On Mon, Nov 17, 2008 at 4:19 PM, Dan Bron <[EMAIL PROTECTED]> wrote:
> I think the colors and solidity are merely hints. Here's a much larger
> hint:
>
> http://en.wikipedia.org/wiki/Image:Dragon_curve_iterations_(2).svg
Ok, that looks reasonably simple.
If I understand properly, the basic structure is two line segments
arranged on a 90 degree angle.
start=: 0 0, 1 0,: 1 1
And the iterative process involves a 90 degree rotation and a
reflection. Specifically, the second half of the iteration retraces
the steps back to the origin but rotated 90 degrees around
what was the end point of the previous rotation.
I would like to use under here, but I can not do so tacitly.
Instead, tacit constructions requires an explicit subtraction
and addition of the end point coordinate (and my attempt
at expressing this explicitly confused me, and I did not
have enough patience to work out how to do that in a
fashion that communicates the ideas clearly):
step=: ],{: +"1 (2 2$0 _1 1 0) +/ .*~ |[EMAIL PROTECTED]: -"1 {:
step^:2 start
0 0
1 0
1 1
0 1
0 2
_1 2
_1 1
_2 1
_2 2
I think that's right, but I don't have a handy plotting
program to represent that graphically (I guess I should
dig out my copy of that fractals and visualization book...).
(If that's not right, let me know... )
--
Raul
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