u/LegalizeAdulthood

Jim Muth's Fractal of the Day for May 22nd, 2003

Jim Muth's commentary for the image: > FOTD -- May 22, 2003 (Rating 8) > > Fractal visionaries and enthusiasts: > > Today's image is what yesterday's should have been. Looking at > yesterday's image one day later, I see that I over-rated it. It > now looks more like a 6 than a 7. But regardless of the true > value of yesterday's image, today's image, which mirror's > yesterday's, rates a true 8. In fact, if I had more time to > color today's image, I might have been able to work it into a > 9-rater. As it is, the colors are a bit gaudy, a flaw which > costs one rating point. > > Today's image is located on the northwest edge of the fan, > where the fan blends into the surrounding area. Like > yesterday's image, today's lies in a vague spiral arrangement in > a kind of pseudo-valley. > > I studied the image for several minutes before I noticed the > claw-like features and named it "Fractal Claws". These claws > are not to be confused with Santa Claus, whose reality lies > somewhere in the range of today's image. In both cases, we can > see the picture but not the object. > > The always-annoying render time of today's image is 15 minutes > on my machine. > > The all-day rain here at Fractal Central on Wednesday made the > fractal cats very unhappy. The temperature of 55F 13C made them > even more unhappy. They spent a few minutes under the cover of > the porch roof, but soon realized that a pleasant afternoon in > the yard was simply not going to happen. They consoled them- > selves by sleeping. > > Today promises more of the same, and in addition, I have more > work to do. So until next FOTD, take care, and is today's > fractal as real as Santa?

PAR file

Fractal_Claws { ; time=0:15:34.54--SF5 on a P200
  reset=2002 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix2 function=recip passes=1
  center-mag=+4.19356285882042800/-1.852233346795663\
  00/4434460/1/-2.5/2.4608337104159439e-009
  params=-10/-1.1/-1/-11/0/525/0/0 float=y
  maxiter=2400 inside=0 logmap=267 periodicity=10
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frm:MandelbrotMix2 {; 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=(((-a*b*g*h)^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.

Jim Muth's Fractal of the Day for May 21st, 2012

Jim Muth's commentary for the image: > FOTD -- May 21, 2012 (Rating 9) > > Fractal visionaries and enthusiasts: > > Today's image rates a 9. In my opinion it is worth it. I have > rarely seen a FOTD fractal image with such a solid-looking ring > filling such a large part of the frame. With perhaps a bit too > much exaggeration, I named it "Beast With 1500 Iterations". > > The parent fractal is a moth-eaten series of bays and other > assorted open areas that came about when I subtracted 0.3 parts > of Z^(2.5) from 0.6 part of Z^(-1.5) and added straight C on > each iteration. > > The most obvious feature of this parent is a twisted Mandeloid > at its the northern end, with the northern side of the main bud > connecting into another, even more distorted, Mandeloid, which > does not appear to be critical. Today's scene is located in > what I take to be the southern branch of Seahorse Valley of the > northern Mandeloid. > > The striking effect of solidity in today's image was created by > rendering the scene with the inside set to 'tdis' followed by > careful coloring. For some reason I declined to award myself > the usual half-point bonus for extra effort on the coloring. A > rating of 9 is exceptional enough as it is, however. > > The name was inspired by those junky old horror movies that I > still enjoy watching. They lacked the super-computerized > special-effect explosions, but made up for it by being so bad > that they were actually good. > > The calculation time of 2-1/4 minutes may not pass in a flash, > but it will certainly pass in two flashes. > > The day brought lots of clouds with a few breaks of sun, as > well as occasional periods of light rain to Fractal Central.
> The temperature of 72F 22C was within a few degrees of normal, > making for a satisfactory day. The day was also satisfactory > for the fractal cats, who watched birds, chased each other up > and down the fractal hallway, fought over the collapsible cat > cube, and asked for an extra treat. > > With all else going well, the fractal humans had nothing to > complain about. The next FOTD will be posted in the near > future. Only time will tell if it goes well. Until next time, > take care, and we think, therefore we might or might not be real.

PAR file

BeastWith1500Iters { ; time=0:02:15.00 SF5 at 2000MHZ
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  formulaname=MandAutoCritInZ function=ident passes=1
  center-mag=+0.6828470067032464/+2.070560323993348/\
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  logmap=82 periodicity=6
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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=(((-a*b*g*h)^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.

Jim Muth's Fractal of the Day for May 20th, 2005

Jim Muth's commentary for the image: > FOTD -- May 20, 2005 (Rating 7) > > Fractal visionaries and enthusiasts: > > I have named today's fractal "Absolutely Glorious". Whether or > not it truly is absolutely glorious is up to the viewer to > decide. The diagonal split cutting close to the center of the > frame spoils the symmetry, but the amberish aura surrounding the > dissected central figure is notable, at least on my CRT fractal > monitor. How it will appear on the newer LED or plasma monitors > will depend on how those monitors are adjusted. > > The image is a scene in East Valley of the prominent midget on > the infinitely divided main stem of the Z^2.000001+C Mandeloid.
> This near-M-set line of fractal exploration is quite rich. It > is surprising how I could have missed it for so long, especially > considering that it could have been done almost as quickly with > the manzpower formula of Fractint. > > I am beginning to wonder what these areas of the near-Mandeloids > look like in the other directions, especially the Julia direc- > tion. It's a good line of thought, so stay tuned and see what > happens. > > The rating of a 7 indicates that I consider today's image above > average. The render time of 6-1/2 minutes means it is slightly > slow. > > An adequate day on Thursday kept the cats out of trouble. It > kept me out of trouble also. But today is starting with rain, > and I doubt that today will be adequate. Regardless of the > weather, the next FOTD will appear in 24 hours. Until then, > take care, and when in doubt, check it out.

PAR file

AbsolutelyGlorious { ; time=0:06:30.47--SF5 on a P200
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandelbrotN passes=1
  center-mag=-1.74853367804061200/+0.000007698676213\
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  maxiter=2500 inside=0 logmap=269 periodicity=10
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frm:MandelbrotN {; Jim Muth
b=p1, z=p2, c=p3+pixel:
z=z^(b)+c,
|z| <= 16 }

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.

Jim Muth's Fractal of the Day for May 19th, 2009

Jim Muth's commentary for the image: > FOTD -- May 19, 2009 (Rating 7.5) > > Fractal visionaries and enthusiasts: > > The parent fractal of today's image is a Mandelbrot set caught > in the act of devolving into the circular hole created by the > iterated non-formula Z+C. This halfway fractal is shaped like a > tear drop with a tiny extra bay on the smooth shore line of its > pointed east end. (I suspect that this tiny extra bay is actually > the extremely shrunken main bay.) > > The west side of the parent fractal has the expected Mandelbrot > buds along its shore. Today's scene is located near the tip of > a filament extending from one of these buds. > > The shape of the parent fractal is symmetrical with respect to > the X-axis, though the bands of the outside=imag coloring > feature are not. Therefore, changing the sign of the Y coordinate > while keeping the absolute value unchanged brings an > entirely different color scheme to the mirrored same scene. > > The name "Tardy Technicality" has little meaning. And why must > a name have meaning or even make sense. (Remember the song > 'Stairway to Heaven'.)
> > The rating of 7-1/2 indicates that the image is good but not > exceptional. One half of the rating is a reward for the effort > I put into the coloring. > > The partly cloudy skies were compromised by an unusually chilly > temperature of 57F 14C here at Fractal Central on Monday. The > fractal cats made themselves comfortable by the heat, which came > on again for an hour. My day was quite busy, but concluded > successfully. > > The next FOTD will be posted in 24 hours, with or without the > approval of the cats. Until then, take care, and be careful of > what you think. Your thoughts are being monitored for illegal > traces of hate.

PAR file

Tardy_Technicality { ; time=0:07:01.77-SF5 on P4-2000
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  formulaname=NewDivideBrot function=recip passes=1
  center-mag=-0.8127135141137847/+0.8410592011071745\
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  maxiter=15000 inside=0 outside=imag
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frm:NewDivideBrot   { ; Jim Muth
z=(0,0), c=pixel, a=-(real(p1)-2),
b=imag(p1)+0.00000000000000000001:
z=z^2*fn1(z^(a)+b)+c
|z| < 1000000 }

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.

Jim Muth's Fractal of the Day for May 18th, 2008

Jim Muth's commentary for the image: > FOTD -- May 18, 2008 (Rating 6) > > Fractal visionaries and enthusiasts: > > We're already 10 or 12 hours late with today's FOTD, so I'll > keep the discussion short. > > Today's image is named "Flight of Fancy". It's an appropriate > name. After all, are not all fractals flights of fancy? > > But we have seen many such squashed-pancake images over the > history of the FOTD, making it difficult to rate today's image > higher than a 6. > > Perhaps the main feature of the image is its celestial blue > colors. The colors might be celestial, but fractals need more > than just fancy colors to gain a superior rating. > > The parent fractal came about when I iterated the formula > Z^(1.57)+C at a level 0.57 units up the logarithmic ladder, > while applying no function. This parent reminds me of a sopping > wet dish cloth slung over the edge of a shelf, but it has a > curious something just off to the west of its main bay, with a > trail of debris leading to this odd thing. Today's image is > located where the debris joins the oddity. > > The calculation time of 4-2/3 minutes is barely within reason, > so waste no time in setting up the included parameter file and > running it. > > Due to the odd hour of my posting, give Paul a chance to run the > parameter file and post the finished image there. > > Saturday began sunny but unusually chilly here at Fractal > Central. Dark clouds moved in during the afternoon, with several > light showers passing over. The high temperature of 57F 14C was > most un-springlike. The fractal cats ignored the weather, and > spent the afternoon chasing each other up and down the hallway. > > In my section, things were rather busy, and will probably remain > so for several weeks. The next FOTD will appear in around 12 > hours. Until then, take care, and move forward.

PAR file

Flight_of_Fancy    { ; time=0:04:40.14-SF5 on P4-2000
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC3 function=ident
  center-mag=-1.114717333522346/-0.1301401672941029/\
  3.823849e+009/1/-90/0 params=1.57/0/0.57/0 float=y
  maxiter=3600 inside=0 periodicity=10
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frm:MandelbrotBC3   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*fn1(p/(2*PI))
  r=real(p2)+PI-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    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.

Jim Muth's Fractal of the Day for May 16th, 2014

Jim Muth's commentary for the image: > FOTD -- May 16, 2014 (Rating A-4,M-8) > > Fractal visionaries and enthusiasts: > > With its rating of a 4, the art aspect of today's image makes > little impact, but its math rating of an 8 gives near full > compensation. > > The image shows perhaps the most convoluted bud I have yet come > upon. This bud appears to have cubic tendencies in much of its > nooks and crannies, while other areas appear almost quadratic.
> The name "Bud Menagerie" refers to this zigzagging bud. > > The parent fractal is a classic Mandelbrot set caught morphing > into a cubic Mandeloid. The most obvious feature is Seahorse > Valley, which has joined its two branches into a kind of narrow > bridge with a large diamond shaped area of chaos at the center.
> Today's image lies within this diamond. > > In addition, the main stem of the parent has spread out into a > broad area of intricate detail, with several large minibrots > centered along the ill-defined negative X-axis. I may check > these minibrots in a future FOTD. > > The image calculates in a measly 1-1/2 minutes, so seeing its > glories will demand little sacrifice. > > Heavy overnight rain ended by late morning here at Fractal > Central today, followed by a cloudy afternoon with a temperature > of 64F 18C. The fractal cats approved of the temperature but > were disappointed by the lack of sun. The fractal humans simply > made it through the day without a notable event happening. The > next FOTD will be posted in two days on May 18. Until then, > take care, and the only sure way to end racism is to stop giving > it so much attention in the media.

PAR file

Bud_Menagerie { ; time=0:01:30.00 SF5 at 2000MHZ
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  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzz }

frm:FinDivBrot-2   { ; Jim Muth
z=(0,0), c=pixel, a=-(real(p1)-2),
esc=(real(p2)+16), b=imag(p1):
z=(b)*(z*z*fn1(z^(a)+b))+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.

Jim Muth's Fractal of the Day for May 15th, 2011

Jim Muth's commentary for the image: > FOTD -- May 15, 2011 (Rating 6) > > Fractal visionaries and enthusiasts: > > Today's discussion is brief because an antiquing trip did happen > on Saturday. > > The image turned up when I decided to see if any rectangles > exist in the (-Z)^(2.003)+C Mandeloid. I found no rectangles > but I did find some interesting other stuff. Today's image is a > sample of that 'stuff'. > > Most of the effect is due to the high-contrast color palette.
> It takes more than sharp colors to create a great fractal > however, so I could rate the image no higher than a 6. > > The name "Many Happy Returns" has nothing to do with the image.
> In fact, I have no idea why I chose it. The words just kind of > popped into my head when I shut off everything else. > > My plans are to eventually post all the past images on my own > web site, but judging from the way things are presently going, I > may never finish the job. > > Heavy clouds and a temperature of 63F 17C cast a pall over > Fractal Central on Saturday. The rain was barely enough to > dampen the sidewalk, but it did dampen the spirits at the fair > for the benefit of the local volunteer fire company. > > The fractal cats, who were left alone all afternoon, had their > spirits dampened also, and gave the humans a sound scolding when > they returned. The next FOTD will be posted in 24 hours. Until > then, take care, and some claim that everything is a dream. If > this is so, then who or what is the dreamer?

PAR file

Many_Happy_Returns { ; time=0:01:06.24-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot5 center-mag=-1.746803722\
  297722/+0.00001106402990913/2.52e+007/1/-57.5/0
  params=0/0/0/0/0/0/0/0/2.003/0 float=y maxiter=1500
  inside=0 logmap=198 periodicity=6
  colors=000HEWCAO87G438fGaWCSL8JA49ipk8rs1I60D40930\
  411ch0Zb0UX0PS0KM0FG0AB055IcM9KBixhGXLAME5B7gSg_N_\
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  5zAtzRlzNezKZzGSzDLzAEz67z3zzwzzUzzszzkzzczzWzzOzz\
  Gzz8zzhzzXzzMzzBzzszzkzzc }

frm:SliceJulibrot5   {; draws all slices of Julibrot
  pix=pixel, u=real(pix), v=imag(pix),
  a=pi*real(p1*0.0055555555555556),
  b=pi*imag(p1*0.0055555555555556),
  g=pi*real(p2*0.0055555555555556),
  d=pi*imag(p2*0.0055555555555556),
  ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
  sg=sin(g), cd=cos(d), sd=sin(d),
  p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
  q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
  r=u*sg+v*ca*sb*cg, 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.

Jim Muth's Fractal of the Day for May 14th, 2010

Jim Muth's commentary for the image: > FOTD -- May 15, 2010 (Rating 7.5) > > Fractal visionaries and enthusiasts: > > Friday turned unexpectedly busy here at FC, so the day's fractal > is a quick one. The parent fractal, which was created with the > FinDivBrot-2 formula, consists of a Mandelbrot set surrounded by > much extra detail. Today's image is located in some of this > extra detail on the positive X-axis. > > I named the image "Mayan Mystery". Something about it reminds > me of the symbolic art of the ancient Mayans of Central America. > > Since so much of the image's worth is in the coloring, I gave > myself a half-point bonus for my color work, bringing the final > rating to 7.5. > > The calculation time of 19 seconds will pass in a flash, or at > least as close as is possible to get to a flash. > > Friday turned surprisingly warm here at Fractal Central, with a > high temperature of 82F 28C and partly cloudy skies. Showers > were in the area during the afternoon, though none fell at FC.
> The fractal cats enjoyed chasing a fly that got inside. One of > them, probably the more agile Cassie, must have caught the fly.
> It disappeared as fast as today's fractal appeared. > > My day was acceptable. I'll be going back to old FC on Saturday > to take care of a few details, so don't be surprised if the FOTD > for May 16 is a day late. Until whenever, take care, and be > fortunate.

PAR file

Mayan_Mystery { ; time=0:00:19.27-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=FinDivBrot-2 function=recip passes=1
  center-mag=+1.29914424038879/0/2.932468e+011
  params=-13/-5000000/0/0 float=y maxiter=450
  inside=0 logmap=68 symmetry=xaxis
  periodicity=6 mathtolerance=0.05/1
  colors=000000c0000c0U0000TST800V1cA0N50BzzcEgz9RPz\
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  Azz5jz3Vz2Fz1rzCdz9Rz6Dz3 }

frm:FinDivBrot-2   { ; Jim Muth
z=(0,0), c=pixel, a=-(real(p1)-2),
esc=(real(p2)+16), b=imag(p1):
z=(b)*(z*z*fn1(z^(a)+b))+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.

Jim Muth's Fractal of the Day for May 13th, 2014

Jim Muth's commentary for the image: > FOTD -- May 13, 2014 (Rating A-7,M-7) > > Fractal visionaries and enthusiasts: > > Today's image came about when I combined negative (1/Z) with > negative (Z) and added (1/C) on each iteration. This expression > has two critical values, +2 and zero. Both critical values > produce similar fractals, which are oriented 180 degrees apart. > > Both parent fractals resemble the east parts of Mandelbrot sets > with the main bud and spike cut off by flat disks. Today's > scene lies in the chaos along the northern edge of the parent > that results when Z is initialized to the critical value of zero > by setting real(p4) to -2. > > I named the image "Maximum Festivity" because of the riot of > overly brilliant colors, which were mostly produced by rendering > the image with the 'outside' set to 'tdis'. In fact, these > garish colors hold down the art rating to an unexceptional 7.
> The math rates a 7 also, mostly because of the non-zero setting > of the real(p4) parameter. > > The image takes a solid 2-1/2 minutes to finish, not so bad as > fractals go. > > Today brought a mix of clouds and sun, and a temperature of 90F > 32C, to Fractal Central. The fractal cats thought it was a > little too warm for comfort, while the fractal humans thought it > was just right. The next FOTD will be posted in a day or two, > or possibly three. > > Until the next FOTD appears, take care, and don't be misled by > conservative deniers of climate change, (aka global warming).
> The world-wide weather records show that it is a fact. And at > the same time don't get caught up in the progressive frenzy to > pass new legislation in the name of fighting climate change. > > Since the climate doesn't obey man-made laws, passing new laws > would amount to nothing more than feeling good while satisfying > various political and economic agendas. With our current lack > of technology, hedonistic life style, and so many nations > developing, there is nothing we would be willing or able to do > that would stop or even slow the warm-up. It would be far > better not to economically cripple ourselves and to use our > resources to prepare for the challenges of the warmer planet to > come.

PAR file

Maximum_Festivity { ; time=0:02:30.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandAutoCritInZ function=recip passes=1
  center-mag=-0.3041584081700229/+0.1763178398559197\
  /142961/1/-65/0 params=-1/-1/-1/1/0/0/-2/0 float=y
  maxiter=3600 inside=0 outside=tdis periodicity=6
  colors=000UzzH0zM4zS9z_CzeHzjMzrSzxYzzbzzgzzmzzrzz\
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  z00z00z00z00z00z00z40z90z }

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=(((-a*b*g*h)^j)+(p4)),
k=real(p3)+1, esc=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+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.

Jim Muth's Fractal of the Day for May 12th, 2003

Jim Muth's commentary for the image: > FOTD -- May 12, 2003 (Rating 7) > > Fractal visionaries and enthusiasts: > > The rush continues here at F.C. The customer is due in three > hours and there is two hours work yet to do. This means another > short FOTD discussion. > > Today's image rates a 7, which is somewhat of an improvement > over the recent days' efforts. > > I named the image "Ghostbusters" because it reminds me of those > mischievous entities that filled the film of the same name some > 20 odd years ago. > > The location of the scene is near the tip of the filament that > extends from the southeast-pointing bud of the obvious Mandel > area of the parent. Actually, the filament goes on forever > until it is absorbed into the ring-like feature. > > The weather was unexpectedly pleasant here at Fractal Central on > Sunday. The forecasted severe weather never developed, and the > sun actually appeared in the afternoon, raising the temperature > to 81F 27C and giving the fractal duo the best romp in the yard > they have had in nearly a week. Their resulting moods were > beyond reproach. > > Today is starting in a far more pleasant manner, with no hint of > foul weather. With things going their way, I expect the duo > will have another pleasant day. My day will turn pleasant when > the work is finished. Until next time, take care, and the > search for truth will never end, because we invent truth by the > act of searching.

PAR file

Ghostbusters { ; time=0:12:13.70--SF5 on a P200
  reset=2002 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix2 function=recip passes=1
  center-mag=-2.98713609027161200/-4.227785958369030\
  00/884250.2/1/25/1.99687892998151595e-006
  params=-10/-1.1/-1/-11/0/525/0/0 float=y
  maxiter=1600 inside=0 logmap=247 periodicity=10
  colors=000C8AD9AEAAFBAGCAHDAIEAKFAMGBOHCPIDRJESKFU\
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  `SzcRzeWzg`zidzkizmJzCJzC }

frm:MandelbrotMix2 {; 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=(((-a*b*g*h)^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.

Jim Muth's Fractal of the Day for May 11th, 2013

Jim Muth's commentary for the image: > FOTD -- May 11, 2013 (Rating 7.5) > > Fractal visionaries and enthusiasts: > > Today's image begins an investigation of the 'hyper' parts of > the HyperMandelbrot set. The investigation will continue in the > days to come, when hopefully, we will stumble upon some far > better hypervistas. > > Today's hyper vista lies in the East Valley area of the minibrot > on the main stem of the parent M-set. > > The name "Hyperscene" is a description. The rating of 7-1/2 is > a come-down, but still a bit above average. The calculation > time of 2-1/4 minutes is fair enough. > > An all-day rain watered down the planned outside activities here > at Fractal Central today. The temperature of 66F 19C was fine, > that is for the ducks. The next FOTD will be posted when it is > ready. Until then, take care, and don't look here for a clever > closing remark.

PAR file

Hyperscene { ; time=0:02:15.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=HyperMandelbrot2 center-mag=-1.7499737\
  29001535/+0.00000626490393988/1.235225e+011/1/100/0
  params=0/0/0/0/0.5/0/1e-050/0 float=y maxiter=5200
  inside=255 logmap=590 periodicity=0
  mathtolerance=0.05/1
  colors=0000FT0FU0FV0FW0FX0FY0FZ0F_0F`0Fa0Fb0Fc0Fd0\
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frm:HyperMandelbrot2 {; periodicity must be turned off
a=(p1),b=(p2):
q=sqr(a)-sqr(b)+pixel,
b=(p3+2)*a*b+p4,
a=q,
|a|+|b| <= 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.

Jim Muth's Fractal of the Day for May 10th, 2007

Jim Muth's commentary for the image: > FOTD -- May 11, 2007 (Rating 6) > > Fractal visionaries and enthusiasts: > > Today's image reminds me of a NDE or near-death experience. I > named it "Toward the Light". All the standard NDE stuff is > there, including the narrow doorway at the end of the brightly-lit > tunnel and the celestial clouds, filled with nebulae of > stars. I leave it to the viewer to decide whether paradise lies > beyond that distant doorway at the end of the tunnel, or the > whole thing is an illusion of an oxygen-starved brain. > > One thing for certain is that today's image rates a 6. I > briefly considered rating it at a 7, but on second thought > decided on a 6. The tunnel effect is not quite strong enough > to earn a rating of 7. > > Actually, the little midget near the center is an exact copy of > its parent fractal, which is a large northwest-southeast-oriented, > flat oval-shaped bay with a field of fractal chaos > extending some distance to the northwest. But today's image is > located off to the side, in some suburban debris on the northeast > side of the large oval main bay. > > The calculation time of 55 seconds is true on the P4-2000 unit, > but even on the P200 the time would be no more than 5 minutes.
> The P4-2000 has 10 times the clock speed of the old P200, but > calculates fractals only 5 times as fast. > > Thursday started fair enough here at Fractal Central, with lots > of sun and a temperature in the 70's F, low 20's C, but clouds > moved in just after noon, and a thunder-shower arrived at 4pm.
> All of this went un-noticed by the fractal cats, who spent most > of the day sleeping like they were already over 15 years old. > > My day was notably average. The next FOTD will appear in 24 > hours. Until then, take care, and search for those elusive > alternate universes.

PAR file

Toward_the_Light { ; time=0:00:55.70-SF5 on P4-2000
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC2 center-mag=+1.1894422532\
  06258/+4.118993571150736/8.056414e+007/1/-100/8.45\
  041294705306534e-005 params=1.11/0/11/3500 float=y
  maxiter=2700 inside=0 logmap=153 periodicity=10
  colors=00000FeQMufQVPO48N89QB9TEAVHAYF4WOBbRCeUCgQ\
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  tz8uz5uz3jz9`zERzJWzL_zMdzNhzOmzPqzQazZbzRbzKbzDWz\
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  AzX9z_9zbQzW_zbhzhqznnzgkzaizWfzPdzJazDEzAHz7Kz5Nz\
  3Qz1Xz5cz8izBKzBMzDNzFOzH }

frm:MandelbrotBC2   { ; by several Fractint users
  e=p1, a=imag(p2)+100, p=real(p2)+PI
  q=2*PI*floor(p/(2*PI)), r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    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.

Jim Muth's Fractal of the Day for May 9th, 2013

Jim Muth's commentary for the image: > FOTD -- May 09, 2013 (Rating 9) > > Fractal visionaries and enthusiasts: > > I have no idea why I named today's image "Out in Left Field", > but that's how it goes sometimes. The lack of a logical reason > for the name is no problem however. With a rating of a 9, the > image needs no fancy, logical name. > > The image is a scene in the East Valley area of a Hyper-Mandelbrot > set that is filling in around the edges of the main > bay and inside the buds. The brilliant white hole at the center > is not an under-resolved minibrot. It is all that remains of > the period-21 bud on the south side of East Valley of the M-set. > The rest of the bud is filled in with patterns similar to those > in today's image, which, like the stack of world turtles, goes > down forever. > > One of these days, someone like Mr. Mandelbrot (may he rest in > fractal land) will determine exactly what is going on in images > like today's. Unfortunately, I am not that person. > > The rating of a 9 is no mistake. The unusually brilliant > colors, for which I am responsible, earn the rating. > > The calculation time of 50 seconds is a joy to experience. It's > so fast that the calculation is dangerously close to finishing > before it starts, thereby creating a time paradox. > > After yesterday's deluge, today, even with its heavy clouds and > chilly temperature of 68F 19C, was an improvement. It was also > the fractal cat's day for a check-up at the doctor. He endured > the discomfort bravely, but showed a bit of resentment when he > returned to FC. > > The next FOTD will be posted when it is ready. Until this > readiness arrives, take care, and the paranormal does indeed > exist. It is nothing more than natural things we do not yet > understand.

PAR file

Out_in_Left_Field { ; time=0:00:50.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=HyperMandelbrot2 passes=1 float=y
  center-mag=+0.27135683245/-0.00622833825/105332
  params=0/0/0/0/0.9/0/1e-020/0 logmap=190 inside=255
  maxiter=1500 outside=imag logmap=190 periodicity=0
  colors=00000210320430540650760860970A80BA0DC0EE1FG\
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  6zz8zz9zz9zz6zz4zz3zz1zzz }

frm:HyperMandelbrot2 {; periodicity must be turned off
a=(p1),b=(p2):
q=sqr(a)-sqr(b)+pixel,
b=(p3+2)*a*b+p4,
a=q,
|a|+|b| <= 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.

Jim Muth's Fractal of the Day for May 8th, 2013

Jim Muth's commentary for the image: > FOTD -- May 08, 2013 (Rating 8) > > Fractal visionaries and enthusiasts: > > Today's image with its lightning-like filaments reflects the > weather today here at Fractal Central. The formula causing all > the bad weather on the screen takes 1.5 parts of Z^(-1.1) and > combines it with 0.3 part of Z^(-7.4) before adding (1/C) on > each iteration. > > The resulting parent fractal is a hugely oversized thing > resembling an upside-down figure eight, with today's scene lying > on the filament extending east from the east branch of the > valley separating the two large lobes of the parent. > > The name "Sinuous Discharge" refers to the image's sinuous outer > curves as well as the electrical effect of the brilliant inner > curves. The rating of an 8 is getting to be a habit, a habit > that I hope continues. > > The calculation time of 1-1/3 minutes is appropriate for the > image, neither too fast nor too slow. But a chore remains -- > the chore of setting up this e-mail as a parameter file and > running it. > > The weather took a turn for the worse here at Fractal Central > today, as a series of severe thunder-storms moved in during the > morning and dropped 3.15 inches, 8cm, of rain by noon. During > the storm an apartment building was struck by lightning and set > afire. The temperature hung around 61F 16C most all day.
> Luckily, the fractal sump pump did its job and we had nothing > worse than a couple puddles on the basement floor. The fractal > cat, who doesn't like thunder, became uneasy until the noise > stopped. > > The next FOTD will be posted in a reasonable time. Until reason > prevails, take care, and presidential assassins are buried in > the U.S. with no fuss; the Oklahoma City bomber, who killed well > over one-hundred, was buried in the U.S. with no fuss; the > Newtown school shooter, who killed 20 children was buried in the > U.S. without a fuss. Why then is there so much silly fuss > finding a place to bury the Boston bomber, who killed only four > people? If we claim it is because he used a weapon of 'mass > destruction', then shouldn't the automatic gun used by the > Newtown shooter and the bomb used by the Oklahoma City bomber > also be considered weapons of mass destruction? > > IMO, everyone, even those we consider the most evil, deserves a > proper burial! God will deal with the evil-doer.

PAR file

Sinuous_Discharge { ; time=0:01:20.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandAutoCritInZ function=recip float=y
  center-mag=+84.76284793287175/+1.51704663727301/\
  119/1/-96./0 params=1.5/-1.1/0.3/-7.4/0/0/0/0
  maxiter=1200 inside=0 logmap=135 periodicity=16
  colors=000A60A80AA0AC0AE0AG0AI0AK0AM1AO2AQ3AS49U5A\
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  NzzOzzQzzRzzSzzUzzVzzKzzF }

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=(((-a*b*g*h)^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.

Jim Muth's Fractal of the Day for May 7th, 2010

Jim Muth's commentary for the image: > FOTD -- May 08, 2010 (Rating 8) > > Fractal visionaries and enthusiasts: > > Today's image, the 8th of the month, rates an 8. It is a scene > in the East Valley of a minibrot in the East Valley of a minibrot > in the East Valley of a minibrot in the East Valley of a > minibrot in the East Valley of a minibrot in the East Valley > of a minibrot in the East Valley of the large minibrot on the > main spike of the Mandelbrot set. I think I have the number of > East Valleys right, but there is no guarantee. The count of > surrounding elements reset itself to a lesser number many times > on the way to the minibrot at the center of the image. > > Perhaps the most unusual thing in the image is how it makes the > normally routine East Valley scenery shine in a new light. I > tried the other outside options on the image, but they produced > results that were either too flat or too chaotic. > > The name "Mysterious East" means just about what it says. > > Unfortunately, the parameter file, using arbitrary precision > math, runs as fast as frozen molasses, taking over 1-3/4 hours > to finish even on the fractal-dedicated fireball P4-2000mhz > unit. > > Friday turned out to be a perfectly normal day both with the > weather and the work here at Fractal Central. The weather was > partly cloudy with a temperature of 70F 21C, which is just about > average. The work was finished by 3pm, which is about average, > and the fractal cats got into trouble, which is also average.
> The trouble arose when Nicholas tried to take Cassie's catnip > mouse and she wanted to keep it. A loud hiss followed by a swat > to Nico's ear gave him other ideas. > > The next FOTD will be posted in 24 hours. Until then, take > care, and changing the past is the reciprocal of knowing the > future. If one is possible, then the other must be possible > also.

PAR file

Mysterious_East { ; time=1:47:46.76-SF5 on P4-2000
  reset=2004 type=mandel passes=1 center-mag=-1.7478\
  549044981009970872626605813389487752/-6.654476e-53\
  /6.673542e+036 params=0/0 float=y maxiter=125000
  bailout=9 inside=0 symmetry=xaxis
  periodicity=6 mathtolerance=0.05/0
  colors=000IABUDOeG_pIkmMbjPVgSMfRFeTEdVEcXEbZEa`E`\
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  RXNUUMXRL_OKbLJeIIhIFXICM }

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.

Jim Muth's Fractal of the Day for May 6th, 2007

Jim Muth's commentary for the image: > FOTD -- May 07, 2007 (Rating 7) > > Fractal visionaries and enthusiasts: > > Today's bright, lacy image lies in the parent fractal that > appears when the formula Z^sqrt(2)+C is iterated 52 levels up > the topless and bottomless complex logarithmic ladder. This > parent reminds me of a distorted Mandelbrot set with its west > side facing southeast. > > Despite its odd shape, the open area at the center is a true > midget, though there is certainly very little of a quadratic > nature about it. > > Today's image is located in the northeast branch of what might > be called Seahorse Valley, since it cuts off a very prominent > period-2 bud. When I saw the image I rated at a 7 almost > immediately. I have no logical explanation to offer for the > name I gave the image -- "Iteration Quest". It sounds kind of > interesting though, and might attract a few viewers. > > And speaking of attracting viewers, when I checked the FOTD web > site today, I couldn't help but notice all the nameless images I > have been posting for the past several months. Without names, > these images are not going to attract many viewers. So from now > on, regardless of how much or how little effort I put into the > FOTD fractals, I will give every one both a name and a rating. > > Today's image takes over 41 minutes to calculate on my P200 > machine. (There is no more P133 machine; it gave up the > iteration last Thursday.) > > Lots of sun and an only slightly cooler temperature of 66F 19C > made Sunday a day to remember here at Fractal Central. The > fractal cats may not remember the weather, but they will > remember the dove that landed right outside their window. > > My day was unusually pleasant. Too bad every day can't be the > same. The next FOTD will appear in 24 hours. Until then, take > care, and don't dare turn a Klein bottle inside-out.

PAR file

Iteration_Quest { ; time=0:41:26.86--SF5 on a P200
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC2 passes=1 float=y
  center-mag=+0.64378755423122760/-0.059667482551642\
  40/8813122 params=1.4142/0/52/0 maxiter=16000
  inside=0 logmap=879 periodicity=10
  colors=000jzzizzhzzgzzfzzeyzdyzcxzaxzZwzWwzTvzQvzN\
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  zYzz_zz_zz_zzbzzbzzdzzdzz }

frm:MandelbrotBC2   { ; by several Fractint users
  e=p1, a=imag(p2)+100, p=real(p2)+PI
  q=2*PI*floor(p/(2*PI)), r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    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.

Jim Muth's Fractal of the Day for May 5th, 2004

Jim Muth's commentary for the image: > FOTD -- May 05, 2004 (Rating 6) > > Fractal visionaries and enthusiasts: > > This will be a short discussion. I am falling behind in my > work and must get caught up before I find myself in another > morass. > > Yesterday's image was a meditation on the negative golden ratio; > today's is a meditation on the negative square root of 2. The > parent fractal is another grossly oversized thing with more > places to investigate than could fit in an infinite universe.
> (oxymoron noted) > > Today's image was rendered with the outside set to 'tdis', which > explains the name "The Total Distance". The inside was set to > 'fmod' to fill in some holes. > > Since IMO the image is a bit above the uninflated FOTD average, > I rated it at a 6. The render time of just over 6 minutes gives > an overall value of 98. > > A sunny but chilly day on Tuesday limited the cats' outdoor time > to under two hours. But this was enough to keep their moods > good. Today is starting sunny and warmer, but showers are > possible later. We'll see how things go for the duo. > > For me, it looks like a normal day. Except for the left-over > sawdust, that fallen limb has been disposed of. Until next > FOTD, take care, and be at ease.

PAR file

The_Total_Distance { ; time=0:06:04.00--SF5 on a P200
  reset=2003 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-1.51093310954631/+1.769058060551924/2.\
  186424e+011/1/-82.5/-0.06180700158054 params=1/-1.\
  414/0.1/-14.14/0/0 float=y maxiter=1000 inside=fmod
  proximity=10 outside=tdis periodicity=10
  colors=000J4EH5CD68B848905B09E0DI0GM0JQ0NV0QX0kG05\
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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=(-a*b*g*h)^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.

Jim Muth's Fractal of the Day for May 4th, 1999

PAR file

Stellar_Nursery    { ; Fractal of the day, 04-05-99
                     ; 4-1/2min at 640x480
  reset=1960 type=formula 
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=-0.09294912167762445/+0.00143386807667\
  271/1.009587e+007/1/180 params=100/1/1/100/-0.99/0
  float=y maxiter=1500 bailout=25 inside=0 logmap=90
  symmetry=none periodicity=10
  colors=000ADa0Cj2AmC9mA8om6qz0or8rgJtUUvFew5ry0zz\
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  }

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=(-a*b*g*h)^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.