Title: Your favorite names of the regions of the Mandelbrot Set Post by: Yggdrasil on October 13, 2014, 08:29:42 AM You all know where the Seahorse Valley and the Elephant Valley are located, and you all know where the Spike is, even if it's sometimes called the Stem or the Far West.
But what are your favorite names for other regions of the Mandelbrot Set, such as the Double Sceptre Valley, the Quad Spiral Valley, the main midgets and other regions? Please reply with simple image with regions marked, like in this link: http://www.nahee.com/Derbyshire/manguide.html Title: Re: Your favorite names of the regions of the Mandelbrot Set Post by: youhn on October 13, 2014, 09:24:37 PM What does a region mean in the mset? In the valley of the main bulb we have those spirals, which are referred to as elephants. Moving west, the next bulb has these spirals. But there is an extra shape. At what seems to be the (infinite) end of the first spiral, a second spiral is added. This seems to be a reflection of what happend along the way at of the branched node of the elephant spiral. Then moving to the third bulb, another shape is attached to the end of the second spiral. While this new shape consists of things we've already seen, it feels kinda new anyway. Now on to the fourth bulb, clearly another piece is added. But to me it looks very much like the last addition. Repeat this process and the additions form antenna's, which is the main shape you seen when looking at the full overview of the mset. Maybe this means we have only a small number of distinct shapes. Naming those seems easier than naming regions. When you start zooming, things get very complicated. Take for example the stacked shape of the third bulb (bulb horizon + bulb + branching node + spiral + another spiral + scepter). You can amplify the shapes by zooming into them. When repetitively aiming for the branching node, the rest of the shapes shrink away. Then to further complicate the naming scheme, we can zoom into the border of a minibrot. Now we can aim for the antenna to let that shape rule. All the others fill the whole area, but are getting so small they appear more like a texture then distinct shapes. Zoom a little further and new shapes pop out, or well, are kinda shaped by morping julias. These are so special and bear little resemblance with the chosen "region". Those morphed things really deserve their own name. The shapes only mean something because of our perspective. The math says they're all connected anyway, so actually it is just 1 shape; The Mandelbrot.
I'll make some black-and-white images to go with the story, somewhere the next few days. Title: Re: Your favorite names of the regions of the Mandelbrot Set Post by: Yggdrasil on October 14, 2014, 08:24:19 AM You're correct of course (a nice visual tour of how the shapes correlate can be found here: http://www.miqel.com/fractals_math_patterns/mandelbrot_fractal_guide.html), but I'm mainly looking for the most widely used colloquial names for the most immediately apparent, surface regions.
Please post images with named regions marked (as you see fit) if you can. It'd be interesting to compare and see which names are most widely used. Title: Re: Your favorite names of the regions of the Mandelbrot Set Post by: youhn on October 14, 2014, 06:34:10 PM I only name about 1% of specific shapes I find, no naming schemes for regions or other more categorically things.
I better continue at http://www.fractalforums.com/fractal-related-links/inner-workings-of-the-mandelbrot-set-1/ Title: Re: Your favorite names of the regions of the Mandelbrot Set Post by: billtavis on January 28, 2015, 12:55:40 AM I like the idea of giving colloquial names to the Mandelbrot set. It helps me navigate and engages parts of my brain other than the strictly mathematical. Basically, I see the set as consisting of "main branches" and "valleys" The first branch is the left tip, which I call the "Needle": (http://i59.tinypic.com/20t04nm.png) Moving to the right, we have the "Antennae Branch": (http://i60.tinypic.com/t526fd.png) followed by "Dragon Valley" and "Sceptor Valley" in the cleft: (http://i57.tinypic.com/vmrww1.png)(http://i62.tinypic.com/20h4oxe.png) Moving right again, we find the "Lightning Branch": (http://i60.tinypic.com/2coh0nk.png) followed by "Double Spiral Valley" and "Seahorse Valley" in the cleft: (http://i57.tinypic.com/sy9dz8.png)(http://i59.tinypic.com/dvhhsh.png) Moving right again, we find the "Y Branch": (http://i61.tinypic.com/2e1r6vk.png) followed by "Elephant Valley": (http://i59.tinypic.com/iyoh9k.png) Every branch represents the transition between valleys, and the branches increase in order when diving into any valley. These patterns of valleys/branches carries through to all bulbs and mini-brots |