Tom Rokicki builds 0, 2, 2+i from 0 in four steps. It's easy to prove that it takes at least three steps ... and I just realized that three steps can indeed be done. So there's a certain sort of "code golf" that can be played with this sort of puzzle. Answer below. 1 6 1 8 0 3 3 9 8 8 7 4 9 8 1. Unfold 0 to 2 2. Unfold 0 to 2+2i (2 is on the crease) 3. Fold 2+2i to 2+i. On Thu, Oct 22, 2020 at 3:12 PM Tomas Rokicki <rokicki@gmail.com> wrote:
Spoiler space.
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Unfold (0,0) to (2,0) Unfold (2,0) to (3,0) (creates (5,0) as well) Fold (5,0) to (3,0) Fold (3,0) to (2,i).
This is just my raster strategy, only using a spiral instead of a raster.
-tom
On Thu, Oct 22, 2020 at 10:50 AM Allan Wechsler <acwacw@gmail.com> wrote:
Okay, two things: a comment about notation, and a starting puzzle.
I mentioned that I could do 0 -> 0, 2+i in two moves. Here is my solution, presented as a way to suggest an unambiguous and fairly terse notation.
1. Unfold 0 to 2+2i. 2. Fold 2+2i to 2+i.
In each case the operation is performed so as to put a copy of the first point onto the second. This specifies the crease axis unambiguously. Some moves are illegal, so it isn't acceptable to say "unfold 0 to 2+i", because there is no permissible crease that does that. The second point has to be a queen's move from the first.
Now the puzzle, the simplest one I haven't been able to do yet:
From {0}, construct {0, 2, 2+i}.
On Thu, Oct 22, 2020 at 1:40 PM Fred Lunnon <fred.lunnon@gmail.com> wrote:
And a dodgy eastern-european billionaire or two? WFL
On 10/22/20, Tomas Rokicki <rokicki@gmail.com> wrote:
This is very nice. Thank you! Now we need some challenges---goal dots, as it were. And a leaderboard! And a world record page, and sponsors, and twitch feeds, and a competition rules committee.
On Thu, Oct 22, 2020 at 3:49 AM Christian Lawson-Perfect < christianperfect@gmail.com> wrote:
I've arguably wasted my morning by making an interactive version of this, as Jim requested: https://somethingorotherwhatever.com/gaussian-origami/ While it sort of works on touchscreens, it's easiest with a mouse.
On Thu, 22 Oct 2020 at 10:56, Tom Karzes <karzes@sonic.net> wrote:
To fold (0,101) onto (51,50), the / fold needs to pass through (0,50) rather than (51,0).
If I understand this correctly, the sequence is:
1. Start: {(0,0)}
2. Unfold(-) through {(0,50.5)} to obtain: {(0,0), (0,101)}
This is a bottom-to-top unfold.
3. Fold(/) through (0,50) to obtain: {(0,0), (51,50)}
This is a nw-to-se fold, so (0,0) is unchanged. This is the first described fold.
4. Fold(\) through (51,1) to obtain: {(0,0), (2,1)}
This is a ne-to-sw fold, so (0,0) is unchanged. This is the second described fold.
This general approach seems to work well when it's possible to isolate a single point on one side of a fold, allowing that one point to be moved without changing any of the others.
In general, if you have a cluster of points, you can replicate it at a great distance away by unfolding about a distant crease line. You then need to eliminate those replicated points by folding inward, until only one replicated point is left. I believe this is always possible (see below).
Once you're down to a single replicated point, you position it at the desired position near the original cluster. The process can then be repeated until the desired set has been contructed.
To reduce a distant replicated cluster of points to a single point, I believe the following will work. Create the replicated cluster vertically above the original by folding upward about a distant horizontal crease line. Then perform a series of \ folds, folding ne-to-sw, until all of the replicated points lie on a single nw-se line. Then perform a series of / folds, folding nw-to-se, until you're down to a single replicated point.
Tom
Tomas Rokicki writes: > Sure. Let's see, 2,1 is odd so set a point at (0,101). > Flip that bad boy up to (51,50) with a / mirror at > (51,0), and then flip it to (2,1) with a \ mirror at > (51,1). > > On Wed, Oct 21, 2020 at 9:08 PM Allan Wechsler < acwacw@gmail.com
wrote: > > > I'm afraid I'm not following the explanation. Can you illustrate by showing > > a construction for {(0,0), (2,1)} ? > >
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