Christian: how big is the original Elm program?
The code is at https://github.com/christianp/gaussian-origami. It's just over 400 lines of elm at the moment. I really really should be doing my actual job, but I think it would help matters to be able to share links to sequences of moves, so I'll try to add that. On Thu, 22 Oct 2020, 21:39 Allan Wechsler, <acwacw@gmail.com> wrote:
I think Tom's 3-step solution is incorrect, and produces i as well as the desired 3 points. But this could be interpreted as a difference of opinion about what the "unfold" operation does. I imagined "unfold" as the union of the original set and its reflection around the crease. Christian's web app agrees with me.
Christian: how big is the original Elm program?
On Thu, Oct 22, 2020 at 4:16 PM Tom Karzes <karzes@sonic.net> wrote:
Nice. I have a different 3-fold solution:
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1. Unfold 0 to 2+2i 2. Fold 2+2i to 2+i 3. Unfold 2+i to 2
Tom
Allan Wechsler writes:
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.
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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}.
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