You've probably posted it for some other reason altogether, but thanks for posting it so you could spur me in new thought-directions! I know nothing about geomancy, so what's inside the "points" doesn't make sense to me, however the geometry itself might be useful.
You're welcome!
Mathematically, the geometry is called a unit-distancetesseract graph. (This is the four-dimensional case of a hypercubic graph.) It's effectively the shape that a four-dimensional cube (e.g. a "tesseract") makes if you squish it flat onto a piece of paper.
How does this relate to geomancy? Geomancy is an elemental symbolic system where there are sixteen symbols, each with some of the four elements (fire, air, water, and earth) are either present or not present. (The meaning of each figure depends on which elements are present: for example, the figure "Carcer" is a combination of fire and earth, and means "separation" since these two elements do not mix well and tend to pull in opposite directions.) Each vertex of the graph contains one figure, and has a line to each figure that varies from it by flipping exactly one element. (That is, each figure links to the four figures that are most similar to it.) There are a lot of ways to assign the figures to the vertices (in fact, around 21 trillion ways), but I chose one that has really elegant properties. (One example is that the direction of each line represents an element; another is that the most "mobile" figures appear at the top and the most "fixed" figures appear at the bottom; another is that the most "passive" figures appear at the left and the most "active" figures appear at the right.)
I posted it as a theme for meditation; walking the paths around the overall figure is useful, I find. (In fact, meditation is where I got this in the first place!)
Would you mind if I also posted your image (with attribution)?
Not at all. In fact, attribution isn't necessary (though you're welcome to credit me or link here if you like). Like everything I post, it's in the public domain.
Also, how do you make all these great charts/images? My question's accompanying images are going to have to be hand drawn.
Oh, dear. That's complicated.
The short version is that there are computer "languages" describing how to draw pictures; in this case, the one I used is called Scalable Vector Graphics (or "SVG" for short). It's a text format (in fact, if you're familiar with HTML, it's very similar), and I wrote it out by hand using a text editor. (The text editor I use is an ancient one called Vi, which is basically Notepad or TextEdit.)
I used lots of trigonometry and analytical geometry (which I worked out by hand on paper using a pencil) to construct it. The lines so happen to have a slope of tan(π/8); this is a complicated irrational number (and there's no way I'm dealing with those by hand), so I used a Stern-Brocot tree to find an appropriate integer approximation (in this case, 17/41); from there it was just a couple quiet hours with a calculator. (I have severe chronic fatigue, so I require an extremely large amount of "down time;" I figure I might as well use it as productively as possible.)
I'm a computer programmer by profession, so these are the kinds of tools I use on a daily basis at work! I picked them up bit-by-bit over the last few decades, and I guess I'm just used to them by now.
no subject
You're welcome!
Mathematically, the geometry is called a unit-distance tesseract graph. (This is the four-dimensional case of a hypercubic graph.) It's effectively the shape that a four-dimensional cube (e.g. a "tesseract") makes if you squish it flat onto a piece of paper.
How does this relate to geomancy? Geomancy is an elemental symbolic system where there are sixteen symbols, each with some of the four elements (fire, air, water, and earth) are either present or not present. (The meaning of each figure depends on which elements are present: for example, the figure "Carcer" is a combination of fire and earth, and means "separation" since these two elements do not mix well and tend to pull in opposite directions.) Each vertex of the graph contains one figure, and has a line to each figure that varies from it by flipping exactly one element. (That is, each figure links to the four figures that are most similar to it.) There are a lot of ways to assign the figures to the vertices (in fact, around 21 trillion ways), but I chose one that has really elegant properties. (One example is that the direction of each line represents an element; another is that the most "mobile" figures appear at the top and the most "fixed" figures appear at the bottom; another is that the most "passive" figures appear at the left and the most "active" figures appear at the right.)
I posted it as a theme for meditation; walking the paths around the overall figure is useful, I find. (In fact, meditation is where I got this in the first place!)
Not at all. In fact, attribution isn't necessary (though you're welcome to credit me or link here if you like). Like everything I post, it's in the public domain.
Oh, dear. That's complicated.
The short version is that there are computer "languages" describing how to draw pictures; in this case, the one I used is called Scalable Vector Graphics (or "SVG" for short). It's a text format (in fact, if you're familiar with HTML, it's very similar), and I wrote it out by hand using a text editor. (The text editor I use is an ancient one called Vi, which is basically Notepad or TextEdit.)
I used lots of trigonometry and analytical geometry (which I worked out by hand on paper using a pencil) to construct it. The lines so happen to have a slope of tan(π/8); this is a complicated irrational number (and there's no way I'm dealing with those by hand), so I used a Stern-Brocot tree to find an appropriate integer approximation (in this case, 17/41); from there it was just a couple quiet hours with a calculator. (I have severe chronic fatigue, so I require an extremely large amount of "down time;" I figure I might as well use it as productively as possible.)
I'm a computer programmer by profession, so these are the kinds of tools I use on a daily basis at work! I picked them up bit-by-bit over the last few decades, and I guess I'm just used to them by now.