My original conception (poorly expressed in my initial posts) was that the "unfold" operation didn't have a preferred side: it simply produced the union of the original set and its reflection. Tom Karzes had a different definition for "unfold": the union of the original set with the reflection of one half-plane. There are other possibilities: unfold could mean, unfold one side of the crease onto the other, deleting whatever was originally on the other side. Or it could only be legal to unfold when one half-plane was already empty. Each of these choices will lead to different puzzles being solvable or not, and will make the minimum number of moves different. I don't have any good reasons to prefer any definition over the other, but discussions should be clear about which definition they are using. What I would really like, from a puzzling perspective, is a set of rules that is "universal" in the sense that any set can be transformed into any other, but some puzzles are insanely hard, and the difficulty is not just correlated with the number of dots. There are endless possible basic operations (union with 90-degree rotation; xor with one-cell shift; and so on and on). But I would like to find a basic toolbox that spawns a nice set of puzzles. On Sun, Oct 25, 2020 at 11:09 AM Tomas Rokicki <rokicki@gmail.com> wrote:
This is great!
I was thinking: is it possible to make "u" unfold and "f" fold, so we don't have to keep hitting the button to switch?
Or if you prefer, make click fold and shift-click unfold?
Or left click fold and right click unfold?
Even though I mostly use vim these days, I'm not a big fan of modality . . .
-tom
On Sun, Oct 25, 2020 at 7:54 AM Christian Lawson-Perfect < christianperfect@gmail.com> wrote:
A little update: I've changed my interactive thing so that you have to click once to select a line, then again to select a side to fold onto. I've also made it keep track of moves and store them in the URL, so you can share solutions more easily. Finally, I changed "unfold" so it only folds the points on one side.
Allan, is it OK if I share this outside math-fun, crediting you with the idea?
On Fri, 23 Oct 2020 at 07:05, Christian Lawson-Perfect < christianperfect@gmail.com> wrote:
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:
1
2
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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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0
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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. > > 3 > > 1 > > 4 > > 1 > > 5 > > 9 > > 2 > > 6 > > 5 > > 3 > > 5 > > 8 > > 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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