Jim Muth's Fractal of the Day for September 1st, 2013

Jim Muth's commentary for the image:

FOTD -- September 01, 2013 (Rating A-8,M-7)

Fractal visionaries and enthusiasts:

Today's image is a non-existent one. The expression behind today's image, Z^0.09+Z^-0.09+C, does not make a fractal.
Try it and see. It merely draws a blank screen of dead inside stuff.

But the Fractint program has inside fills that can make something dead come alive, and in today's image, the 'FMOD' inside fill with a proximity of 0.65 has brought a basically dead screen to a zombie like life.

I have given the art aspect of the image a rating of a very honorable 8, while the math aspect comes in at a 7. I spent quite a bit of time on the impossible task of smoothing out a 256-color GIF palette. The result is moderately successful.

The name "FOTD with FMOD" simply states the situation as it is.
The calculation time of 6 minutes is slow however.

A mix of sun and clouds with a temperature of 88F 31C made today ideal for most any outdoor activities here at Fractal Central, including water things. The humidity was a bit on the high side, but simply added to the summer atmosphere. The fractal cat spent most of the day asleep on the entertainment center, the rest of the day watching the local pigeons. The humans survived the day without mishap.

The next FOTD will soon be posted. To see how soon, check back frequently. Until soon arrives, take care, and why did God set standards of behavior that, because of the weaknesses He Himself built into us, are impossible for any human being to achieve?

PAR file `` FOTD_with_FMOD { ; time=0:06:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-421.878100629715/+0.1550629443494898/\ 12782.1/1/-45/0 params=1/0.09/1/-0.09/210/5000/0/0 float=y maxiter=1200 inside=fmod proximity=0.65 logmap=yes periodicity=6 colors=0000lp0lq0lo0kq0kq0kq0jp0ip0hp0gn0gn0fn0fl0\ el0el0dk0ck0bk0bi0ai0ai0ag0g0_g0Zf0Yf0Xf0Xd0Wd0Vd\ 0Vb0Ub0Ub0Ta0Sa0Ra0Q_0Q_0P_0OY0OY0NY0NX0MX0LX0LV0K\ V0JV0IU0IT0HT0HR0GR0FR0ER0ER0DR0DO0CO0BO0BN0AN09N0\ 8L08L08L07J06J05J04I04I02I02G01G01G01E00E00E00D10E\ 31G51I62J82L92NB4ND4OE6QG6RI6TJ8VL8XN9XO9YQB_RBaTD\ bVDdXDfYEf_EgaGibIkdKlfMngOniQpkSqlUsnWtpYwqZxs_xt\ zwazxbzzczzdzzezzfzzgzzhzzizzjzzkzzlzzmzzlzzkzzjz\ zizzhzzgzzfzzezzdzzczzbzxazwzt_zrZzqYzoWznUzlSzkR\ ziQzhQzfQzdQzbQzaQz_OzYOzXOzVOzTOzROzQKzQKzOKzOKzN\ KzNKzNKzLJzLIzLHzJGzJFzIFzIFzIFzGFzGFzGFzEFzEFzDFz\ DEzDEzBEyBExBEw9Eu9Es9Eq8Eo8Em6Ek6Ei6Cg4Ae49c48a26\ _24T24M13K1Dt0Ds0Ds0Ds0Ds0Ds0Et0Ds0Ds0Ds0Ds0Ds0Ds0\ Ds0Ds0Ds0Ds0Ds0Ds0Ds0Bs0Bs0Bs0Bs0Bs0Bs0Bs0Bs0Bs0Bs\ 0Bs0Bs0Bs09s0Dt0Dt0Dt0Dw0Dw0Dx0Dx0Dx0Dz0Dz0Dz0Dz0D\ z0Dz0Dz0Dz0Dz0Dz0Dz0Dz0Dz }

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 made bad apple using only mandelbrot fractal formulas. I am so proud of this. Maybe color pallete can be adjusted but i got too used to it by now.

I was trying to make an icon and got this when fiddling with the settings. The checker pattern comes from XORing z - c against zi - ci.
I've used that before, but I found this one rather striking.

Hello, yet another IFS situation with double modulus framework for spirals and pre_waves/mobius with splits for everything else. Quite simple hybrid system and very slow to render due to the hybrid empty transform trick. Main image and details are 1080x1350px crops from 7200x9000px render, I got lazy on the render time as there is some dots and unclear portions, good enough for internets.

Instagram link, because I might forget to post here.

Created with the very old app Fractal Explorer.

I designed this 3D fractal album artwork for my latest album release: Fractal Archive.

Fractal Archive is a collection of dark psychedelic ambient compositions, designed to explore the infinite depths of 3D fractal rendering and the complex weirdness of nature's inner workings.

(an exploratory sonic experience)

The 3D fractal artwork was rendered in mandelbulber, and the 3D Ul was designed in Blender.

The release is now available across digital streaming platforms, here is the spotify link if you want to check it out!

I made a «digital sand clock» with Hilbert Curve filling. Check out how your time is wasted, one pixel at a time. Standalone html is here

Jim Muth's Fractal of the Day for August 31st, 2012

Jim Muth's commentary for the image:

FOTD -- August 31, 2012 (Rating 8)

Fractal visionaries and enthusiasts:

Today's image lies in the parent fractal that results when the expression Z^1.7+C is iterated 11 levels up the complex logarithmic hyperladder with the recip function applied. (The 'hyperladder' could more correctly be called a hyperspiral or hyperhelix.)

This parent fractal resembles a distorted Mandelbrot set that has been rotated so that its East Valley lies on the northwest side of the main bay, while its main period-2 bud sprouts from the southwest side. A long, twisting filament with a large minibrot extends southwest from this bud, but we are not interested in this filament. For today's image we check the southeast shore line of the misplaced East Valley.

We find some curious elephant pieces in this area, but we bypass the pachyderms to check a high-order star, where we find today's scene. The rating of an 8 indicates that I consider the image to be an above average one found in the range of exponents between 1 and 2.

The name "Shattered Dreams" is un-necessarily foreboding. The image is actually rather bright and cheerful. The calculation time of 6 minutes drags a bit, but relief lies at the web sites.

The morning fog cleared off by 10am, leading to a sunny hot afternoon with a temperature of 91F 33C. The fractal cats remained in full summer mode all day, except for a brief moment of excitement when Nicholas got wind of an unwanted tomcat in the area. The humans spent much of the day preparing for the big week-end. The next FOTD is not scheduled to be posted until September 4, but even then, no guarantee is given or implied.
Until whenever, take care, and be extremely cautious before you believe the promises of the political candidates.

PAR file `` Shattered_Dreams { ; time=0:06:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip passes=1 center-mag=-0.1238618515707104/+0.2069993477786224\ /2.660665e+007/1/-177.5/0 params=1.7/0/11/0 float=y maxiter=5000 inside=0 logmap=702 periodicity=6 colors=000000988AA9BCACEBDFCEGDFIEGKFHMGFOHEQICSJB\ UBJPNRJYZDhf8sfAqfCofEmfGmfImhKmjMmmOmpQmqSmuSmrQe\ oLYjHQgCIe8Ac43dCEiKOnRZsZhwertbpr_opXnmUmkRliOkfL\ idIhbFg_CfY9eW7dUAaTC_SFYRHWPJUOMSNOQMQOKTLJVJIXHH\ _FFaDEcBDf9Ch7Bj5sksohplfniclfajcZh_XeXUcUSaRP_ONY\ PMXQMWQMVRMURMTSLSSLRTLRULQULPVKOVKNWKMWKLXKKXKKZM\ J_OIQHbRHcTGdVFfWFgYEh_DjDkbCldBmeBldCkcDjbEiaFh\ Fg_GfZHeYIdXIcWJbVKaULTL_SMZRNPQQRRT_SV_yJQzMS\ oURdaQUiQJqP9xP8mITaRMQEEi73kE9lKFmRLnXRpbXqibro\ hsunopikkegfacaX_XTXTPYNMZIJ_CG7D2BpVHevMoyiMuhD\ ShNhNbhOehOahLbgIcfGcfDdeBde0ikEejRbjc_jpXjkdhfkg\ aszXzzRrzMkhGUjBKl6Am8Kh9UdBc_CcWDwSFwNzzJzrFzdazR\ wsOuqLspIqnFomCmk9kj7jmFhoMfqTescugbwnyu_0cs1cp2\ cm2ckAcjImiQmhYmgemflmemmanmYnzUozQozNizSczWYz_Tzd\ NzhzzlzzpzzqzzqzzqzzrzzrzzrczXbzXbzWazW`zMczIgzEjz\ Anz6qz2kzIpzGuzEvzHwzKxzN }

frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2PIfn1(p/(2PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } ```

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 falsification here! True 3D fractal artwork created in Mandelbulber software.
Alien Mandala - Mysterious Sacred Geometry Motion Loop.

Jim Muth's Fractal of the Day for August 30th, 2010

Jim Muth's commentary for the image:

FOTD -- August 30, 2010 (Rating 6)

Fractal visionaries and enthusiasts:

Today's image is a scene in the Rectangular (imag(c),imag(z)), orientation of the Z^2+C Julibrot. The scene is located near the -1.416 point of the main spike of the Mandelbrot set.

The rating of a 6 is a come-down from the lofty ratings of the past several days, but the image is still worth a look, and the calculation time of just over 2-1/4 minutes will cause little inconvenience.

The name "Total Abstraction" refers to the nature of the four- dimensional Julibrot figure, as well as all other 4-D things.
The curious thing about this is that when one or two dimensions of the total abstraction are discarded by taking slices, the slices prove to be very real.

This abstract stuff becomes quite clear when the image is seen.

The sky was once again cloudless here at Fractal Central on Sunday, but the temperature of 90F 32C was a bit too warm for human or cat comfort. The fractal cats took up residence on the cool kitchen floor, while the humans took it easy on the porch.

The next FOTD will be posted in 24 hours. Until then, take care, and as I see it, the concept of meaning is an invention of intelligent minds. Since the universe apparently has no mind, how then can it have a meaning apart from what we give it? But at the same time, what is the evolutionary advantage of this human tendency to waste mental energy searching for meaning and even to invent meaning where none exists?

PAR file `` Total_Abstraction { ; time=0:02:15.37-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=1 center-mag=0/-0.028319668443599/3349.992/4.7924/180 params=90/0/0/90/-1.41665335/0/0/0/2/0 float=y maxiter=5000 inside=0 periodicity=6 colors=000UQwUQwUQwUPwTPwTPxTOxSOxSOxSNxSNyRNyRMyR\ MyRMyQLwPKuOKtOJrNJpMIoMHmLHkKGjJGhJFgIFeHEcHDbGD\ FCZECYEBWDBVCAT000C9RB9QA8O98M97L86J76H75G65E54D44\ B439328226214113001JMxILvIKtHKsHJqGJpGInFImFHkEHjE\ GhDFgDFeBDbBDBCBCZACYACW9BW9BU9AS89R89P78O79M6AL\ 6BJ5CI5EG4HF4KD3PC3UA2Z92c71h61m40r30v1Az6Kx5Pv4Ut\ 3Zr2cp1hn8ml7rj7vh7zf6vd6rc6ma6h_5cY5ZW5UU4ST4QR4O\ P4MN3KL3IK3GI2EG2CE2AC28A1691471250130010L1xK0wK0v\ K0uK0uJ0tJ0sJ0sJ0rI0qI0pI0pI0oH0nH0nH0mH0lG0lG0kG0\ jG0iF0iF0hF0gF0gE0fE0eE0eE0dE0cD0bD0bD0aD0C0C0_C\ 0ZC0ZB0YB0XB0WB0WA0VA0UA0UA0T90S90S90R90Q80P80P80O\ 80N70N70M70L70L70KA5JFAIKFJPKKUPPZUUcZZhccmhhrmmvr\ rzvvuzzszzqzzozzmzzkzzizzgzzezzcyzbxzawzvz_uzZtzY\ szXrzWqzVpyVoxUnwUnvTmuTluTltSksSjrRiqRipQhpQgoQgn\ PfmPelOdkOdkOcjNbiNbhMagMfL_fL_eLZdKYcKYbJXaJWaIV\ `IV_IUZHTYHTXGSXGRWGRVFQU }

frm:SliceJulibrot4 {; draws all 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), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^real(p5)+c |z|< esc } ```

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.