perplexus.info :: Shapes : Various Valleys, More Mountains

Various Valleys, More Mountains (Posted on 2006-07-26)

Fold a strip of paper in half two times and unfold. Put the strip on its side and adjust each angle to 90 degrees. It will look something like this:

___   
   |  |
   |__|

If you could fold the paper in half an infinite number of times and adjust every angle to 90 degrees what appears to be a fractal would be formed.

Is it a fractal? If so, what is its fractal dimension?

Submitted by Jer

Rating: 2.5000 (2 votes)

Solution: (Hide)

This shape that arises is a fractal because it shows self-similarity. Since it fills the plane its dimension is 2. It is actually a well known shape called the Dragon Curve.
The following is a quote from http://library.thinkquest.org/26242/full/fm/fm8.html
"Since the motif has 2 identical line segments of sizes 0.5·sqr(2), the dimension is log 2 / log (2·sqr(2)) = 2"
or see also http://en.wikipedia.org/wiki/Dragon_curve

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Thoughts	K Sengupta	2023-08-07 23:58:36
Dimension	vswitchs	2006-08-20 16:51:23
Another thought	Tristan	2006-08-15 23:51:26
Spoiler link	Tristan	2006-08-11 02:30:49
Some possibly enlightening sites	Jer	2006-07-27 14:51:04
this is wierd...	laura	2006-07-27 12:18:24
Have you ever...	Federico Kereki	2006-07-27 08:08:38
?	Hugo	2006-07-26 18:02:30

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