As laser cutting and 3D-printing projects piled up, I was spending more time slinging points and paths -- aka vectors.
Inkscape, the free, open source vector program, is the default doorway to vectors. If you had the cash, you might spring for Adobe Illustrator. But Inkscape's stripped-down interface is well suited to the struggle to understand vectors.
Vectors versus Pixels is a common topic on the Web. It comes up a lot as people try to push pixel-based images -- .jpg's and .png's -- into vector jobs. Like laser cutting, or large, high resolution imagery.
The difference is that vector images consist of mathematically defined paths. Pixel-based images, frequently called "raster" or "bitmap" images, consist of an array of pixels, which together create an image.
Many comparisons emphasize that vector images don't lose resolution when you make them bigger; raster images tend to fall apart. This is related to your interest: that vector images are more precisely defined.
You're starting to like points and paths over splashes of dots. You can do more with them, like use a line to laser-cut a shape.
One image you play with: a photo you took outside of Fab@CIC. You use Inkscape to convert it to a vector image. It's now the lead image on this post.
A larger, uncropped version of the image is below. (Of course, both had to be exported to .pngs to display here on the web, but you get the idea).