Looks beautiful, when can I play? 
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No one is stopping you from starting a game (although perhaps a separate thread would be a good idea then) 
You’d need to find a way to draw the moves, I guess. Also, with Penrose tiling, you’re going to have a hard time with coordinates, but you could just number them and refer to that
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Sorry, “rediscovered”
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Well, technically, I’d say I discovered it independently, but wasn’t the first one to do so. It’s not my most creative variant either, just a different graph to play on, and this graph is pretty famous anyways. The Penrose dual might be new territory, though, who knows…
Rediscovered sounds more like discovering someone else’s idea and bringing it back under the spotlight.
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I smell a new Leibniz-Newton controversy!
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Before someone beats me to it…
A good variant for playing on the tiles instead of the intersections, I guess. It’s quite disorienting and especially hard to figure out how to hane around those pentagonal corners.
There are a lot of star points, but oh, you can’t play on them.
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Exactly 
I’ll only be able to play on mobile…
So, I played around with making something to create custom graphs to play Go on.
One thing that I want to try, is to use some physics-based techniques to get the graph to look nicely and untangled, by the edges wanting to grow to a preferred size (like springs), and having vertices wanting to be as far away from each other as possible. It’s not exactly working, yet, but at least it already looks funny:
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I think you should have to play on a moving board, like that
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It’s now exactly working, the mistake was that the ‘spring-like’ edges were only pulling on one of the two vertices they were connected to, which is why it seems to be pulling itself along.
Now I have a quivering graph that settles in a local minimum in terms of tension, but not in the global minimum:
I think perhaps a genetic algorithm may work better: give every node several random nudges in different directions, and settle with the option with least overall tension. Let’s see. Maybe a combination of both may work.
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So, by putting in some controls I can adjust the physical constants or make one kind of force stronger or the other kind of force stronger. By doing that, you can nudge the graph to become roughly the shape you want:
After it’s roughly satisfactory, lowering the effect of all forces makes it settle into a pretty nice form:
I also made a genetic algorithm, but it behaves weirdly. I’m not sure what it does or why it does what it does. Here it is taking only local tension into account:
Somehow it wants to shrink the outside, which is weird. The nodes should be repelled by having edges that are too short, so why does it want to shrink?
Using global tension doesn’t make things better:
In fact, after switching back from global to local, it’s clear that the local computation makes the central areas distribute more evenly than the global one:
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Well there is this minimal surface idea, that things want to be like circles, spheres, bubbles etc to minimise surface tension.
Could be an effect related to that?
Perhaps, but locally it only receives force from the two neighbouring nodes, and when it gets closer to them, that force is directed outwards.
Perhaps I have the direction incorrect or something… I should sleep first, though.
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I’m totally not of that field, but I remember one of my friends with a biochemistry major told me about the difficulty of imagining proteins because they’re so entangled.
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I found out the problem while trying to fall asleep: I summed the forces first and then tried to minimise the size of the sum, instead of minimising the sum of the sizes of the forces. A node that is under a lot of tension, but gets pulled in opposite directions, would be minimal in the first case, but not in the second.
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Probably I don’t know what the forces being used are, but I look forward to more graphics
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These graphics are awesome.
I just had a thought - would an extra degree of freedom (allowing the nodes to move around in 3 or more dimensions) help them to settle faster?
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Could also consider playing in 3 or more dimensions…
Surprised no one has mentioned Calabi-Yau manifold yet
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11,6
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