The Geometron Shape Table

In Geometron, "shape" means something specific, yet circular: shapes are the action glyphs in the shape table. Shapes are how the general geometry actions of the 0300 action layer get to creating extremely specific languages. It is this specificity that more than anything marks Geometron as different from other types of language. By far the best way to understand why the concept of a table of action glyphs which can reference itself is powerful is to just construct a few tables and show rather than tell how this system works. There will be examples of building shape tables here, and then more complete and distinct examples in another chapter.

The very first shape in the table is one that we almost always leave alone: the square. The square is made up of four lines, four rotations, and four movements forward:

One reason it's important to almost never edit this particular shape is that it's used in all the standard symbol glyphs as the container. For example the symbol glyph for the square, which is at address 01200 is
This square is the simplest possible square. But to show the power of shapes built on shapes I'm going to use that square to make a square that is more convient for building things out of. This will be the same size square, but with the point of action at the center instead of the corner. To do that we shrink the cursor by 2x, move it, expand it, draw the square, and reverse the shrink-move process. The spelling of this glyph is shown here, along with the symbol glyph:
Note that as we build up these shapes it is a good idea to be always creating symbol glyphs as we go. It's not technically required, but it allows us to read the glyph spelling of each new glyph, which can make documentation of the end result possible in a way that is totally self-contained without reference to either a human or computer language--and that's a very useful thing!

With this square, I'll now add another extremely simple shape, the move-and-draw-square(I've added a rotation to make the canvas cleaner):

"So what?" you might ask. Does this really save that much time? Well, if we now add that move-square as a command and build a art program on it, let's see how easy it is to build things quickly. I'll start with a couple examples then give you an interactive canvas to play with.

This is four boxes stacked:

And now we can use that to make a square made of squares:
Now we put that shape into another shape with zooms and movements to get to the center, to build a fractal zoom art pattern:
Note that this whole thing is built on the foundation of just one shape, which is built on the square. Changing that shape can then change the whole thing. Here is the same shape but with just the change of the base shape: Now we put that shape into another shape with zooms and movements to get to the center, to build a fractal zoom art pattern:
And now with another shape just because we can: Now we put that shape into another shape with zooms and movements to get to the center, to build a fractal zoom art pattern:
This kind of switching out of one shape for another in a huge system of shapes is not just of artistic interest. This is the kind of thing that enables Geometron to be of industrial utility.

Now you will build things out of shapes.

Geometric Recursion

What if a function just links directly back to itself? Let's try this.
This glyph calls itself. This is the path to infinity, zero, madness, and demons. And it can indeed lead your computer to insanity just sure as demons did to Aleister Crowley. The way to break this knot of insanity is with what I call the Explode Index. We keep resetting this index from time to time, at any reset event or command. If, in the middle of a glyph calling itself, Explode Index gets bigger than a certain point, it breaks out. I do this manually, I'm sure there are other ways, but simplest ways are best for our purposes.

We must manage madness, tame it, and use it.

Shape Languages

Here, in the shape table section, it's important to go over the various specific shapes that get the most usage. Each basic shape can create a whole language. Doing this with the equilateral triangle was one of the initial catalysts that started the whole thing.

What follows then is building up a language based on simple shapes and some simple variations on those shapes. This is worth doing slowly and with a lot of annotations and examples, since it's such an important case. I believe that with this case described explicitly enough here that many readers will be able to modify this to their needs or use it as is, to create a vast wealth of art in this medium. But all that requires that this section err on the side of being overly verbose instead of leaving things as an "exercise for the reader[one of my least favorite phrases in math and physics books]".

I'm also going to err on the side of too many shapes, most of which you will never use, rather than not enough. Fill up the table! Why not? Let's build a commons of shapes that is really universal to start from.

That being said, I'm starting with a study of the equilateral triangle. I begin with the simplest possible triangle:

From this we can build a bunch of other triangles by rotating the first one around, then rotating the cursor back to where it started:
And some more:
These and two more make a whole set of triangles:
Six triangles make a hexagon. Now I will make a more interesting triangle to make other types of art.
These are the same symbol glyphs, but notice that now the triangles are smaller than the unit of the lattice. This makes an interesting effect of outlining.

Moving on to the next triangle project is the geometry of curved corners. Square root of three must be very carefully used here.

This creates a triangle with circular arcs for corners, as a closed figure, centered on the start/end location of the cursor. It took me quite a few tries to get this right, and it's easy to make a triangle that looks about like it's centered on the right place, but turns out to be off by a little bit by misusing the combinations of square root of 3 zoom and zooms by 2x. It's important to have the shape really centered in this way so that we can build up from this in a simple way.

To start with, we apply a minor scale zoom, then write that curved triangle, then un-apply it as follows:

With this whitespace border added, we can chain them together into a unit cell of two from which structures can be built:
Having built this foundation, it only takes a couple actions to build a recursive tentacle spiral out of this basis:

remaining elements of shape chapter:

Shape Table Workflow

The workflow of using Geometron shape tables differs significantly from that of traditional methods. While it is common when using existing design software to have a library of commonly used elements to draw on, and to edit that library as needed, Geometron takes this process to the next level, and has more complex dependencies which have both upsides and downsides.