Welcome to Fractal Forums

A Seahorse Odyssey XXIX

(http://nocache-nocookies.digitalgott.com/gallery/11/511_15_04_12_4_37_56.jpeg)

http://www.fractalforums.com/index.php?action=gallery;sa=view;id=11010

On the hair inside the seahorse-head spiral near the microbrot is this seahorse jewel. The microbrot tendril's influence is buried deep in the heart of that central twinned spiral and won't become apparent for several more zooms.

Beautiful, looks almost like a Julia set with tendrils

It basically is, although this is a Mandelbrot image. The earlier posts titled "A Seahorse Odyssey" something are all outzooms from here, leading back to a big minibrot at a shallow magnification.

The phenomenon is more general; zoom into the "nodes" along the filaments around a minibrot and you'll find what I call "jewels" that are basically copies of disconnected Julia sets that are held together by more filaments. If you're in the minibrot's Seahorse Valley you get Seahorse Valley Julia sets, for example.

In this instance, we're in Seahorse Valley of a shallow minibrot and close to a tendril of a much deeper minibrot. The nearly-straight whiskers are filaments of the shallow minibrot, so the jewels are Seahorse Valley ones and are large compared to the filament. ("A Seahorse Odyssey XXVIII" has most of the filament, and the jewels can be seen as diamond-shaped objects strung along it that are fairly large.) Zooming deep into this jewel should reveal one associated with the deep minibrot, much smaller compared to the filament. The deep minibrot's filaments are the seahorses and spirals around here, so the deep jewel's features will be held together by a tapestry of seahorses and seahorse tails rather than just whiskers. But any sufficiently deep zoom into these, in turn, will end up showing areas that are separated and held together with only whiskers. Such zooms will be forthcoming in this series.