                                    class Animal {

                                                                                                    Circle circles_[13];

                                                                                                    }

                                                                                                      • gnramires

                                                                                                        yesterday at 6:25 PM

                                                                                                        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

                                                                                                          yesterday at 6:26 PM

                                                                                                            interface Animal {
                                                                                                              Circle[13] circles();
                                                                                                          
                                                                                                              // Leftover from Intro to CS, remember to remove
                                                                                                              void make_sound();
                                                                                                            }

                                                                                                      • dukeofdoom

                                                                                                        yesterday at 5:26 PM

                                                                                                        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

                                                                                                        • deadbabe

                                                                                                          yesterday at 5:19 PM

                                                                                                          Could an AI generate art like this and actually utilize perfect circles, to create whatever you ask?

                                                                                                          • lingying

                                                                                                            today at 8:25 AM

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                                                                                                            • today at 10:56 AM

                                                                                                              • yesterday at 3:44 PM

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                                                                                                                    • ajross

                                                                                                                      yesterday at 3:50 PM

                                                                                                                      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

                                                                                                                          yesterday at 4:03 PM

                                                                                                                          Is it impossible, in this day and age, to enjoy a post without thinking about LLMs? It's like an obsession.

                                                                                                                            • generationP

                                                                                                                              yesterday at 4:18 PM

                                                                                                                              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".

                                                                                                                                • jstanley

                                                                                                                                  yesterday at 4:42 PM

                                                                                                                                  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.

                                                                                                                                  • floxy

                                                                                                                                    yesterday at 4:40 PM

                                                                                                                                    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

                                                                                                                                        yesterday at 5:03 PM

                                                                                                                                        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.

                                                                                                                                • y1n0

                                                                                                                                  yesterday at 4:18 PM

                                                                                                                                  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.

                                                                                                                                  • ajross

                                                                                                                                    yesterday at 5:28 PM

                                                                                                                                    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.

                                                                                                                                    • elpocko

                                                                                                                                      yesterday at 4:24 PM

                                                                                                                                      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

                                                                                                                                          yesterday at 5:00 PM

                                                                                                                                          Calm down dude, for fuck's sake. Read yourself back.

                                                                                                                                  • abeppu

                                                                                                                                    yesterday at 4:11 PM

                                                                                                                                    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

                                                                                                                                        yesterday at 4:52 PM

                                                                                                                                        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

                                                                                                                                      yesterday at 4:22 PM

                                                                                                                                      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.