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Dark Temple at SunriseWhere There's Smoke?Forms of Dusk
Where There's Smoke?
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Description: There are no iteration bands here ... only smoke, flames, and minibrots. Fractal detail fills nearly all of the image.

The mapping used to generate this image is

z_{n + 1} = \frac{z_n + \frac{1}{\sqrt{3}}a}{b(z_n^3 - \sqrt{3}az_n^2 + cz_n + \frac{1}{\sqrt{3}}ac)} + d

and the image is in the a-plane with upper left corner 0.26422942305 - 2.1472630887i, lower right corner 0.31023820036 - 2.1817696717i, z0 = a, b = 0.073049 + 0.039934i, c = -1.804256 + 2.869793i, and d = -0.119048 + 0.083333i.

For most of the a values in the image, except in the minibrots, the dynamics possesses no attractor and the Julia set is the whole Riemann sphere. Elliptic Harlequin coloring (UF users have access to this via, IIRC, akl-m-math.ucl) gives the tools needed to visualize the dynamics without any attractor to target. The result resembles smooth iteration coloring, without need for convergence to any attractor, and makes visible the dendrites that completely occupy the space around the minibrots. This location is in a seahorse valley, shallow and on the double-spiral side, giving the usual shapes for such an area, but fattened to fill space with infinite smoke-swirl detail as there is no fixed attracting basin to capture most of the points as there is in the normal Mandelbrot Set's seahorse valley.

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Filesize: 479.93kB
Height: 960 Width: 1280
Discussion Topic: View Topic
Keywords: spacefilling;mandelbrot;elliptic harlequin;seahorse valley 
Posted by: Pauldelbrot May 03, 2013, 10:20:35 AM

Rating: **** by 23 members.

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Comments (4) rss
Fractal Senior
Posts: 7044

formerly known as 'Trifox'

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May 04, 2013, 10:05:30 AM
the still frame section is meant for the "anything goes" section, nice though
i have moved it to the still frame!!
Fractal Senior
Posts: 1616

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May 04, 2013, 12:25:54 AM
Very soft and smoke-like
I think it would have been better with some enhancements to the flames, to make them fit in the environment more.
Then as Alef and Pauldelbrot said, I don't see the connection with axolotl.
Fractal Senior
Posts: 2592

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May 03, 2013, 09:48:38 PM
Isn't this basically an "anything goes" section?
Fractal Supremo
Posts: 1174

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May 03, 2013, 03:28:42 PM
Cool, but don't gives even alightest tought about axolotl.

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