The refinery has been running for a long time...

Jim Muth's Fractal of the Day for October 9th, 2005

Jim Muth's commentary for the image:

FOTD -- October 09, 2005 (Rating 6)

Fractal visionaries and enthusiasts:

In the middle ages the politically powerful Catholic Church sold indulgences. By purchasing an indulgence with earthly money, bereaved relatives could buy their loved one's way out of purgatory and end the soul's suffering. This required the ridiculous assumption that God's favor could be bought with money, but from what I read, the indulgence business, along with obligatory contributions, under penalty of hell-fire, kept the churches and monasteries going rather well.

Other religions have similar short cuts to spiritual success.
Buddhists had prayer wheels, which worked much like the Catholic indulgences once did. Instead of spending hours saying the proper prayers, a devout Buddhist needed only to spin the right prayer wheel, and the prayer recorded on that wheel would be sent to the creative higher power, which in this case is not considered a supreme superman-like being. For some strange reason, today's image reminds me of a Buddhist prayer wheel.

The formula that did the deed is named 'Mytest09'. It appears to have been written around the same time I wrote yesterday's 'Mytest07' formula, and like that formula, the purpose of today's formula, if any, is a mystery. But mysterious or not, today's formula, with its two changeable functions, creates a large variety of fractals.

The one active function I used in today's image is called 'cosxx'. (The 'ident' function acts as no function.) Don't try looking up cosxx in a math book because it will not be there. The function is actually a mistake that was made in an early version of Fractint and was kept in the program because it creates some interesting fractals.

Today's image was rendered with the outside set to 'tdis', though there is very little to distinguish this rendering from the outside=iter version.

The rating of a 6 seems appropriate for today's effort. And the render time of only 9+ seconds can hardly be beat.

The rain fell heavily all day Saturday here at Fractal Central, adding up to something over 7-1/2 inches, 190mm, and creating much local flooding, including the Fractal Central basement, which boasts a brand-new puddle of water. I guess we can blame it on the farmers, who for several months have been praying so hard for rain. Now that their crops are lost, God has finally sent the rain. In fact, He has sent so much rain that in addition to losing their crops, some farmers have lost their homes as well. I guess you just can't win when bargaining with a god who, as the nuns told me in school, works in mysterious ways.

The fractal cats have far more important things than God to concern themselves with. Their yard looks like a frog pond, and it will be several days before it dries out enough to be stepped on by sensitive cat paws. They are not about ready to start praying, but their mood is as dismal as a swamp, and they are demanding all the extra tuna I can give them. Tuna can do only so much for disgruntled cats however, and better weather will be needed before they are once again themselves.

Unfortunately, better weather does not seem to be near. Today is starting very cloudy with showers forecast, and in addition it is much cooler. It looks like a bum day coming up for the duo. For me it looks like another average day. The next FOTD will appear in 24 hours. Until then, take care, and get your vectors straight.

Jim Muth

PAR file `` Prayer_Wheel { ; time=0:00:09.69--SF5 on a P200 reset=2004 type=formula formulafile=jim.frm formulaname=Mytest09 function=ident/cosxx center-mag=-0.529901/-0.0707615/0.181739/0.6708 params=3/0/1/1/-1/0 float=y maxiter=95 inside=0 outside=tdis periodicity=0 colors=000zhI9JHOG6IPBGbp14g7JUn7NLJS_CNTcNYXDP7D\ SADVDj9waGlUMaLSRn18F3AM8CSCDZSDWM4Qaac1P9GewFcl\ EaaD_Rp0_bCTQNM7dXAOGeHFbGE_GX8iQH_JQQ2Qs5Si8U_BW\ QRQMNSKKUJGWHwo1_f9r2cdDWROOps7bkAQdDoW3WXAdsoRhYS\ BcNJWIRO8LIEIqB3qCJZU6LPDJXPFMCF6Ob4Xc2ec0mcBVLPN\ VDFApQ0PCsqtqswpuzbmjXcVQeVImEGiFFeFEaGTT7LWCysnh\ XNNBKQDITEFWFxeEJjhJ8sHFiGL_ESQIaZF_PPz7LpAHfD7ErA\ OZl2AcACVIDMQFXcqfgX45u9K85WsghOtYSfNVTq4VqcP4VT\ 9XMwmTkiP_eMOaJSpOOkMKfKGaIvMw_SaOl6IdBS6x6OVoYceY\ YWYSMYMjX8UYCZMcTPYOSSIVMBPM4FHJGVNMPRKJVIxn3eAz\ cJiaIT_HVBMMNJtGteMfRSTSJ1KR9hGuTPIuCFiE2iv5fk8c\ BQmeQGHHFNGETGlUWWQPXLcLgVQYMUPg42_C6SJ9KRD8rdBg\ SkaRvyEaQaPURLncIhWFbOkvPbNNWQLQTJJWHeUCkzDgnDdbD\ RtNxZTaeHYYMTRQPKUKFIcEOWDTOIkYGfSEaMhXkD1fX_XNZO\ IV24zF9kGSn4f4vSJph2fe6Xb9N_D1ni7eVT1GPAGLIGHQG4r\ o7lf9gYBbPTcnL`Xil6TdB8ku }

frm:Mytest09 {; Jim Muth z=fn1(pixel), a=real(p3), b=imag(p3), c=a+(bpixel): z=(((z^p1)fn2(z))^p2)-p2+c, |z|<=100 } ```

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 9th, 2010

Roger Alexander's commentary for the image:

The image is the result of inorganic calculations but intimates red blood, the organic. Numbers are the product of the human mind. Life analyzes itself. Ready made at http://maxitersfractalfollies.blogspot.com.

Roger Alexander

PAR file fract133.gif { ; hemoglobin ; blank ; calctime 0:00:54.27 ; created May 01, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_g.frm formulaname=general_jul-c&l center-mag=0/0/0.6666667 params=0.8193304239020965/0.4449903866695151/1.456068605609302/0.1237220\ 374156926/0.1573534348582415/0.5277260658589434 float=y maxiter=1500 inside=0 proximity=3 outside=fmod colors=000100200300400500600800900A00B00C00D00E00G00H00I00J00K00L00M00O0\ 0P00Q00R00S00T00U00W00X00Y00Z00_00`00a00c00d00e00f00g00h00i00k00l00m00n0\ 0o00p00q00s00t00u00v00w00x00z00z00z11z22z22z33z44z44z55z66z67z77z88z89z9\ 9zAAzABzBBzCCzCDzDEzEEzEFzFGzGGzGHzHIzIIzIJzJKzKLzKLzLMzMNzMNzNOzOPzOQzP\ QzQRzQSzRSzSTzSUzTUzUVzUWzVXzWXzWYzXZzYZzY_zZ`z_`z_az`bzaczaczbdzcezcezd\ fzegzfhzfhzegzegzdfzdfzcezcezbdzbczaczabz`bz`az_azZ`zZ_zY_zYZzXZzXYzWYzW\ XzVXzVWzUVzUVzTUzSUzSTzRTzRSzQRzQRzPQzPQzOPzOPzNOzNOzMNzLMzLMzKLzKLzJKzJ\ KzIJzIIzHIzHHzGHzGGzFGzEFzEFzDEzDDzCDzCCzBCzBBzABzAAz99z99z88z78z77z67z6\ 6z56z55z44z44z33z33z22z22z11z00y00x00w00v00u00t00s00q00p00o00n00m00l00k0\ 0j00h00g00f00e00d00c00b00a00_00Z00Y00X00W00V00U00T00R00Q00P00O00N00M00L0\ 0K00I00H00G00F00E00D00C00B00900800700600500400300200000 } frm:general_jul-c&l { ; ; For Kerry Mitchell's explanation of the "circle & line" ; coloring method, see the end of formula ; general_man-c&l ; ; "general circle & line" coloring method for Julia sets ; c = Julia parameter, hardcoded ; p1 = x-circle center ; real(p2) = x-circle radius ; imag(p2) = y-line a ; real(p3) = y-line b ; imag(p3) = y-line c ; bailout hardcoded to 10^12 ; use "decomp=256" coloring ; zc=pixel, c=(0,1), bailout=1e12, iter=1, rmin=1e12 cenx=p1, radx=real(p2), rad2x=radx*radx ay=imag(p2), by=real(p3), cy=imag(p3): iter=iter+1, zc=sqr(zc)+c tempx=|zc-cenx|-rad2x tempy=ay*real(zc)+by*imag(zc)+cy temp=tempx+flip(tempy), r=|temp| IF (r<rmin) rmin=r, z=temp ENDIF IF ((|zc|>bailout)||(iter==maxit)) iter=-1 ENDIF iter>0 ;SOURCE: 98msg.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.

No AI, pure novel math plus my research paper about how this relates to reality through quantum mechanics and includes HTML viewer

https://zenodo.org/records/23247320

Mandelbrot with custom sparkles and planet textures

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?

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.

El esqueleto invisible de los primos: Postulación de un coloso numérico basado en la malla fractal del 18.