r/fractals

Created with the now deprecated app Fractal Explorer.

Jim Muth's Fractal of the Day for August 19th, 2008

Jim Muth's commentary for the image: > FOTD -- August 19, 2008 (Rating 8) > > Fractal visionaries and enthusiasts: > > The formula for today's image adds a very small bit of Z^(-20) > to Z^2 to produce a Mandelbrot set with disks of Z^(-20) stuff > at the centers of all the bays and buds. The image is located > on the X-axis, in the detail at the east edge of a disk almost > filling the large period-2 bud of the M-set. More than anything > else it resembles a surrealist's spider-web. > > I named the image "Stars of Iteration", which sounds a little > poetic and in a way describes not only today's fractal, but all > fractals. And then I rated it at an 8. I considered adding a > half point for my coloring, but decided that I did not do quite > enough color tweaking to merit the extra half-point. > > The calculation time of only 42 seconds is fast enough to cause > no impatience. > > With a temperature of 88F 31C here at Fractal Central on Monday, > it was just a bit too warm to be perfect, but all else was the > picture of perfection. The dynamic fractal cats, who never stop > reiterating, agreed. Just after lunch they spotted an unfamil- > iar manx cat in the yard next door, and with a volley of hisses > and growls, sent it on its way. I did not tell them that the > cat was ready to move on anyway, and their empty threats had > nothing to do with its departure. > > Otherwise the day was uneventful. The next FOTD will be posted > in 24 hours. Until then, take care, and to become famous, solve > the measurement problem.

PAR file

Stars_of_Iteration { ; time=0:00:42.84-SF5 on P4-2000
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandAutoCritInZ function=ident passes=1
  center-mag=-0.9160783767764306/0/8.62e+008
  params=1/2/1e-018/-20/0/0/0/0 float=y maxiter=1450
  inside=0 logmap=153 symmetry=xaxis periodicity=10
  colors=0000EC0FF0GI0HL0IO0JQ0LT0NW0PZ0Ra0Td0Vg1XiD\
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  zzzzzzzzzezzNzz4zz6zz7zz8zz9zzAzzCzzDzzEzzFzzGzzIz\
  zJzzezzfzzgzzhzzhzzezzbzz }

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.

Mandelbrot Mix4 at the edge — a glowing boundary where darkness dissolves into an organic sea of purple and coral cells.

Rendered with FractalForgeASMLab.

Created with the very old app Fractal Explorer.

Jim Muth's Fractal of the Day for August 18th, 2011

Jim Muth's commentary for the image: > FOTD -- August 18, 2011 (Rating 7) > > Fractal visionaries and enthusiasts: > > I believe in honesty in advertising, and when a fractal falls > flat, I admit it. I realize that no one gets rich by being > totally honest about their product, but no one gets rich from > finding fractals either, so I've got nothing to lose by telling > it like it is. > > With a rating of an everyday 7, today's deep scene in the > Mandelbrot set barely deserves the word 'deep'. At the modest > magnitude of only 7*(10^15) it is barely beyond conventional > math range, but at least IMO, it has a certain interesting > quality about it that raises it to FOTD standards. > > The scene lies in the East Valley of a larger minibrot on a side > filament of the main filament extending from the bud on the > north shore line of the period-2 bud of the M-set. > > I named the image "Elephant Trek". I see a few hints of > elephant parts in the scene, though not quite enough trunks and > heads to fully justify the name. > > The parameter file takes 25 minutes to finish. > > The day began mostly sunny here at Fractal Central, and > continued this way through a good part of the afternoon. At > post time, showers were in the area, though none had yet reached > FC. The temperature of 86F 30C brought out the best in the > fractal cats. They spent most of the time sleeping. > > While the cats were taking it easy, the humans were doing what > needed to be done. When the necessities were finished, we took > it easy also. It is hardly necessary to state that the next > FOTD image will be posted in 24 hours. Until then, take care > and when I was a youngster, I knew that science and technology > would be our salvation. But now I'm not so sure. What it is > doing is making us ever more dependent on the high priests of > the 'Church of Science and Technology'. > > I recently overheard a young boy (probably an internet addict), > ask how people ever got along when they didn't have cell phones > and the internet. Well, I was around before cell phones and the > internet, getting along quite well, the same as everyone else, > and I can state that we managed life the same as we are doing it > now without the next big technological advance, which will not > be developed for another 50 years.

PAR file

Elephant_Trek { ; time=0:25:10.06-SF5 on P4-2000
  reset=2004 type=mandel passes=1 center-mag=-1.0188\
  8639656655182417/0.30447073015893949152/7.411e+015\
  /1/-10/0 params=0/0 float=y maxiter=7500 bailout=16
  inside=0 logmap=1110 periodicity=6
  colors=000F0AF0AF0AE0AE0AE0AE0AE0AE1AE2AE3AE4AE5AD\
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  `gziazfWzdRzbLz`GzZPzcTzO }

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.

a headache and this thing

20 years ago I wrote an app that wraps bitmaps around the iteration boundaries of a Julia or Mandelbrot fractal. A few days ago I converted that app to Processing 4.0 with the help of Claude AI. Here are the results in 8x8 anti-aliased 4k resolution. Also some movies:

Julia set zooms and morphs:

Cat: https://youtu.be/WHsyn8N9N24

ET: https://youtu.be/tH5TucwHDAE

Cobra: https://youtu.be/-wpJ01GqZyI

Created with the very old app Fractal Explorer.

Jim Muth's Fractal of the Day for August 17th, 2012

Jim Muth's commentary for the image: > FOTD -- August 17, 2012 (Rating 6) > > Fractal visionaries and enthusiasts: > > Today we check the 'Zexpi' fractal, or at least one of the > infinity of Zexpi fractals. The one we are checking looks > nothing at all like the familiar one, which closely resembles > the cubic Mandelbrot set. Instead of sitting upright, today's > parent Zexpi has been turned on its side, with two main buds on > the western lobe of the main bay and only half of a bud on the > eastern lobe. > > I created this parent by calculating the formula Z^(PI)+C at a > level 15.5 rungs up the logarithmic hyperladded with the 'ceil' > function in effect. I think this is the first time I have used > this function, which is one of the rounding functions. Today's > scene is located on the west side of the main bay, in the debris > near the X-axis. > > The rating of a 6 is average and indicates that I see nothing in > the image to get excited about. The name "Primarily PI" shows > that this is the first in a series of images based on the Zexpi > fractal. The calculation time of a mere 20 seconds is about > what the image is worth. > > Increasing clouds marred the early part of the day here at > Fractal Central, and rain spoiled the latter part. The fractal > cats approved of the temperature of 86F 30C however. > > The humans made it through the day with little of the excitement > that makes interesting reading. The next FOTD will be posted > before too long. Until whenever, take care, and why are the > 99-percent so offended by the wealth of the 1-percent? Could it > be envy?

PAR file

Primarily_PI { ; time=0:00:20.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=ceil logmap=37
  center-mag=-0.9369868294821131/+0.0378608092734622\
  /1.568021e+011/1/132.5/0 params=3.14159265358979/0\
  /15.5/0 float=y maxiter=2400 inside=0 periodicity=6
  colors=0000FI0EL0DN0CP0BR0AT08V56aA4iG3tM8wTBwUEwV\
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  HzTHzUHzUHzVHzVHzWHzWHzXHzXHzYHzYHzZHzZHz_Hz_Hz`Hz\
  `HzaHzaHzaHzdHzgHziIzhJzh }

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 August 16th, 2004

Jim Muth's commentary for the image: > FOEFD -- August 16, 2004 (Rating 7) > > Fractal visionaries and enthusiasts: > > As has become the usual state of affairs lately, the work is > still heavy here at Fractal Central, and the discussion will be > brief. > > Today's fractal image features spirals -- brilliant, sparkling > spirals everywhere, a good reason to name it "Spiral Spangled".
> Those sparkling small spirals, and the large main spiral > surrounding the central midget, raise the rating of the image to > a respectful 7. The conveniently short render time of 4 minutes > gives the image an even more respectful overall value of 162. > > The image lies near the end of a filament extending from a bud > on the north shoreline of the main bay of its parent fractal.
> This parent was created by combining 4 parts of Z^(0.5) with 2 > parts of Z^(-1.5) and adding (1/C). > > The parameter file renders in just over 4 minutes on my now-antique > fractal-dedicated machine. It will go faster on a newer > unit. > > Storm Charley passed by Saturday with 0.08 inch 2mm of rain and > a wind gusting to 5mph 8kph. The fractal cats watched the non-excitement > from the dryness of the porch. Sunday stayed dry all > day, giving the dynamic duo much time in the fractal yard.
> Today is starting sunny. It looks like another good day for the > fractal duo. > > For me it looks like work, and there is no better time to get > started than now. Until the next FOEFD appears in a few days, > take care, and dig deeply.

PAR file

Spiral_Spangled { ; time=0:04:19.91--SF5 on a P200
  reset=2003 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=b
  center-mag=-0.21650624140427070/+0.019943127229515\
  34/4.234284e+009/1/37.5/-0.000450000450211679448
  params=2/0.5/1/-1.5/1/-70 float=y maxiter=1000
  inside=255 outside=imag logmap=113 periodicity=10
  colors=000G0oD0jB0e80a50Z10W03R09O0QN0UN0YN0aN0cN0\
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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.

Mandelbrot set at (-1.8603864897749156, -0.0000634054575759), with a height of 1.4 * 10^(-12).

its [-3z / sqrt(z^2 + 1)^5 + c] where white is stable orbit