Current project(s) - the mathematical side of doodling

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Nishat's paper covers the exact question of this thread. Thanks for finding it!

My terminology's likely to be way off as I'm not a mathematician, and so far I only very briefly skimmed the first paper that you linked, meaning I've certainly overlooked the vast majority of it.

What I'm specifically interested in right now is generating legitimate transformations of one glyph into its neighbouring glyphs in the graph.


Other goals are currently secondary and most likely have pre-existing technical implementations.

SVG appears to be a sensible format to continue with

 

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Of interest here.

Only just noticed these, btw. Will have to plough through them in due course

 

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I may have figured it out. If so, soon I'll post a little program to generate and display all square glyphs for a given size.

 

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I may have figured it out. If so, soon I'll post a little program to generate and display all square glyphs for a given size.

This is what @Hyper Turtle was working towards before we ran out of steam back then. Do you think the program can be adapted to the question of 'neighbouring mutations', if you haven't already written it with that feature in mind?

If you need me to clarify with examples, let me know and I'll happily explain further, but that feature is one of the keys to the 'dancing glyphs' project as I envisage it in its fullness.

And thank you so much for dedicating some time to this

 

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Do you think the program can be adapted to the question of 'neighbouring mutations', if you haven't already written it with that feature in mind?

If my approach (following the Muchas Crowley paper) is correct, I have an idea about how to go about it, yes. There are two constraints that must be followed by a cell: not cause any of 4 forbidden patterns, and if it's an exterior cell, be connected to the outer layer through a single path.

So one could examine all the cells of a valid configuration and check which ones could be switched from inner to outer without violating the constraints, and then switch a random one of those. I'm not sure this will be possible for every valid configuration, but it's a start. If it works, I'll look into extending it to handle cases where more than one cell at a time are switched while still preserving continuity. But I don't want to get ahead of myself.

And thank you so much for dedicating some time to this

My pleasure, I like the idea so I have been thinking about it from time to time. It's fun.

 

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Is it helpful to have the nearest neighbours of each glyph clearly defined? This is at least the way I've been handling the question in my own mind, but maybe that's just another variation of brute-forcing it, or even a different way of saying the same thing.

 

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Is it helpful to have the nearest neighbours of each glyph clearly defined? This is at least the way I've been handling the question in my own mind, but maybe that's just another variation of brute-forcing it, or even a different way of saying the same thing.

Not with the approach I'm using, but that's just because what is helpful for a human and what is helpful for a computer are often very different things. For a program, checking whether every cell in a grid can be mutated without creating invalid patterns is close to nothing, even if the grid is quite large. Whereas for a human it would be unbearable.
There may be methods where that's useful, and I'm not sure if my approach will work.