7 ms·
Drawing an elephant with four complex parameters (2008)
- tabtab 9y agoThis parametric equation set draws a hamburger: x=sin(tan(t)) and y=cos(t) Picture: http://uncyclopedia.wikia.com/wiki/File:Hamburger_plot_ies.PNG http://uncyclopedia.wikia.com/wiki/File:Hamburger_plot_ies.P...
- nabla9 9y agoVisualization of the same technique: https://www.reddit.com/r/Art/comments/7wztif/generative_art_%E3%81%98%E3%82%83%E3%81%8C%E3%82%8A%E3%81%8D%E3%82%93_video_2018/ https://www.reddit.com/r/Art/comments/7wztif/generative_art_...
- tabtab 9y agoThe medieval astronomers had it right: epicycles work! However, they didn't reflect the actual mechanism behind planet movements, but merely predicted them. "Circular regression", essentially. The ancient Greeks used threaded pegs to make puppet shows etc.: the first programmable robots. I'd like to see possible emulations of such.
- tzs 9y agoHomer Simpson in 1000 epicycles: https://www.youtube.com/watch?v=QVuU2YCwHjw https://www.youtube.com/watch?v=QVuU2YCwHjw
- ourmandave 9y agoAnd a blind man felt the elephant and declared, "It's a computer screen." https://en.wikipedia.org/wiki/Blind_men_and_an_elephant https://en.wikipedia.org/wiki/Blind_men_and_an_elephant
- tlarkworthy 9y agoSlightly cheating by using complex numbers so there is 8 degrees of freedom instead of 4. But bravo anyway, it was a great exercise.
- 983 9y agoOne might also argue that choosing a non-continuous sequence of Fourier-coefficients is not perfectly honest, since it allows for encoding information in the coefficient indices.
- soVeryTired 9y agoI'm not sure counting the number of real numbers that you have to input is quite the right way to think about this. I could encode instructions to draw an arbitrary shape in a single real number if I wanted: .00011110 could be interpreted as a square if I take pairs of digits to be successive (x,y) coordinates (my example becomes (0,0), (0,1), (1,1), (1,0)).
- tlarkworthy 9y agoDegrees of freedom expresses a bound on the complexity of things you can represent. The motivation of this work was a conversation about the over complexity of a scentific model. You literally count the free params and if there are loads of parameters you need zillions of observations to pin them down due to the curse of dimensionality. It's the same concept in parametric statistics: https://en.m.wikipedia.org/wiki/Degrees_of_freedom_(statistics) https://en.m.wikipedia.org/wiki/Degrees_of_freedom_(statisti... Non-parametric statistics work by fitting models of infinite degrees of freedom. But then you need fancy math to figure out how complex your model currently is and how your data supports it.
- logfromblammo 9y agoAnd the professional digital modeler that just found a way to cut 20 triangles out of the trunk wireframe just rolls their eyes and goes back to fine-tuning the skeleton so that the active forelimb doesn't pinch in the "skull-crush execution" animation.... The described technique is interesting, but elephants are 3-dimensional objects with a somewhat more detailed contour, so I'm going to have to declare that the well-known saying remains unimplemented. I think Dyson could have retorted, "Yes, but my model will be finished long before you have discovered your fourth parameter."
- leblancfg 9y agoWell, if they can use complex numbers, I think quaternions[0] are fair game for a 3D elephant. [0]https://en.wikipedia.org/wiki/Quaternion https://en.wikipedia.org/wiki/Quaternion
- logfromblammo 9y agoThat seems like cheating. If you can use quaternions to squeeze out more degrees of freedom, you could also use octonions. You could use any number of additional dimensions that square to -1.
- Myrmornis 9y agoI thought those things weren't so easy to come by -- that was why Hamilton was excited enough to carve it into a bridge wasn't it?
- logfromblammo 9y agoI think the difficulty is actually in arranging them such that they combine to make an interesting algebra.
- EtDybNuvCu 9y agoWe lose features too, as we climb in complexity. Lucky 10000: https://en.wikipedia.org/wiki/Cayley–Dickson_construction https://en.wikipedia.org/wiki/Cayley–Dickson_construction
- rogerallen 9y agoBonus points for the first to reimplement this in PyTorch or Tensorflow.
- 983 9y agoHere you go: https://github.com/983/Elephant/tree/master https://github.com/983/Elephant/tree/master
- rogerallen 9y agoCongratulations, full bonus points awarded! Seriously, that's very cool. Well done.
- 983 9y agoThanks :)
- skinner_ 9y agoAwesome! You are amazingly fast! I've tried to add neural time warping to it, but it did not help yet. L1 loss on the parameters did help reducing the parameter count on the fancy elephant task. Here are a couple of failed runs: https://users.renyi.hu/~daniel/elephants/ https://users.renyi.hu/~daniel/elephants/
- rafael859 9y agoHeh, I find these more interesting than the successful ones.
- deleted 9y ago[deleted]
- thom_nic 9y agoI'm currently taking Andrew Ng's Machine Learning course on Coursera; I immediately thought of using logistic regression to find this shape algorithmically. I know the premise of the paper is "with four parameters." But: with enough polynomial terms it should be easy to get much closer to the example in figure a than the one shown in figure b, no?
- enriquto 9y agothis is actually a standard first example in Fourier analysis, since more than a hundred years ago
- chaosopher 9y agoA mechanical harmonic (Fourier) analysis device: https://www.youtube.com/watch?v=NAsM30MAHLg https://www.youtube.com/watch?v=NAsM30MAHLg
- Sharlin 9y agoSee also: Mechanical Laser Show [1] [1] https://youtu.be/_dtBUiaAqRE https://youtu.be/_dtBUiaAqRE
- ttoinou 9y agoAre all parameters not described equals to zero ?
- bakul 9y agoOrigamists create an elephant with nothing more than one fold! See some minimalist elephant designs by David Mitchell and Paul Jackson: http://www.origamiheaven.com/pdfs/elephantsextreme.pdf http://www.origamiheaven.com/pdfs/elephantsextreme.pdf
- jerrre 9y agoThis is beautiful! Any hints where to find more like this?
- bakul 9y agohttp://www.origamiheaven.com/ http://www.origamiheaven.com/ & http://www.origami-instructions.com/ http://www.origami-instructions.com/ have many examples with instructions for single sheet designs.
- mar77i 9y agoThat was both satisfying - I wasn't promised more than what I got - and disappointing - I totally expected something fancier from "Orgamists", something I couldn't do myself.
- bakul 9y agoMost anyone can "do" origami given instructions. But no one came up with a single fold design until David Mitchell did -- minimalist designs are only easy in hindsight. At the other extreme we have Robert Lang's amazing creations (which may require many more than four complex parameters!). http://www.langorigami.com/artworks/mammals http://www.langorigami.com/artworks/mammals