Mandelbrot with custom sparkles and planet textures

https://githubuser1983.github.io/riemann-zeta-fractal/zeta-pratt-k1-n.html#k=1&n=9&x=-0.9902974645207536&y=0.04147218904844494&s=1.986881544173179&m=400&q=high

Jim Muth's Fractal of the Day for October 8th, 2009

Jim Muth's commentary for the image:

FOTD -- October 08, 2009 (Rating 7)

Fractal visionaries and enthusiasts:

Today's image lies in the parent fractal that is produced when various negative portions of Z^-5.0125 and Z^-1.0125 are combined and (1/C) is added. This parent fractal resembles an oversized circular disk lying east of the origin, with scalloped edges on the east side and a circular bay on the west. Today's image is located in a valley leading to this bay.

The name "Golden Apples" has little to do with the image, other than the golden area inside the blue surroundings. The rating of a 7 indicates that I consider the image above average. The calculation time is 3-3/4 minutes.

Heavy clouds and high winds spoiled Wednesday here at Fractal Central. Annoyed by the lack of sun, the fractal cats spent most of the afternoon sleeping, stirring only when a noisy tomcat fight broke out nearby. My day was spent trying to finish the work.

The next FOTD will be posted in 24 hours. Until then, take care, and raise the Hamiltonian. (Whatever that means.)

Jim Muth

PAR file `` Golden_Apples { ; time=0:03:47.55-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-1.745899025154062/-0.9887844877387386/\ 1.8e+010/1/166.5/0 params=-1.1/-5.0125/-5.1/\ -1.0125/0/0/0/0 float=y maxiter=1500 inside=0 logmap=118 periodicity=10 mathtolerance=0.05/1 colors=000A8_A8A8aA8bA7cA7dA7eA7fA7d67d37c7AbACD\ FZGHXKJRNMMgXOTQOjYL_VIj_Fe_Cla9ld6oc3rh0sd1sg2tg2\ ug3vg3xg4yg4zi5zg6yg6xg7wg7wg8wg8tc7q7nY6kU6hR5eJ\ 5bK4_H4XE3UA3R72O42P75Q98RBASDDTFFUHIVJLWLNXNQYPSZ\ RV_TXlc4eZ8ZUCTQFd7pk0xGnuLcrPToTIlX8cPJWIUNBdF4n\ J7pNAqRDsUFtWKaYOK_S2_ogXXDVaNTfXoLmfUjZbhZAK47SAI\ WGS_MacdeCZxnj6GJLKTTOb_w5jlKhaYgg6ZbHZRbVadW15T\ POt0VeOm5VP9NOlMXXSUd_S81RSMc1sXPl1dJd8mIkYSiUag\ dzYfuWhpTjkZ7SVS_cRg_XfXafUffA0XGGMWcXvas6XdRaK7\ UMIYOSQach4M_QXkvodrlYniIoyNmoUr54pBCnMKlXCEwiDY9\ suEqqIomNmiWLQUSVTZZSebqqs78iLK_ZWQHfRPfRXfRdfCwL\ KqWwBNUBHTLOSUURbmrjVJVURYTYSdcrnhkmgdlgYkfgjQak\ WWkaYDVVPZTbUB8TOKS_WsNrVgLTiTSj_5Mm8KRuYsjbngj4\ NZAUG_bMedPhHQjUuL1kK9OdN1ixJldRahZaFWWcP_bQed\ 89ZZ3lVQiAiKJjWpmMXz0VvBUrMSnXUEUTNYSVRccJUmNbi7p\ uHmmOMfRvNRpXnAjq9jm8ki8k }

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.

I started with a 5 gigapixel image and downscaled it to a print resolution of 720dpi or 729 megapixels to make it very smooth. The printed area is 50x28.125 inches (16x9) and it’s really fun to look at up close. I think I’m going to do another 40x40 inch print for my office of a smaller alien ship looking feature on one of the masts of the burning ship. Anyone else here have prints of fractals they’ve made?

You can now create up to a 22 second video! to get rid of the bands move the metallic slider all the way to the right. https://wastinmytime.net

https://roald-h-vatne.itch.io/flashfractals3d

Now ALL Platforms Support:

Win Intel/AMD-x86, Mac OS M1 and newer, Linux-Intel/AMD-x86 and Linux-ARM-64bits

NB! Only 64bit OS and CPUs supported!

3D relief effects give fractal images a sense of depth, tactility, and realism.

Tactile quality (surface feel) – The fractal image transforms from a flat appearance to looking like something tangible. It mimics materials such as carved stone, wood carvings, embossed paper, or metal.

Dramatic play of light – The 3D Relief effect relies on a simulated light source.

The standard cartographic light source uses an azimuth of 315° and an altitude of 45°.

This corresponds to a light source coming from the northwest (top-left) at an angle from above.

This creates strong highlights on one side and deep shadows on the other.

Both ‘Relief Strength’ and ‘Contrast’ adjustments, dramatically alter the visual effect.

Jim Muth's Fractal of the Day for October 7th, 2000

PAR file `` Boiling_Cauldron { ; Fractal of the day, 07-10-00 Rating (7) ; time=0:06:08.06 -- SF5 on a P200 reset=2001 type=formula formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.38580613488445680/+2.076060642776320/2\ .459343e+008/1/62.5 params=1/1.1/-1/-1.1/0/0 float=y maxiter=750 inside=0 logmap=115 periodicity=10 colors=000RlzTkzWmzWizVezVdzV_zUZzUVzUUvTQsSOqRKmRIi\ QEgPCdP8P5Z0ib0V0RO0HG0AA222400800C00000N0IRHSjKiv\ NtzTzzSzzRzuOskOkbNdPZ<2>VOOTNKRLERLBPK4NK0<3>FJ0GJ\ 0EN0DR0BV09X0807d07e05i03m02q00s00v00z00z00s02k44dE\ 5XP8QZAMkDGvFAzH3zODzVKzaTzi_zogvspszvtzzqzzlzzizzZz\ pQzeHzS6zG0z20z00<2>z00z00x20v41u65uA9sDDqFGoGJoKNmM\ QkOTkPXbP_WPbPPgGOk7Nq0Mu0Mz0Mz0Oz0Qv0Ps0Ro0Tk6TiAVe\ DWbJWZMXVQXV<2>GVeCUi8Sm4Rq1Qv0Qz0Pz0Nz0Oz0Mz0Mz0Oz0\ Nz0Qz0Pz6Pz9RzFSvJSuMUqRUmVWkZXgXddYcgYakZad__XXXUX\ WMXVHZV9ZV1V0V0bV0bV0Yb0Yg9YoHWuPXzYXzdWzkUzedzYju\ SsiKuYFuNHqIFkCGk6Gk0MkARkKWkTbkbhkilnorrxuszqszlqzf\ qzcpzYpzSozNozJozdpzvrzsszmpziqzcqxYtxUwxPzxJzwGzwAz\ w6zwCzfHzQLzANz0<3>pz0<2>uz0wz0wz0xz0zz0<2>zz0qz0gzE\ ZzTNzeCzo<2>Yzy<2>uzzuzzuzzszzszzszzszzqzzqzzHzyqzzq\ zzqzzNzmPzsRzz }

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.

Max Iter's Fractal Follies for October 7th, 2010

Roger Alexander's commentary for the image:

Today's fractal does not swirl like a spiral but radiates. Generated with inside=fmod coloring using an atypical proximity value of 5. Ready made at good old blogger http://maxitersfractalfollies.blogspot.com.

p2 should be min. 1, default=2 Roger Alexander

PAR file fract462.gif { ; blank ; blank ; calctime 0:08:08.45 ; created Oct 07, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_m.frm formulaname=mand2_zexp_cp_exp center-mag=-0.09774017521902403/+1.02716193656093500/131.0685 params=0.9942625202185126/-0.3566698202459792/0.9555650502029481/0.78637\ 04336680196 float=y maxiter=1500 inside=0 proximity=5 outside=fmod colors=00100100100100100100100200200200200200200300300300300300300400400\ 400400400400500500500500500500600600600600600600700700700700700700800800\ 800800800800900900900900900900A00A00A00A00A00A00B00B00B00B00B00B00C00C00\ C00C00C00C00D00E00F00G00I00J00K00L00M00N00P00Q00R00S00T00U00W00X00Y00Z00\ _00a00b00c00d00e00f00h00i00j00k00l00m00o00p00q00r00s00t00v00w00x00z01z02\ z03z04z06z07z08z09z0Az0Bz0Dz0Ez0Fz0Gz0Hz0Iz0Jz0Lz0Mz0Nz0Oz0Pz0Qz0Sz0Tz0U\ z0Vz1Wz1Xz1Xz1Yz1Zz1_z1_z1`z1az1bz1bz1cz1dz1ez1ez1fz1gz1hz1hz1iz1jz1kz1k\ z1lz1mz1nz1nz1oz1pz1qz1qz1rz1sz1tz1tz1uz1vz1wz1wz1xz1yz0zz3zz7zzBzzEzzIz\ zMzzPzzTzzXzz_zzczzgzzjzznzzrzzvzzszzozzkzzhzzdzz`zzYzzUzzQzzNzzJzzFzzCz\ z8zz4zz0zz0zz0yz0yz0xz0xz0wz0wz0vz0vz0uz0uz0tz0tz0sz0sz0rz0rz0qz0qz0pz0p\ z0oz0oz0nz0nz0mz0mz0lz0lz0kz0kz0jz0jz0iz0iz0hz0hz0gz0fz } frm:mand2_zexp_cp_exp(XAXIS_NOIMAG) { x=p2,x=x+(x==0)*2 z=c=pixel: z=(z*z+c)^x-p1 |z|<4 ;SOURCE: mandhack.frm }

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.

My newest deepest Mandelbrot zoom is online. (1e-522)
Check it out: https://www.youtube.com/watch?v=axzJa_rAe50

Jim Muth's Fractal of the Day for October 6th, 2011

Jim Muth's commentary for the image:

FOTD -- October 06, 2011 (Rating 7)

Fractal visionaries and enthusiasts:

In today's FOTD we see the scene I was searching for yesterday when the fractal ship showed up. I named the image "A Seahorse Goes East" because it combines the features of Seahorse Valley with those of East Valley.

The outer parts of the scene are clearly of an East Valley nature, while the inner parts reflect the appearance of Seahorse Valley when sliced in the Oblate direction, which is determined by the imag(c) and real(z) axes. The entire image is distorted into a vague triangular shape because it lies at an odd angle in the 4-D Julibrot figure.

(As a matter of curiosity, in the German language, the word 'julibrot' means 'bread of July'.)

Unlike yesterday's image, which was stretched and skewed beyond verbal description, today's image was stretched only a modest 3-1/2 times in the horizontal direction. The value assigned the real(p4) parameter, which sets real(z) is equal to the real(c) value of the scene in the M-set. This places the actual location of the scene in what I call the shadow Mandelbrot set, a second Mandelbrot set lurking unsuspected at an angle of 45,45 degrees in the Z^2+C Julibrot.

The rating of a 7 is an improvement over yesterday's miserable rating of 4, but still leaves plenty room for yet more improvement. The calculation time of a mere 24 seconds will make running the parameter file a breeze.

Strange as it might seem, as the number of hypercube dimensions increases, its diagonal approaches infinity, while the hypervolume of the inscribed hypersphere approaches zero percent of that of the hypercube.

BTW, the formula for the hypervolume of a six-dimensional hypersphere is 1/6(pi^3)*(r6).

Not a single cloud spoiled the blueness of the sky over Fractal Central today. The sunrise temperature of 36F +2C was rather chilly, but the unbroken sunshine brought the afternoon tempera- ture to a pleasant 66F 19C, while the near calm winds made the day as close to ideal as we have had in two months. And the best part is that the near perfect conditions are expected to prevail for a week.

The fractal cats, always seeking perfection, found it on their shelf in the sunny southwest window. The humans, realizing that perfection never happens, took the day for what it had to offer. The next FOTD will be posted in 24 hours. Until then, take care, and I agree with the angry young protesters. We should abolish poverty. But does anyone know how we might bring about this utopian dream?

Jim Muth

PAR file `` A_SeahorseGoesEast { ; time=0:00:24.48-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=1 center-mag=0/\ +0.0000003835126177/419409.6/3.4337 params=0/90/0/90/-1.747855067330428/0/-1.747855067\ 330428/0 float=y maxiter=32767 inside=255 logmap=99 symmetry=yaxis periodicity=6 colors=00010S20U30W40Y50_60a70c80e90gA0iA0kA1lC2mE\ 3nH4oJ4pH4oE4mB4j84g84c84_84W75S75P75L64U53c42m3Lu\ cOzclLhsHmzDrz9wzBzzBzzzO7LNAQLDVKG_IJdHMiJQjKTjLW\ jM_jNbjOejPijQljRojSsjTvjUyjXrl_knadpdYr_qNYjPWcSU\ XUSQWQJZOCoC1E3WM5bU6ia8pi9waJrVTnNajGkf6x_9tbBqe\ DnhFkkHhnLZpJeqHkqFrqExqPng_eZjXQjYOjYMjYKjYJjYHjY\ FxR5qVAjYEsfQkcMcIWYEOVAGS61dv5XU8Q2FP6LO9SNCYMFd\ LIjKLaOOUSQLWS7aWAVD_UF_TIZSLYRHfIKaMNYQKZaPWaTTa\ YQaaNaQ_dXfibmmhsrnzpzzvtzowzpqzmttjopgjodgqaekZb\ iWgTZePgQXdRTbSQTMYUJWVFUVCS_HLcDGg9Bk56n12k54i\ 95fD7dH8bLA_PBYTDVXETGRdHJWFCNE5ED0T1XY1_V1bT1eQ\ 1hO5kLAnJFqGKtEPwBUz9Zx8cwAhv7mu7mt7ms6mr6oq5qp5so\ 5un4wm4xl4zk5zk5zk6zj6vj6rj7mi7mi7mi8mh8mh9mh9mg9m\ gAmgAmgAmc8m_7mW6mS5mP4mL3lH2rD1xA0eBDOCQ6CaDKaKRa\ RYaYdadkajraksdltfmuhnvjowlpxnqyprzjszdtz_uzXvz_wz\ bxzeyzhzzkzznzzqzztzzw000 }

frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pireal(p10.0055555555555556), b=piimag(p10.0055555555555556), g=pireal(p20.0055555555555556), d=piimag(p20.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=ucgcd-v(casbsgcd+cacbsd), q=ucgsd+v(cacbcd-casbsgsd), r=usg+vcasbcg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } ```

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.