SF0 / teucer / Manual Fractal Art

15 + 180 points

Manual Fractal Art by teucer, help im a bear

April 30th, 2008 6:18 PM

INSTRUCTIONS: Produce a piece of fractal art. Documentation should include both the artwork and a discussion of the mathematics that helped you create it.

The artwork must be executed without the aid of a computer.

The Dragon Curve. Objectively the prettiest of the simple fractals. Protagonist of Jurassic Park. Therefore an obvious choice for painting on Doktor Harmon and JJason's apartment wall.

First, we modeled it with toothpicks for practice:

iteration 4 dragon curve

Hmm, too simple.

an iteration 6 dragon curve

A bit better...

iteration 8

Getting there...

Ah, there we go. So, with that as a guide, we sketched it on the wall. Using an appropriate plumb bob for guidance, of course.

Then we painted it in Suddenly Sapphire, though Sir Moss-a-Lot was a tempting alternative.

final

One (1) iteration 10 dragon curve, painted (and touched up with Sharpie) on an apartment wall!

EDIT: It has come to our attention that we are missing out on the math here. This is actually incredibly simple, as such things go. At each iteration, every line is replaced with two lines, forty-five degrees off from the original; which direction they go alternates. Not coincidentally, since folding a strip of paper hamburger-style has the effect of breaking it into two strips, this curve is the result you get if you fold such a strip repeatedly, always folding the newest fold toward the other end rather than vice versa, then unfold it so that all folds are right angles.

Because each straight line gets replaced with an iteration-one curve, and each iteration-one curve with an iteration-two curve, and so forth, the curve is self-similar - and thus, a fractal. This is, of course, only a ten-iteration approximation of it.

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(no subject) +1

posted by Lincøln on April 30th, 2008 6:32 PM

There is so much win here. That plumb bob is particularly awesome. As are the toothpicks, and the tape, and the paint, holy crap. Win.

(no subject)

posted by C.M. Gonzalez on May 1st, 2008 8:31 AM

Hamburger-style?

(no subject) +2

posted by teucer on May 1st, 2008 9:39 AM

At least when I was little and doing artsy things in elementary school they would refer to folding paper in half "hot-dog-style" and "hamburger-style." "Hot-dog-style" was also called "lengthwise" and involves the fold being parallel to the long sides of the paper; "hamburger-style" doesn't have any other term for it that doesn't sound really stilted (widthwise? shortwise?) and means the fold is parallel to the short sides of the paper.

Unlike the hot-dog one, it doesn't look much at all like a hamburger bun, but my teachers didn't like it when I mentioned this fact.

(no subject)

posted by C.M. Gonzalez on May 1st, 2008 10:31 AM

Oh, I gotcha. Neat.

(no subject)

posted by meredithian on May 1st, 2008 9:49 AM

i am in the process of doing this task. your fractals are of a totally different pattern than the ones i am trying out, which are decidedly more simple. way to go!