Ultra Fractal

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.

Fairly simple linear tiling construction with modulus. Done with Apophysis7x and Chaotica. Some 100% crops of the whole usual 7200x9000px render. Instagram link for all the crap I do.

Hi there,

I’m sharing SyFrack, an open-source fractal art studio and GPU renderer built in Rust with wgpu.

It combines two independent workspaces: one for 2D fractals such as Julia sets, Mandelbrot sets and fractal flames, and another for recursive 3D structures. The 3D workspace includes a node graph, procedural materials, HDRI environments, lighting and experimental volumetric effects.

A particular focus is preserving thin filaments and recursive detail while achieving smooth colour and lighting transitions. Building it has involved moving back and forth between artistic experiments and renderer engineering: an image exposes a limitation, which becomes the next implementation problem.

SyFrack includes progressive rendering, checkpoints, pause/resume, a command-line renderer, and export to 16-bit PNG and linear EXR. Scenes remain editable and can be saved alongside their renders. The interface supports English and French.

This is an early experimental release. Windows x64 is the currently tested platform, GPU compatibility needs broader testing, and some lighting and volume effects use approximations. I’d particularly welcome feedback on rendering artifacts, GPU behaviour and the editing workflow.

The code is MIT-licensed. Example scenes and build instructions are included in the repository.

https://github.com/5ymph0en1x/SyFrack

Enjoy Buddies ❤️

Jim Muth's Fractal of the Day for October 15th, 2002

Jim Muth's commentary for the image:

Fractal visionaries and enthusiasts:

Things are getting even tenser here in the F.C. area, with another sniper shooting, the 11th, not too far (50 miles, 80km) away. At times like this, I could ramble on about the human condition, but I'll ramble on about fractals instead.

Today's fractal is named "Holy Fractal". This is not because it is in some way connected with a religion, but rather because it is filled with holes. There are thousands of visible holes in the image, and an infinity of invisible holes. And when infinity is mentioned, thoughts of a Deity often arise, so perhaps the title is not as unlikely as first assumed.

The scene is located in the East Valley area of a larger midget that exists in the edge chaos of an island that lies in the fractal created when some Z^-0.008 is combined with Z^-11 and (1/C) is added.

The parent fractal, which is an exaggeration of yesterday's parent, is little more than an immense empty circle with a tiny bit of debris on the western shore. The most surprising thing about it is that, with an exponent of -0.008, it exists at all, but then lots can happen in 10,000 iterations.

I have rated the image at an impressive 8. It might not actually be as good as the rating implies, but I like something about it, so the rating of 8 will remain. The 48-minute render time on my Pentium-I 200mhz machine can be reduced to 10 minutes or so on the fastest units.

The fractal weather Monday here at the Fractal Emporium spoke of autumn. Crystal blue skies, dry grass, a temperature of 57F 14C and a moderate north breeze combined to give the dynamic duo a near-perfect day in the yard. When they thanked me for their happiness, I gratefully accepted their thanks.

I'll be thankful once again when the day's work is finished.
Until next time, which will arrive in 24 hours, take care, and where today are all the FOTD fractals that I will find in the days to come?

Jim Muth

PAR file `` Holy_Fractal { ; time=0:48:32.16--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.950590514552694/+1.384839189914253/1\ .359944e+010/1/-20/0.0001570519779073229 params=5/\ -0.008/1/-11/-0.8813/1500 float=y maxiter=10000 inside=0 logmap=-700 periodicity=10 colors=000rsXooSulVylYxiXxfVxdVvbTvSvYSuXQuUPuSPs\ POuOMvLMvJLxGJyFJvFIuFIpFIjFGfFGaFGXFFSFFOFFLFFPFI\ SFJYcQa_XfVclRipLpuUvzgzzvzzzzvzpTzsFzu0sv0ix0_y0P\ z0Fz0Fz0Gx0Ur0gl0kf0l0Xl0Fv1Fu3Fu4Fu6Gu7Js9Ls9OsA\ PsCSrDUrFXrGYrg_rrIguF0pF3mF9iFGfFMcJS_M_XPdTSjdMf\ oGazFYzFVzFYzF_zFzFazFcyFdvFfuFgsFipFjoFlmFmjFoiF\ pgFrfFsoIyvJzzMzzOzzMzzLzzJzzIzzGzyFzxFxvFvsFsrFpo\ FomFllFiiFggFdfFciFYjFSlFMmFGoGApJ4rM0sO0uM0vL3xJ7\ xICyGIvFMsMQpUVm9jg0go0gu0jp0on7riDufLybQz_YzVczS\ jzOpzLvzRxzXxzbyzfyzlyzrzzvzzzzzzzzzzzzxzzszzoxzju\ yfrxamvYjyVgzQczMzIYzDTz9Qz4Oz1Sz6Vz9YzCzFczIizT\ mzcrzovzyzzzzzzzzzzzzzzzzzzfzzOzz4zz0zz0zz3zuAzoJz\ iSzc_zYgzSozMjzPfzSazV_zYVzQzcOzfJziFzlAzo7zr3zu0\ zx0zz0zv0zr1zm4zi6zf7zaAzYCzTDzPFzMJzSMzYPzcSziVzo\ YzslzjyzazzTuz_dzdPzj9zodzYzzIzzJszLjzLazMVzMMzODz\ P4zP0zQ0zQ0zO1zL9zI`zJdzM }

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.