There Be Ter-Dragons

January 9, 2017 9:38 AM

Brainfilling Curves, by Jeffrey Ventrella, is an explanation and exploration of various subspecies of fractal curves, including fat dragons, Gosper islands, and the occasional aggressively self-touching specimen. Also in PDF if you like.
posted by cortex (6 comments total)

now I want a sockpuppet account named aggressively self-touching specimen
posted by hippybear at 9:42 AM on January 9, 2017 [11 favorites]

A rep-tile is a plane figure that tiles the plane and can be divided into several smaller copies of itself. Some examples are shown below at left. At right are pertilings (fractal rep-tiles) of a specimen I will show you later.

This can be used to make pretty pictures. For example, you can take an image and recursively subdivide it into tiles, stopping your subdivision when the pixels in a given tile are similar enough, and giving each tile a solid color. Many computers ago (and sadly before the advent of cloud storage) I made a program that did this with Gosper islands (well, a sort of built-out-of-hexagons finite approximation thereof).
posted by a snickering nuthatch at 9:53 AM on January 9, 2017

cortex, you must really hate that stencil-cutting machine ...
posted by scruss at 11:14 AM on January 9, 2017

I'm right now working on a sort of interactive music box that uses dragon curves to generate a melody. This isn't really new territory, and the concept, as applied to music, produces very 'theoretically correct" melodic patterns.

I only mention this because the book that exposed me to the idea barely scratched the surface. This site is really comprehensive in real world examples and mathematical examples. So cool, thanks!
posted by lownote at 11:32 AM on January 9, 2017

I like this taxonomy of squiggles.

Especially this guy which makes me feel like I'm wearing a bell bottom jumpsuit about to enter the botanical pod of my space habitat.
posted by fleacircus at 8:51 AM on January 11, 2017

This rabbit hole is relevant to my interests (it's basically taken up all of my non-working time since Monday).

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posted by sparklemotion at 3:19 PM on January 11, 2017