
Drawing an elephant with four complex parameters (2008) - Myrmornis
http://fermatslibrary.com/s/drawing-an-elephant-with-four-complex-parameters
======
ourmandave
And 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)

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bakul
Origamists 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)

~~~
mar77i
That 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
Most 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)

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nabla9
Visualization of the same technique:

[https://www.reddit.com/r/Art/comments/7wztif/generative_art_...](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/)

~~~
tabtab
The 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
Homer Simpson in 1000 epicycles:
[https://www.youtube.com/watch?v=QVuU2YCwHjw](https://www.youtube.com/watch?v=QVuU2YCwHjw)

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tlarkworthy
Slightly cheating by using complex numbers so there is 8 degrees of freedom
instead of 4. But bravo anyway, it was a great exercise.

~~~
soVeryTired
I'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
Degrees 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_(statisti...](https://en.m.wikipedia.org/wiki/Degrees_of_freedom_\(statistics\))

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.

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tabtab
This parametric equation set draws a hamburger: x=sin(tan(t)) and y=cos(t)

Picture:
[http://uncyclopedia.wikia.com/wiki/File:Hamburger_plot_ies.P...](http://uncyclopedia.wikia.com/wiki/File:Hamburger_plot_ies.PNG)

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logfromblammo
And 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
Well, 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
That 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
I 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
I think the difficulty is actually in arranging them such that they combine to
make an interesting algebra.

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chaosopher
A mechanical harmonic (Fourier) analysis device:
[https://www.youtube.com/watch?v=NAsM30MAHLg](https://www.youtube.com/watch?v=NAsM30MAHLg)

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rogerallen
Bonus points for the first to reimplement this in PyTorch or Tensorflow.

~~~
983
Here you go:

[https://github.com/983/Elephant/tree/master](https://github.com/983/Elephant/tree/master)

~~~
rogerallen
Congratulations, full bonus points awarded!

Seriously, that's very cool. Well done.

~~~
983
Thanks :)

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Sharlin
See also: Mechanical Laser Show [1]

[1] [https://youtu.be/_dtBUiaAqRE](https://youtu.be/_dtBUiaAqRE)

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thom_nic
I'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
this is actually a standard first example in Fourier analysis, since more than
a hundred years ago

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ttoinou
Are all parameters not described equals to zero ?

