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Author Topic: Exploring a Mandelbrot Spiral  (Read 874 times)
Description: First post: a set with over 60 images, over 1000 in the whole Mandelbrot gallery
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timothychase
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« on: August 19, 2013, 09:10:56 PM »


cover to the set spiral-02 by timothy_chase1, on Flickr

The image is from a Flickr set exploring a spiral region belonging to a branch within the seahorse valley of a mini-Mandelbrot.  The set is part of a collection that includes over a thousand images from the Mandelbrot object, each desktop-sized if you download the original.

The images for this set were created using Fractal eXtreme.  For those who are interested, there is enough information in the set write up to reproduce the palette, and there are coordinates for each image, such that you could replicate the entire set, then modify the palette to something more your liking and further explore the region.

On the web pages devoted to individual images, in addition to the hyperlinks to the left and right of the image, there are mouseover hyperlinks to zoom into other images in the set.  In the write-up below a hyperlink taking you back up to the parent.  Consequently, in addition to the linear sequence of Flickr sets there exists a tree-like organization that permits you to zoom in by navigating down into the branches and zoom out by going back towards the trunk.

The spiral is essentially a doubled logarithmic spiral of infinite descent composed of 9-branch structures separated by two-fold symmetry embedded Julias.  The set is a study of the region surrounding the mini-Mandelbrots at the heart of these Julias, demonstrating how the further one descends into the spiral the more winding of spirals surrounding the mini-Mandelbrots will occur.  However, there are mini-Mandelbrots with surrounding regions that display quite different structures which exist within the spiral, e.g., in the 9-branch structures.
« Last Edit: August 19, 2013, 09:41:16 PM by timothychase, Reason: Wanted to link to the set itself, not just to the image » Logged
Pauldelbrot
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pderbyshire2
« Reply #1 on: August 20, 2013, 08:14:21 AM »

Repeating Zooming Self-Silimilar Thumb Up, by Craig
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timothychase
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« Reply #2 on: August 20, 2013, 07:26:19 PM »

Your videos are beautiful, Pauldelbrot.
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Pauldelbrot
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pderbyshire2
« Reply #3 on: August 22, 2013, 06:59:29 AM »

Your videos are beautiful, Pauldelbrot.

Thanks!
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cKleinhuis
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« Reply #4 on: August 22, 2013, 07:07:13 AM »

the colors in this are nice, as is the location!
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divide and conquer - iterate and rule - chaos is No random!
mclarekin
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« Reply #5 on: August 22, 2013, 09:05:59 AM »

yes, very  nice image, like it a lot, smiley smiley smiley
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Theramin
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« Reply #6 on: August 22, 2013, 04:47:44 PM »

That is beautiful! I love the turquoise-y/aquamarine(?) blue background.

I wish I knew how to do such stuff (WITHOUT a learning curve)  cheesy
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Nahee_Enterprises
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« Reply #7 on: August 30, 2013, 12:31:53 AM »

The image is from a Flickr set exploring a spiral region belonging to a branch within the seahorse valley of a mini-Mandelbrot.
.......     The images for this set were created using Fractal eXtreme.

Greetings, and welcome to this particular forum !!!     cheesy

I have found that Fractal eXtreme is very good at producing these type of fractal images.  You have a nice set of images, and a very large connected collection.
 
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