This could probably be extended to more than two images. Don't know how far you can push it before the images look too contrived to be interesting.
In thinking how I would start, I imagined starting with only one kind of shape, except filling/flattening out the edges/corners. Then come up with a dual picture that depends on 2 arrangements of the pieces. Finally adjust the edges of the piece shapes without breaking the 2 selected arrangements but allowing all the other possible arrangements to collapse down.
It's like making a repeating/tiling shape where you start with a blank tiled plane then start drawing anywhere, all the repeated places also get drawn in, and you keep drawing/undoing until you like what you see. i.e. 'maintain the constraint from the beginning'. The tricky bit is in the drawing/painting. I imagine the same could be done with this jigsaw, blank the pieces, show both arranged blanks, and let someone paint on the pieces updating both as you go. When you like what you see, you're done.
Check out Stave Puzzles if you want to get into insanely difficult jigsaw puzzles with multiple solutions. Some have multiple solutions (3+) and some go 3 dimensional. I have one that is either a 3 or 4 leaf clover.
I feel like using AI to make optical illusions have been some of the more interesting things to come out of the generative image AI thing.
I suppose when it comes down to it, image AI could be viewed as a fancy way to interopolate between human meaningful images where the inbetween values are still human meaningful. I wish that the AI discussions had more of a focus on that, as it seems unique and novel, and much more interesting than the tired moral panic around "what is art?"
There was a post a while back about making QR codes that look like other things that was also super cool.
It’s kind of a shame they had to use AI to get the images to tessellate properly. Seems like there should be some math there.
Escher would do something more with this if he were alive.
It’s not like they just wrote a prompt and got a result. It sounded like a very hands-on process.
While they used the same process generative AI uses, it doesn’t sound like they really used AI.
They literally explained how they used GenAI and to generate the image.
As Steve Mould describes it, solution is very mechanical. You start from chaos and gradually improve it so that it matches two different image classes. Pattern-matching is not considered AI nowadays.
Uh, that's literally how Stable Diffusion works, and I think it's considered GenAI?
I'm not sure how jigsaws are usually modelled in maths. I feel like there should be a graph model? Perhaps each piece could be labelled and have 'dangling' half-edges that are coloured such that they can only be connected to the appropriate partner.
Then a two solution jigsaw would be a set of these pieces that reconstruct into two different labelled graphs.
Hmm ok I realise this is all very dumb, as it's the labelling (the image!) that is the tricky part here ...
It seems like there's a simpler, lazier solution to having a puzzle with just two solutions.
Just make two corners diagonal from each other interchangeable, then simply print "this side up" on one of the corner pieces and have the image be a rotational illusion that look like different items when rotated 180°
And in the video Matt talks about the effort he went to in order to avoid trivial solutions like that. He wanted to find the least trivial one he could.
Or don't print an image at all, leave it a solid color, and then you have four solutions - two landscape, two portrait - if you leave yourself restricted to 90° angles.
(Technically eight, if you also flip the puzzle upside down.)
Trivial solutions aren't interesting solutions.
Or just flip over a normal jigsaw and give yourself a challenge.
Long before this Matt video, I've done just that. A generator of devilish no-image jigsaw puzzles :-) which I indeed wanted to do a little Show HN someday. I made a small python script call a SAT solver to create a MxN puzzle with only 1 solution but only a few jig shapes, so maaany 'almost solutions'. Then I laser cut a plastic board and made it real, and gave one copy to a friend. At least a nice use of SAT solvers that is more efficient than Matts brute force approach.
The most recent one I did had a grid of letters on the back, to make sure things align. I wonder if that would make it easier or harder to solve than if it were a single color
There's a jigsaw brand (impossipuzzle, I think) that does something like that to make them as difficult as possible. They're printed on both sides, and the rows/columns are cut from different sides.
I have aunts that took almost a year solving one that was an 5*7 foot picture of baked beans and chips. Most of the patterns are repetitive and non-distinct on purpose.