Manual Fractal Art by help im a bear, teucer
April 30th, 2008 6:18 PMFirst, we modeled it with toothpicks for practice:
Hmm, too simple.
A bit better...
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.
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.
finished product
a suddenly sapphire dragon curve with blonde beauty highlights!
iteration 0
to make a dragon curve: start with a straight line
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crumple it up a bunch, then repeat on each individual straight line!
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an iteration 6 dragon curve
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me starting the final model. currently at iteration 2. by the way, since each iteration divides the line segment length by root 2, it is easier to iterate two steps at a time.
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here is iteration 4
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starting iteration 6
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completed iteration 6
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beginning of iteration 8
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working through it
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done! and starting iteration 10.
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in this picture you can maybe see that each iteration is present at the start of each subsequent iteration. see the tiny iteration 6 at the beginning of this partial iteration 10?
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about a quarter of the way iterated...
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maybe a third...
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halfway done...
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iteration 10!
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another angle
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with the floor cleared
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doktor harmon made this nifty plumb bob out of wire
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close-up on our drafting. we're not very good at that bit it turns out!
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doktor harmon drawing things on a wall
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i join him. i am so helpful
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we marked off the bits we had already copied with crosses
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then we covered everything with masking tape so we could paint!
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doktor harmon painted it, then left for journey to the end of the night chicago.
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upon return, this remained! there are still a few erors. five to be exact are visible. can you spot them? it is a fun game!
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awww that's cheating. you cheater. here i am covering them up with paint.
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i am not very tall ok
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doktor harmon is also capable of wielding a sponge brush
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a close up, in which we have started filling in the individual lines with blue sharpie
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waiting for the paint to dry
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here is a neat angle!
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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.
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!
This is wonderful. Everyone should have this kind of painting on their walls.
i am not very tall ok
Neither am I!
You guys did a fantastic job on this. It's awesome.
I just want to say, this praxis just ruined my life. I've spent the past two days drawing out colorful illustrations of this very fractal for this very task only to find out that you guys did it first. Now what am I gonna do?
Good job though. :)
Do a different art project with the same fractal. It's pretty enough for more than one!
pretty sure one of the saddest things in my life is knowing that this is painted over.
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.