Lovely pics! Do any of those curves give rise to interesting number sequences (giving say the number of square cells, or blobs, or curve segments), as they grow? For some animations in the OEIS, which certainly are associated with sequences, go to https://oeis.org/A139250, scroll down to the second link (David Applegate, The movie version), pick any of a hundred different sequences from the drop-down menus, and click Next repeatedly - or click Run. The E-toothpick sequence, A161328, is especially pretty - and no recurrence is known for it .... Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Wed, Dec 27, 2017 at 8:08 AM, Tom Karzes <karzes@sonic.net> wrote:
Here's an inside-out version, showing that the inside and the outside, while visually distinct, may be freely interchanged:
http://www.karzes.com/ghack14-inv-twin-1.gif
Tom
Tom Karzes writes:
Here's a twindragon version of the same thing, formed by gluing together two Heighway dragons:
http://www.karzes.com/ghack14-twin-1.gif
Given that this is now a closed curve, it would almost certainly look better filled, but, still lazy...
Tom
Tom Karzes writes:
Nice - I like it!
I have some Heighway Dragon renderings that use different styles for left- vs. right-turns, resulting in a nice inside vs. outside distinction. Here's one of them:
http://www.karzes.com/ghack14-1.gif
For more examples, see:
http://www.karzes.com/dragon.html
They would probably be more dramatic if I shaded one side of the curve, but I'm too lazy.
Tom
Bill Gosper writes:
Looking to illustrate spacefilling by using continuously varying colors, with no tricky phases and sampling frequencies, I found gosper.org/blackdrag.png ​which looks nice all black yet shows the course of the spacefill, using only actual dyadic rationals from the Dragon recursion. The trick is to replace every triad of consecutive points by a triangle with those vertices. It might be tweakable into one of those inside|outside https://pictures.abebooks.com/isbn/9780262630221-us-300.jpg Minsky-Papert perceptron confusers. Not that gosper.org/mediandrag2.png isn't confusing enough. --rwg
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