Jim Muth's Fractal of the Day for October 17th, 2012

Jim Muth's commentary for the image:

FOTD -- October 17, 2012 (Rating 7.5)

Fractal visionaries and enthusiasts:

The parent fractal of today's image is one of the most unpromising of all time -- little more than a large open circle with degenerate buds along its circumference. But the east side of this circle holds hints of Mandelbrot stuff, and as one looks closer, the hints prove to be entire worlds. Today's scene lies in a remote non-critical valley near an unpromising bud in this island of chaos.

To create the parent circle, I combined 1/2 part of Z² with 1/10 part of Z³ on each iteration, then and added 1/C. Perhaps the most interesting feature of the image is its combination of open areas, straight spokes and spirals. The spokes and spirals explain the name.

The rating of 7-1/2 includes a half-point bonus for my work on the colors. It really did take nearly 1/2 hour to get the colors almost right.

The calculation time of 15 minutes will pass slowly.

When the morning fog cleared off, sunshine ruled the roost here at Fractal Central today. A few decorative angel-hair cirrus clouds in the afternoon merely added to the splendor. Fractal cat Nicholas passed the afternoon sleeping in the sun. From the way he sometimes behaves since Cassie's departure, I would assume he is interacting with her conscious left-over energy field. (Could I call it her spirit without arousing the wrath of rationalists who know that conscious spirits do not exist?
[I guess it's all right as long as I consider such belief to be merely a comforting and harmless fantasy.])

FL passed the day putting her garden to sleep; I passed the day pondering the mysteries of existence. The next FOTD will be posted when the time is right. Until whenever, take care, and how can we make statements about the existence of things like spirits when we can't even agree on whether the Mandelbrot set actually exists? (I, for one, have seen nothing of the set more than a lot of pictures.)

Jim Muth

PAR file ` Spokes_and_Spirals { ; time=0:15:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=t center-mag=-0.307016313251/+0.219156404541/6.96e+9\ /1/-7.5/0 params=0.5/2/0.1/3/0/0/0/0 float=y maxiter=5700 inside=0 logmap=784 periodicity=6 colors=000CDNDEOEFPFGQGHRHISIJTJKUKLVLMWMNXNOYOPZP\ Q_QR`RR_RRYRRXQRZPR_PR`ORbNRcNRdSRgXRjaRmfRpeQndPl\ dOkcQibRgbSfaUdaVc`Wa_Y__ZZZ_XYaVYbUXcSXdRVkJTrCRy\ 5Pz0Oz0Oz1Nz3Nz4Nz5My7Mx8Mw9LvBLuCKtEKsFKrGJqIJpJJ\ pKHnJFlJEjJChJBfI9dI8bI6`I5ZH3XH3VH3TH3RH3TG7UFBWF\ EXEIZEM_DQaCTbCXdB`eBdgAgh9kj9ok8rl8mqEhuJ3hH4dF6`\ D8XBAUACQ8EM6GI4IF3KH6MI8OKAQLCSMETOHVPJXQLZSN`TPa\ URZWOWXLTZIQ_GOaDLbAId8Fe5Cg2Ah0NXjMYiMZhLZgL_fL_e\ K`dKacJacJbbJbaIc`Id_HdZHeYHeYUhbzrzznjvkhthfredoc\ bmjYZhVXgTVfQTeNRcKPbINaFLCJ_9HZ7FYCIYGLYKNYOQY\ SSXWVX_XXd_XhaXldWpfWtiWxkWznWzp3Re4Pc7ObANDM_GLZ\ JKXLJWOHVRGTVFSZERbDPiCOiBNnCPpCRpDSzDUsDWzEX_EzZE\ zYFzXFzXFzWGzVGzVGzEJz3LzANzMOzYPgiQlrRq4g35e45c46\ b5758Z69Y79W7AU8BT8E5C4B4Aj39j38j27t16t15t0_z0\ _z0_z0_z0_z0_z0_z0iz0iz0iz0rz0rz0rz0rz0rz0rz0rz0rz\ 0rz0rz0rz0rz0rz0rz0rz0rz0 }

frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-abgh)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k((a(z^b))+(d(z^f)))+c, |z| < l } ```

Want to render these yourself and explore further? Try out the PAR file in Iterated Dynamics, an open source fork of FRACTINT that can render these PAR files. See the online help for instructions on using Id or press F1 anywhere in the program for context-sensitive help.

Ultra Fractal

Check it out, lots of options, web based.

With a depth of 1e-1052, this is my deepest zoom so far. Its based on Maths Towns "The edge of infinity" location, but with my own coloring. Check out the full version:
https://www.youtube.com/watch?v=TbGMHNEyBgc

Playing around with layered images of differing coloring algorithms. Two images of the same coordinates of the Mandelbrot set been used. An orbit trap variant and distance estimation. One layer used a soft focus effect and difference blending. The result is rather random, but I like it somehow.

Mandelbrot set with an XOR pattern applied to the polar displacement of (z, zi).

Editable here.

3d render made with my own software + a few 2d caleidoscope passes in good old GIMP ^^

Max Iter's Fractal Follies for October 16th, 2010

Roger Alexander's commentary for the image:

  Today's post marks the passing of Benoit Mandelbrot, father of fractal geometry. 

As a tribute to Benoit Mandelbrot's contribution to the field of fractal geometry today's fractal image is of the default original Mandelbrot set. The plotting does not use the usual inside and outside mappings but rather uses the distance estimator method with a two color map. This plotting method was chosen because I find it enhances the demonstration of the complexity of the basic Mandelbrot set. According to the Fractint manual "The distance estimator method widens very thin "strands" which are part of the "inside" of the set. Instead of hiding invisibly between pixels, these strands are made one pixel wide." At the usual http://maxitersfractalfollies.blogspot.com.

Roger Alexander

PAR file Benoit_Mandelbrot { ; distance estimator method ; fract474.gif ; calctime 0:01:00.47 ; created Oct 16, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=mandel passes=1 center-mag=-0.5/3.33067e-016/0.837633 params=0/0 float=y maxiter=1500 inside=0 outside=1 distest=1200/71/800/600 colors=0000Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0X\ z0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0X\ z0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0X\ z0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0X\ z0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0X\ z0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0X\ z0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0X\ z0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0X\ z0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0X\ z0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0X\ z0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz }

Want to render these yourself and explore further? Try out the PAR file in Iterated Dynamics, an open source fork of FRACTINT that can render these PAR files. See the online help for instructions on using Id or press F1 anywhere in the program for context-sensitive help.

Fractal: Mandelbrot Center: -0.8376333428333328 / 0.2048731871666665 Width: 5.3333333333333345e-06 Render Algorithm: Stripe Average Maximum iterations: 900 Output: 1’920 x 1’080 Samples: 15’360 x 8’640 (8x) Renderer: Direct, double Render time: 55.903 s Iterations: average 285.09629, minimum 159 Color Mapping: Linear Smooth color: yes

Editable at http://weirdly.net/mandelbrot/?config=v1,-1.7699183163365715,-0.009843823600744261,6e-9,4.15129151291513e-9,1024,128,0.19841,0,1,0.67841,0,1,0.958,0,1,-2.01159,-0.44159,1110011000,01110011001,001110011001,1,1,1,0,0,1,5,2,2,3,addition,4,1,0,2,-89.97732882889666

The mini renderings nested in it are created by taking the displacement of (z, zi), and passing that into the Mandelbrot function as a new coordinate to calculate, summing the results.

Jim Muth's Fractal of the Day for October 16th, 2000

PAR file `` Fractal_Foliage { ; Fractal of the day, 16-10-00 Rating (6) ; time=0:06:50.51 -- SF5 on a P200 reset=2001 type=formula formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-8.938876274351706/-9.976549500589202/452\ .3876/1/-79.999 params=-11/-1.1/-1.11/-2.222/-0.9/200 float=y maxiter=1800 inside=0 logmap=98 periodicity=9 colors=000S0SvAuo7rg3o0mS0jL0gD0d60cC0dI6fMGgSQiXj\ aYlSpiSilPfo9cp0al0di0gf3jc6mFo_FfYT_XTQV_JTCSg3Q\ g0Qv0IzC9zY0zF0z00v0<3>0T00M00G0DFMTFgiFzcDv_CoVCgQA\ L9TG9MC7F777<2>FGfIJrJLz9Lc0LF0L00O30QD0TO0XY0_i0as\ 0dz0gz3da6a09f6AjCDoIFsOGvSP0iQQXQzLMrJ<3>AGD77CFYFM\ vGJpTGlfDgso07j71<2>as0<3>mg1pd6sc9mQPgFcc3rY6rT9sOC\ sIFuCIu7LuDOvIPxMQxTSyTzgVzoYzz_zzzzazvczzdzyizylz\ xoxxruxurvxpvzmvzluzjszj<2>oximxilvgjvgiuggsffsfdrfc\ pdapdododapccpccpadradrfr`<2>gs_dma<3>YVmXQpTLrSG\ uQCxO6zM1zL0zJ0zL0vM7lOFaPLSQSIS_7Sd0OV7LMGGDPD3_90g\ 60p70r71s99u9Iv9PxAXyAczAlzCszCzzCzz<3>PzzTzyXzx_zva\ zufzs<3>szmvzlyzjzziszgjzgczfVzfMzfFzd6zd0zd<3>0zj0z\ l0zl<2>0zp0zr0zr<2>0zv0zx0zx0zs4zo9zjDzfIzcMz_QzVVzQ\ YzOPzGGzA7z40z00z00z01z46zACzGIzMMzSSzY }

frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-abgh)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k((a(z^b))+(d(z^f)))+c, |z| < l } ```

Want to render these yourself and explore further? Try out the PAR file in Iterated Dynamics, an open source fork of FRACTINT that can render these PAR files. See the online help for instructions on using Id or press F1 anywhere in the program for context-sensitive help.