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cubic mandebrots
by David Lowenstein 05 Mar '04

05 Mar '04

http://www.hypercomplex.org/quats.htm http://www.mathcs.sjsu.edu/faculty/rucker/cubic_mandel.htm

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FOTD 05-03-04 (Cubic Mandelbrot [4])
by Jim Muth 05 Mar '04

05 Mar '04

FOTD -- March 05, 2004 (Rating 4) Fractal visionaries and enthusiasts: Today there is some good news and some bad news. The good news is that I will take steps to assure the unbroken continuity of the daily FOTD's. I will put several images and discussions into a spare directory and hold them for use on the days when I lack the time to find a new image and write a new discussion. The bad news is that it will take several days to create the backup supply of FOTD's. As a result, today's FOTD will be the last until March 9th. On the Fractint list, Tony Hanmer wrote: >In a formula such as MandelbrotMix4, are there enough midgets >to make very tiny jumps from one to the next, such that each >midget stays the same size and orientation but only its surroun- >ding detail changes slightly? This would lead to animations >with a stable midget, which would be amazing to see. The answer is yes. The number of midgets that could be created with the MandelbtotMix4 formula is one of the higher infinities, and animations such as you describe would be fascinating to watch. But making animations with the M-Mix4 formula raises problems. When the parameters are changed, the detail around the midgets does indeed change. And the size and orientation of the midgets remains nearly unchanged. But the midgets jump around in a totally unpredictable manner, and are quickly lost beyond the edges of the screen. As a result, it becomes neces- sary to track the midgets down, and when they are finally found, sometimes with much difficulty, it is nearly impossible to posi- tion them in exactly the same spot on the screen. The resulting animations are jerky and very unpleasant to watch. Not much need be said about today's image. It is a scene in a remote valley in the northwest quadrant of the cubic Mandelbrot set. The image has been running for the last hour while I have been busy at other tasks. The rating of a 4 hardly makes the render time of over 1-1/4 hours worth the effort. The overall value comes in at a nominal 5. The image may be seen with much less effort by viewing it on Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> But before going there, give Paul a chance to render and post the image. The light rain on Thursday morning ended before noon, leading to a cloudy and mild afternoon. Before venturing outdoors, the dynamic duo checked the temperature and found it was 52F 11C. They decided this was acceptable, and spent several hours in the yard, nibbling the new grass. This morning is starting with similar weather. We shall see what the duo decides. My decision is to attack the pile of work still before me, so until next time, which will not be until March 9th, take care, enjoy fractals while you have them, and be certain you will always have them. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Cubic_Mandelbrot { ; time=1:16:36.22--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotCube passes=1 center-mag=-0.25362329215568170/+1.276686610281370\ 00/2.409843e+009/1/2.49999017136973389/7.615552049\ 72785837e-006 params=0/0/0/0 float=y maxiter=75000 inside=0 logmap=-4088 periodicity=10 colors=000TKUSKVRKWQKXPKYOKZNK_MK`LKaKKcKKeKKgKKjK\ KmMKpOJpQIrWLtUOvWRxYUy_Xza_zcbzeezghzhkzgnzgqzcry\ _sxWtwSuwOvwKwwGxwXywOzwFzw6zu8zs9wqAuoCsmDqkEoiFm\ gFkeGicGgcHedHcfHaiI_kIYmJWoJWmJVkPWhTVcOU`MSZLPVK\ JAJMAIOBHRBGTBISCJSDKSEMRFNRGORHQQIRQJSQKTQL`VJh_I\ odHl_MiVRgRWcTU_VSYXQWZOX`MYbKZdI_fG`hEagIbfLceOdd\ RecVfbYga`h`ci_gjZjkYmlYpmXnmWlmVjmUhmTfmSdmRbmQ`m\ PZmOXmNVmMTmLRmKPmJNmIMmESmAXmDUmFRmHOmJLmLJmNGmPD\ mRAmT8mQ7mO7mM6mK9mICmGFmEImCLmAOmERmIUmMXmQ_mUbmY\ em`hmdkmhnmlqmptmtwmwzmvzmuzmtzmszmrzmqzmpzmozmnzm\ mzmlzmkzmjzmizmhzmhzm`zmUzmNzmGzm9zmBzmDzmFzmHzmJz\ mLzmNzmOzmRzmOzmMzmJzmHzmEzmCzmAzmCzmEzmGzmIzmKzmM\ zmOzmPzmRzmTzmVzmXzmZzm`zmazmZzmXzmVzmTzmUzmUzmUzm\ UzmUzmUzmUzmUzmUzmRzmNzmJzmEzmAzm6zm9zmCzmFzmIzmLz\ mNzmQzmTzmWzmZzmazmczmXzmQzmJzmCzm6zm8zm9zmAzmCzmD\ zmEzmGzmHzmIzmKzmLzmMzmMz } frm:MandelbrotCube {; Jim Muth real(c),imag(c) z=p1, c=pixel+p2: z=z*(sqr(z))+c, |z| <= 16 } END 20.0 PAR-FORMULA FILE==================================

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FOTD & Midgets
by Tony (Anthony) Hanmer 05 Mar '04

05 Mar '04

Greetings Jim, I admit to being fascinated by the endless supply of regular midgets from which you feed us, each with its own entirely novel surrounding! For a while, long ago, I found myself lazily wishing that you'd apply such creativity to other fractal types; but then I got into the rhythm of the FOTD and reached the above conclusion. Which leads me to my question. In a formula such as MandelbrotMix4, are there enough midgets on hand to make very tiny jumps from one to the next, such that each midget stays the same size and orientation but only its surrounding detail changes slightly? This would lead to animations with a stable midget, which would be amazing to see. Tony Hanmer Tbilisi, Republic of Georgia _________________________________________________________________ Tired of spam? Get advanced junk mail protection with MSN 8. http://join.msn.com/?page=features/junkmail

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FOTD 04-03-04 (High-Order Valley [3.5])
by Jim Muth 04 Mar '04

04 Mar '04

FOTD -- March 04, 2004 (Rating 3.5) Fractal visionaries and enthusiasts: With the work still backed up, I had time for only an almost- automatic trip into the Mandelbrot set. My destination was the eighth valley out the negative X-axis, where I stopped and found a midget near the surface of a spiral. The broken, chaotic nature of the scene is typical of the area, which is one of the most difficult to explore in the M-set. The maxiter of the image is an immense 250,000, and even this fails to fully resolve the midget at the center. The logmap of close to a negative 34,000 confirms the difficulty of the area. Since I put almost no effort into the image, and because such fractals have been seen often, I could rate the image no higher than a 3.5. I gave the image a fractional rating to spare it the indignity of a rating of a shameful 3. When the render time of 39 minutes is considered, the overall value comes in at a not very impressive 8.9. I named the image "High-Order Valley" because it is located in a valley of high order. The best way to see the image is to download it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Tuesday and Wednesday were quite pleasant here at Fractal Central, and the cats enjoyed the conditions to the utmost. But this morning is starting with a light rain. The cats already look unhappy. I'll be unhappy until I finish the pile of work before me. Until next time and next fractal, take care, and things will get better. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= High-Order_Valley { ; time=0:39:23.39--SF5 on a P200 reset=2003 type=mandel passes=1 center-mag=-1.40114016879128400/+0.000003334519280\ 19/1.183764e+011/1/132.500439777237176/-0.00037265\ 1854078746847 params=0/0 float=y maxiter=250000 bailout=9 inside=0 logmap=-33650 periodicity=10 colors=00060R00U00W00Z03a06d09g0Bj0Em0Hp3Ks6Nv9RyB\ UzEWzHWzKUzNUyRRvURsWNpZNmaKjdKggKgjHmmEpmBspBvp9z\ s6zv3zv3zy0zy0zz0zz0zzBzzUzzgzztzztzzszzrzyqzsrzjs\ zdtzZuzRvzKszEmz6iv0dp0Zj0Wd0RZ0KU0HN0BH09E0djazzm\ zzmzzdzyKza3vH0m00d00R00U00W00Z00Z00a00d00g00g00j0\ 0m00p00p00s00v00y00y00z00z00z00z00v00m00d03WBENRUE\ dg6ps0zz0zz0zz0zz0zz0zz0zz0zz0zz0vz0mz0dz0Uz0Kz0Bz\ 03z00z00z00z00z00z00z00z00z30z60zB0yH0pN0zmHza0jR0\ U90RB0NE0NH0KK0KK0HN0HR0EU0BW0BW09Z09a06d06d0Bd0Hg\ 0Kj0Rm0Up0Zs0av0gy0mz0pz0vz0yz0zz0zz0zz0vz0jz0Zz6N\ zEBzR0zZ0zj0zp0zs0zv0zy0zz0zz3zz6zzBzzHzzNzzRzzWzz\ azzdzzjzzpzzvzzyzzzzzzzzzzzzzzzzzzzzzzzzzzyzsvzjsz\ amzUjzKgzBdz3az0Zz0Wz0Uz0RzKWzNZzNdzNgzNmzRpzRvzRy\ zRzzUzzUzzUzzUzzWzzWzzWzzKzzWzzdzzmzzvzzzzzzzzzvzz\ pzzmzzjzzgzzdzzazzZzzZzzWzzUzzRzzNzzKzzKzyHzsEzpBz\ j9zgBzZ9zd9zg6zj6zm3zp3zs } END PARAMETER FILE=========================================

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just a question
by David Lowenstein 03 Mar '04

03 Mar '04

what is the 32-bit color version of a map? http://spanky.triumf.ca/pub/fractals/formulas/noel1.frm http://www.mathcs.sjsu.edu/faculty/rucker/cubic_mandel.htm I think Noel giffin should call his inductive fractals rudt sets since they both come from the same diagonalization. -david

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chaos download and rudy set
by David Lowenstein 03 Mar '04

03 Mar '04

http://www.mathcs.sjsu.edu/faculty/rucker/chaos.htm

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[Fractint] you can get the chaos soucecode and program at rudy rucker's website.
by David Lowenstein 03 Mar '04

03 Mar '04

It also has info on cubic mandelbrots and the rudy sets. -david

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No FOTD for 03-03-04
by Jim Muth 03 Mar '04

03 Mar '04

Fractal fans: Due to the non-fractal work load, there will be no FOTD for March 3. This time I will not unexpectedly post a FOTD at a later hour. The next fractal will appear on schedule on March 4. As soon as I can get around to it, I will put aside a couple extra images and discussions to post in a hurry on very busy days like today. Take care and see you in 24 hours. Jim M.

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multifractals?
by David Lowenstein 03 Mar '04

03 Mar '04

http://www.angelfire.com/nc/HUMMINGBIRD1/images/multifractal.jpg http://munin.hsh.no/home/gw/public_html/proj/two_phase_flow2.html http://bg.mypagesonline.com/multi/ http://www.physionet.org/tutorials/multifractal/dimension.htm when several different distorted fractals appear in the same object, is this a multifractal? -david

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about multifractals
by David Lowenstein 03 Mar '04

03 Mar '04

http://www.math.yale.edu/mandelbrot/webbooks/wb_multi.htm http://maxvalue.com/tip048.htm http://citeseer.ist.psu.edu/riedi97inversion.html http://www.umich.edu/~lowbrows/reflections/1998/dsnyder.3.html http://www.fractalmovies.com/index.php4?mode=list_dir&dir_ID=47 multifractals are objects composed of several fractals, each having different scales. I think that is the definition of a multifractal! -david

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more on multifractals
by David Lowenstein 03 Mar '04

03 Mar '04

http://mathworld.wolfram.com/MultifractalMeasure.html http://www.math.ohio-state.edu/~edgar/preprints/mauldin/

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[Fractint] julie brot wonders if multifractals can be implemented in fractint!
by David Lowenstein 03 Mar '04

03 Mar '04

http://classes.yale.edu/Fractals/MultiFractals/welcome.html http://www.amazon.com/exec/obidos/tg/detail/-/0387985395/002-8379713-787204… http://www.amazon.com/exec/obidos/tg/detail/-/1584881542/002-8379713-787204… http://mathworld.wolfram.com/Multifractal.html

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gnofract4d
by Vortex Swirling 03 Mar '04

03 Mar '04

--- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.605 / Virus Database: 385 - Release Date: 3/1/2004

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maybe there can be fractint for ecomstation?
by David Lowenstein 02 Mar '04

02 Mar '04

just an idea! -david www.ecomstation.com a version of os/2!

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FOTD 02-03-04 (Back to Work [6])
by Jim Muth 02 Mar '04

02 Mar '04

FOTD -- February 02, 2004 (Rating 6) Fractal visionaries and enthusiasts: The non-fractal work is unexpectedly heavy again here at F.C., so today's discussion will have to be short and to the point. The point is that today's image is a scene in the fractal which results when 9.9 parts of Z^(-0.41) are subtracted from 0.9 parts of Z^(1.4) and (1/C) is added. This fractal resembles a distorted Mandelbrot set with East Valley on its southern side. The scene of today's image is located in the interior of this valley. The coloring is different from my usual rather somber palettes. Instead of dark blues and purples, I have colored it in bright oranges and tints of white, with a little green and black thrown in for emphasis. The image was calculated using the outside=tdis option, which, in this image, gives more bands than the normal equal-iteration method, and therefore smoother colors. I named the image "Back to Work" because that's what I have to do as soon as I post this letter. The image has been rated at a 6. The render time of 8 minutes gives an overall value of 68. And the minor task of rendering the image from the included parameter file may be avoided by downloading the completed GIF image from Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Another near perfect late winter day here at Fractal Central on Monday kept the two fractal cats happy. The sun and temperature of 57F 14C were pleasant for people also. Today is starting cloudy with light rain, but the rain is already moving out. I expect better things to come by afternoon. For me, the work is heavy today, but I always manage to find time enough for another fractal. Until tomorrow, when that fractal will appear, take care, and have you tried the miracle fractal diet? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Back_to_Work { ; time=0:08:48.22--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.10212840421265620/+0.057868193267248\ 99/3.902478e+008/1/180 params=0.9/1.4/-9.9/-0.41/0\ /525 float=y maxiter=1200 inside=0 outside=tdis periodicity=10 colors=000QhVOiWNhVNgVNfUNeUNdTNcTN\ bTNbSNaSN`RN_RNZRNYQNXQNWPNWPNVONUONTONSNNRNNQMNPM\ NPMORLOSLOTKOUKOVJOWJOXJOYIOZIO_HPaHPbGPcGPdGPeFPf\ FPgEPhEPiDPjDPkDTjHXiL`hOdgSgfVkeZodbscewbizblyahy\ aeyabyaZy_WxYTxWQxXMxYJxZGw_Dw`9wa6wb3wc0vd3ve6vf9\ ugCuhFuiIujLukOulRumUunWuoZupauqdurgusjutmuupuvsuw\ vuxxuxuuwssvpqtnprkopinnfmldljakh_J31L52M72O93PB3Q\ D4SF4TH4VJ5WL5XN6ZP6_R7`T7bV7cX8eZ8f`9gb9idAjfAkhA\ ikBgnCfqDdsEbwFazGrzHzzIzzJzzKzzLWzKXwJYuJZsI_qH`o\ HanGclFdkFejEfiDggDhfCieBjdBacLTcVKbcBbm3bv5`t6Zs8\ Yq9WzBmzCTzESzFQjHOiINhKLfLKeNIcOHbQFaRD_TCZUAXW9W\ X7VZ6T_4S`3Ra5Ta6Ua7Vc8Wh9YmAZrB_wC`wDarEcmFdhGedH\ fdIgdJieKjeLkeMleNmdOncPnbQoaRp`Sp_TqZUrZUrVRnSPkP\ NhMKeJIbGG_DEXCHVBKUANTAQR9TQ8WP7ZN7aM6dL5gJ4jI4mH\ 3pF2sE2vD4tF6sG8qI9pJBnKDmMFkNGjOIhQKgRLfSMeUNeVNd\ WOdYPdZPc_Qc`RbbRbcSbdTafTagUahV`iVdRSfT } 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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 28-02-04 (Cellular Patterns)
by Jim Muth 02 Mar '04

02 Mar '04

At 05:44 AM 3/1/04 -0700, SherLok Merfy wrote: >Before I become a shill for the LCD monitor >makers, you are probably sitting in front of >the strongest source of radiation, . . . True. My fractal-dedicated P200 machine is equipped with an old-style CRT monitor. And these devices are high radiation emitters, as any radio that picks up the AM band can prove. But all the machines I use in my regular work are equipped with the newer non-CRT monitors. In my original letter I was referring to the microwave radiation emitted by cell phones held against the head. The results of some of the studies that have been done can be found at: http://www.wave-guide.org/library/studies.html I also wonder about the radiation that fills the so-called 'wireless office'. This topic really should be discussed on the philofractal list. Are you subscribed to that list? Jim M.

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Re: [Fractint] MIMING for FRACTALS
by gnome＠hawaii.rr.com 01 Mar '04

01 Mar '04

----- Original Message ----- From: SherLok Merfy <brewhaha(a)freenet.edmonton.ab.ca> Date: Monday, March 1, 2004 12:44 pm Subject: Re: [Fractint] MIMING for FRACTALS > On Mon, 1 Mar 2004, Paul N. Lee wrote: > > I sit corrected regarding IFS. So far, I've got a request to my > sysadmin for writing text/XFractint in as the type for .par , .frm > , and > .map > > Transformational operations and rates derived from triangles are a > hard stone to cook, now, because I still hav trouble getting past > usingFDESIGN to draw. There's an interactive tutorial in Java > around somewhere, > but that's for when I'm at the library or my neighbour's place (if > I can > keep his browser from seeking porn and spam and telling me to hide > my IP > number)*. Perhaps it's my goal (my font, which is itself built upon > transformational rules), but I don't see how those triangles work > out to > "FRACTINT", or "DUG", either. > > * I don't know why it took me so long to think of it, but disabling > JavaScript seems like the most obvious way to do that. It's just > that he'll probably want me to turn it back on. Download, install, and run Spybot Search & Destroy. If he uses Internet Explorer, he probably has a few tons of spyware running on his PC. David gnome(a)hawaii.rr.com

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FOTD 01-03-04 (Florida Interlude [6])
by Jim Muth 01 Mar '04

01 Mar '04

FOTD -- March 01, 2004 (Rating 6) Fractal visionaries and enthusiasts: Recently on the Fractint list I saw an image posted that shows disconnected features in the Julibrot. The image started me wondering. It is known that the classic Mandelbrot set is connected, but the perturbed M-sets are not. And it is known that Julia sets are either connected or disconnected, depending on whether their corresponding Mandelbrot points lie within the M-set itself. But, to my knowledge, has it ever been determined whether or not the four-dimensional Julibrot is connected? Does every apparently disconnected point have a filament leading through hyperspace back to the central hyperbay? I rather suspect that the Julibrot is connected, but this is based on intuition. I have not seen it proved and I could easily be wrong. . . . Now on to today's image . . . To find today's image, I took Z^(-1.2), combined it with 0.2 parts of Z^(2.1), then added (1/C). The resulting fractal consists of a large, distorted Mandeloid with a smaller, discon- nected Mandeloid some distance to the east. To locate the scene of today's action, I checked the East Valley of the larger Mandeloid, which in this case is on the north shore of the main bay. The scene of today's action lies in the interior of this valley, disconnected from the rest of the fractal. As is always the case, the disconnected nature of the general area is reflected in the disconnected nature of the features surrounding the central midget. The curving, feathery filaments add just enough artistic touch to qualify the image as FOTD for the first day of March. I had intended on naming the image "Fractal Interlude", but for some reason I wrote "Florida Interlude". The mistake seemed as good as my original intent, so I let it stand. Not much need to be said about the rating of 6, which is the most common FOTD rating. When adjusted for the render time of 4.07 minutes, the rating jumps to a 98. Those who choose to download the finished product from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> will have little reason to concern themselves with the render time. The cats had a near perfect day in the Fractal Central yard on Sunday. With a temperature of 66F 19C and lots of sun to lounge in, the duo had nothing to do but nothing all day. And they do nothing very well. When evening arrived, they came indoors with their tails straight in the air, ready for their dinner. Today is starting in a similar manner. Hopefully, things will go just as well for the duo. I have a bit of work to clear away before I can declare my day a success. And the best way to finish a job is to start it. Until the next glorious or not-so-glorious fractal appears, take care, and watch for hit-and-run fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Florida_Interlude { ; time=0:04:04.09--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-1.59508887023064300/+0.219397667625330\ 00/40616.79/1/165/-7.78849103266754383e-009 params=1/-1.2/-0.2/2.1/1/0 float=y maxiter=620 inside=0 logmap=74 periodicity=10 colors=000FGQG8QHBSIDUKFWMHYOJ_RLaTNcVPeXRgZTi`Vkb\ XmcZoc`qc`tcbufaxgaxibxkbxmcwoewqhwskuumrwomvmhukc\ thZseUrbPq_KpXKoUKnRLmOLlLLkILjFLfJIbMG_PEWSBTV9PY\ 7M`4Ic2Ff0Ec2E`4EY6EV8ESADPCDMEDJGDGIDDKDAMBHJ9NHF\ TFKZCPdAUj8Zp6cq7hq7mrAqrKtsUwsczthztcruUmuKhvBcvB\ olAl_9pO9tD8x28zrOxsNvtMtuLrvKpvKmnHkgFi_CgTAeWCcY\ Eb_G`aI_dKYfMXhOVjQTlSSoUQqWPsYNu_Mw`PtYSrWUpUXnSZ\ lQajOdhMfeKicIkaGn_EqYCsWAvU8xS6uS7sS7qS8oS8mS8lcJ\ koUjmd_mdPmdEmdGmLIm1Km3Lm4Mm5Nk6Pj8Qi9RpASwBRuAQt\ 9Qs8Pr8Pq7Op6No5Nm5Ml4Mk3Lj2Ki2Kh1Jg0Jf0Kd4Kb8K`CL\ ZGLYKLWOMUSMSWMR_UZS`eLglDns6jp9fnCblFZiIVgLReONbR\ J`UFZXBXZDYXEYWGZVHZUGaUFdUEgUDjUCmUVqYlt`hpaelaai\ aZeaWcaScaPcaLcaIcaFcaBca8ca5ca8cZBeXDgVGiTIkRLmPN\ oNQqKSsIVuGXwE_xCazAdz8fz6gz7hz7iz7kz7mz7oz7qz7szT\ uzRwzPzzOzzMzzLzzJzzIzzPzzVzzazzUzzUzzUzzUzzUzzUzz\ UzzUzzSzzNzzIzzEzzBzz9zz7 } 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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 27-02-04 (Iterative Currents [6])
by Jim Muth 01 Mar '04

01 Mar '04

FOTD -- February 27, 2004 (Rating 6) Fractal visionaries and enthusiasts: While working with today's image, I discovered that there is a problem with the type=mandel formula in Fractint. As a result, I needed to write a new version of the SliceJulibrot formula to calculate today's image, which is a different view of yester- day's type=mandel image. This new version, SliceJulibrot3, is included in the parameter section at the bottom of this letter. The new version calculates the square root of the number entered as (p4), or the starting point of Z. I needed the new version because the high-speed type=mandel formula in Fractint calcu- lates the square root of the complex number that is entered as the starting-point parameter rather than the entered number itself. (Actually, I already knew this, but for some reason it did not come to mind.) As mentioned above, today's image is a different view of the spectral bud that was illustrated in yesterday's FOTD. But the angle of today's view is close to 90 degrees from that of yester- day's view, and as a result, the spectral bud has been stretched to a few near-straight features in the background. The fore- ground spiral however has really come to life, and has changed into a sinuous series of curves, which no longer form a perfect spiral, but are rather pleasant to look at anyway. These swirling features inspired the name "Iterative Currents". While studying the image, I got the distinct impression of convection currents swirling on the surface of a newly-poured cup of hot coffee. My original impulse was to rate the image at a 7, but then I realized that some people do not drink coffee, and dropped the rating to a 6. Combined with the render time of just under 16 minutes, this gives an overall value of 38. With more work, the coloring could have been better, but I spent so much time trying to find why the first formula didn't work that I had too little time to devote to coloring the image. The finished image is available on Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A lack of sun and a temperature of 41F 5C here at Fractal Central on Thursday kept the cats' outdoor time limited to less than one hour, but, perhaps due to their increasing age, this was all the duo needed to satisfy their ever-shrinking urge for adventure. Today is starting sunny and milder. This promises good things for the duo. For me, the work is still heavy. But it is not heavy enough to keep me from fractal land, and whatever I find there will become tomorrow's FOTD. Until then, take care, and keep your fractals in alphabetical order. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Iterative_Currents { ; time=0:15:54.50--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=SliceJulibrot3 passes=1 center-mag=-0.00263587632006605/+0.004641457407512\ 89/79.37667/23.269/0/-32.6192430711928907 params=82.7/-41.3/-91.4/74.8/-0.23020724/0.6448031\ 5/0.3991/-0.6312 float=y maxiter=40000 inside=0 logmap=464 periodicity=10 colors=000pzMpyMpxNpxNpxOpxOpxOpxPpxPpxQpxQpxRpwRp\ wSpwSpwTpwTpwUpwUpwUpwUpwUpvUpvUpvUpvUpvUpvUpvUpvU\ pvUpvUpuUpuUpuUpuUpuUpuUpuUpuUpuUpuUptUptUptUptUpt\ UotUotUotUotUntUnsUnsUmsUmsUmsUlsUlsUlsUksUksUksUj\ sUjrUjrUirUirUirUhrUhrUhrUhrUgrUgrUgrUfqUfqUfqUeqU\ eqUeqUeqTdqTdqSdqSdqRdqRdpQdpQdpPdpPdpOdpOdpNcpNcp\ McpMcpLcpLcoKcoKcoKcnJcnJcnJcnJcmIcmIcmIcmIblHblHb\ lHblHakGakGakGakG`jF`jF`jF`jF_iE_iE_iE_iEZhDZhDZhD\ ZhDYgCYgCYgCYgCXfBXfBXfBXfBWeAWeAWeAWeAVc9Vb9Ua9U`\ 9TZ8TZ8SZ8SZ8SZ7SZ7S_7T_7T_6U_6U`6Tb5Uc6Ud7Vd8Ve9V\ cAWbBWaCW_DXZEXYFYYHYYKYXNZXQZWTZWW_WZ_Va`Vd`Ug`Uj\ aUnaTqaTtbSwbSzcSzcRzcRzdRzdTzdVzeXzeZzf`zfbzfdzgf\ zghzgjzhkzhkzilzimzinzjozjpzjqzkrzkrzlrzlrzlrzmrzm\ rzmrznrznrzmrznrznrznrznrznrznrznrznrznrznrznrznrz\ nrznrzorzorzorzorzorzorzorzorzorzorzorzorzorzorzpr\ zprzprzprzprzprzprzprzprz } frm:SliceJulibrot3 {; draws most 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), c=p+flip(q)+p3, z=r+flip(s)+sqrt(p4): z=sqr(z)+c |z|<=9 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 29-02-04 (Odd Mandelbrot [5])
by Jim Muth 29 Feb '04

29 Feb '04

FOTD -- February 29, 2004 (Rating 5) Fractal visionaries and enthusiasts: Today's image for leap-day has been named "Odd Mandelbrot". This is because it is a view of a midget sliced in an odd direction of the Julibrot somewhere between the Mandelbrot and Julia orientations. In the odd slices of the Julibrot, the midgets, or holes as they could more properly be called, can assume any shape whatever. The hole at the center of today's image is clearly not a per- turbed Mandelbrot midget. Such fragmentary midgets never have the straight edges seen in today's image. Nor could it be a Julia set. They also never have features with straight edges. It is actually a slice through the Julibrot oriented half way between the Julia and Oblate orientations. (The Oblate orienta- tion is determined by the imag(c) and real(z) axes.) The straight line through the northwest corner of the hole is an example of one of the features I have named bridges, which are actually parts of Mandelbrot valleys seen from the side. As I mentioned in recent discussions, these odd planes of the Julibrot can be rather unattractive, mostly due to the stretch- ing, which produces a feeling of stress. After considering today's image for several minutes, I decided to rate it at a 5. When the speedy render time of 2-2/3 minutes is taken into consideration, the overall value registers a 187. This makes running the parameter file worth the effort. Those who would rather have their fractals already cooked may download the fin- ished image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A nice warm late winter day with lots of sun and a temperature of 59F 15C made the fractal cats nice and happy on Saturday. They enjoyed several hours in the yard, romping as much as 13-year-old cats can romp, which is not much. When evening came and the sun went down, they strolled back indoors without com- plaint. Today is starting even warmer. How active can the duo get? As for me, I'm simply going to take it easy. After all, it is the seventh day of the week, a divinely ordained day of rest. Yes, I know that the calendar says it is the first day of the week, but the calendar is wrong. Creation began at 9am on a Monday. Until next fractal, take care, and see you in fractal land. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Odd_Mandelbrot { ; time=0:02:40.70--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=1 center-mag=+0.00000000000151219/-0.000000000003180\ 98/1.776313e+010/0.6892/50/1.31075705844807544e-014 params=45/0/90/0/-0.6351285303263351/0.49205751226\ 41822/-0.635128530326335/0.4920575122641822 float=y maxiter=18000 inside=0 logmap=169 periodicity=10 colors=000qOPnPNkQKhRFeSCbTAZU9VU8QV7MW6HV1IW5JX9K\ XCLYGMYJNZNO_QP`UQaYRa`SadT`gU_kU_hUZkUXnMWqIVtLUw\ OTvRSvURvXQv_PvbOveQwhTwjWwlZwkawhcwebwbaw_`wX_wUZ\ xWYvXXtYWrZVp_Un`TlaSkcRidQgePefOcgNahP_hIghMbiQZg\ UUfYQeaLdeHciCbm8alA`kC_kDZjFYiHXiI_hKdgMhgNlfPpeR\ teSp`PlXMhSJdOG`JDXFAVOBTXBReBPnBOz6NwBNuGNrKMpPMm\ TMkYLhaLff8kcLdgXZXiTIjN4kU6a`7Tf9JmA9tC0zD4xF8vGC\ tIGrJKpKOnMSlNWjO_hQcfRgdSkbUi`ViWZhZWi`UjbSkePlgN\ niLplIrnGwpEzrCzlFrfIm`LhWNcQQZKTUEWP4TK9YYEbkJgxO\ ksRhoTfkWdgYbb``ZbZVeXRgVNiTQjSSkSUkSXlSZmR`mRcnRe\ oRgpReqOerMfsKgtIhuGivEjwCkxAly8mz6nz4oz2pz8qzDrzI\ szNtzSuzXvzZwz`xzayzbzzczzdzzezzfzzgzzhzzizzjzzkzz\ lzzmzzkzzjzzizzgzzfzzezzizzmzzpzzozzozzozzozzozzoz\ zozzozznzznzznzznzznzznzznzzszzpzznzzlzzjzzgzzezzc\ zzazzZzzXzzVzzTzzQzzOzzMzzIzzKzzMzzNzzPzzQzzSzzUzz\ VzzXzzfzzizzkzzmzzpzzrzzt } frm:SliceJulibrot2 {; draws most 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), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 28-02-04 (Cellular Patterns [6])
by Jim Muth 29 Feb '04

29 Feb '04

At 12:58 AM 2/29/04 -0800, you wrote: >The effects of EM radiation have not been >determined, studies done have never conclusively >shown that there is a problem, . . . Let's move this off-topic subject to the philofractal list. Studies have indicated that there *might* be a problem with the microwave radiation from 217 pps cell phones. The article that caused me to raise the topic advises that we keep hand-held cell-phone use to a minimum. The article appears on page 115 of the Feb. 22, 2003 issue of 'Science News' magazine. >. . . in fact a few studies show the opposite, >a reduction of certain cancers. I assume you are referring to the high-energy radiation used in radiation therapy. Jim M.

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Front end
by Brian Rankin 27 Feb '04

27 Feb '04

Hi. I once had,but since have lost a utility for entering formula into fractint.I fount it before in a Fractint site but can't locate it now.I am gratefull for any help. Brian. ________________________________________________________________________ Yahoo! Messenger - Communicate instantly..."Ping" your friends today! Download Messenger Now http://uk.messenger.yahoo.com/download/index.html

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FOTD 26-02-04 (Spectral Bud [4])
by Jim Muth 26 Feb '04

26 Feb '04

FOTD -- February 26, 2004 (Rating 4) Fractal visionaries and enthusiasts: I'm busy again today, so the discussion will once again have to be brief. Today's trip takes us into the depths of the Mandelbrot set, to a fine spiral and the ghost of a bud. Images such as today's are what sparked my interest in the four- dimensional aspect of fractals. When I began exploring the perturbed M-sets, I found it puzzling that the low-iteration features should change so quickly when the starting point of Z is changed, while the high-iteration features, such as the background buds, remain unchanged. After a bit of thought, I realized that regardless of where the points start, if they do not escape first, they will eventually settle into the same orbits as the points that start at zero. In today's image, the foreground spiral consists of the low- iteration points that have escaped before settling into the conventional M-set orbits, while the background bud consists of the high-iteration points that have endured many iterations and found the time to settle into the M-set orbits. I named today's image "Spectral Bud", which is a recognition of the ghostly nature of the background bud. Pictures such as today's can be given a striking three- dimensional appearance by using the 'ranges' feature of Fractint, though I lacked the time to use this feature on today's image. I could honestly rate today's image no higher than a 4. When the render time of 2-1/2 minutes is considered, the overall value comes in at 152. The image may be seen either by running the included parameter file, or by downloading the completed image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather was pleasant here at Fractal Central on Wednesday, though it was a bit chilly. The temperature of 43F 6C was tempered greatly by a warm sun, which made the cats' two hours in the yard a pleasant experience. When the day ended, they settled for the evening without complaint. Today is starting similarly. For me, things are a bit more settled today, but still relatively busy. If all goes well, I'll finish in time to find a top-rated fractal. If not, I'll find a medium-rated fractal. Until next time, take care, and find only good fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Spectral_Bud { ; time= 0:02:38.35--SF5 on a P200 reset=2003 type=mandel passes=1 center-mag=-0.23028521918996140/+0.644699549704085\ 40/1847.458/1/-5/-3.77822773067748585e-014 params=0.3991/-0.6312 float=y maxiter=100000 bailout=9 inside=0 logmap=49 periodicity=10 colors=000LKULKULKULKUKKUKKUKKUKKUKKUJKUJKUJKUJKUI\ KUIKUIKVIKVHKVHKVHKVHKVGKVGKVGKVGKVHKVGKVGKVGKVGKV\ GKVGKWGKWGKWFKWFKWFKWFKWFKWFKWFKWFKWFKWEKWEKWEKWEK\ WEKXEKXEKXEKXEKXDKXDKXDKXDKXDKXDKXDKXDKXCKXCKXCKXD\ KYDKYDKYDKYDKYDKYCKYCKYCKYCKYCKYCKYCKYCKYBKYCKYDKZ\ DKZEKZEKZEKZFKZFKZFKZFKZGKZGKZGKZHKZHKZHKZHKZJKYJJ\ YJJYKJYKJYKIYKIYLIYLHYLHYMHYMHYMGYMGZNG_NG`OF`PFaP\ FbPEcPEdQEeQEeRDfRDgRDhRDiRCiSCjSCkSBlTBmUBmUBmUAm\ VAmVAmVAmW9mW9mW9mW8mX8mX8mX8mY7mY7mY7mX6mY7mZ8mZ9\ m_Am_Bm`Cm`DmaEmbFobGqcGscHudIwdJxeKyeLzfMzgNzgOzh\ PzhPziQziRzjSzkTzkUzlVzlWzmXzmYznYznZznZzkwzkwzlwz\ lwzmwzmwznwzowznwznwznwznwznwznwzmwzmwzmwzmwzmwzmw\ zlwzlwzlwzlwzlwzlwzkwzkwzkwzkwzkwzkwzlwzkwzjwzjwzi\ wzhwzhwzgwzgwzfwzewzewzdwzdwzcwzbwzbwzawz`wz`wz_wz\ _wzZwzYwzYwzXwzXwzWwzVwzVwzUwzUwzTwzSwzSwzRwzQwzQw\ zPwzPwzOwzNwzNwzMwzMwzLwz } END PARAMETER FILE=========================================

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FOTD 24-02-04 (Iterative Diversion [6])
by Jim Muth 25 Feb '04

25 Feb '04

FOTD -- February 24, 2004 (Rating 6) Fractal visionaries and enthusiasts: Big changes are coming. In a year or two, Fractal Central will be moving from its current location near the northeast corner of Baltimore MD to somewhere in south or central Pennsylvania. The exact location is yet to be determined. Fractal headquarters will be moving because the fair city in which it is now located, (Charm City they try to call it), has sunk to levels that have gone beyond unbelievable to downright comical. I'll not go into lengthy details, since discussing politics on the list is off topic, but as a single example, believe it or not, the city school system, which recently was granted a multi-million funding increase and boasts something like a 33-percent literacy rate among its 12th grade graduates, is insolvent, and looks like it will soon go into receivership. Now that I have gotten that off my chest, on to the fractal. For today's trip into Fractal Land, I have returned to the traditional Mandelbrot set and the valley of the large period-3 north bud, where I found today's midget. The shape of the midget is familiar. Most of the impact, (if that's what it might be called), is a result of the coloring. I named the image "Iterative Diversion" because it is a brief diversion from my excursions into the other planes of the Julibrot. The rating of a 6 combined with a render time of 9 minutes gives an overall value of 66. For tomorrow's image I will show one of the strange things that happens to today's image when it is viewed from a different direction. Until then, be aware that the finished GIF file of the image is available for download on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather remained pleasant all day here at Fractal Central on Monday, with lots of sun and a temperature of 48F 9C. These conditions kept the fractal cats satisfied from dawn to dusk. Today is starting cloudy and chilly, with the possibility of a little snow. We'll see how it goes. For me, the work is slightly heavy -- nothing that I cannot finish in plenty time to find another fractal. So stay tuned for more wonders. Until next time, take care, and iterate well. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= IterativeDiversion { ; time=0:09:09.85--SF5 on a P200 reset=2003 type=mandel passes=1 center-mag=-0.12942475470355410/+0.649525362441421\ 70/3.099803e+008/1/-24.9999914072450728/-1.7447611\ 8168162553e-005 params=0/0 float=y maxiter=100000 inside=0 logmap=5777 periodicity=10 colors=000NotLnuKmwJlxLkuMjsOipPhnRglSgiUfgVeeXdbY\ c`ZcZUcbPceKciGclEcbCcTBcJ9c98c0OcORcVTcaJcSFcWBc_\ 8cc7he7eg7ch7`j6Zl6Wm6Uo6Rp5Pr5Mt5Ku5Hw5Fx8LlBQ`FM\ cIJeMGgPDiSAlW7nZ4pa1rd4of7liAikDfmFcpI`rLYuOVwRSy\ TQcSXIRcNSfRTiVUkZUncVqgWskXvoXxlWviVugUtdTrbSq_Rp\ YQnVPmTOlQNjOMiLLhJKfGJeEIdHObJTaLZ_OcZQiXSnWUsVZH\ K_ML`QMaUNbYNcaOdePeiQfmQgqRhuShySbrQYkOSdNNYLHRKC\ KI7EHKKDWQ9gW5s`1jV8bPEUJLMDRD7Y52cD6YKATREOZIJeME\ lP9mNBgMCcLDmJFnIGnHHnFJnEKoDLoBNoAOo9PeGOWNNNUNUZ\ H`bBgf5nj0og0pd0qa0rZ0sX0tU0tR0uO0vL0wJ0xG0yD0zA0z\ 80rY1tI2qN2nS3lW3iZ6fX8dYAaYC_YEXZGUZIS_KP_MN_OPYM\ RWKTUIVTGXREYPC_NAaM8cK6eI4gG2hF1gF1gF1fG1fG1eH1eH\ 1dI1JEQJFPKGOKHNLIMLJMMKLMLKNMJNOINQIOSHOUGPWFPYEP\ _DQaDQcDReCRgBSiASk9Tm9Tm8UmAUm6Vm5Vm5Wm4Wm3Xm2Xm1\ FlAGk9Hj9Hi9Ii8Ih8Jg8Jf8Kf7Le7Ld7Mc6Mc6Nb6Na6O`5O`\ 5P_5QZ4QY4RY4RX4SW3PipOlr } END PARAMETER FILE=========================================

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FOTD 25-02-04 (Bite the Bullet [2])
by Jim Muth 25 Feb '04

25 Feb '04

FOTD -- February 25, 2004 (Rating 2) Fractal visionaries and enthusiasts: I am brimming over with philosophy today, both scientific and political, but unfortunately, or perhaps fortunately, because of the general turmoil, I have no time to write it. So instead of blathering, we will go directly to the abbreviated discussion of the image. Today's image is a different view of the same scene that appeared in yesterday's image. The magnitude and maxiter are the same, but, using a different formula, the render time has jumped from 9 minutes to 95 minutes. This is a fine demonstra- tion of the efficiency of the Fractint Mandel formula, which was used to calculate yesterday's image. Yesterday's Mandelbrot image showed the real(c) and imag(c) axes of the scene. Today's image shows the imag(c) and imag(z) axes. I call this orientation the 'Rectangular' because the slice through the origin of the Julibrot in this direction is shaped quite like a rectangle. When seen from this particular direction, the hole that appeared as a midget in yesterday's image is shaped more like a bullet. In recognition of this fact, and considering the plight of the local school teachers, I have named the miserable picture "Bite the Bullet". Since today's image is basically a repeat of yesterday's, complete with the same color palette, I could rate it no higher than a 2, which, combined with the render time of 95 minutes, gives an overall value of a pathetic 2, perhaps the all-time lowest value. At times like this it is best to avoid needless frustration by giving Paul a chance to render and post the image, then download- ing it from his FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather was cold and rainy here at Fractal Central on Tuesday. The temperature of 36F 2C, while not quite cold enough for snow, was certainly cold enough to chill the whiskers and ears of the cats, who passed the day sleeping by the heat and glancing at the birds flying past. Today is starting sunny and cold, but promises to turn warmer. The cats have yet to make their judgement on the weather. For me, I've got quite a load of work to accomplish and the local agitation, (the fractal lady is involved in the school situation), is helping none at all. I'll try to have a fractal ready by post time tomorrow, but there is no promise. Until next time, take care. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Bite_the_Bullet { ; time=1:35:29.99--SF5 on a P200 reset=2003 type=formula formulafile=slices.frm formulaname=Rectangular passes=1 center-mag=0/0/2.171274e+008/0.002123/-0.035408778\ 9311406873/-89.8977468907879 params=-0.12942475461\ 27244/0.6495253624666402/-0.1294247546127244/0.649\ 5253624666402 float=y maxiter=100000 inside=0 logmap=5777 periodicity=10 colors=000NotLnuKmwJlxLkuMjsOipPhnRglSgiUfgVeeXdbY\ c`ZcZUcbPceKciGclEcbCcTBcJ9c98c0OcORcVTcaJcSFcWBc_\ 8cc7he7eg7ch7`j6Zl6Wm6Uo6Rp5Pr5Mt5Ku5Hw5Fx8LlBQ`FM\ cIJeMGgPDiSAlW7nZ4pa1rd4of7liAikDfmFcpI`rLYuOVwRSy\ TQcSXIRcNSfRTiVUkZUncVqgWskXvoXxlWviVugUtdTrbSq_Rp\ YQnVPmTOlQNjOMiLLhJKfGJeEIdHObJTaLZ_OcZQiXSnWUsVZH\ K_ML`QMaUNbYNcaOdePeiQfmQgqRhuShySbrQYkOSdNNYLHRKC\ KI7EHKKDWQ9gW5s`1jV8bPEUJLMDRD7Y52cD6YKATREOZIJeME\ lP9mNBgMCcLDmJFnIGnHHnFJnEKoDLoBNoAOo9PeGOWNNNUNUZ\ H`bBgf5nj0og0pd0qa0rZ0sX0tU0tR0uO0vL0wJ0xG0yD0zA0z\ 80rY1tI2qN2nS3lW3iZ6fX8dYAaYC_YEXZGUZIS_KP_MN_OPYM\ RWKTUIVTGXREYPC_NAaM8cK6eI4gG2hF1gF1gF1fG1fG1eH1eH\ 1dI1JEQJFPKGOKHNLIMLJMMKLMLKNMJNOINQIOSHOUGPWFPYEP\ _DQaDQcDReCRgBSiASk9Tm9Tm8UmAUm6Vm5Vm5Wm4Wm3Xm2Xm1\ FlAGk9Hj9Hi9Ii8Ih8Jg8Jf8Kf7Le7Ld7Mc6Mc6Nb6Na6O`5O`\ 5P_5QZ4QY4RY4RX4SW3PipOlr } frm:Rectangular {; Jim Muth imag(z),imag(c) z=flip(real(pixel))+p1, c=flip(imag(pixel))+p2: z=sqr(z)+c, |z| <= 16 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 23-02-04 (The Fractal Hill [7])
by Jim Muth 23 Feb '04

23 Feb '04

FOTD -- February 23, 2004 (Rating 7) Fractal visionaries and enthusiasts: Though today's image might not be the most beautiful scene ever discovered in the Z^2+C Julibrot, it must be one of the most unusual. Viewing the image, we once again find ourselves in the East Valley area, but what has happened to the valley we know so well? Where are the elephants? In today's image there is not the slightest sign of the ponderous pachyderms that live in the vicinity. Don't panic. The elephants have not stampeded off. They have simply been squashed beyond recognition, leaving us with some- thing that resembles a surrealistic mathematical hill standing on an alien planet, under a very earthly blue sky, complete with a haze layer near the horizon. Nothing beyond the basic equal-iteration bands has been used to render the scene. The only extraordinary aspect of the image is the fact that it has been stretched in the vertical direction almost 100000 times. Things become quite squashed as we near the tip of East Valley and view it from the unimaginable direc- tion of today's image. The stretching I did on the image was necessary so that it would consist of more than a straight, featureless razor-edge. I named the image "The Fractal Hill". It does rather resemble a hill, and it most certainly is a fractal. I put some extra effort into coloring the scene, which raises its rating to a 7. When the render time of over 10 minutes is considered, the overall value comes in at a 67. And when the pre-rendered image is downloaded from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> the value increases several-fold. With lots of sun and a temperature of 50F 10C, Sunday was fair enough here at Fractal Central. The cats must have thought so also, because they spent over three hours lounging in the yard, and when they came in, only a small bit of tuna was needed to keep their moods up. Today is starting sunny and pleasant once again. We shall see how the cats' day goes. For me, it will be another relatively uneventful day -- that is unless finding a great fractal can be considered a big event. Regardless of what happens, the next FOTD will appear in 24 hours. Until then, take care, and there's a hill beyond the hill beyond the hill . . . Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Fractal_Hill { ; time=0:10:23.02--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=1 center-mag=+0.25009805052166050/+0.519661012667224\ 50/28984.82/9.451e-005/90/3.64113739159677152e-011 params=45/90/0/0/0/1e-006/0/0 float=y maxiter=100000 inside=255 logmap=297 periodicity=10 colors=000PNzQOzRPzSQzTRzUSzVTzWUzXVzYWzZXz_Yz`Zza\ _zb`zcazdbzeczfdzgezhfzigzjhzkizljzmkzmlzmmzmmzmmz\ mmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmm\ zmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzm\ mzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmz\ mmzmmzlmzlmzkmzkmzkmzjmzjmzimzimzimzhmzhmzhmzgmzgm\ zfmzfmzfmzemzUmLUmMUkLUjLUiLUgLUfLUeLUdLUbLYaLZ`M_\ ZOZYQYXSXWUWUWVTYUS_TQaSPcROhQNrPLkOKbNJZKHSKGSKFS\ KESKCSKBSKASK8SK7QK6OK5MK3KK2IK1IK0IKANKKSPUXUbaZa\ aiaacaaUaaUaaA`aB`aB`aC`aC`aDcaE_aE_aF_aF_aG_aHWaH\ ZaIZaIZaJZaJZaKYaLYaLYaMYaMYaNXaOXaOXaPXaPXaQXaRWa\ RWaSWaSWaTWaUVaUVaVVaVVaWVaWVaXWbXWbYWbYWbYWbZWbZW\ b_Wb_Wb_Xb`Xb`XbaXbaXbaXbbXbbXbcXbcYbcYbdYbdYbeYbe\ YbeYbfYbfYbgZbgZbgZbhZbhZbiZbiZbiZbjZbj_bk_bk_bk_b\ l_bl_bm_bm_bn`cm_bm_bm_bm`em`emaemaembembdmcdmcdmc\ dmccmccmccmccmcbmcbmcbmcb } frm:SliceJulibrot2 {; draws most 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), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 22-02-04 (Where are the Elephants [3])
by Jim Muth 22 Feb '04

22 Feb '04

FOTD -- February 22, 2004 (Rating 3) Fractal visionaries and enthusiasts: Today's image is not particularly attractive. I warned that the odd planes of the Julibrot can sometimes be stressful to look at. But it is still an interesting view of what happens to the elephants in East Valley when the angle of view is changed to something totally new. In today's image we have stationed ourselves at the origin of the Julibrot, which is also the origin of the Mandelbrot set, and we are looking east toward East Valley. The four- dimensional Julibrot figure is oriented in our 3-D space so that the X-axis of the image is the imag(z) axis of the Julibrot and the Y-axis is the imag(c) axis. What we see looking east has been stretched 250 times in the vertical direction. If this had not been done, the image would have consisted of nothing but a few horizontal lines and bars. And after stretching the scene, what do we see? East Valley is sometimes called Elephant Valley because the features there resemble elephants. The name is well earned. The East Valley features resemble elephants more closely than the Seahorse Valley features resemble seahorses. But here we are in East Valley, and "Where are the Elephants"? The elephants are all around us, but only bits and pieces of them are recognizable. Look closely and you will see parts of trunks here and there, half-elephants touching trunks, and disembodied parts of bodies scattered about in a totally disorganized manner. The elephants are here indeed, but we have missed them, for, though they lie very near, they are in the fourth dimension, leaving us only hints of their true nature. After careful consideration, I decided today's image was worth no more than a rating of a below-average 3. This rating combines with the render time of 2-1/2 minutes to give an overall value of 119. The finished image has been posted to Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> from where it may be conveniently downloaded. The Saturday temperature of 50F 10C was fair enough here at Fractal Central, but the wind, which gusted to over 40mph 64kph was far too much for the cats, who spent most of the day sitting on their shelf by the window, watching the trees blowing and the birds flying by. An extra treat of tuna in the evening restored their good spirits. With nothing much to do for the rest of today, I am going to do nothing much. Sometime this evening I'll see what I can find in the Julibrot that will rate higher than today's 3. Until next time, take care, and there are more wonders in the fourth dimension than can be imagined by the mind of man. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ WheresTheElephants { ; time=0:02:31.05--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=1 center-mag=-0.00704999421812261/+0.295991068831446\ 40/742.8395/0.004019/90/1.912220382038754e-013 params=90/90/0/90/0.27555/0/0/0 float=y maxiter=10000 bailout=9 inside=0 periodicity=10 colors=000GsLJnNLjPOfQQbSTZUVVVYRX_NYZJ`ZGbZDdYAfY\ 7hY4jY1lS8cNEWHLNCRF7X7A_ECbLFeSHhYJkdMnkOqrQsxNmr\ KhlIcfFZ`CUVAPP7KJ5FEDLHLRJSXM_bOfhRnnTutVtfQsULrG\ Gq3C`3IK3OTBY`IfhPoZTcQWSHZG8a5CdCGgJKjQOmXSpbQoVO\ nONnGLm9Km2QdJVW__OpZSqYWrX_sWbtVfuUjvTnwSqxPiyMby\ JVyHOyEGyB9y92yB1vC1sD1qF0nG0kH0iI4mI8pICsIGvIKyAU\ u2cr3`q4Yq4Vp5Sp5Po6Mo6Ko9IkCGgFFcID_KBXNATQ8PT6LV\ 5IU9OTCUSGZRJdQNjPQoSTkUVhWYeY_a_bZbdWdgSfiPhlMjnI\ mqFosCqv8sx5uz2qx5nv7ju9gsBdqD`pGYnIVlKRkMOiOLhQIj\ TGlWEmZCoaAqd8rg6tj4vm2wpFniSebdXWpPPtdOwsNsrLprJm\ rHjrFgrDdrBar9Zr7o1Yk7_hCaeIcbNe_TgWYiTckQhmNnoKsq\ GokDkeAh_7dU4aOLhGao9rv2mt5is7dr9`qBWoDSnFNmHJlJEj\ LAiN5hP1gR4eV7dYAc`DbcGafJ`iM_lPZoSYrUXuTVtSUtRTsQ\ SsPRsOQrNPrMOrLMqKLqJKpIJpHIpGHoFGoFFoEKqDOrCSsBWt\ A`v9dw8hx7ly6pz9lyBiyDeyFbyI_yKWyMTxOPxRMxTJxVFxXC\ xZ9xUCxPExKGxeOf_WaTcWMkQ } frm:SliceJulibrot2 {; draws most 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), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 21-02-04 (That's the Way It Is [5])
by Jim Muth 21 Feb '04

21 Feb '04

FOTD -- February 21, 2004 (Rating 5) Fractal visionaries and enthusiasts: Today's image is a simple view of the Julia set of Seahorse Valley. If this is doubted, start the included parameter file, then bring up the X screen, drop the maxiter to 100 and restart the image. After a few seconds, the screen will show a near- perfect Julia set with the inside colored a brilliant orange. Why then did I choose this very-familiar Julia set to be the FOTD for today? The answer is obvious when the maxiter is raised to 1000000. The Julia set turns out to be not a Julia set after all, but rather a slice of the Julibrot that has been double-rotated 1/10 of 1 degree from the Julia orientation. (Double rotation is a new motion, not possible in 3-D space.) This slight rotation has made a great change in the resulting almost-Julia fractal, which is now magically filled with curious detail. The detail filling the Julia set is actually a greatly magnified image of the Oblate aspect of Seahorse Valley. It has been magnified 573, or tan(89.9), times in fact. (The Oblate aspect is what appears on the screen when the real(z) and imag(c) axes of the Julibrot are pictured.) To see the unmagnified oblate aspect of Seahorse Valley, change the real(p1) and real(p2) parameters to zero. This can be done in equal increments to make things more interesting. Now, to prove that it is actually Seahorse Valley we are investigating, drop the maxiter to 1000 and change the imag(p1) and imag(p2) parameters to zero, while leaving the real(p1 and p2) parameters at zero. If this is done in equal increments, you will see the Mandelbrot set gradually take shape and rotate into its proper position, with Seahorse Valley at the center of the screen. It has been Seahorse Valley we have been investiga- ting all along. This magnification of the Mandelbrot aspect as the Julia orientation is approached is one of the most puzzling things in the Julibrot. I am reasonably certain of what is happening here, but a visualization is totally beyond me. In fact, I cannot even come close. All I can do is sit back and say "That's the Way It Is", which is the name I gave the image. The rating of a 5, when adjusted for a slow render time of almost an hour, gives an overall value of 8.5. The hour wait for the parameter file to run may be cut drastic- ally by visiting Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and downloading the completed image from there. A very pleasant Friday here at Fractal Central made for very happy cats. The temperature reached only 52F 11C, but the wind was light and the sun, which is just now clearing the holly trees in the afternoons, was warm, making the cats' time in the yard very pleasant. At the end of the day no treat was needed. For me, the work is heavier than usual for a Saturday. But it is nothing that cannot be finished in time to find a fractal. Until next FOTD, take care, and do fractals exist on the planet Pluto? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ ThatsThe_Way_It_Is { ; time=0:58:58.38--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=1 center-mag=-4.44089e-016/3.33067e-016/0.8503401 params=89.9/90/89.9/90/-0.75/0/0/0 float=y maxiter=1000000 inside=255 logmap=yes periodicity=0 colors=000A0EB0GC0ID0KE4MD7OCAQCDSBGUBIWALY9O_9Ra8\ Uc8We7Zg6ai6dk5gm5in7km9lmAmmComDpmFqmGrm8oj9lhAii\ AfdBc_C`VCYRFVQISPLPPOMORJNYINRJgZKmhIjiHgjFdkEalD\ ZmBWnATo8Qp7Nq6Kp7Lp8Mp8Mp9NpANpAOpBOpCPpCQpDQpERp\ ERpFSpFSgIW_L_SOcKRgCUjEWiGXhIZgK_fM`eNbePcdRdcTfb\ VgaWhaYj`_k_amZcnYeoXfqXhrWjsVluUnvTowTmsSkpSjmRhj\ RggQedQcaQbZP`VP_SOYPOWMOVJNTGNSDMQAMP7MNHOLZQJcRH\ hTGiUIgWKeXLcYNaZO_`QYaRWbTUcVSdWQfYOgZMh`KiaKkcKl\ eKmfKnhKoiKqkJrlOsnRtoUuoXvo_vpbwpewphwqkxqnxqqyrt\ yrwzryzrwznuzjrzgozcmz`kzXizUgzQeyNcyJaxG_xHYwIWuI\ UsJSqJQoKOmKMkLKiLIgMHeMIcNKaNL_ONYOOWPQUPRSQQQRPO\ SOMTOKUNLVMLWLMXLMYKMZJN_IN`INaHObGOcFOcFOTEFIE7KH\ 8LJ9MMANOBORCPTDQVERYFS_GTbGUdHVgIWiJXkKYnLZpM_sN`\ uOawOdpRfiUhcXkX_mRboKerEht7kv1mt3nr4np5nn6nl8nj9o\ hAofBodDobEo`FoZGpXHpVJpTKpRLpPMqNOqLPqJQqHRqGSqIV\ kKXeM__NaUPdORfITiCUk6zl7 } frm:SliceJulibrot2 {; draws most 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), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 20-02-04 (Seahorse Lake [6])
by Jim Muth 20 Feb '04

20 Feb '04

FOTD -- February 20, 2004 (Rating 6) Fractal visionaries and enthusiasts: Last evening I got into a discussion with the fractal lady, who is of the opinion that I am spending too much time concerning myself with such useless things as fractals and fantasies of the fourth dimension. She seemed to think that this is something only little boys do before they grow up and learn to think like sensible, practical men. When such discussions arise, I totally agree with her opinion, leaving nothing to disagree about, but to myself I often wonder how useless the fourth dimension actually is. One thing the fourth dimension most definitely is good for is fun. And if Einstein had thought it childish to consider the fourth dimension, what kind of world would we live in today? Perhaps we would not have developed computers and discovered fractals, and today's image would not exist. Today's scene reminds me of a lake with reflections shimmering off the wave tops, but it is actually a view of Seahorse Valley sliced in an unimaginable direction. These reflections needed no special formula to bring them to life. They are an actual part of the Julibrot itself. Perhaps this area should be known as "Seahorse Lake", which is the name I gave the image. Due to time limitations, I am unable to write a description of the orientation of today's image, but I will go into the curiosities of four-dimensional geometry in future FOTD's. For now, enjoy the image. It is a very fast one. I have rated today's image at a 6, which combines with the render time of just over one minute to give an overall value of 508. The image may also be viewed by going to Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A very pleasant and sunny late-winter day with a high temperature of 56F 13C here at Fractal Central on Thursday gave the intrepid cats a long, pleasant afternoon in the yard. When evening came, they settled down without complaint. The best news is that today looks to be a repeat. For me, the work is rather heavy, but it is under control, and will be finished in plenty time for another trip to the fourth dimension to find another fractal. The fractal I find will appear as tomorrow's FOTD. Until then, take care, and the everyday world we live in is four-dimensional, so what's the fuss about? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Seahorse_Lake { ; time=0:01:11.01--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=1 periodicity=10 center-mag=-0.0812181/5.55112e-016/3.045118/0.62/9\ 0/3.885780586188e-016 params=45/90/0/90/-0.75/0/0/0 float=y maxiter=50000 inside=0 logmap=yes colors=000dAjcAibAhaAg`Af_AeZAdYAcXAbWAaVA`UA_TAZS\ AYRAXQ9WP9VO9TN9SM9QL9OK9MJ9KH9IB9GA9EMMMQQQSUUX__\ beelpouyxntvgot`jsVeqO`oHWnARl4Nk5Pj6Qi7Rh7Tg8Ug9V\ fAWeAYdBZdC_cC`bDbaEc`Fd`Ff_GgZHhYIiYIkXJlWKmVKnVH\ gNEeFBc7Ca8D_8EY9FW9GU9GUAHUAIUBJUBKUBKUCLUCMUCNUD\ OUDOUEPUEQUERUFSUFSUFTXHTZJU`LUbMVdOVfQWhSWjTXlVXn\ XXpYTqWPoVLmUHkTDiSCgQBeOBcNAaLA_K9YI9WH8UF8WEAYGC\ ZHE_JG`KIaLKbNLcONdPPeRRfSTgUVhVWiWYjY_kZal_cmaenb\ focdqaer`gsZitYkuWmvVowUquSstRurQwqPzoNwnMumLskKqj\ IohHmgGkfFidDgcCeaBc`Aa_9_`CY`EW`GUaJSaLSaNTbQVbSW\ bUXbWYcVZdU_dT`eSafSbfRcgQdhPehPfiOfiNgjMhkLikLjlK\ kmJlmImnInoHooGppFppFnqImqKlrNjrPisRhsUftWetYdu`cu\ bavd`vg_wiYwkXxnWxpVxrWvqXtqYrqZpq_nq`lqajpbhpcfpd\ dpebpe`pfZogXohVoiTojRokPolNnmLnnJnoHnpFnpEnmDlkDk\ iDjgDieDhcDgaDf_DeYDdAKUWDcq7pp6lp6ho5eo5ao4Yn4VZT\ c_Re`QfaOgbMhcLidJjeIlfGm } frm:SliceJulibrot2 {; draws most 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), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 14-02-04 (Unwhisked Whiskbroom [5])
by Vortex Swirling 20 Feb '04

20 Feb '04

Jonathan, Thanks. Looks like Fractint once again has more flexibility than I can imagine. By changing the 3rd setting from the bottom from 1 to 2 it achieved what I was trying to do. --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.590 / Virus Database: 373 - Release Date: 2/16/2004

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FOTD 14-02-04 (Unwhisked Whiskbroom [5])
by Vortex Swirling 20 Feb '04

20 Feb '04

Edwin, I'll take note of that map, I find those color transitions quite nice. I tried rotating the "test par" image and found it to have a very cool effect, a sort of strobe with changing colors moving up slowly. General question. For coloring, is there a way to force the (for a lack of a better word) pool color to not change? What I noticed during the color rotation cycle is that the background goes through the color progressions. I've always accepted that it is this way, but it might be nice to be able to lock that background into a single color. I would have liked that to remain black all through the color rotation. I don't think it can do that. Now more specifically for Edwin, is this to say that there is something Fractint can't do? That you had to write a separate program (that I being an XP head can't run)? I know a Mandelbrot can be converted into a Julia as it is. This would seem to mean that if there were an option to only rotate by a few degrees (if I've been understanding Jim Muth's talks on this) it might be able to do this. While rotating into these other planes it might even be fast enough to do it as a movie? Or at least make a movie of it by collecting snapshots quite quickly. Just some thoughts here, I'll let the experts have at it if they want. --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.588 / Virus Database: 372 - Release Date: 2/13/2004

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Re: FOTD 19-02-04 (The Golden M [5])
by Jim Muth 19 Feb '04

19 Feb '04

At 01:50 PM 2/19/04 -0600, Paul Lee wrote: >But, this [outage] has only affected one of my websites at >AT&T. The actual webpage for today's FOTD by Jim Muth may >be viewed by going directly to the following URL: > > http://home.att.net/~Fractals_3/FotD_04-02-19.html > >Hopefully, service will be restored shortly. :-) I could save a few steps for those who pick up the FOTD's from Paul's web page by from now on listing the URL that will take the viewer directly to the FOTD of that day. It would be easy to adjust the year-month-day part of the address, but I would need to know when the ~Fractals_3 part of the URL changes. Jim M.

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FOTD 19-02-04 (The Golden M [5])
by Jim Muth 19 Feb '04

19 Feb '04

FOTD -- February 19, 2004 (Rating 5) Fractal visionaries and enthusiasts: With an unexpected load of work to get out, I have time for only a short discussion of today's image. The image is a scene in Seahorse Valley. It looks nothing like the familiar valley because it is sliced through the Julibrot in a new direction. To visualize the direction, imagine the Seahorse Valley area of the M-set extending as a 3-D figure in front of and behind the screen as it would when the real and imaginary parts of Z are perturbed equally. Then imagine a horizontal slice through this 3-D figure cut 0.05 above the X-axis. And then imagine yourself looking down on this slice from above. Or better, forget the imagination. From this angle, Seahorse Valley appears as a 'bridge' spanning the width of the Julibrot. The impossibly straight edges are typical of scenes in the odd planes. There is an explanation for why this is so, but it will have to wait until I have more time to write it. Until then, enjoy Seahorse Valley as you have never seen it before. I named the image "The Golden M". The reason for the name is obvious when the image is seen. The rating of an average 5 combines with the render time of 16 minutes to give an overall value of 31. The value may be increased by downloading the finished GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The sun shone and the temperature rose to 46F 8C on Wednesday here at Fractal Central. The cats enjoyed the pleasant conditions to the best of their ability, and when the sun went down, came inside without complaint. Only a small treat was needed to satisfy their meager desires. Today is starting cloudy, but it is still mild. It will be another good day for the cats. For me, it remains to be seen how the trip into the fourth dimension will go. But however it goes, whatever I find there will appear as the next FOTD. Until then, take care, and keep your feet on the ground and your head in the clouds. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Golden_M { ; time=0:16:10.54--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=t logmap=yes center-mag=-0.00128325508607199/-0.000000000000004\ 55/159.0018/0.01505/90/-5.05012698326368081e-014 params=45/90/0/0/-0.75/0.05/0/0 float=y maxiter=100000 inside=0 outside=summ periodicity=10 colors=000NuPNrQOpSOmTPkVPhWQfYQcZR``RZaSWcSUdTRfT\ PgUMiUKjWJiXIiZHh_GhaFgbEgcEgeDffCfhBeiAek9dl8dm8d\ bIaTRZJ`W9iTDeVHbWL_XPXYTUZXR_`OadLbhIclFdpCet9fw6\ gqHdlRbg`_hjYmqWmoTmmQmkNmiJmgFmeBmd8meAmfCriAml9m\ n7uq6xr5uo4sk4qh4qe4pc4oa4n_4mZ3mY3nX3oW3pV3qU3rZ3\ rV3rT7mRBhOFcMIZJMUHQPFUKFXEH`8Id7Kh6Mk5No4Ps3Rw3S\ z8XrD`kIddNhYSmRXqKauDfy6bu9_qCXmFTjIQfKYbNJ_QGWTD\ SV9PYaL`mHmcEeUHrcKmcMcmKccScEUcHXcJZcLacfdhQfmSim\ VlmXnmZqm`smZpmYmmWmmVmmTmmSmmQmmOmmNmmLcmacmZQmXO\ mUMmRKmPImMGoKEpGGqDHrAJr7Ks4Ls8NtCOtGPtKRtOStSTtW\ Vt_WtcXtgZtk_to`tsbtwctzdtxfqvgouhmsjmqkmplmnmmlon\ kpoiqphrqfqrepsdotcnubmvalw`kxblycmzdnzfozgpzhqzir\ zkszltzmuzovzpwzqxzryzpzzozzmzzlzzjzzizzhzzfzzezzc\ zzbzz`zz_zzZzzbzzezzhzzkzznzzozzpzzpzzqzzqzzrzzszz\ szztzztzzuzzvzzvzzwzzwzztzzrzzozzmzzjzzhzzfzzczzaz\ z_zzYzzWzzUzzSzzQzzOzzMzz } frm:SliceJulibrot2 {; draws most 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), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END 20.0 PAR-FORMULA FILE==================================

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-32767 limit on zoom-out demo.
by SherLok Merfy 19 Feb '04

19 Feb '04

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Re: FOTD 18-02-04 (Where is the Seahorse [5])
by Jim Muth 18 Feb '04

18 Feb '04

At 10:57 AM 2/18/04 -0600, Paul Lee wrote: >Sorry for the lateness of putting up Jim's current FOTD >image, but I when it rendered in about 2 seconds, I >figured something was not quite correct. I did not realize that an earlier version of the formula existed with the same name. The image on the web site is the correct one. I have renamed the new version of the formula SliceJulibrot2 as Paul suggested. Jim M.

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FOTD 18-02-04 (Where is the Seahorse [5])
by Jim Muth 18 Feb '04

18 Feb '04

FOTD -- February 18, 2004 (Rating 5) Fractal visionaries and enthusiasts: Since yesterday, I have reworked the Julibrot rotation formula and given it a new name. The only change is that the angles of rotation are now entered as degrees rather than fractions of pi. This makes it easier for me to work with. It's hard enough trying to think in four dimensions without doing the conversion math. The new formula is included in the parameter file at the bottom of this letter, but the [frm:] that I have inserted in front of the formula name must be removed before the formula can be copied into a formula file. Using the new formula, today's image takes us to the area we know and love so well -- Seahorse Valley of the Mandelbrot set. But where are the seahorses? Actually, they are in the picture, but they are distorted to such a degree that they have become totally unrecognizable. The thing we know as Seahorse Valley is actually nothing more than a particular part of a two-dimensional slice down the center of the four-dimensional Z^2+C Julibrot figure. This slice is known as the Mandelbrot set. But Seahorse Valley is not limited to two dimensions. It actually extends off into two more dimensions, both of which are perpendicular to the familiar Mandelbrot aspect of the valley, making the entire valley a true four-dimensional object. These two extra dimensions, when displayed on the screen, create the familiar Julia set associ- ated with Seahorse Valley. A slightly distorted version of this Julia set may be seen by making one full outzoom from today's image. The Julia set is distorted because it is not a true Julia set. The orientation of the image on the screen has been slightly rotated in four different directions from the true Julia orientation. The spirals appearing on the tips of the valleys are Julia features which are familiar enough, but what is that straight- edged border cutting diagonally through the scene? It is not part of a Julia set, nor is it a part of the Mandelbrot set. It is the edge of something entirely new, which I call a bridge, a true 4-D object totally impossible for mere 3-D beings to visualize. These straight edges are one of the most common features of the odd slices of the Julibrot, and make up an entire world in themselves. We will be seeing many more of them as we delve deeper into the hyperspace of four dimensions. Today's image, which consists mostly of gaudily colored spirals and a straight edge, has been named "Where is the Seahorse". The name was inspired by the fact that, though the scene is Seahorse Valley, no seahorses are recognizable. The comb-like fringes throughout the image are true features, and not artifacts. These fringes are also very common in the odd slices of the Julibrot, especially in the areas associated with Mandelbrot valleys. Sometimes these odd slices are rather unpleasant appearing, as illustrated by today's image, which I could rate at only a 5. Taking the render time of 23 minutes into consideration gives an overall value of 21. Today's hyper-image may be seen by starting the parameter file and sitting back to watch the fun, or by downloading the finished GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> thereby saving time but missing the fun. The temperature reached 36F 2C and the clouds increased threateningly on Tuesday here at Fractal Central, but the forecasted snow never arrived. The cats not only approved of the situation, they actually found the courage to endure over 1/2 hour in the yard at the warmest time of the day. And when evening came, no treat was needed. Today is starting sunny and milder. It should be an even better day for the local cats. For me it will be an average day. Most days are. And when I start pondering the fourth dimension, that will also be part of an average day. Until next FOTD, take care, and where does one look to find this fourth dimension we hear so much about? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ WhereIsTheSeahorse { ; time=0:23:49.82--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=SliceJulibrot passes=t center-mag=-1.11565/-0.0388942/7.803134/1/-35.0000\ 000000000142/3.85524945301085609e-014 params=86/89/89/89/-0.75/0.03/0/0 float=y maxiter=65000 inside=0 logmap=yes periodicity=10 colors=000bOScNQdMPeMNfLMgKLhKJiJIjIGkIFlHEmGCnGBo\ F9pE8qD6rE7qF8oG9mG9kHAiIBgJCeJCcKDaLE_LEYMFWNGUOH\ TOHRPIPQJNRKLRKJSLHTMFUKGTMGSNGROGQPGPQGPRGOSGNTGM\ UGLVILWKKUMKSOLUQMWSMXUNZWN`YOa_OcaPdcPfeQhgQiiRkk\ QkmRloSmpTnnUolVojWpiXqgYreZsc_sa`t_auYbvWawXcvXev\ YgvYhvZjvZlvZmv_ov_qv`sv`tvavvaxv`zyayvbxscxpdwmev\ jfvgfudgtahtZisXjsUkrRkqOlqLmpInoFooCpn9pn7okAohDo\ eFobIoRKoQNoPPoNSoMUoKYoIaoFbo9coIcnNblRajU_hWZfYY\ d_WbaV`cUZeVXgWVgWTgXRfXRfYTfYUfZVe_Xe_Ye`Ze``daad\ abdbddceccfcdhcdiceicejceigZhkTfpMetFey8dx9dwAdvAd\ uBdtBdsCdrCdqDdpDdoEdnEdmFdlFclGckGcjHciHchIcgIcfJ\ ceJcdKccKcbLcaLc`Mc`MdaNdaOdaPebQebRebSecSfcTfcUfc\ VfdWgdXgdXgeYgeZhe_he`hfahfaifbigcigdigejgfjhfjhgj\ hikikkimkioljqkiskhukhwkgxkgzkfzjezjezjdzjdzjczjbz\ ibziaziazi`zi_zi_zhZzhZzhYzhXzhXzhWzgWzgVzgUzgUzgT\ zeSzgTzhTziUzkQzmQzmPzmOz } frm:SliceJulibrot {; draws most 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), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 17-02-04 (A Very Deep Scene [6])
by Jim Muth 17 Feb '04

17 Feb '04

FOTD -- February 17, 2004 (Rating 6) Fractal visionaries and enthusiasts: While working on the Julibrot rotation formula last evening, (I wanted to make a few changes.), I took a short diversion into the very-deep, unexplored depths of the Mandelbrot set, down to where no one has gone before and the patterns around the midgets are all circles. The exact location of today's scene is on a filament of a larger midget, which in turn is on a filament of a still larger midget that lies on a filament extending from the northern shoreline of the large period-2 bud of the M-set. I named the picture "A Very Deep Scene", a name that needs no explanation. When the time came to rate the image, I decided on a 6. All images this deep should be at least a little above average. When the two-hour render time is considered, the overall value drops to a measly 4.9. But the value may be increased immensely by downloading the finished GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> I sent the image to Paul in a separate e-mail earlier this morning, so it should be posted very soon. Monday, the Presidents' Day holiday here at Fractal Central, passed like any other day. I didn't even realize it had been a holiday until the day was nearly over. Holidays mean little when every day is a holiday, filled with the joy of fractals. Well, there is that slight matter of the design work that must be done on schedule, but that also is more fun than labor. The fractal cats must have agreed, for despite the below freezing temperatures of 30F -1C that kept them indoors, their spirits remained high. This morning is starting cloudy, with possible snow threatening. We'll see what happens with the cats if the conditions deteriorate. For me, the immediate task is to finish the modicum of work so that I can get back to the Juli- brot formula. If I find anything, I'll present it as tomorrow's FOTD. Until then, take care, and though the attributes of the Julibrot are impossible, we explore it anyway. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Very_Deep_Scene { ; time=2:02:27.65--SF5 on a P200 reset=2003 type=mandel passes=1 center-mag=-1.013604105547047168538693807702/0.373\ 6435665162143165812429607776/4.737036e+026/1/-177.\ 5/2.03941030729737349e-013 params=0/0 float=y maxiter=7500 bailout=9 inside=0 periodicity=10 colors=000VTzROzSPzTQyUQwVglYej`cic`gfZfiXdlUcoSar\ Q`qPZqOXqNVqMTpLRpKPpJNpJLoIJoHHoGFoFDnEBnD9nC7nC5\ lLDkULjbTik`hsggqefpceobdn`cmZblYajW`iU_hTZgRYfPYe\ OXgRWhTViVUjXUkZTl`SmbRndQofQphR`eRLbUN_XPY_RWbTTe\ VRgXPjZMm`KpbIsdFvfDxhBtdAqaAnZAkWAhT9eQ9bN9_K9XH9\ YJAZKB_LC`MD`NEaOFbPGcQHcRIdSJeTKfULfVMhTViRckPllO\ tfRkaTcXWVSYNN`EIb6Ja7Ja7J`7K`7K_7K_8LZ8LZ8E5YF6ZG\ 8_H8`I9aJ9bKAcLAdMDeNFfOHgPJhQLiRNjSPkTRlUTmVVnVXo\ WZpY`q_as`ctbeudgvejvdmwcpxbsyfuzWT9UVASYCP_DObENe\ GMhHKkIJnKHqLFtMLwPQzRVzT_ZWdUYiQ_nLasHdxCfz8hz4jz\ 8grBekFccI`XMZPPXISVHXUH`UHeTGiTGnSarSfvSkwTmwTowU\ qwUrwUswVtwVuxVvxWwxWxxWyxXuxXqxXmu_knaiichdff_hdV\ jcQleSjgTiiUhkVgnWeqXdtYcwZaz__y`Zy`Zy`Zz`Zz`Zz`Yz\ `Yz`Yz`Yz`Yz`Xz`Xy`Xy`Xy`XzdWzhWzlVzoVzsUzvUzzUzzT\ yzSszSnzVjaYgY`dVcaRfZNiWKlTGoQCrN9tMrdQqgUqjYqm`q\ odqrhqulqxoqzjlzfgzbbzZYz } END PARAMETER FILE=========================================

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FOTD 16-02-04 (Triple Point [7])
by Jim Muth 16 Feb '04

16 Feb '04

FOTD -- February 16, 2004 (Rating 7) Fractal visionaries and enthusiasts: This happens every time I start thinking about the fourth dimension. Today's image starts what may prove to be a lengthy journey in the oblique slices of the four-dimensional Z^2+C Julibrot figure. The formula I use for this exploration was developed about five years ago by John Goering and revised slightly by me. I have not posted this particular version previously. Since I will be using it often in the days to come, be sure to remove the frm: from its name and copy it into your formula file. This formula does not draw every possible slice through the four- dimensional figure, but it draws more slices than any other in my vast collection. It can do a smooth rotation from the Julia to the Mandelbrot aspect. And it reveals one of the least known oddities of the world of fractals -- that there are two slices through the Julibrot that produce a Mandelbrot set. One of these slices is drawn when the (p1) and (p2) parameters of the formula are set to zero. I leave it to the intrepid fractalists to find the parameters that reveal the second Mandelbrot set. One hint -- the (p1) and (p2) parameters need to be varied only somewhere between +1 and -1. Today's image is another view of the orange midget of yesterday's image, using the same color palette. I have named it "Triple Point". There is not much to be said about it, except that it is a remote slice of the Julibrot, which appears as though it is being pulled in three directions. The rating of 7 and render time of 7 minutes give an overall value of 84. Starting with tomorrow's FOTD, I'll do some heavy-duty exploration of the fourth dimension. But before that time arrives, save a few minutes by downloading the finished image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunday was sunny here at Fractal Central, but the temperature hovered around freezing all day. This was too chilly for the fractal felines, who spent the day indoors, seeking the warmest spots they could find. Thomas managed a few hits at his old playtoy before he settled for the day. Tippy just settled. Today is starting even colder, with a temperature of 14F -10C. The cats, who are growing slower every year, will likely have another inactive day. As for me, when the work is finished, I'll have a fractal day. Until next time, take care, and don't get dizzy trying to figure those Julibrot rotations. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Triple_Point { ; time=0:07:11.60--SF5 on a P200 reset=2003 type=formula formulafile=julibrot.frm formulaname=SliceJulibrot passes=1 center-mag=+0.00000000000130513/+0.000000000008816\ 47/2.524132e+011/0.03598/101.821445919962812/-76.3\ 113167840462694 params=0.83333/0.5/0/0/0.351424051\ 7840664/0.06386667204878391/0.3514240517840664/0.0\ 6386667204878391 float=y maxiter=5000 inside=0 logmap=-820 periodicity=10 colors=00001P02P03P14Q25Q36Q47R58R69R7AQ8BQ9CPADPB\ EPCFPDGQEHRFIQGJRHKSILTJMUKNVLOWMPXNQYNRXOSXPTXQUX\ RVXSWXTYXT_X`bageenkjuonvhgwa`wWUxPNyIGyCAxFBxHCxK\ DxMDwPEwRFwTFwWGwYHv`IvbIveJvgKviKueJtbIs_IrXHqUHp\ QGoNGnKFmHFlEEkBEfDLbERZGXVHbQIeMKgILiEMgCOeBPd9Rc\ 8SbAUcCVcEWcGYcIZcK_dMadObdQcdSfdUheWjeYme_oe`meXk\ iTilPgpLesHcwDZztiTqgVofXleYjd_hc`ebbcaca`eZ_gXZhU\ YjSXkQWmNVnLUpJTqLVmMWjNYgPZdQ``RaYTbVUdSVeOXgLYhI\ ZiFXjHWjIVjJUjKTjLSjMQkOPkPOkQNkRMkSLkTPgSTdRWcQ_c\ PbcOfcNicMmcLpcKtcJwcJscHocFkcEgcCdcA`c9Xc7Tc5Qc4O\ cBMcIKeOIgVGi`EkgCpmAtt9xzCvuEtpGrkIpgKobNqYPsTRuP\ TwKVxFXzBZzL`zVbzc`z_ZzWXzSVzPTzLRzHQzEQzIQzLPzPPz\ SPzWPzZPzbPzeRzcSzbUz`Vz_XzZYzX_zW`zVazTczSdzQfzPc\ zO`zVgzUdzYaz`ZzcXzeVzdTzcVzbYza_zaaz`cz_fzZhzYjzY\ lzXozWqzVszUuzUnzSgzQ`zOUzMOzLVzJ`zIgzHmzGtzFzzEwz\ LtzRrzXozblzhjznczVezThzR } frm:SliceJulibrot {; draws most oblique slices pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1), b=pi*imag(p1), g=pi*real(p2), d=pi*imag(p2), 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), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 15-02-04 (Mandelbrot Aspect [7])
by Jim Muth 15 Feb '04

15 Feb '04

FOTD -- February 15, 2004 (Rating 7) Fractal visionaries and enthusiasts: Yesterday's FOTD made such an abomination of such a great scene that I feel compelled to make restitution. I do this by presenting the same scene in its Mandelbrot aspect as today's FOTD. In an attempt to atone for my wrongdoing, I have given the scene a new color palette, one that might be even a bit too intense. But, after what I did yesterday, the midget in question deserves all the help it can get. I named the image "Mandelbrot Aspect" because that's what it is. But let's not forget the five other mutually perpendicular aspects of this four-dimensional scene. The Julia aspect is only one of these. Perhaps I'll see what can be done with today's midget in the other perpendicular directions and present these as the next five FOTD images. I'm once again getting the urge to ponder the fourth dimension, and we all know what happens when I do that. I seem to remember writing in an FOTD discussion about five years ago about a four-dimensional Titanic striking a four- dimensional iceberg. I half finished the description of what a three-dimensional person standing on the deck might see, and then I dropped the topic. Of course, the whole thing might be pure fantasy, since stable planetary orbits are not possible in spaces of four or more dimensions. I originally rated today's image at an 8. Then I noticed that the colors were a bit too strong for comfort, and dropped the rating to a 7. But a seven is still above average, and combined with a render time of 45 seconds gives an overall value of 921. For those who would rather not render, the completed GIF image is available on Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The clouds hung tough on Saturday here at Fractal Central, and the temperature stopped rising before it reached 41F 5C. For proper comfort, the fractal cats demand either full sun or a temperature above 50F 10C. Since neither of these conditions prevailed, the cats were not satisfied, and showed their dis- satisfaction by returning inside only a few minutes after they had gone out and looking as unhappy as they could. I let them look unhappy for a few hours, then gave them a treat of salmon. I hope they enjoyed their special treat, for the salmon is gone and the next treat will be the standard tuna. Today is the seventh day of the week. (Our calendar is wrong. Monday is actually the first day of the week.) It's a day of rest both for the Deity and the created. And, being among the created, I intend on resting. The best source of relaxation I know of is a computer screen on which a fractal is taking shape. I wouldn't be surprised if that's where I find myself in a few hours. Until next time, take care, and if I was not created, I must be a lucky accident. The chances of such an accident must be far greater than one in a googolplex to the googolplex. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Mandelbrot_Aspect { ; time=0:00:45.70--SF5 on a P200 reset=2003 type=mandel passes=1 center-mag=+0.35142405178407020/+0.063866672048795\ 94/3.309344e+011/1/107.500211829640378/-0.00010569\ 7737740419184 params=0/0 float=y maxiter=5000 bailout=9 inside=0 logmap=-820 periodicity=10 colors=00001P02P03P14Q25Q36Q47R58R69R7AQ8BQ9CPADPB\ EPCFPDGQEHRFIQGJRHKSILTJMUKNVLOWMPXNQYNRXOSXPTXQUX\ RVXSWXTYXT_X`bageenkjuonvhgwa`wWUxPNyIGyCAxFBxHCxK\ DxMDwPEwRFwTFwWGwYHv`IvbIveJvgKviKueJtbIs_IrXHqUHp\ QGoNGnKFmHFlEEkBEfDLbERZGXVHbQIeMKgILiEMgCOeBPd9Rc\ 8SbAUcCVcEWcGYcIZcK_dMadObdQcdSfdUheWjeYme_oe`meXk\ iTilPgpLesHcwDZztiTqgVofXleYjd_hc`ebbcaca`eZ_gXZhU\ YjSXkQWmNVnLUpJTqLVmMWjNYgPZdQ``RaYTbVUdSVeOXgLYhI\ ZiFXjHWjIVjJUjKTjLSjMQkOPkPOkQNkRMkSLkTPgSTdRWcQ_c\ PbcOfcNicMmcLpcKtcJwcJscHocFkcEgcCdcA`c9Xc7Tc5Qc4O\ cBMcIKeOIgVGi`EkgCpmAtt9xzCvuEtpGrkIpgKobNqYPsTRuP\ TwKVxFXzBZzL`zVbzc`z_ZzWXzSVzPTzLRzHQzEQzIQzLPzPPz\ SPzWPzZPzbPzeRzcSzbUz`Vz_XzZYzX_zW`zVazTczSdzQfzPc\ zO`zVgzUdzYaz`ZzcXzeVzdTzcVzbYza_zaaz`cz_fzZhzYjzY\ lzXozWqzVszUuzUnzSgzQ`zOUzMOzLVzJ`zIgzHmzGtzFzzEwz\ LtzRrzXozblzhjznczVezThzR } END 20.0 PAR-FORMULA FILE==================================

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FOTD 14-02-04 (Unwhisked Whiskbroom [5])
by Vortex Swirling 15 Feb '04

15 Feb '04

Edwin, Any tips on how to translate one of the .fct files so that that the picture can be generated in Fractint with one of Jim's formulas? I'd just love to generate Kandy Pop and rotate the palette for fun! --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.588 / Virus Database: 372 - Release Date: 2/13/2004

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FOTD 12-02-04 (Unwatched Watchtower [4])
by Jim Muth 15 Feb '04

15 Feb '04

FOTD -- February 12, 2004 (Rating 4) Fractal visionaries and enthusiasts: What evil has befallen the splendid midget that appeared as yesterday's FOTD? Where we once had a lovely, perfectly symmetrical pattern, we now have a mis-shapen, distorted thing that is downright stressful to look at. I have used the same color palette, so what could have caused this abomination? Actually nothing evil was done to the glorious scene of yesterday. I simply shifted my point of view, took a 'photograph' of the same scene from a different direction, and named the picture "Unwatched Watchtower". As I have said often in the past, the Mandelbrot set, the perturbed M-sets and the Julia sets are slices of a single four-dimensional object known as the Julibrot. Since this Julibrot object is four-dimensional, it may be sliced in new ways that produce neither Julia nor Mandelbrot sets, but entirely new aspects of the familiar Julia and Mandelbrot scenes. Today's image illustrates what happens to yesterday's "Watchtower" image when it is seen from one of these new directions. Some slices taken in new directions reveal aspects that are virtually the same as the familiar Julia and Mandelbrot aspects; other slices reveal grossly stretched and distorted aspects such as we have in today's image. In order to fully comprehend why this is so, it would be necessary to visualize the entire inside of the Julibrot, which would be difficult for even a four- dimensional person, not to mention a mere three-dimensional one. To try to understand what is happening in images such as today's I reduce the problem to three dimensions and imagine taking a blob of white silly-putty and a blob of black silly putty, and combining them into a single lump. Then I knead the lump slightly, so that the black and white putties just start to blend, forming well-defined arms and filaments that twist and turn through the interior of the combined blob. Then I cut the combined blob in half to reveal inside features much like those in today's image. The features have not really been stretched, the apparent stretching is due to the angle at which some of the twisting and turning features have been sliced. All this stretching and distorting has taken its toll on the superb original image. Today's version is worth no more than a humble 4, which equals slightly below average. Considering the render time of 7-1/2 minutes, this results in an overall value of 52. The 7-1/2 minute wait while the parameter file runs can be avoided by downloading the completed GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather on Wednesday here at Fractal Central was very average, with lots of sun but a chilly temperature of 39F 4C. The cats' behavior was also very average. After an uneventful hour in the yard, they came inside and settled by the heat for a long sleep. Today is starting cloudy and cold, with snow not far to the south. As long as it stays to the south, the cats will not be worried. My only concern is to get the waiting work finished, a task that will take about two hours to accomplish. Then I'll see what I can find in Fractal Land. The best of what I find will appear as tomorrow's FOTD. Until then, take care, and watch for lurking Julibrots. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ UnwatchedWatchtowr { ; time=0:07:39.12--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=1 center-mag=+0.00000000000227835/+0.000000000001655\ 24/9.466954e+011/0.07488/-42.1987606685050665/-86.\ 2801728293503629 params=19.055/-104.667/2/0/-1.861\ 19088257009/0.000407298011669/-1.86119088257009/0.\ 000407298011669 float=y maxiter=7500 inside=0 periodicity=10 colors=000NleRuhVzkTzlRxmQunOroMopL\ lpJiqIgrGdsEatDZtBWu9Tv8Qw6Nx5LxJT_W_CUZGTZJRZMQZP\ OZSNYWLYZKYaIYdHYgFXdEXbDW_CWYBWVAVT9VQ8VO7UL6UJ5U\ H5UI5TJ5TJ7JY7JY7JY7JY7KY7KY7KY7KY7KY6LX6LX6LX6LX6\ MX6MX6MX6MX6NX6NX6NX6NX6NXyHvwIuvItuIttIssIsrIrqIr\ oIqnJqmJplJpkJojJoiJngJnfJmeKldKlcKkbKkaKj_KjZKiYK\ iXLhWLhVLgULgSLfAAAAAAAAAAAAAAAAAAAEAAEAAEAAEAAEAA\ EBAECAEDAEEAEFAEGAEHAEIAEJAEKAELCEMFENIEPLGROIURKW\ UM_WOcZNicMnhLrmOwrRywUzzWwwbrrgmmjhmmcmoZmqUmsUnu\ WowYqyZsz`uzawzbuvbrqbmlchgcc`cZYcUVdPTeNRfRPgWNh_\ LicJjgHklFlpDmtBnx9nvHdtPVsXMqdCpl3kk6fj9aiCYhFTgH\ OfKKeNFdQAcT6cV7bW7aX8`X8_Y9ZZ9YZAX_AX`BW`BVaCUbCT\ bDScDRdDRdFVgGYiHakIdmJhoKkqLgmMcjN_gOWdPSaQOZRKWS\ GTTCQU8NU5KSISRU_PfgOrnNsoNspNsqNsrMssMstMttMtuLtv\ LtwLtxLtyLtyNnvOitPdrQZpRUnSPkTJiUEgV9eW4c87mEEmKL\ mQSmWZmadmYajV_hRXfOVdLSaHQ_ENYBLWFV_Jcb } frm:multirot-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 13-02-04 (Whisk Brooms [5])
by Jim Muth 15 Feb '04

15 Feb '04

FOTD -- February 13, 2004 (Rating 5) Fractal visionaries and enthusiasts: Today's image was never supposed to be. I announced earlier today that there would be no FOTD for February 13. But the other work went faster than expected, and I managed to find the time for a quick trip into the star of the period-5 radical on the northeast shore of the Mandelbrot set. I stopped at a point on an arm of the star at a magnitude just before the switch over to arbitrary precision math becomes necessary, and zoomed into the nearest midget. The result is pretty much as expected, with spiky filaments radiating and branching from the central midget. For some strange reason I named the image "Whisk Brooms". One benefit of stopping just before the switch over to arbitrary precision math becomes necessary is the extreme speed of the image, which renders in only 17 seconds. Unfortunately, the ordinariness of the scene cut a couple points off the rating, but with a render time of mere seconds, even an image with a rating of a 5 has an overall value of 1786, making it well worth the effort of running its parameter file. As always, the finished GIF image is available on Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A cloudy and chilly day here at Fractal Central on Thursday kept the dynamic cats' outdoor time limited to under 15 minutes. But the brief outing in the 41F 5C degree air seemed to satisfy them, and only a small treat of tuna was needed in the evening to keep their moods livable. The work today was heavy, but the Friday 13th jinx did not appear, and the work was finished faster than at first seemed possible. Until tomorrow's FOTD, which hopefully will appear on schedule, take care, and God made fractals at the same time that he made the universe. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Whisk_Brooms { ; time=0:00:16.87--SF5 on a P200 reset=2003 type=mandel mathtolerance=/1 center-mag=+0.43792435442605380/+0.341892138828262\ 40/1.312819e+012/1/142.836672263020262/-0.000 params=0/0 float=y maxiter=1500 bailout=9 inside=0 logmap=322 periodicity=10 colors=000HMcINdJMeJMfKMgKMhLMiLLiMLjMLkMLlNLmNLnO\ KnOKoPKpPKqPKrQKsQJsRJtRJuSJvSJwSJxQKyOKzMKzKKzIKw\ GKtFLqDLnBLk9Lh7Le5Lc3Ma4L_4KY4KX4JW4JU4IT4IS5HR6G\ Q7GP8FO9FNAEMBDLCGKCKHDOLESOEWRF_UFcXGg`GkcGofHsiH\ ulHvmKwmNvlQujStiVsgZrfaqdepcioaln`lmallbmlcmldkle\ jlfhlhglhelicljblk`kl_kmZknYkoYkpXkqXkrWksVkuVkwUk\ yXkzUkwRgtPdrM`mKXhHUcFQZCMUAJPCMRDPUFSYGV`IYdJ`gL\ ckMfnOirPluNivMfvLdvKawJZwIXwHUwGRxFPxEMxDJyCHyBEy\ ACyFEvJGsNIpRKmWMj_OgcQdgSaiSYkT_iS`gRaeQccPd`OeZN\ gXLhVKiTJkQIlOHmMGoKFpIEqHDpHDpHDpGCoGCoGCoFCoFBnF\ BnEBnEAmEAmDAmDAmD9lC9lC9lC9lFBhIDdLE`KGXKHTKFQKAM\ K0IK0EM0AP06S03V03Y03`00c13f15i27p59rACtFEvKGxPIzU\ LzZNzcPzhRl5Tk6Wm6Yn6_p7aq7dr7fr8hs8ju5ns8lrAkpCjo\ EinGhlIgkLeiNdhPcgRbeTadV`bYZa_Y`bXZeWYhVYkUXnUZq9\ atBcwDezFgzGizIlzKnzMpzNrzPtzRvzSrzWnzZjzbfzebziZz\ lUzrVzoWzmWzkXziYzgYzeZzc } END PARAMETER FILE=========================================

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FOTD 14-02-04 (Unwhisked Whiskbroom [5])
by Jim Muth 14 Feb '04

14 Feb '04

FOTD -- February 14, 2004 (Rating 5) Fractal visionaries and enthusiasts: After saying that there would be no FOTD for February 13, I went ahead and posted one anyway. If this created a minor bit of confusion, those who were confused have my apologies. This morning I found a note from Paul, suggesting that I post my FOTD's the night before the day on which they are due. This is a good idea. I will resume doing this in the near future. I shifted to morning posting because I am always more alert and energetic in the mornings, and can write better. I will adjust my schedule to write the FOTD's a full day in advance, on the morning of the day before, and post them the evening before. The "Unwatched Watchtower" FOTD of two days ago showed a distorted version of a fine midget in the Mandelbrot set. In a letter with quirky spelling that was posted to the Fractint list on Friday, SherLok Merfy commented that the image was a mixture of Mandelbrot and Julia features. In a way, this is what the image of two days ago is. Today's image consists of the same mixture. It is not a Mandelbrot image; it is not a Julia image. It is not actually a distortion of either of these. It is a legitimate aspect of the Julibrot in its own right. By returning to the default magnitude, keeping the (p1) and (p2) parameters unchanged and changing only the (p3) and (p4) parameters, the entire fractal world glimpsed in today's image can be fixed and thoroughly examined, a world as varied as the Julia and Mandelbrot worlds themselves. But as today's image shows, this new world is not all beauty. Like the 'real' world, it holds scenes that are not pretty. Also like the real world, these not-very-attractive scenes hold a strange fascination, and with a bit of effort can be turned into works of art -- kind of like turning a sow's ear into a silk purse. Today's image demonstrates a bit of this artistic regeneration. The regeneration was not great, but it was enough to raise a total loser to a rating of a 5, which is average. There is actually a fine Mandelbrot midget or Julia set lying at the center of the basin in the image. All that is needed to see one of these aspects is to rotate the point of view to the proper direction. I named today's image "Unwhisked Whiskbroom" because it is a distortion of an area similar to the one that appeared in yesterday's image. The render time of 5-1/4 minutes combined with the rating of 5 produces an overall value of 96. The image can be seen and perhaps enjoyed by running the parameter file or by downloading it from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Friday started very busy here at Fractal Central, but the rush was cleared away far sooner than expected. This made the fractal cats quite happy. (They get jealous when I give the computer more attention than I give them.) The weather was pleasant, with sun and a temperature of 45F 7C. This made them even happier. When they ended the day with their faces in their food dishes, eating a treat of salmon, no less, their happiness was complete. Today is starting cloudy but mild. Anything could happen both in the 'real' world and in the fractal world. Check back in 24 hours to see what the 'anything' turns out to be. Until then, take care, and if you don't find a fractal lying on the side- walk the next time you go out walking, look for a meme. They are almost as rare. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ UnwhiskdWhiskbroom { ; time=0:05:14.61--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=1 center-mag=+0.00000000041173934/-0.000000000085871\ 50/2.510428e+010/0.01217/11.9165416490383649/85.78\ 47425758229463 params=90.663/54.828/2/0/0.35142405\ 17840664/0.06386667204878391/0.3514240517840664/0.\ 06386667204878391 float=y maxiter=5000 inside=0 logmap=641 periodicity=10 colors=000FH0GIKHJQIKTJLWKMZLNaMOcNPeOQgQRiSSkUTmW\ UoXVmZUm`SmbQmdOleMlgKiiIhkGfmEenCdmEalGZkHXjJViLT\ iMRhOPgPNfRLeTJeUHdWFcYDbZBa`9aa8Z`AW_CUZDRYFOXGMW\ IJVJGULEUMF`HFfDFm8Fs4Eo3Ek3Dh3Dd2Ca2CY2CV2BR1BN1A\ K1AG09D0990960C84EA8GCCIEGKFKMHOOJRQLVSMZUObWQfYSj\ _Tm`VkaXibZgb`ecacdcbee`egZfhXgjVglThnSipQjqOjsMku\ KlwIlxHjxGhxGfxFdwEbwD`wDZwCXwBVwATwARw9Pw8Nw7Lw7K\ v8Kv8Ku8Ju9Ju9Jt9ItAItALO3LO3LO3LO4LO4LO4LO4NQ8PRC\ QTGSUKTWOVXSWZVY_Z_ab`bfbdjcenegrfhucisairZjpXjoUk\ mSklPljNliKmgImfFndDncAoa8o`Dl_Hj_Lg_Qe_Ub_Y`_aZ_f\ W_jU_nR_sP_wM_zK_zI_zLayObwRctTdrWeoZfmagjchgfjeik\ bll`nmYqnWtoTwpRyqSvrStrSrrTorTmrTkrUirUfrUdrVbrV`\ rVYrWWrWUrWSrURqTRqSRqQQqPQqOQqNPqLPqKPqJOpIOpGOpF\ NpENpDNpBMpAMp9Mp8Mp9Om9Pk9Qi9Rg9Se9TcAUaAV_AWYAXW\ AZTA_RA`PBaNBbLBcJBdHBeFBfDBgBEhAHiAKjANjAQkASlAVl\ AYmA`n9cn9eo9hp9TF6RD4PA3 } frm:multirot-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================

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No FOTD for February 13
by Jim Muth 13 Feb '04

13 Feb '04

Because of too much real work, which must be done, there will be no FOTD for Feb 13. The fractals will return on schedule on Feb 14. Jim M.

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Re: [Fractint] FOTD 12-02-04 (Unwatched Watchtower [4])
by Fr. Jim Lacasse 13 Feb '04

13 Feb '04

Jim, The Unwatched Watchtower in view is about an 8. Great color. Have a good day. Fr. Jim >>> jamth(a)mindspring.com 02/12/04 07:08AM >>> FOTD -- February 12, 2004 (Rating 4) Fractal visionaries and enthusiasts: What evil has befallen the splendid midget that appeared as yesterday's FOTD? Where we once had a lovely, perfectly symmetrical pattern, we now have a mis-shapen, distorted thing that is downright stressful to look at. I have used the same color palette, so what could have caused this abomination? Actually nothing evil was done to the glorious scene of yesterday. I simply shifted my point of view, took a 'photograph' of the same scene from a different direction, and named the picture "Unwatched Watchtower". As I have said often in the past, the Mandelbrot set, the perturbed M-sets and the Julia sets are slices of a single four-dimensional object known as the Julibrot. Since this Julibrot object is four-dimensional, it may be sliced in new ways that produce neither Julia nor Mandelbrot sets, but entirely new aspects of the familiar Julia and Mandelbrot scenes. Today's image illustrates what happens to yesterday's "Watchtower" image when it is seen from one of these new directions. Some slices taken in new directions reveal aspects that are virtually the same as the familiar Julia and Mandelbrot aspects; other slices reveal grossly stretched and distorted aspects such as we have in today's image. In order to fully comprehend why this is so, it would be necessary to visualize the entire inside of the Julibrot, which would be difficult for even a four- dimensional person, not to mention a mere three-dimensional one. To try to understand what is happening in images such as today's I reduce the problem to three dimensions and imagine taking a blob of white silly-putty and a blob of black silly putty, and combining them into a single lump. Then I knead the lump slightly, so that the black and white putties just start to blend, forming well-defined arms and filaments that twist and turn through the interior of the combined blob. Then I cut the combined blob in half to reveal inside features much like those in today's image. The features have not really been stretched, the apparent stretching is due to the angle at which some of the twisting and turning features have been sliced. All this stretching and distorting has taken its toll on the superb original image. Today's version is worth no more than a humble 4, which equals slightly below average. Considering the render time of 7-1/2 minutes, this results in an overall value of 52. The 7-1/2 minute wait while the parameter file runs can be avoided by downloading the completed GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather on Wednesday here at Fractal Central was very average, with lots of sun but a chilly temperature of 39F 4C. The cats' behavior was also very average. After an uneventful hour in the yard, they came inside and settled by the heat for a long sleep. Today is starting cloudy and cold, with snow not far to the south. As long as it stays to the south, the cats will not be worried. My only concern is to get the waiting work finished, a task that will take about two hours to accomplish. Then I'll see what I can find in Fractal Land. The best of what I find will appear as tomorrow's FOTD. Until then, take care, and watch for lurking Julibrots. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ UnwatchedWatchtowr { ; time=0:07:39.12--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=1 center-mag=+0.00000000000227835/+0.000000000001655\ 24/9.466954e+011/0.07488/-42.1987606685050665/-86.\ 2801728293503629 params=19.055/-104.667/2/0/-1.861\ 19088257009/0.000407298011669/-1.86119088257009/0.\ 000407298011669 float=y maxiter=7500 inside=0 periodicity=10 colors=000NleRuhVzkTzlRxmQunOroMopL\ lpJiqIgrGdsEatDZtBWu9Tv8Qw6Nx5LxJT_W_CUZGTZJRZMQZP\ OZSNYWLYZKYaIYdHYgFXdEXbDW_CWYBWVAVT9VQ8VO7UL6UJ5U\ H5UI5TJ5TJ7JY7JY7JY7JY7KY7KY7KY7KY7KY6LX6LX6LX6LX6\ MX6MX6MX6MX6NX6NX6NX6NX6NXyHvwIuvItuIttIssIsrIrqIr\ oIqnJqmJplJpkJojJoiJngJnfJmeKldKlcKkbKkaKj_KjZKiYK\ iXLhWLhVLgULgSLfAAAAAAAAAAAAAAAAAAAEAAEAAEAAEAAEAA\ EBAECAEDAEEAEFAEGAEHAEIAEJAEKAELCEMFENIEPLGROIURKW\ UM_WOcZNicMnhLrmOwrRywUzzWwwbrrgmmjhmmcmoZmqUmsUnu\ WowYqyZsz`uzawzbuvbrqbmlchgcc`cZYcUVdPTeNRfRPgWNh_\ LicJjgHklFlpDmtBnx9nvHdtPVsXMqdCpl3kk6fj9aiCYhFTgH\ OfKKeNFdQAcT6cV7bW7aX8`X8_Y9ZZ9YZAX_AX`BW`BVaCUbCT\ bDScDRdDRdFVgGYiHakIdmJhoKkqLgmMcjN_gOWdPSaQOZRKWS\ GTTCQU8NU5KSISRU_PfgOrnNsoNspNsqNsrMssMstMttMtuLtv\ LtwLtxLtyLtyNnvOitPdrQZpRUnSPkTJiUEgV9eW4c87mEEmKL\ mQSmWZmadmYajV_hRXfOVdLSaHQ_ENYBLWFV_Jcb } frm:multirot-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE================================== _______________________________________________ Fractint mailing list Fractint(a)mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint

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[Fractint] Jim Muth's Feb 10, '04 FotDay with arbitrary precision math
by Hal Lane 13 Feb '04

13 Feb '04

################################################################ [I like this image a lot, Jim. It shows many classic fractal elements, despite not having a visible miniature Mandelbrot set.] When I rendered Jim Muth's Feb 10, '04 Fractal of the day - 'Order from Chaos' at 1024 x 768 I thought I could see the effect of Jim's turning off arbitrary precision math. To confirm this I turned it on and rendered the image. Some rectangular-looking patches of color now varied smoothly in size. This improvement came at the cost of a 27 hour compute on my P400, but visibly improved the image. Long compute time images can be done conveniently as Disk/RAM 'Video' images. My rendition below includes: - my longtime favorite color map: Leather Gem - arbitrary precision math I obtained the Leather Gem color map from an entry to a Fractal Art contest. It seems to have slightly more muted colors than Fractint automatically generates. It also has smooth color gradations that do not show banding between adjacent iterations for most of its range of colors. To get Jim's 5 minute render, turn the arbitrary precision math off -- as Jim did -- by adding: mathtolerance=/1 to the parameter file below. - Hal Lane ######################### # hallane(a)earthlink.net # ######################### START 20.0 PAR FILE================================ Order_fm_Chaos2 { ; time=26:51:35 CPU=P400 1024x768 Jim Muth's ; Feb 10,'04 Fractal of the day with the ; Leather Gem color map and arbitrary ; precision math turned on. - Hal Lane reset=2003 type=mandel passes=1 center-mag=-1.77551631029264878/0.004553217222571274/3.305215e\ +013/1.0404/13.9106570650115682/-0.977835246052904727 params=0/0 float=y maxiter=80000 bailout=9 inside=0 periodicity=10 sound=off colors=YD0Q82O61M41<3>Q71R81S91fM5<3>iO5jP5kQ6<9>UB3S92Q82<3>I\ 10931A00<3>VK0_P0dU0<3>zm0<3>zb0z_0zX0zU0<3>`F0UC0O80H40<2>A47\ 73A73C<3>56K47M48O39Q2AS<8>9QaASbATc<3>E`hFbiGdi<3>JklKmmJkj<7\ >CURBSOAQM<3>6GB5E86G9<9>EWHFYIGZJ<2>JdMKfNLhM<5>bmDenBhoA<3>t\ s3wt1sr2<5>Zf8Vd9SbA<3>DVF<4>CPCCNBCMA<2>BI9BH8BH8<3>AE79D6DE6\ <3>UI9YJAaLBeMCgODjQF<9>tgGuiGvjG<2>ypGzrFzrK<3>yufxukxvqwww<3\ >rhh`F0`F0<5>UA0T90S80R80Q70P60<3>L30K30J20I10I10<16>UB2UB2VC2\ <3>YE3<2>S92 } END 20.0 PAR FILE================================ ################################################################ --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.581 / Virus Database: 368 - Release Date: 2/9/04

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The Face Of Wegner (Tim's Error)
by SherLok Merfy 12 Feb '04

12 Feb '04

Tim's_Face { ; He looks even more ghastly as a negativ. reset=2003 type=tim's_error function=tanh center-mag=-0.0868849/-9.46742e-005/2.491917/1.5675/90/3.8857805861880\ 4789e-016 params=0/0 float=y maxiter=255 inside=maxiter potential=255/255/0 colors=0000001zz<28>XggYggZff<2>bddcccf__<3>oIIrEEu99w55z00<34>H0iG0jF\ 0k<3>90q70s60t<2>20x00z01y<46>0s70t60u5<2>0x20z02z2<23>mzmozoqzq<2>wzw\ zzzzz000zzU00fzz000z0f0zzz000zzU00fzz000z0f0zzz000zzU00fzz000z0f0zzz00\ 0zzU00fzz000z0f0zzz000zzU00fzz000z0f0zzz000zzU00fzz000z0f0zzz000zzU00f\ zz000z0f0zzz000zzU00fzz000z0f0zzz000zzU00fzz000z0f0zzz000zzU00fzz000z0\ f0zzz000zzU00fzz000z0f0z }

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Latoocarfian parameters (last part)
by Gerald K. Dobiasovsky 11 Feb '04

11 Feb '04

For what it's worth, here is the rest of the bunch of the Latoocarfian parameters... Gerald ;------------------ Start of PAR --------------------- Number_31 { ; reset=2001 type=latoocarfian function=cos/sin/sin/cos corners=-4.953885/4.521355/-3.675321/3.431109 params=-1/-1/2/-2 float=y maxiter=1000 colors=(a)chroma.map } Number_32 { ; reset=2001 type=latoocarfian function=sin/cos/cos/sin corners=-6.870226/6.437695/-5.112576/4.868364 params=1/1/3/-3 float=y maxiter=1000 colors=(a)chroma.map } Number_33 { ; reset=2001 type=latoocarfian function=asin/sin/asin/sin corners=-5.681818/5.681818/-4.261364/4.261364 params=3.14159265358979/3.14159265358979/-2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_34 { ; reset=2001 type=latoocarfian function=sin/asin/sin/asin corners=-5.126411/6.237226/-1.816774/6.705953 params=3.14159265358979/3.14159265358979/-2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_35 { ; reset=2001 type=latoocarfian function=sin/asin/sin/asin corners=-5.737359/5.626277/-1.816774/6.705953 params=2.71828182845905/3.14159265358979/-2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_36 { ; reset=2001 type=latoocarfian function=sin/acos/sin/acos corners=-13.02041/0.1814591/-1.771725/8.129679 params=2.71828182845905/3.14159265358979/-2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_37 { ; reset=2001 type=latoocarfian function=cos/asin/cos/asin corners=-3.924439/-2.621505/2.5883915/3.5655919 params=2/2/-2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_38 { ; reset=2001 type=latoocarfian function=cos/asin/cos/asin corners=-5.015268/-1.530677/1.77027/4.383713 params=2.71828182845905/2.71828182845905/-2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_39 { ; reset=2001 type=latoocarfian function=acos/sin/acos/sin corners=-5.120538/1.324287/0.6601826/5.493801 params=2.71828182845905/2.71828182845905/-2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_40 { ; reset=2001 type=latoocarfian function=acos/sin/acos/sin corners=-3.975715/7.109383/-2.655415/5.658409 params=2/2/-2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_41 { ; reset=2001 type=latoocarfian function=acos/cos/acos/sin corners=-3.975715/7.109383/-2.655415/5.658409 params=2/2/-2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_42 { ; reset=2001 type=latoocarfian function=cos/asin/sin/acos corners=-10.72341/10.51473/-4.929214/10.99939 params=2/2/-2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_43 { ; reset=2001 type=latoocarfian function=cos/asin/sin/acos corners=-3.351484/3.50045/-1.772775/3.366175 params=2/2/-1/0.5 float=y maxiter=1000 colors=(a)chroma.map } Number_44 { ; reset=2001 type=latoocarfian function=acos/sin/cos/acos corners=-2.435012/5.283331/-1.395576/4.393181 params=2/2/1/1 float=y maxiter=1000 colors=(a)chroma.map } Number_45 { ; reset=2001 type=latoocarfian function=acos/sin/cos/acos corners=-1.236156/4.537164/-1.194501/3.135489 params=2/1/1/1 float=y maxiter=1000 colors=(a)chroma.map } Number_46 { ; reset=2001 type=latoocarfian function=acos/sin/cos/acos corners=-2.859903/6.16091/-1.930376/4.835234 params=3/1/1/1 float=y maxiter=1000 colors=(a)chroma.map } Number_47 { ; reset=2001 type=latoocarfian function=acos/sin/cos/acos corners=-5.692019/8.993026/-2.515938/8.497845 params=3/2/2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_48 {;a and b control the Lissajous coefficients ; reset=2001 type=latoocarfian function=acos/sin/cos/acos corners=-2.591823/5.749282/-1.572917/4.682912 params=3/2/2/1 float=y maxiter=1000 colors=(a)chroma.map } Number_49 { ; reset=2001 type=latoocarfian function=acos/sin/sin/log corners=-6.161078/9.721416/-8.4665/3.44537 params=1/1/1/1 float=y maxiter=1000 colors=(a)chroma.map } Number_50 { ; reset=2001 type=latoocarfian function=acos/sin/sin/cos corners=-2.755082/5.694404/-3.349552/2.987563 params=2/2/2/1 float=y maxiter=1000 colors=(a)chroma.map } Number_51 { ; reset=2001 type=latoocarfian function=acos/sin/sin/cos corners=-3.592511/6.331539/-3.86708/3.575958 params=1/2/2/1 float=y maxiter=1000 colors=(a)chroma.map } ;------------------- End of PAR -----------------------

7 11

FOTD 28-01-04 (The Quintessential Midget [8])
by Jim Muth 11 Feb '04

11 Feb '04

FOTD -- January 28, 2004 (Rating 8) Fractal visionaries and enthusiasts: Unless I am mistaken, today's FOTD is the third consecutive one that rates an 8. Combined with the render time of 19 minutes, its overall value is 41. This unexpected spate of excellence might have been equalled sometime in the past, but at the moment, I cannot recall when. But how did this excellence come about? Surely the extra time available for fractal exploration, due to the bad weather and resulting lack of work, is largely responsible. When I saw the golden ratio mentioned on the list, having nothing else to do, I was inspired to venture into the fractals that this mysterious number can produce. Turning to the MandelbrotMix4 formula, I checked the fractal that results when 0.8 parts of Z^(1.618) are subtracted from 0.8 parts of Z^(-1.618) and (1/C) is added. This fractal is an oversized thing consisting of three main Mandeloids, the largest of which barely appears in the southwest corner of the default screen. In today's scene I ignored this giant Mandeloid, which is mostly off the screen, and turned instead to the larger of the two Mandeloids that fit entirely onto the screen. This Mandeloid appears to be in what I call a condition of stress, as though it were ready to be cut off by a too-small escape radius. But stressed as it might be, the midget still has some interesting areas to check. The area I chose is the interior of the west branch of the valley leading to the large southern bud of this midget. Hidden there, deep in a cut-off area of interest, I found the midget that appears in today's image. And what a splendid midget it is. It is so splendid in fact that I named it "The Quintessential Midget", a title that is too long to fit into the allotted space in the parameter file. Actually, the midget looks as though it could use a few more iterations. This could easily be done, but if I raised the maxiter, it would mess up the color palette, which is what really makes the image. The render time of 19 minutes is a small price to pay for such a fine example of a midget. And there is even better news -- the completed GIF image is available for download on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Freezing drizzle prevailed all day Tuesday here at Fractal Central, making the area roads an ice-skating rink. The drizzle did not stop until it was replaced by heavy snow around sunset. With a temperature of 25F -4C, the day was a true winter wonder- land. Unfortunately, the fractal cats do not enjoy wonderlands, and passed the day indoors by the heat. I have lost track of the snow depth this morning. It appears to be around 1 foot in the U.S. measuring system, or 30cm in the rest of the world. Whatever the exact amount of snow, the dynamic duo will have another indoor day. For me, the work appears to have come to a halt, probably because everyone is snowed in. This means a good opportunity to find more great fractals. Any success I might have in Fractal Land will appear as tomorrow's FOTD. Until then, take care, and keep those fractals iterating. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ QuintesentialMidgt { ; time=0:00:00.00--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.39979361592270500/-0.608017365655577\ 00/4795150/1/-75/-1.8414457056414868e-008 params=-0.8/1.618034/0.8/-1.618034/0/0 float=y maxiter=2400 inside=0 logmap=305 periodicity=10 colors=000HEZJEVLERMENRCTVBY_9bc8gh6ll5qj6sh7tf8ud\ 8vTIoHRi5_c4`a4a_4bY4bX3cV3dT3eR3eQFdZQdg`dodephep\ keqoeqreqUmaSgdQbgPYjNTmLOpKJsIEvH9xLBwPDwTFwXHw`I\ wkBmv4duB_tHWtNSsTNrZJrdFnaLk_RgYXdWb`UhYSnUQtROzT\ LxUJvVGtWErYCpZ9n_7l`5kD7y9Bq6Fi3Ia4Oe5Th6Yl7bo6Xi\ 5Rc4LY3FS29MfspiodllToiIq`FrSCsJ9tA6u23t45s67s79r9\ BrADqCFqDHpQJzzzzzmzwMxgGsUHn9Ii8Jd8J_7KV7LQ6ML6MK\ INKTOKdPKoPK_WKKbK5hzPkrabjmUcyMWvSOtXGrb8pg0nlAqq\ KtvUwzUwzUwzUwzUwzUwzDP6W9IG49icjYUZNKNBABDqoftncb\ RaM3TK4LJ5CH64G7HQJUZVfgepTgzEhjFlWGpHHt2HxQnkYsPd\ w2J7DRc1DK0gXnC5a9gLxmGcXAKG5H`yBOd5CKdBrF5LfzMWeG\ LSBAE5cu7Uf5KT3N4VH5ZB5a56e06h0IW0UJ6QGBNEGKBMH9RE\ 6WB4YH7_M9aRCcWEe`HfeJidPkcUmb_oadr`it_ovZtxYyuZwr\ ZvoZum_tj_sg_re_qZ`iTaaNaUTeVYhVckVhnVkqUnsWqvYtx_\ wzaxzcyzezzgzzizzkzzmzzozzqzzszzuzzvzzwzzxzzyzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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 } END 20.0 PAR-FORMULA FILE==================================

4 4

FOTD 11-02-04 (Watchtower [8])
by Jim Muth 11 Feb '04

11 Feb '04

FOTD -- February 11, 2004 (Rating 8) Fractal visionaries and enthusiasts: In yesterday's FOTD we tried to show what happens in filaments along the shorelines of midgets that lie on the negative X-axis of the Mandelbrot set. This first attempt was only moderately successful. Today we make the second attempt -- one that is somewhat more successful. We jump to a midget on the X-axis a short distance beyond the largest midget, and examine the filaments near its shoreline. The filaments here are covered with tiny nodes which remind me of long fences with watchtowers positioned every kilometer or so. These fractal watchtowers are islands of chaos with smaller midgets at the center. Today's image illustrates one of these watchtowers -- an island of chaos sitting in a prairie of order. I named the image "Watchtower" and rated it at an 8. The rating might be a bit excessive, but I do rather enjoy the image. When combined with the render time of 44 seconds, the image has an overall value of 1067. (I really must bring some consistency to the way I determine the overall value.) The image may be seen by running the attached parameter file and enjoying the lightning-fast rendering show, or by taking a trip to Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and downloading the completed GIF image from there. Tuesday turned out to be the best day in over a month here at Fractal Central. The temperature of 52F 11C, gentle breezes, and warm sun, gave the cat duo all they could ask for. They explored the yard from noon until sunset, somehow managing to stay out of trouble for over 5 hours. Today is starting colder, but not extremely so. It remains to be seen what the cats will make of the day. I'm going to make another work day of it. About 4 hours of work waits in the rack beside the desk, and the only way to move it to the finished rack is to get started. So until next FOTD, take care, and how many fractals could fit on the head of a pin? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Watchtower { ; time=0:00:43.45--SF5 on a P200 reset=2003 type=mandel passes=1 mathtolerance=/1 center-mag=-1.86119088257009000/+0.000407298011668\ 70/2.823726e+012/1/-7.27769909978726215/0.00000603\ 84787128533 params=0/0 float=y maxiter=7500 bailout=9 inside=0 symmetry=none periodicity=10 colors=000NleRuhVzkTzlRxmQunOroMopLlpJiqIgrGdsEatD\ ZtBWu9Tv8Qw6Nx5LxJT_W_CUZGTZJRZMQZPOZSNYWLYZKYaIYd\ HYgFXdEXbDW_CWYBWVAVT9VQ8VO7UL6UJ5UH5UI5TJ5TJ7JY7J\ Y7JY7JY7KY7KY7KY7KY7KY6LX6LX6LX6LX6MX6MX6MX6MX6NX6\ NX6NX6NX6NXyHvwIuvItuIttIssIsrIrqIroIqnJqmJplJpkJo\ jJoiJngJnfJmeKldKlcKkbKkaKj_KjZKiYKiXLhWLhVLgULgSL\ fRLfQLePLeOMdNMcMMcKMbAEAAEAAEAAEAAEBAECAEDAEEAEFA\ EGAEHAEIAEJAEKAELCEMFENIEPLGROIURKWUM_WOcZNicMnhLr\ mOwrRywUzzWwwbrrgmmjhmmcmoZmqUmsUnuWowYqyZsz`uzawz\ buvbrqbmlchgcc`cZYcUVdPTeNRfRPgWNh_LicJjgHklFlpDmt\ Bnx9nvHdtPVsXMqdCpl3kk6fj9aiCYhFTgHOfKKeNFdQAcT6cV\ 7bW7aX8`X8_Y9ZZ9YZAX_AX`BW`BVaCUbCTbDScDRdDRdFVgGY\ iHakIdmJhoKkqLgmMcjN_gOWdPSaQOZRKWSGTTCQU8NU5KSISR\ U_PfgOrnNsoNspNsqNsrMssMstMttMtuLtvLtwLtxLtyLtyNnv\ OitPdrQZpRUnSPkTJiUEgV9eW4c87mEEmKLmQSmWZmadmYajV_\ hRXfOVdLSaHQ_ENYBLWFV_Jcb } END PARAMETER FILE=========================================

1 0

FOTD 10-02-04 (Order from Chaos [5])
by Jim Muth 10 Feb '04

10 Feb '04

FOTD -- February 10, 2004 (Rating 5) Fractal visionaries and enthusiasts: With today's image we tunnel quite deep into the Mandelbrot set. At the end of our trip we find ourselves in a remote valley just off the northwest shoreline of the main bud of the large midget on the negative X-axis. This area consists of areas of wild chaos interspersed with relatively orderly and almost straight filaments. The nature of the general area, with its mixture of order and chaos, is reflected quite well in today's image, which I have named "Order from Chaos". The magnitude of the image is really in the range of arbitrary precision math, but I have forced the program to use the conven- tional math routine by including the 'mathtolerance=/1' entry in the parameter file. In such a chaotic image, the resulting breakdown in resolution is barely noticeable, and the time saved is a sizable part of a day. One result of forcing the use of conventional math is the unwanted stretching and skewing, which is reported on the 'tab' screen of the image. This distortion is barely noticeable, but those who wish to render the image marginally more accurately may be re-enable arbitrary precision math by striking the 'g' key and entering the command 'mathtolerance=/0'. The 'logmap' method of coloring does not work with today's image. The 'tdis' option runs very slowly. The other outside coloring options either create too much chaos or run far too slowly. The best method I found of coloring today's image is also the simplest -- outside=iter logmap=0. When the time came to rate the image, I was undecided whether to consider the overworked nature of the M-set. Is today's image really that unusual? After almost 20 years of exploration, is there anything truly new to be found in the M-set within the range of conventional math? One would think so. At the magni- tude of today's image, the entire M-set would be about as large as the solar system. And except for the X-axis symmetry, no two spots of the M-set are identical. But the differences are often infinitesimal, and for all practical purposes, the major varia- tions have long since been found. Considering all this, I rated today's image at an above-average 6, which, with the render time of just under 5 minutes, gives an overall value of 125. I must get a machine fast enough to make arbitrary precision math prac- tical. Way down deep is where the undiscovered M-set goodies lie. To see the image, run the included parameter file and sit back to watch the fun, or go to Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and download the image from there. The clouds moved in quickly here at Fractal Central on Monday, but the temperature reached 46F 8C, which was mild enough for the fractal cats to enjoy a full 90 minutes in the yard. They must have enjoyed their outing. When the day ended, they were content to settle down without a special treat. Today brings both work and fractals for me. The work I will finish; the fractals will never be finished. I shall return in 24 hours with more goodies, some concrete, some abstract. Until then, take care, and the search for truth is all too often hindered by the difficulty in recognizing and accepting it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Order_from_Chaos { ; time=0:04:50.28--SF5 on a P200 reset=2003 type=mandel passes=1 bailout=9 center-mag=-1.77551631029264878/0.0045532172225712\ 74/3.305215e+013/1.0404/13.9106570650115682/-0.977\ 835246052904727 params=0/0 float=y maxiter=80000 inside=0 periodicity=10 mathtolerance=/1 colors=000_hnaiocjpekqflrdiocgmcekccicagc_ecYccWcc\ UccSccQccOccMccKccIcdGcdEcdCceAce8ce6cf4cf2cf0cg6c\ gCcgIchKchKchKciKcjKckKclKcmKcnHcoCco7cpAcpDcqGcrI\ csLctOcuRcvQewPgxOiyNkzMmzNnzOpzPrzQryRovPosOmpMhm\ LckKZiIUgHPeFKcEFaDA_BAZAAY8AX7AW6AV4AU3AT2AS4AR6A\ Q7AP9AOBANCAMEALGAKHAJJAILAJMAKNALOAMPANQAORAPSAQT\ BRUCSVDTWEUXFVYGWZHX_IY`IZaJ_bK`cLadMbeNceOcgPchQc\ iRajS_kTYlTWmUUnUSmUQlUOjUMhUKgUNeSPcQRbQU`SWZUYYW\ `WZbU`dTbgRdiPfkOhhNgfNfcNeaNd_McXMbVMaSM`QL_OLZLL\ YJLXHLWJNVKOULPUMQTNRTOTSPUSRVRSWQTXQUZPV_PW`OXaOZ\ bN_dM`eMafLbgLchKdiKbgLaeL`cL_aLZ_LYYMXWMWUMVSMUQM\ SPNRNNQLNPJNOHNNFOMDOLBOK9OJ7OI6OK5MM5LO5KQ5IR5HT5\ GV5EX5DZ5C_5BXCEUJHRQJOXMLcOIjRGpTKlVNhXQdZT``XXb_\ TdbPfeLhhIjaMfWPbQTZJWWD_S7bO1eL7gMChNIiNNjOSkOYmP\ bnQhoQmpRrqRnmPjjNfgLbdJZaHWZFSVDOSBKP9GM7EYbGZcI_\ dK`eMafObhQciSdjUekWflYgm } END 20.0 PAR-FORMULA FILE==================================

1 0

FOTD 09-02-04 (Apples and Oranges [7])
by Jim Muth 09 Feb '04

09 Feb '04

FOTD -- February 09, 2004 (Rating 7) Fractal visionaries and enthusiasts: Today's image takes us once again to that ultimate fractal reality, the Mandelbrot set, for a brief stay in one of the more remote valleys. I call the M-set the ultimate fractal reality with some misgivings. I am not certain that such a thing as fractal reality exists. As far as that goes, I am not even certain that such a thing as physical reality exists. (I am reasonably certain that I exist however.) But if anything like ultimate fractal reality does exist, the Mandelbrot set comes as close to filling that definition as we have yet come. The scene of today's action lies in a spiral deep in the outer side of the right branch of the valley leading to the large period-4 bud on the northeast shoreline of the main bay of the Mandelbrot set. The features that appear in the image are familiar to those with experience exploring the M-set. This familiarity cost the image one full rating point. But to make up for the familiarity, the coloring is somewhat unexpected, and this originality added one full point to the rating. As a result, we have an image with a rating of a 7 and, due to the short render time, an overall value of 321. I named the image "Apples and Oranges". The tiny orange spots remind me of oranges. The apples were added just to make a more interesting name. There are two ways of viewing the image: first, by running the included parameter file; second, by downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> It remained sunny but breezy and quite cold here at Fractal Central on Sunday. The temperature never rose above freezing, which kept Tippy the tabby indoors. Thomas, the rusty, ventured out onto the remaining ice for a few minutes before deciding that comfort was the better part of valor, and hastily retreat- ing back inside. They both ended the day with a treat of left- over salmon. Today is starting milder. Hopefully, it will be better for the duo. For me, it looks like today might be a bit on the busy side. But unless an avalanche of unexpected work arrives, I'll find time to dredge up another fractal worthy of FOTD status. Until tomorrow, when that next fractal will appear, take care, and see you then. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Apples_and_Oranges { ; time=0:02:10.88--SF5 on a P200 reset=2003 type=mandel passes=1 center-mag=+0.25604\ 36923746491/+0.4940656109920195/3.6466e+007/1/177.5\ /1.38515831929475475e-008 params=0/0 float=y maxiter=15000 inside=0 logmap=1560 periodicity=10 colors=000D7WD5YC3ZC2_B4ZB5YB6XB7XB8WA9VAAUABUACTA\ DSAER9FR9GQ9HP9IO9JO9KN8LM8ML8NL8OK8PJ8QI7SI7TH7UG\ 7VF7WF7XE6YD6ZC6_C6`B6aA6b95c95d85e75f65g65h54i44j\ 34k34l24m14n16m37l48l59k6Bk7Cj9DjAEiBGiCHhDIhFJgGL\ gHMfINeJOeLQdMRdNScOTcPVbRWbSXaTYaU_`V``Xa_YbZZdZ_\ eY`fYbgXciXdjWekWflVhnVioUjpUkqTlrTmqSjpRhpQfoPdnO\ bnN`mMZmLWlKUkJSkIQjIOjHMiGKhFIhEFgDDgCBfB9eA7e95d\ 83d81eA3eB4fD6fE7fF8gHAgIBgJDhLEhMFiOHiPIiQKjSLjTM\ jUOkWPkXRlZSl_Tl`VmbWmcYmdZnf_ngaoibojdokepmfunhzo\ izqkzrlztmzuozvpyxrxyswztvyuuzvtzwszxszyszzszzszzs\ zzszzswwsvwsvwsvwsvwquupttossnsrmrplqokqnjpmiolhoj\ gnifmhelgdlfckdbjcajb`ia_h_ZhZYgYXfXWeWVeUUdTTcSSc\ RRbQQaOPaNO`MN_LM_KNZKOYKPYKQXKRWKSWKTVKTVKUUKVTKW\ TKXSKYSKZRK_QKaQKcPKeOKgOKiNKkNKlMKmLKnLKoKKpKKqMK\ rOKsQKtSKuUKvWLwYLx_MyaMzcMzcNzcNzcOzcOzcOzcPzcPzc\ QzcQzcQzcRzcRzcRzcSzcSzcT } END 20.0 PAR-FORMULA FILE==================================

1 0

Fractint version 20.3 patch 1
by Jonathan Osuch 08 Feb '04

08 Feb '04

Fractint and Xfractint version 20.1 patch 1 is now available on the developer's web site. What's new: Fixed the float bailout for the lambdafn fractal type when the EXP function is used so the float and integer images match. Jan Andres contributed Xfractint fixes that allow compiling with newer versions of gcc because varargs.h is no longer supported. Enabled the use of the long double type on Solaris. Moved the getwd() macro definition in prompts1.c after the #include lines, to avoid the mess that happens when the prototype for getwd() is included but it's already defined as a macro. Added some Solaris-specific comments to the Makefile. Fixed the sound in Xfractint so the beep turns off now. Changed lsys.c to use inline1 instead of the reserved word inline. Jonathan

1 0

FOTD 08-02-04 (Jungle Lushness [6])
by Jim Muth 08 Feb '04

08 Feb '04

FOTD -- February 08, 2004 (Rating 6) Fractal visionaries and enthusiasts: I named today's image "Jungle Lushness". Perhaps I should have named it something like "Too Lush". The image has almost too much richness. No jungle on earth was ever as lush as the scene in the image, not even in the deepest depths of the Amazon rain forest. This over-abundance of detail and color has cost the image one full rating point. After careful consideration, I could give the image a rating no higher than a 6, which is still somewhat above average, but falls short of the 7 that I first considered. The parent fractal was created by combining 1 negative part of Z^(-1.1) with 0.1 negative part of Z^(-11) and adding (1/C). This parent is several orders too large to fit on the default screen, but a single outzoom reveals the most interesting parts. The interesting part of the parent consists of an oversized banana-shaped hole with a Mandelbrot set lying at its southwest extremity. The banana-shaped hole splits the East Valley of the M-set as it joins with the set. Today's scene is located on the shoreline of the hole, near the point where it joins the M-set. The traditional equal-iteration-band method of rendering today's scene produces a very interesting image -- almost good enough to be a FOTD. The evaporated version, which appears as today's FOTD, is improved just enough to be the version I chose. As an 'evaporated' image, today's scene consists entirely of trapped inside points made visible by the 'bof61' inside fill. This fill traces quite faithfully the foundation features of the 'real' image that has been evaporated, but adds bells and whistles that the real image never had. Sometimes a humdrum scene can be improved by evaporating it, sometimes not. The only way to find out is to go ahead and evaporate an image and see what can be done with the ghostly remains. There are also 'half-evaporated' and 'extra-condensed' versions of images created by negative exponents of Z, but I have yet to do much investigating in these areas. The render time of today's image is 13-3/4 minutes. Combined with the rating of a 6, its overall value is 44 -- a value that is not too bad. The image may be seen quicker by downloading it from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Saturday turned into a quite pleasant day here at Fractal Central, when sun and an unexpectedly warm temperature of 43F 6C prevailed most of the afternoon. The cats enjoyed the few spots where the sun is now shining above the holly trees in the early afternoon, and ignored the remaining ice. But this morning things are again frozen solid. It once again feels like winter. I doubt that the duo will have a second good day. My day will probably be average . . . most days are . . . that is unless something unexpectedly good or bad happens. Since nothing like this is likely to occur, the day will probably pass with nothing more notable taking place than the appearance of the next FOTD fractal image. When that happens, we will have found tomorrow's FOTD. Until then, take care, and does the brain create the mind, or does the mind create the brain . . . or is it all just one big fractal? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Jungle_Lushness { ; time=0:13:47.67--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-1.38105363973058900/-5.353386666406572\ 00/1.344518e+009/1/-137.5/0.000903528871152227409 params=-1/-1.1/-0.1/-11/0/1e+100 float=y maxiter=2000 inside=bof61 periodicity=10 colors=000ePadQ`dSZcTXcVVbWUbYSaZQa`O`aN`cL_dJ_eIm\ ulnqmnnnojnogopdop`pqYpqVqrRrrOrsLssHstEttBtmHfAMT\ EKSHIRKGQNEQQCPTAOW8NZ6Na4Md2Lg0LXHNMYPBmQEiTHeVKb\ XMZ_PWaSScUOfXLh_HjaEl_JnZNpYSrXWtW_vUdwThySlyRqyQ\ uyPyyOvyOtyOrwOptOnqOlnOjkNghNeeNcbNa_N_XNYUNWRNUO\ LSPJRPHPPGOQEMQCLQBKQ8KN6KKEEIM8GT3FS6HS8JRALRCMRE\ OQGQQIRPKTPMVPOWRLaSJfTHkVFpWDuXByY9yWAyUBySCyQDyO\ ExMFvKGuIGtGHrEIqCJoAKn8Lm6Mk4Nj2NivEfuHhuJjtLltNn\ tPpsRrsUtrWvrYxr_yqayqcyqeyr`ysXutSouOjvJdwF_xBVxH\ _xNdxThyZmydryjwypyimuVjpGgk1df8_eFVeMQdTLd_GcfBcG\ DyHLyITyI_yJgyJnyOosSokXod`oXeoQioImoBijJeeQb`XZWc\ WRjTQgQPeNOcLNaIM_FLYCKWAJU7IS4HQ2HOKRUa`Zrjcogfle\ hickfamc_p`YrYVuVTwSRyPPyMNyJLyOQyTVyZ_ycdyhiyV_jb\ bhZabflnkomekb_gSUdIQ`HMXHITGEPGDOKDONDNRDNUCMYCM`\ CMdCLgCLkBKnBKrBJuBJyBJyDLsEMkFNcGPWHQOIRGJUKaCTbE\ WcFYdG_eHafIcgJegKgfMeeNc } 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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 07-02-04 (Amber Mandeloid [7])
by Jim Muth 07 Feb '04

07 Feb '04

FOTD -- February 07, 2004 (Rating 7) Fractal visionaries and enthusiasts: Here in Fractal Central territory it's the 100th anniversary of a memorable day. In the rest of the world, it's just another day. Today is the 100th anniversary of the great Baltimore fire -- the world's least-known conflagration. On this day in 1904 someone threw a cigarette butt down a ventilation grate and started a fire that burned over 1500 buildings in the downtown area. Only one person was reported as killed -- a drunk who was pulled from the harbor -- but it has always been uncertain that the death was actually due to the fire. Refusing to admit defeat and without federal assistance, the city pulled itself from the disaster and rose to be the nation's largest seaport for most of the 20th century. Only toward the end of the century did the bottom fall out. It now appears our no-longer-fair city leads the nation in everything bad and is in last place in everything good. The reasons for the decline are as numerous as the people still living in the city, which is where I still live by less than 1/2 mile, though this will likely change within two years. The connection of the fire to today's fractal is straight- forward. The fire started as a simple lit cigarette; today's fractal started as a simple mathematical expression -- (Z^2)-0.25(Z^3)+C. Like so many other things of the world around us, and even of the worlds within us, a fire has a fractal nature. Like fractals, a spark can find itself in con- ditions that are stable, neutral or unstable. If a tiny flame finds itself in stable conditions such as a burning match on a concrete sidewalk, it will quickly be extinguished. If the con- ditions are neutral, such as the flame of the wick of a large candle, it will continue unchanged indefinitely. But if the con- ditions are unstable, such as a flame in a large pile of waste paper, the flame will quickly grow without limit, as did that cigarette spark back in February of 1904. The parent fractal of today's image resembles a Mandelbrot set rotated 180 degrees. Its East Valley, which is now on the west side, is split down the middle into two separate valleys, leaving two entirely new shorelines along the interior edges of the valleys. Today's scene is located along one of these shore- lines, rather deep in the valley. In this area, the 'outside' parts of the fractal do not have the smooth, unbroken nature that we find in the 'outside' parts of the M-set. They are more like a swiss cheese in which the holes have been organized to form a regular pattern that can itself become the most important feature. In today's image however, it is not the holes that are the most important feature, it is the coloring. The amber ring close around the central midget is so brilliant that I named the entire image for it. The name I chose is "Amber Mandeloid". The rating of a 7 that I gave the image is above average, but the overall value has been cut to a measly 13 by the render time of over 53 minutes. In a few days I will adjust the method of calculating the overall value, or perhaps drop it entirely. The wait of nearly an hour for the parameter file to finish running may be avoided by downloading the completed image from Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy rain all day Friday here at Fractal Central led to localized flooding and unhappy cats. The high temperature of 36F 2C helped not at all. It took almost a whole can of tuna to restore the spirits of the dynamic duo. Luckily, today is starting better. That's it for now. Until next FOTD, take care, and fill in the blanks before you leave. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Amber_Mandeloid { ; time=0:53:24.50--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=ident passes=1 center-mag=-0.00161624027746348/+0.000070489860749\ 22/1.182809e+009/1/-155/1.14853522872881975e-008 params=1/2/-0.25/3/0/0/0/0 float=y maxiter=10000 inside=0 outside=tdis periodicity=10 colors=000kqihypdzxczz`zyYzuWxpTqkRkhOdcMZZJTVIMRF\ GMDAIA4D90AA76CF3DM0FV0Ga0Ii0Jq0Jy0Mx0Ov0Pu0Rs6TqC\ VpGWpMYnRZmY`kcaihchndhs`cfYWWVPJRJ9OD0L90PzsJnxFe\ zA_z4Wy0Tx0Qx0Nw4Kw7HwCEtFFoJHhMIcRJZWQ`ZUZcYZfZWk\ `TncOsdLvfIxiJykJzmJznLzpLzqLzuMzvMzxMzyOzzOzzOzzO\ uzIczCOy6MsCLmIJhOIaTGYZGRdFMkDGpCCvA6zA1zFJzJazZf\ dnkJzn0vd4nW9fMDZDJR4OJ0Tz7zzCuzGmzLdvOYqTPmYGh`9c\ d1Zi0Vm0`i0dh0kf0pd0vc0za0z`0zZ0zW0xT0qP0kM0dJ0ZG0\ TD0LA0F70940310000000000000011344979DADJDGPILWLO`O\ TfRYmV`sYdx`hsYipWkmVmiRndPpaOqZLsWJuRIvOFxLDyICzD\ 9zA7z76z44zA3yG3qL3kR3cY3Wa1Ph1In1As14y10z10sJAhaV\ Yum`mkadkdYifPiiJikChn4hp0fs0fu0fp0Zm3TiDLfMFaW9Zf\ 1Wp0Ty0Ps0On0Mh0Jc0IZ0GT0FO0CI0AD09907304003001000\ 0010030040060460970F90LA0PC0WC0`94a7Cc6Jd4Rf3Zh1fi\ 0mk6nfApaFpYJqVOqPVsLZsIcuDhv9mv6sx1xx0zy0zy0zz0zz\ 0zn0pc0aT6PGDC6L00T03W0AY } 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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 06-02-04 (Roulette Festival [7])
by Jim Muth 06 Feb '04

06 Feb '04

FOTD -- February 06, 2004 (Rating 7) Fractal visionaries and enthusiasts: For some reason, when I studied today's image in search of a name, I thought of a roulette wheel. Then I noticed the carnival-like colors, and named the image "Roulette Festival". The scene illustrated in the image lies in the fractal that results when ten parts of Z^(-1.3) are combined with one part of Z^(-13) before (1/C) is added, and the whole thing is iterated at a maxiter of 256 with an escape radius of 100. This parent fractal is an oversized thing with many supernume- rary bays and valleys. To find today's image I ignored the many obvious bays and valleys, and checked a small area of chaos on the southwest edge of the part of the fractal that fits on the default screen. When I first saw the inner details of this area, I had little hope of finding a midget there, but, being intrepid, I pushed onward into the wilderness, drawn by an unknown power. The progress was slow at first, with one dead end after another. I went farther -- into a tiny sub-area of chaos. Once again things looked bleak. All around me were the chaotic areas that I knew held no hidden midgets. But one of those chaotic areas was different -- it was doubled in a symmetrical manner. There at last, at the center of symmetry, I found my quarry. The trophy appears as today's FOTD. The image rates a 7. Combined with the render time of just over one minute, its overall value comes in at a whopping 614, which is totally out of proportion. I really must change the way I calculate overall value. As it is now calculated, the render time has far too much importance. Perhaps I should do something like multiply the regular rating by the reciprocal of the square root of the render time. Well, that's a problem for another day. Today's problems are small. The image may be viewed by running the attached para- meter file or by visiting Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and downloading the finished image from there. Both methods require about the same amount of time. Clouds and freezing temperatures kept the fractal cats confined to the indoors on Thursday. Their moods showed their disappoint- ment, though the evening treat of tuna cheered them somewhat. Today is starting with freezing rain and a coating of ice. I assume the rain is still freezing. The outside sensor of the F.C. thermometer is covered in ice, and reads 32F 0C. This may or may not be accurate, since the reading cannot rise above freezing until the ice melts. With rain and ice prevailing, I expect further deterioration in the cats' moods. It looks like a rather slow day for me. The work is minimal and with the roads slippery no new work is likely to arrive. I'll probably spend a good part of the day in Fractal Land, wherever that is. The best of what I find there will appear as tomor- row's FOTD. When I finish my trip in Fractal Land, I might start thinking about things such as the nature of reality, and we know what happens when I do that. Until the next FOTD, take care, and fractals must prove something about reality, but I'm not sure what. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Roulette_Festival { ; time=0:01:08.54--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.83439334781566500/-1.203480149355678\ 00/2.550009e+008/1/142.5/5.37021542955373743e-005 params=10/-1.3/1/-13/0/0 float=y maxiter=256 inside=0 outside=tdis periodicity=10 colors=000_mza1aa4bb6edAfeBhfDjfGlhImiLojMqjPrlRtm\ SvnVxoWzoZzq_zrbzsdzsezrdxrbnqadq_Vq_LhdO_hRSjTVhR\ YfO_eLbdIdaGf_DiZAlY6mV4oT1rS0tR0vP0qT4mWFiZOeaWad\ dYflMDPPBTSBWVA_Y8dL8TLFSd4nf4qi3tl1xn1zq0zs0zo0zi\ 3tf8kbDbYIWUKRRIOOGLLEKKCNKAPK8RJ9SIA`I8dG6hG4lF3o\ F1sD0xD0zJ6tODoTLlYRfaYafbYjiSvsOqpLlmIgjFbgBYd8Ta\ 4PZ1MW0UT0WQ0cA0m30z00j3AS8L8BVBDYFD_IDaLDdODfRFhT\ FjWFmZFnaFqdGsfGtiGxlGzmGzoJxqLtrMrsOotRmvSjxTfzVd\ zYazZZz_WzaTzeSxiRvmPsoOqsMmxLjzJhzIezGbzGdzDdzBdx\ Adt8dq6dm4dj3df1db0dZ0dV0dR0dO0aT0ZY1Wb4Tf8RjBOoFL\ sIIxLFzOBzRAzT800F34LGBPTIVdPZoVdz_hzelz_nzWqzRtxM\ xtGzrBzo4zm0zj0zhDteTnbhhatedvdevbfxahx_ixYjxWlxVm\ xTnzSozPqzOrzMszLtzJvzIxzGszGozFlzFhzDdzD_zBWzBSzA\ OzAJz8Fz8Az86z4Rz1hz0xzqtxtoxxlvzftzbszYrzTqzPqzVl\ z_fxebrjYmnThsOaxJWzDRz8Pz6Pz4Pz3Oz1Oz0Oz0Rz3Sz6Tz\ AVxFWtIYrLZoO_mSajVY0WZ0Y } 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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 05-02-04 (Crazy Man, Crazy [8])
by Jim Muth 05 Feb '04

05 Feb '04

FOTD -- February 05, 2004 (Rating 7) Fractal visionaries and enthusiasts: We have a fractal for today -- an image with a rating of 7 that I found at the zero level of the Z^2.1+C Mandeloid. I hesitate to call the zero level the ground level, since the 3.14159... or pi level is a more appropriate candidate for ground level of the MandelbrotBC1 formula, at least when the 'floor' function is used. The parent fractal is a twisted version of the classic M-set, which closely resembles the midget at the center of today's image. The largest bud of the parent is attached to the north- west shore of its main bay, and is squashed on the right side. A tiny, almost invisible valley lies on this squashed shoreline. Today's scene is located rather deep in this valley. Today's picture gives an unusually strong impression of being a photograph of an actual three-dimensional scene in some other reality. How is this possible? Nothing but numbers are involved in the creation of the image, and numbers are abstrac- tions -- ideas that might have no existence other than in the mind of man. It's "Crazy Man, Crazy", which is what I named the image. And it could get even crazier. Since I arranged the colors with the intent of creating the impression of an actual three- dimensional object, perhaps I am the creator of a reality. In fact, I could consider myself the creating god of as many infinite fractal universes as I care to create. I might wonder if there are conscious beings in any of the universes I create. If there are, I wonder if they believe in me. Returning to our present reality, today's image, with its render time of 28 minutes, has an overall value of 25. That value may be increased significantly by downloading the completed GIF picture from Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Tuesday was wet here at F.C., and the cats were unhappy. On Wednesday the sun appeared and the temperature reached 41F 5C. The cats were happier, but the sloppy snow in the yard made their paws too wet for comfort. Today is starting colder and the sun is gone. It remains to be seen how the duo will take these conditions. With the work once again under control, my day promises to be busy but not overly rushed. The fractal that I find will appear as tomorrow's FOTD. Until then, take care, and never forget that any fractal, no matter how good, can always be made a little better. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Crazy_Man--Crazy { ; time=0:27:51.78--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor inside=0 center-mag=-0.54888974079389370/+0.824478167923077\ 90/1.096037e+008/1/10/-3.4330458e-007 params=2.1/0\ /0/0 float=y maxiter=12000 inside=0 periodicity=10 colors=000z0dz0iz0nz0sz0az0Hz40z00z00z00xA0xL0vU0v\ a0ui0ur0sz0sz0mz0fz2az4Uz6Nz8Hz8Fz6Dz4Az28z26x04x0\ 2v02v00u00s00s00r00p00p00n00n0DHLEIQFJTGKWHLZIMbJN\ fNJmQFsNQu0Sz0YzRcrShgUm_WraYuc_xeazgcziezkgzmizok\ zqmztmzwkzzizzgzzezzczzazz_zzYzzWxzUuzSszQvzOzzMzz\ KzzKzzKzzKzzKzzKzzKzzKzzKzzKzzLszmNzgLzbJzZHzUHuQF\ nLDiFAbAAW48Q06J04A04402800D20H60LA0PF0SJ0WN0ZQ0bU\ 0fY0ia0md0pg0si0vbPLfNHgLDiJ8kJ4mP8nSApWFpZHrbLsgN\ ukQunSvrWxuYzzazzbzzfzzgzzkzzmzznzznzsnzmnzdnzYnzP\ pzHpz6pz0pz0pz0pz0rz0sz0uz6uzFvzLxzQxzWzzazxgzvmzs\ rzpvznzzpzzpxvrvrrvmrugssbsrYsrSupNunHunAmrNdsYWuf\ NvpDxx2zz0zzDxzSuzfszupzzmzzkzzizzgxzgszfnufipddid\ ZdbUZbPUaJPaDJZ6DZ2AgF8nQ6va4zk6zr6zxS4zD2z00p02b0\ 8d0Cd0Hd6LdDPfJSfPWfS_fYcgbfggigmmgrpivtizwizyizwg\ xtfvpdsmbpkanhZkdYg`YfXWbVUZQSYNQUJPQFNPDNNzmNziNx\ gNudNpbNkZNgYz0Hz0Nz0Uz0Z } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(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 } END 20.0 PAR-FORMULA FILE==================================

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More Latoocarfian pars
by Gerald K. Dobiasovsky 05 Feb '04

05 Feb '04

Here's the second part of my Latoocarfian experiments... Gerald ;-------------------- Start of PAR --------------------- Number_16 { ; reset=2001 type=latoocarfian function=cos/cos/cos/cos corners=-3.239746/3.268721/-2.061837/2.819514 params=1/2/2/1 float=y maxiter=1000 colors=(a)chroma.map } Number_17 { ; reset=2001 type=latoocarfian function=cos/cos/cos/cos corners=-2.728477/3.344381/-1.898483/2.65616 params=2/1/2/1 float=y maxiter=1000 colors=(a)chroma.map } Number_18 { ; reset=2001 type=latoocarfian function=cos/sin/cos/cos corners=-0.8342913/4.801321/-2.150194/2.076515 params=2/1/2/1 float=y maxiter=1000 colors=(a)chroma.map } Number_19 { ; reset=2001 type=latoocarfian function=cos/cos/cos/sin corners=-3.549054/4.58101/-3.085613/3.011934 params=2/1/2/-1 float=y maxiter=1000 colors=(a)chroma.map } Number_20 { ; reset=2001 type=latoocarfian function=cos/cos/cos/sin corners=-2.126971/1.577737/-1.70435/1.07418 params=2/1/-2/1 float=y maxiter=1000 colors=(a)chroma.map } Number_21 { ; reset=2001 type=latoocarfian function=cos/sin/cos/log corners=-8.501247/7.952012/-8.349628/3.990316 params=2/1/-2/1 float=y maxiter=1000 colors=(a)chroma.map } Number_22 { ; reset=2001 type=latoocarfian function=cos/sin/cos/log corners=-8.501247/7.952012/-8.349628/3.990316 params=2/1/2/1 float=y maxiter=1000 colors=(a)chroma.map } Number_23 { ; reset=2001 type=latoocarfian function=cos/sin/cos/log corners=-8.501247/7.952012/-8.349628/3.990316 params=2/2/2/1 float=y maxiter=1000 colors=(a)chroma.map } Number_24 { ; reset=2001 type=latoocarfian function=sin/sin/sin/sin corners=-4.117647/4.117647/-3.088235/3.088235 params=1/1/-2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_25 { ; reset=2001 type=latoocarfian function=cos/sin/sin/sin corners=-4.117647/4.117647/-3.088235/3.088235 params=1/1/-2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_26 { ; reset=2001 type=latoocarfian function=sin/sin/sin/sin corners=-4.117647/4.117647/-3.088235/3.088235 params=2/2/-2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_27 { ; reset=2001 type=latoocarfian function=sin/sin/cos/sin corners=-4.117647/4.117647/-3.088235/3.088235 params=1/1/-2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_28 { ; reset=2001 type=latoocarfian function=cos/cos/cos/cos corners=-3.228235/3.228235/-1.575636/3.266717 params=1/1/-2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_29 { ; reset=2001 type=latoocarfian function=cos/sin/sin/cos corners=0.3911148/3.654111/-1.575826/0.8714209 params=1/1/2/-2 float=y maxiter=1000 colors=(a)chroma.map } Number_30 { ; reset=2001 type=latoocarfian function=cos/sin/sin/cos corners=-4.953885/4.521355/-3.675321/3.431109 params=2/1/2/-2 float=y maxiter=1000 colors=(a)chroma.map } ;-------------------- End of PAR -----------------------

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No FOTD for Feb 4
by Jim Muth 04 Feb '04

04 Feb '04

Disappointed fractal enthusiasts: I regret to announce that, due to technical difficulties, (I am falling behind in the real work.), there will be no FOTD for February 04. The ongoing FOTD will return on schedule on February 05. Jim M.

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Mentor Needed - OT
by BillatNY＠aol.com 04 Feb '04

04 Feb '04

A friend of mine, a High School teacher, has a student who is interested in fractals and chaos theory. The student would like to correspond with someone who can impart some knowledge and answer a few questions. Is there any mathematically minded person out there who wouldn't mind taking this on? If so, please contact me off-line. Thanks in advance. Bill Rossi http://members.aol.com/billatny/ http://www.arts4u.org/rossi/

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Re: [Fractint] FW: The Google logo includes fractal motifs today!
by Gerald K. Dobiasovsky 04 Feb '04

04 Feb '04

David wrote: >I doubt that it's causing any more problems for site owners >than simply being Googled in the first place. I do think it's different. Googling for, say, "fractals" or "fractal images" you have to have a particular interest in those subjects beforehand. But in this case *every single Google user* was confronted with these strange-looking logo adornments. I bet many people clicked on it ("Looks strange! What is this all about?") and probably many of those clicked on some of the thumbnails too, causing more traffic to the listed sites than usual. Paul N. Lee wrote: >Actually, the search values have changed from "julia fractals" >to the now "gaston julia". >Makes a big difference in what one retrieves. No doubt. Have missed the change completely (that is, didn't remember it had not been "gaston julia" the first time). Speaking of memory deficits (and to add something of substance to my post), here are a few of a number of pars I've completely forgotten of (note the reset version and the inspired titles) :o) Chroma.map is nice for these, but you might try to set the background color to black (for better contrast)... Regards, Gerald ;-------------------- Start of PAR ------------------- comment { Some Latoocarfian parameters... } Number_01 { ; reset=2000 type=latoocarfian function=sin/sin/sin/sin corners=-4.032258/4.032258/-3.024194/3.024194 params=-1.57/1/2/-1 float=y maxiter=1000 colors=(a)chroma.map } Number_02 { ; reset=2000 type=latoocarfian function=sin/sin/sin/sin corners=-4.032259/4.032259/-3.024194/3.024194 params=-2/1.6/-2/1 float=y maxiter=1000 colors=(a)chroma.map } Number_03 { ; reset=2000 type=latoocarfian function=sin/sin/sin/sin corners=-4.032259/4.032259/-3.024194/3.024194 params=-1/1/-2/1 float=y maxiter=1000 colors=(a)chroma.map } Number_04 { ; reset=2000 type=latoocarfian function=sin/ident/ident/sin corners=-4.032259/4.032259/-3.024194/3.024194 params=-1/1/-1/1 float=y maxiter=1000 colors=(a)chroma.map } Number_05 { ; reset=2001 type=latoocarfian function=sin/sin/log/sin corners=-7.029945/7.029945/-7.158452/3.386466 params=-1/1.57/1.57/1.57 float=y maxiter=1000 colors=(a)chroma.map } Number_06 { ; reset=2001 type=latoocarfian function=sin/cos/sin/cos corners=-3.917366/3.779929/-2.877736/2.895236 params=-1.57/1.57/1.57/1.57 float=y maxiter=1000 colors=(a)chroma.map } Number_07 { ; reset=2001 type=latoocarfian function=sin/cos/cos/sin corners=-3.917366/3.779929/-2.877736/2.895236 params=-1.57/1.57/1.57/1.57 float=y maxiter=1000 colors=(a)chroma.map } Number_08 { ; reset=2001 type=latoocarfian function=cos/cos/log/sin corners=-6.884047/7.488664/-7.236758/3.542775 params=1.57/1.57/1.57/1.57 float=y maxiter=1000 colors=(a)chroma.map } Number_09 { ; reset=2001 type=latoocarfian function=sin/cos/cos/sin corners=-1.196632/1.385777/0.7858341/2.722641 params=1.2/-1.3/1.4/1.5 float=y maxiter=1000 colors=(a)chroma.map } Number_10 { ; reset=2001 type=latoocarfian function=cos/sin/sin/cos corners=-3.197433/3.406192/-2.259031/2.693688 params=1.35/-1.35/1.35/1.35 float=y maxiter=1000 colors=(a)chroma.map } Number_11 { ; reset=2001 type=latoocarfian function=cos/sin/cos/cos corners=-4.21411/3.942568/-3.168432/2.949076 params=1.57/-1.57/1.57/1.57 float=y maxiter=1000 colors=(a)chroma.map } Number_12 { ; reset=2001 type=latoocarfian function=cos/sin/sin/cos corners=-2.699419/4.188871/-1.929178/3.23704 params=1/1/2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_13 { ; reset=2001 type=latoocarfian function=cos/cos/cos/log corners=-9.79141/10.13312/-7.986742/6.956654 params=1/1/2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_14 { ; reset=2001 type=latoocarfian function=sin/log/cos/log corners=-12.22598/7.698548/-7.986742/6.956654 params=1/1/2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_15 { ; reset=2001 type=latoocarfian function=cos/cos/cos/sin corners=-2.730775/3.777692/-1.87091/3.01044 params=1/1/2/1 float=y maxiter=1000 colors=(a)chroma.map } ;----------------------- End of PAR -------------------

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Re: [Fractint] FW: The Google logo includes fractal motifs today!
by gnome＠hawaii.rr.com 04 Feb '04

04 Feb '04

I just redid the search for julia fractal and get about 1240 hits. I doubt that it's causing any more problems for site owners than simply being Googled in the first place. Anyone see any of their own images up there? David gnome(a)hawaii.rr.com ----- Original Message ----- From: "Paul N. Lee" <Paul.N.Lee(a)Worldnet.att.net> Date: Tuesday, February 3, 2004 2:14 pm Subject: Re: [Fractint] FW: The Google logo includes fractal motifs today! > Gerald K. Dobiasovsky wrote: > > > > The search result now brings up only > > three pages contrary to the last time > > I clicked (about 20 hours ago), so Google > > staff seems to have realized (probably > > by receiving lots of not too friendly > > mails) they're causing problems for image > > site owners. > > Actually, the search values have changed from "julia fractals" to the > now "gaston julia". > > Makes a big difference in what one retrieves.

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FW: The Google logo includes fractal motifs today!
by Hal Lane 04 Feb '04

04 Feb '04

################################################################ - Please go to at least the 3rd or 4th or later Google result page of thumbnail images and view these images. The images on the 1st couple of pages are being over-viewed and causing *severe* problems for the owners of the pages. - Or wait until Wednesday February 4th or later to do the search described below. - Hal Lane ######################### # hallane(a)earthlink.net # ######################### -----Original Message----- From: Hal Lane [mailto:hallane@earthlink.net] Sent: Tuesday, February 03, 2004 3:55 PM Subject: The Google logo includes fractal motifs today! The Google logo includes fractal motifs today! I first learned that Google's main page logo changes when I saw the pictures they added around the letters of 'Google' on Thanksgiving and the Fourth of July. I learned that they occasionally have whimsical additions to their logo when I observed monkeys and bananas on one occasion (see below). Today Feb 3, '04 at 7:00am EST I found fractals worked into their logo. The 'G' in 'Google' is nestled in the lake of a Mandelbrot set, 'L' is from Seahorse Valley and the equation Z(n+1) = Z(n)^2 + C appears -- among other items. And the word 'Google' is clickable! Clicking it does a search on the words: julia fractals in Google's image data base and finds 1,270 images -- many of which appear quite interesting. Also, you can do the search yourself: - go to Google's main page (regardless of whether the Google logo has fractal pictures added to it) - click on the word 'Images' above the search text box - type in the search terms: julia fractals - receive a page from Google with many thumbnail images on it. - click on an image to see the *page* that the image is on (in the bottom subwindow) - click on See full-size image. - (in the top subwindow) to see the image if it is not in the bottom subwindow - note that there are many pages of images (see the list of pages at the bottom of the page) - Please go to at least the 3rd or 4th or later Google result page of thumbnail images and view these images. The images on the 1st couple of pages are being over-viewed and causing severe problems for the owners of the pages. - Or wait until Wednesday February 4th to do the search defined above. ################################################################ --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.576 / Virus Database: 365 - Release Date: 1/30/04

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Re: [Fractint] Google logo includes fractal motifs today!
by gnome＠hawaii.rr.com 03 Feb '04

03 Feb '04

And if you click on the fractal Google logo, it does a nice little search for "juli fractals" in the Google image base. David gnome(a)hawaii.rr.com ----- Original Message ----- From: Kevin Sexton <sexton(a)QNET.COM> Date: Tuesday, February 3, 2004 5:23 am Subject: Re: [Fractint] Google logo includes fractal motifs today! > while you look at it click on it, I'm sure they are tracking > clicks on > the logo > > Hal Lane wrote: > > > ################################################## > > > > The Google logo includes fractal motifs today! > > I first learned that Google's main page logo changes > > when I saw the pictures they added around the letters > > of 'Google' on Thanksgiving and the Fourth of July. > > > > I learned that they occasionally had whimsical additions > > to their logo when I observed monkeys and bananas > > on one occasion. Today Feb 3, '04 at 7:00am EST > > I found fractals worked into their logo. The 'G' in > > 'Google' is nestled in the lake of a Mandelbrot set, > > 'L' is from Seahorse Valley and the equation > > Z(n+1) = Z(n)^2 + C appears -- among other items. > > > > It seems we have a fractal enthusiast in a fairly > > high place in the Google organization... > > > > If you miss seeing this and wish to, I could put it up > > on my web site temporarily. > > > > - Hal Lane > > > > ######################### > > # hallane(a)earthlink.net <hallane(a)earthlink.net> # > > ######################### > > ################################################## > > > >------------------------------------------------------------------ > ------ > > > >_______________________________________________ > >Fractint mailing list > >Fractint(a)mailman.xmission.com > >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint > > > > > > > _______________________________________________ > Fractint mailing list > Fractint(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >

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Fwd: Fractint list and Fractal Universe 2006
by Jim Muth 03 Feb '04

03 Feb '04

>This is an open call for you to submit your fractal >artwork for consideration for inclusion in the >Fractal Universe ® Calendar 2006. >All the information you will need is detailed on the >following website: http://www.fractalforum.com >Please make your submissions and any additional >enquires you may have via the contact form on the >above website. >Linda Allison and Tina Oloyede

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Google logo includes fractal motifs today!
by Hal Lane 03 Feb '04

03 Feb '04

################################################## The Google logo includes fractal motifs today! I first learned that Google's main page logo changes when I saw the pictures they added around the letters of 'Google' on Thanksgiving and the Fourth of July. I learned that they occasionally had whimsical additions to their logo when I observed monkeys and bananas on one occasion. Today Feb 3, '04 at 7:00am EST I found fractals worked into their logo. The 'G' in 'Google' is nestled in the lake of a Mandelbrot set, 'L' is from Seahorse Valley and the equation Z(n+1) = Z(n)^2 + C appears -- among other items. It seems we have a fractal enthusiast in a fairly high place in the Google organization... If you miss seeing this and wish to, I could put it up on my web site temporarily. - Hal Lane ######################### # hallane(a)earthlink.net # ######################### ################################################## --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.576 / Virus Database: 365 - Release Date: 1/30/04

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FOTD 03-02-04 (Path to Nowhere [8])
by Jim Muth 03 Feb '04

03 Feb '04

FOTD -- February 03, 2004 (Rating 7) Fractal visionaries and enthusiasts: Is there anything as useless as a fractal? Yes. It is the pile of 15-year-old books about using outdated computer programs, which is lying in the closet in the far corner of F.C. Some of those books were outdated when I bought them. Some of them must have been outdated by the time they were printed. And, speaking of being useless, who ever determined that fractals are useless. As I see it, we merely have yet to discover most of the uses fractals might have. Take today's fractal for example, which certainly has a small amount of use as a source of entertainment. It is a scene in the Z^2.01+C Mandeloid 315 levels up the logarithmic spiral. At this level the figure is rotated 180 degrees, so that East Valley is on the west side of the screen. Lying on the negative real axis, East Valley has had some odd things happen to it. To start, it has broadened significantly. No longer does it terminate in its usual sharp point. Instead, the valley ends abruptly in an almost straight wall. The edges of this wall hold some interesting features composed almost entirely of discontinuities. Today's scene lies in a small area of chaos near the edge of the straight wall that marks the terminus of East Valley. Surrounded by delicate fingers of chaos, the midget is one of the more unusual ones to have made the lofty status of FOTD. After a brief consideration, I rated it at a 7. If I had had more time to work on the colors, I might have worked it up to a rating of 8. Combined with the render time of 13-1/2 minutes, the rating gives the image an overall value of 59, which is not all that bad. The name I gave to the picture is "Path to Nowhere". When I thought of the name, I had in mind a trip into East valley in expectation of an infinite journey, only to find that the valley comes to an abrupt end at an impassable wall. The fun way to see the image is to run the included parameter file and watch the scene gradually come to life on your screen. The convenient way is to download the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Monday was a warmer day here at Fractal Central. The afternoon temperature reached 34F 1C, but this caused the snow in the yard to start melting. The fractal cats, who dislike wet paws, checked the melting ice and decided to venture no farther than the bottom porch step. This morning, the temperature is 36F 2C and a cold rain is starting. It looks like the big snow-and-ice storm that was forecasted will not develop. This is good for the humans, but with the rain, the dynamic cat duo will have another bad day. My day will turn better when I finish the work that I have scheduled to be completed today. Then I will start the search for the next FOTD fractal. Until tomorrow, take care, and wait for that next fractal. It could be a winner. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Path_to_Nowhere { ; time=0:13:34.16--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-0.25283251275150080/-0.006577498609819\ 30/4.376921e+010/1/177.5/3.10523039630319908e-005 params=2.01/0/315/0 float=y maxiter=1800 inside=0 logmap=370 periodicity=10 colors=000VUUmWUmWUmWUmWUmWUmWUmWUmWUmWUmWUmWUmWUm\ WTnWSoWUpVUqVUrUTsUStTQuSQvROvSQvTRvUSvVTvVUuWVtXW\ tYXsZYrZZq__q``paaobbq`fobclceidfefhbgi_hkWjlTkoQl\ qMntJovGpyDpzCmzBjyAfx9cw9`v8Xu7Ut6Qs6Ns5Kr4Gr3Dr0\ Br2Ar3Aq4Ap5Ao6An7Al8Ak99iA9gB9eD9cE9aF9`G9ZH9XI8V\ J8TK8RL8QM8OO8MP8KQ8IR7GS7FT7DU7BV79W77X75Y42`74e9\ 5`B6bD8dF9eHAfJChLDiNEjPFjRHkTIlVJmXLnZMo`NobPpdQq\ fRrhSsjUslVtnWupYvrZwt_xy_rv`qs`pq`onanlaniamgbldb\ kbbj_cjYciVchTdgQdfOdfLeeJedGecEfbBfe7gb9f_BfXCfVE\ fSFfPHfNIfPKeQLeRNdSOdTQcURcVTbWUbXWbYXaZZa__``a`b\ b_cd_deZegZfhZgjYhkYimXjnXkpWlqWmsVntVouVlsTiqRfoO\ cmMalKZjIWhGTfDQdBNb9K`7KY3JZ4I_5I`6Ha7Hb8Gc9GdAFe\ BFfCEfDGgEIhFKiGMjHOkHQlISmJUnKWoLYoM_pNaqOcrPesQg\ tRiuSkvTmwUowUqxVsxVuyVwyVyyWzzWzzWzzWzzXzzXzzXzzX\ zzWzzWzzWzzWzzWzzWzzWzzWzzWzzWzzWzzWzzWzzWzzWzzYzz\ XzzWzzUzzUzzUzzUzzUzzUzzU } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(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 } END 20.0 PAR-FORMULA FILE==================================

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Internet Wayback Machine
by Vortex Swirling 03 Feb '04

03 Feb '04

Paul, Your welcome. Just for the fun of it I tried it on the FOTD page. It seems the last cache was made on June 30, 2003. If I go into it from there it finds that FOTD there with its full graphic. Then I went to the Jan 17, 1999 cache and found some FOTD's there, again with their full graphic. I've looked at the source of this html and what they have done is to redirect the links within the pages to point deeper into their cache. That is, if you click on a link within the cached page, you stay in the Wayback archive. You have to wonder where they are getting all the space to store this. They claim to be located in the Presidio. Gerald, That page is recent, but I stopped looking for it in the last few months of 2003 when I found the Wayback. I used Dogpile to determine the new page showed up sometime in October which is reassuring. I had looked for it quite obsessively at one time and used terms like home page etc. It would be interesting to find a search engine that might tell you about the page it finds. When it appeared, who own's the domain, etc all in one click. --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.576 / Virus Database: 365 - Release Date: 1/30/2004

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FOTD 28-01-04 (The Quintessential Midget [8])
by Jim Muth 02 Feb '04

02 Feb '04

At 10:52 AM 1/28/04 -0600, Paul Lee wrote: >Jim Muth wrote: >> >> FOTD -- January 28, 2004 (Rating 8) >> >> The render time of 19 minutes.... >> >> START 20.0 PAR-FORMULA FILE================================ >> >> QuintesentialMidgt { ; time=0:00:00.00--SF5 on a P200 >> reset=2003 type=formula formulafile=allinone.frm The answer is simple -- I forgot to type in the actual, render time, which is 0:19:21.24 Jim (the penitent) M.

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FOTD 02-02-04 (A Nest of Undines [8])
by Jim Muth 02 Feb '04

02 Feb '04

FOTD -- February 02, 2004 (Rating 8) Fractal visionaries and enthusiasts: The first day of February, the day of the great computer virus attack, has come and gone, and not much has happened -- at least as far as I have heard. This is just about what I expected. These over-hyped disasters never seem to happen. Of course, I never had reason to worry. With the precautions I take, I have absolutely 100-percent total immunity, (no exaggeration), to electronic viral attack. But though I was not concerned about my own computer safety, I was surprised when a friend called yesterday to ask if it were safe to go on the internet. I told her that the risk was slight, and settled down to wander in Fractal Land. I gave the name "A Nest of Undines" to the image I soon found. An undine is a female nature spirit who supposedly lives in the water, just as gnomes live in the earth and sylphs live in the air. I have no idea what a group of undines would be called. I doubt that it would be a bevy. I guess a nest is as good as anything. There is nothing really watery about today's image. I simply liked the sound of the name. The image is an evaporated one, created by combining 7 negative parts of Z^(-1.4142) with 0.7 negative parts of Z^(-14.142) and then adding (1/C). Since the image has been evaporated, it consists of nothing but trapped 'inside' points, which have been brought to life by rendering it with the inside set to bof60. The image is one of the few in which the 'bof60' inside fill draws the best picture. Normally, this fill draws little more than chains of bubbles, which can sometimes be quite attractive, but often are boring. In today's image however, the bubbles have been caught up in the discontinuities and ripped to shreds, so that they resemble the shape of bananas more than spheres. Another unusual feature of the scene is the almost total lack of symmetry around the central midget. This is a result of the rather low maxiter of the image. I feel that the rating of an 8 is justified. Due to the extra effort I put into its coloring, the image is one of the more unusual ones of recent weeks. Combined with the render time of 29-1/2 minutes, this gives an overall value of 35. The wait for the image to calculate can be avoided by downloading the already-rendered image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Of course, then you miss the fun of doing it yourself. Sunday was a bit milder here at Fractal Central. The tempera- ture reached a high of 32F 0C, but the yard is still shaded by the holly trees and the snow is still 15cm deep on the ground. The cats passed the day wishing for better things. Today looks like a repeat. We'll see how it goes. The work looks as though it will be heavy today. If I am smart, (which I am), I'll start on it without delay. The next FOTD is due to appear in 24-odd hours. But an ice storm is also due in 24 hours, and the reliability of the electric service here at Fractal Central in ice and wind conditions cannot be under- estimated. Until tomorrow, when the next FOTD will hopefully appear, take care, and keep searching for stray fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Nest_of_Undines { ; time=0:29:37.95--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.54156745632081060/+1.201010131049127\ 00/1170.852/1/-35/-7.59461937782646146e-014 params=-7/-1.4142/-0.7/-14.142/0/1e+100 float=y maxiter=1200 inside=bof60 periodicity=10 colors=000zb8zb8zb6zb4vb1ub0qb0nd0md0hd0ed0dd0`d0Y\ d0Wd0Sd0Od0Md0Oe0Qe0Se0Ug0Ug0Wg4Yh8ZhAZhF`kIbkKdkO\ emSemWgmYhn`kndkngmohnomoooomqmknhimefkbcj_aeXZdUW\ bQUZMRYKOWHHUDDQ88O44M11K00H00F00D00A00H08K0HO0QS0\ YW4eZ6nb8ueAzhDzmAzk8xk6vh4si1pi0mi0jh0gf0ee0bd0`d\ 0Yb0Vb0Sb6PgOEidzqszvzzzqzzdqzOZz8Hz6Kz1Mz0Qz0Sz0W\ z0Yz0`z0bz0ez0gz0kz0mz0nz0hz0dz0`z0Wz0Sz0Mz0Iz0Dz1\ 8z41z60zSK0QO0OQ0OS0MW0MY0KZ0K`0Id0Ie0Hg0Hk0Fm0Fn0\ Do0Ds0Au0Av08z08z06z06z0Az0Fz0Iz0Mz0Qz0Uz0Yz0`z0dz\ 0gz0hz0mz0oz0sz0vz0zz0zx0zx0zx0zx0zx0zx0yyKxzUwzUv\ zIvz0vz0vz1vz8vzDvuHvnMvhQvbWvWZvObvHgv8kv1nx0kx0g\ z0ez0bz0Zz0Yz0Uz0Qz0Oz0Kz0Iz0Fz0Az08z04z00z00z00z0\ 0z00z00z00z00z40z80zF0zI0zM0zS1zW4zZ8zbAzgDzkHznIz\ sKzvOzzQzzSzzWzzYzzZzzbvzd0zq6zkIzdUzZduSnoKxkFze6\ z`0zY0zZ0zZ0z`4z`8zbDzbHzbKzdOzdSzeWzeZze`zhYzkWzn\ UzoSzsQzeQz`IzbHzbFzbDzbA } 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 } END 20.0 PAR-FORMULA FILE==================================

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Internet Wayback Machine
by Vortex Swirling 02 Feb '04

02 Feb '04

Too bad the manguide and the short manfaq couldn't be hosted at spanky. The manguide is rather unique in that I haven't seen anyone else annotate the Mandelbrot set in that way. I wonder if Paul would mind? I wonder where and who Paul actually is? --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.576 / Virus Database: 365 - Release Date: 1/30/2004

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FOTD 01-02-04 (Golden Bud [4])
by Jim Muth 01 Feb '04

01 Feb '04

FOTD -- February 01, 2004 (Rating 4) Fractal visionaries and enthusiasts: Today's image is named "Golden Bud". This does not imply that the bud is a golden color. I gave it that name because the parent fractal was created by using the golden ratio, or 1.618, twice. Actually, the bud, or the interior of the bud, is an electric blue color. The generating formula of the image is Z^1.618+C. This means that each bud in the resulting fractal will have 0.618 part of one lobe. But unlike the buds of the whole Mandeloids, where all buds are of a similar shape, the buds of the fractional Mandeloids have no fixed shape. The missing part of the next- higher whole bud can take any shape whatever. The next-higher whole bud in today's instance is the near-per- fect circle of the buds of the classic Mandelbtot set. The 0.382 part of a circle that is missing has been eroded rather equally from the entire perimeter, leaving a rather squat bud with assorted nooks and crannies. Some of these crannies might hold some interesting scenes. The drawback to the exploration is the extreme slowness of the area. I wanted to give the image a rating higher than the 4, but in all honesty I could not. I worked on it for my own amusement rather than to make as good a picture as possible. Combined with the render time of 22 minutes, the image has an overall value of 18. The completed GIF image is available on Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> It remained very cold all day Saturday here at Fractal Central, and as a result, the fractal cats remained very close to the heat. At one point, Thomas did check the conditions on the porch, but the temperature of 19F -7C and lack of direct sun was far too chilly for his ears. He turned around after only two minutes and came back inside to enjoy the heat. This morning is starting about the same; I suppose the cats will have a repeat day. So far, my day has been uneventful, but the fractal lady has that 'lets go shopping for antiques' look in her eye. I fail to see what's so interesting about stuff that others no longer want, but who knows . . . on rare occasions something worthwhile does turn up. One thing certain to turn up however is the next FOTD, which will appear tomorrow. Until then, take care, and older is not always better. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Golden_Bud { ; time=0:22:18.97--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=mandelbrotbc1 function=floor center-mag=+0.19019301420027440/-0.004400056781287\ 68/31007.75/1/24.86/-1.94137206310784904e-011 params=1.618/0/1.618/0 float=y maxiter=15000 inside=255 logmap=187 periodicity=10 colors=000bXqbYocZnc`lcakdbiLQHOMHQHGRIHRIHRJHRJIR\ KIRKIRLJRLJRMJRMJRNKRNKROKROLRPLRPLRQMRQMRRMUFRSLO\ RRMPWJOaHNfFMeGMdHLcILcJKbKKaLJ`MJ`NI_OIZPHYQHYRGX\ TGXUFWWFWXEWZEV_DV`DVbCUcCUeBUfBThATi8RkATjBUiCViE\ WhFYgGZgI_fJ`eKaeMcdNdcOecPfbRhaSiaTj`Vk_Wl_XnZZoY\ _pY`qX`tVasWarXaqXbpYboZbnZcm_cl_ck`cjadiadhbdgcef\ ceededdecefbffaff`gg_hgZhgYikctghpgXiZJVP4IR5HS5HU\ 6HV6GX6GY7G_7F`8Fb8Fc8FcCHcFJcILcLNcOPcRRcUTcXVc`X\ ccZcf`cibcldcofcrhcujdzfcxkcvpcttbrybpzcrzbnzajz`f\ z_bwZZsZVpYRlXNhWJeVFaWASVBWVCZUDaUDdUEgTFjTFmSGpS\ HsSHvRIyRJzQHzRJzSKzSLzTMzTNzUOzUPzVQzVRzWSzWTzXUz\ YVzYWzZXzZYz_Zz__z``z`azabzaczcczdczeczgczhcziczlb\ zkczjczjdzidzhdzhezgezgezffzefzefzdgzdgzcgzbhzbhza\ hzaiz`iz_iz_jzZjzZjzYjzXjzWjzVlzUlzTmzSmzRozQozPpz\ OpzNrzMrzLrzLrzNszOszQszRszStzUtzVtzXtzYuzYuzZuzZu\ z_vz_vz`vz`vz`vzavzavzmzz } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(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 } END 20.0 PAR-FORMULA FILE==================================

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Internet Wayback Machine
by Vortex Swirling 01 Feb '04

01 Feb '04

The FOTD's are annotated quite nicely by Paul Lee with various web links. In the past there was a link to Paul Derbyshires "Quck Guide to the Mandelbrot Set" when describing various regions of the Mandelbrot set. The last known site where this guide posted seems to have gone 404. I been checking from time to time to see it might have found a new home. Then I found out about the Internet Wayback Machine at http://www.archive.org/web/web.php With it, you can find cached copies way back to 1996. A page might be cached several times. I was able to display the most recent cache of Paul Derbyshires Guide by going to this link. You can go there directly: http://web.archive.org/web/20030618092046/http://www.globalserve.net/~derby… --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.573 / Virus Database: 363 - Release Date: 1/28/2004

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FOTD 31-01-04 (Sevateem [7])
by Jim Muth 31 Jan '04

31 Jan '04

FOTD -- January 31, 2004 (Rating 7) Fractal visionaries and enthusiasts: I have no idea what the name of today's image has to do with its actual appearance. The name is one I invented on a whim, pure nonsense, a word such as one might find in the 'Alice in Wonderland' books. But such nonsense is not surprising in this modern-day world of science, where we have books of popularized quantum physics speaking nonsense such as Carroll never dreamed of when he wrote his 'Wonderland' books, and then declaring the nonsense to be a model of some strange kind of 'reality'. At least I make no claims that today's fractal is real -- not real in the every-day objective sense, that is. The image is a scene in the fractal that results when 1/3 part of Z^4.5 is added to Z^2.5 and 1/C is then added. This parent fractal appears as a fragment of a Mandeloid that fills the screen, with a sharply-defined but very distorted Mandeloid just off the bottom of the screen. In today's image, I ignored this distorted Mandeloid and concentrated on the large fragment. Today's scene is located at the edge of one of the arms marking the entrance to a partly-obscured bay on the southern edge of the fragment. As is frequently the case in fractals where two or more powers of Z are combined, certain parts of the image appear eroded, and filled with holes of all shapes. Today's image lies in such an area, and the greater part of it consists of such 'inside' holes. I have made this 'inside' area do things by rendering it with the 'fmod' option, with the proximity set to 0.25. The result is a FOTD that rates a 7 -- not as good as I might have hoped for, but certainly better than some of the images that have made it to FOTD status. Is the image worth the 11-minute render time that, combined with the rating of 7, results in an overall value of 63? This is a question which each individual must answer for himself. But the question may be eliminated by downloading the finished GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and avoiding the rendering stage entirely. Friday was a very busy day for me here at Fractal Central. For the fractal cats it was a boring day. The temperature of 23F -5C and brisk winds kept them confined to their beds by the heat. In the evening, they demanded a treat of tuna, which I gave them willingly. After all, I had ignored them all day. This morning is even colder. It looks like another day curled by the heat for the dynamic duo. For me it looks like a far slower day. If I'm clever enough, I might get through the whole day without doing a bit of useful work. And I'll return on schedule in 24 hours or so with another fractal. Until next time, take care, and be forever fractalish. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Sevateem { ; time= 0:11:11.01--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.16960004342521910/-0.655188865003747\ 20/1.131122e+008/1/-100/-4.45595079812122208e-006 params=1/2.5/0.333/4.5/0/0 float=y maxiter=1500 inside=fmod proximity=0.25 periodicity=10 colors=00076G6CO4IT4M_3Sd3Xj1apAcLD_GFVCGSDGQFGPGG\ OIGMJGJLGIMGGOGFPGDQGCSG9TG7VG6XG4YG3_G1`G0aG0cG0d\ G0fG0gG0iD0lA0o73r46u1Ax0Dz0Iz0Lz0Pz0Sz0Vz0Yz0_z0`\ z3az7cxCdsGfpLglPiiTjfYlaam_foXdpVcrVcrVasV`sV`uV_\ vVYvVYxVXxVXyVVzVTzVTzVSzVQzVQzVPzVOzVOzVMzVMzVLzS\ JzPIzOGzLFzJDzGCzDAzC9z97z7Gz3Or0Xj0ca0jV0iY0i`0ic\ 4if9iiDilIioMirQiuVix_arYVmYPgYIcYCYYl0Qi0Sf4XdC`a\ JdpQiqcmrdisedtfaugYvhTwiQxjMykIzlFzmAzn6zo3zo0zp0\ zm1zi7zdDy`JuYPrTVm0`i0ff0l`0fV0aP7YJFTDMP9TLLMIXG\ GgADs4Cz09z07z09z09z49z79zAAzFAzIAzLAzPCzSCyXCx_Cv\ aDufDsiDslDpjGmiIjgJgfMddOcdP`cQYaTV`VS_XQ_YVaXYcV\ `fTcgSfjQilPloOopOssMvuLyxJzyIzzGzzFzzDzzDzzAzz9zz\ 7zz6xz4sz3py1my0jx0gv0cu0`u0Ys0Vr0Sp0Pp0Qu0Sx0Tz0T\ z0Vz0Xz1Xz3SzAOsIQmMSgPVaSXXV_QY`M`aGldAofWjiXmjap\ n`iobcqcgsfjujmvmpxpsxsvxuyywzyxzzxzzwzvwzruzmrxin\ sdjo`fjXafSYaOUYJQTFGPAAL } 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 } END 20.0 PAR-FORMULA FILE==================================

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No FOTD for Jan. 30
by Jim Muth 30 Jan '04

30 Jan '04

Due to other work there will be no FOTD for January 30. The FOTD will return on schedule on January 31. Jim M.

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Re: [Fractint] Jim, what is going on here?
by Jim Muth 29 Jan '04

29 Jan '04

At 12:07 PM 1/28/04 -0500, Hal Lane wrote: > >Jim, I tried raising the maximum iterations to 10,000 as I >prefer well iterated, clearly defined midgets. And true to >your promise -- some of the colors changed in the center 1/4 of >the image. > >I assume that by "mess up the color palette" you mean that >some of the image *data* changed when maxiter was increased and >thus got mapped to different colors....If my assumption is >right, why do those pixels change color? The colors changed when the maxiter was increased because the 'logmap' was used with the image. When the logmap is set to zero, the 256-color palette is repeated over and over, one color per iteration band, until the maxiter is reached. Increasing the maxiter produces no change in the colors that are already on the screen. It merely adds additional rounds of the palette to the new higher-iteration features. When the logmap feature is activated, the color palette is applied only once across the entire range of iterations. The individual bands are increasingly broadened as the iteration count increases. In this case, increasing the maxiter will broaden and therefore change some of the color bands already on the screen. Jim M.

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FOTD 29-01-04 (Fractal Cesspool [4])
by Jim Muth 29 Jan '04

29 Jan '04

FOTD -- January 29, 2004 (Rating 4) Fractal visionaries and enthusiasts: Today's image is named "Fractal Cesspool". Yes, I realize that it is an unpleasant sounding name, but the experience of unpleas- antness is a natural part of existence in the physical world. Why should unpleasantness not be a part of the world of fractals? The image, which consists of squirmy bits and pieces, is not actually as unpleasant as the name implies. It is merely a part of the fractal that results when 1/2 part of Z^(1.5) is subtrac- ted from 5 parts of Z^(-0.5) and (1/C) is added. As is so often the case, the parent fractal consists of numerous disconnected Mandeloids. Today's scene is located in the chaos surrounding one of the largest irregular ones. The rating of a 4 is a big come-down from the recent run of 8's, but when the render time of 3-1/2 minutes is taken into consider- ation, the overall value is 115. The image can be viewed either by running the included parameter file or by downloading the finished GIF image from Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> As expected, the cold, ice, and high winds here at Fractal Central kept the fractal cats sulking indoors all day Wednesday. The temperature reached a high of 28F -2C, which is not unbear- ably cold, but the wind made it feel like Barrow, Alaska. The good news is that Fractal Central just missed being part of the big power failure that struck most of northeast Maryland on Wednesday when transmission lines swinging in the high wind came together and shorted out. That 250,000-volt arc must have been truly spectacular. So far today appears acceptable. The temperature promises to rise to freezing, the cats have not yet become active, the work is at a minimum, and the electricity is on. Hopefully, the day will remain acceptable. Until next time, take care, and be kind to orphan fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Cesspool { ; time=0:03:28.50--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.14173382183010250/-0.013860991553163\ 99/3.737725e+008/1/-142.5/-1.92086317268858053e-007 params=5/-0.5/-0.5/1.5/0/525 float=y maxiter=450 inside=0 logmap=56 periodicity=10 colors=000oKKmKKkKKiKKgKKeKKcKKaKK_KKYKKWKKUKKSKKQ\ KKPKKOKKNKKMKKLKKKKKJKKIKLHKPGKSFKVFNYEQ`ETbDWdCZh\ D`kCbnBeqBhtAkwAmzBmzBlyCkyCjxDiwDhwEgvEfvHewJdwLc\ xObxQayS`yV_zXZzZYzYXtXWnWViVUcVSZ`QSeOLjMEoM7tQ0o\ S9jUIeWR`Y_W_hY_h__ha_hcaeeccfd`hfZjgWkiUmkRmKSlKQ\ jJPhINgILeHKdGIbGGaFF_EDZECYDEXDGWDHVDJUDLTDMSDORD\ PQDRPDTODUNDWMDYLDZKD`KDaFMgAVl5cr0lw3ju5ht8fsAdrD\ bqF`oIZnKXmNVlPTkSRiUPhXNgZLf`JecUYfdQgcUgcXhc`hcc\ hcfibjibmjbqjbtjbwedvaevYfuTguPhuLitHjtCkt8ls4ms0n\ s1mo2ml2lh3le3ka4kZ4jV5jS6jO6iL7iH7hE8hA8g79g39g0D\ e6GgBJiGMkLPmQSoVVq_Ysd`uicwnfxshyojzllzhnzepzarzZ\ tzVvzSwzPvzNvzMuzLuzKtzJtzIszHszGrzErzDqzCqzBpzApz\ 9oz8oz7pzCqzGrzKszPtzTuzXvzawzexziyznzzrzzvnz0lz6j\ zBhzGfzLdzQczVhzglzsmzqmzpnzonznozmozlpzkpziqzhqzg\ rzfrzeszdszcszbrzcqzdpzepzeozfnzgmzhmzhlzikzjjzkjz\ kizlhzmgzngznczklzPszMzzJ } 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 } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] FOTD 28-01-04 (The Quintessential Midget [8])
by Jim Muth 29 Jan '04

29 Jan '04

At 08:54 AM 1/29/04 -0500, Vortex Swirling wrote: >If I zoom out some on the parent fractal I can see the largest mandeloid >fully. Can there images produced using the >MandelbrotMix4 formula such that you could continue to zoom out and find >them in the largest possible field? Or is there a limit to how far out >they can occur? There is no limit to how far out fractals can exist. They can be infinite on the large acale as well as on the small scale. Jim M.

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FOTD 28-01-04 (The Quintessential Midget [8])
by Vortex Swirling 29 Jan '04

29 Jan '04

--- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.573 / Virus Database: 363 - Release Date: 1/28/2004

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Domain has no parent.
by SherLok Merfy 29 Jan '04

29 Jan '04

> 5. [1]Fractint Development Team Homepage > http://www.fractint.org/ > 4. [2]A URL specified by the user > http://www.fractint.org/ftp/current/dos/fradev.zip > 3. [3]400 Bad Request > http://www.fractint.org/../ftp/current A few _anchors_ (that don't specify the domain) _like_ [3] are on [5]. While some browsers might see what happens when they snip the .. that doesn't make sense to your server on your site's base page, Lynx 2.7.1 (remote version beyond my direct control) doesn't happen to be one of them. I was kinda hoping that Tim would fix those when release three of version twenty gets the name fradev.zip , but then I realized that this might not take any action on his part. ...It's getting smaller. ...Someone knows what he's doing! ...I wish it was me. :-)

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Re: FOTD 28-01-04 (The Quintessential Midget [8])
by Jim Muth 28 Jan '04

28 Jan '04

At 11:39 AM 1/28/04 -0600, Paul Lee wrote: >Just curious, how come your 'Startup Parameters' >in the SSTOOLS.INI file do not already accomplish >such for your saved PAR files?? As in the >following: > > COMMENT=time=$calctime$--$vidkey$_on_a_P200 Yes, I have thought about it. I just have never gotten around to doing it. The problem is that I often calculate the FOTD images on other machines, and must convert the time to the P200 standard. >And, ever think of expanding your COMMENT >parameter to something like: > COMMENT=(c)_Jim_Muth_--_$date$_-_$time$_/ > time=$calctime$_on_a_P200_at_$xdots$x$ydots$_/ > Video=$vidkey$_using_FractInt_$version$.$patch$ I have thought of a lot of things I might do. I like to keep the parameter file uncluttered, and most of the above information is available elsewhere. But, if a great public outcry should arise, I could do this. Jim M.

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Jim, what is going on here?
by Hal Lane 28 Jan '04

28 Jan '04

######################################################### > FOTD -- January 28, 2004 (Rating 8) > Actually, the midget looks as though it could use a few more > iterations. This could easily be done, but if I raised the > maxiter, it would mess up the color palette, which is what > really makes the image. Jim, I tried raising the maximum iterations to 10,000 as I prefer well iterated, clearly defined midgets. And true to your promise -- some of the colors changed in the center 1/4 of the image. I too like the image coloring better when the midget is underiterated. But as I said, I prefer well iterated midgets. Is there a way for me to have my cake and eat it too? <---<< My experience when adding iterations to an inside=0 fractal is that a few more black pixels get colored in as they escape prior to the new higher maxiter value. I don't remember seeing existing pixels change color. I assume that by "mess up the color palette" you mean that some of the image *data* changed when maxiter was increased and thus got mapped to different colors... (Color palettes remain constant entities unless specifically changed -- which I did not do.) If my assumption is right, why do those pixels change color (iteration count)? <---<< In your image, presumably they were assigned a color because they escaped at an iteration count less than your maxiter=2400. Why would those pixels escape at a different iteration count when maxiter was raised? <---<< - Hal Lane ######################### # hallane(a)earthlink.net # ######################### ######################################################### --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.572 / Virus Database: 362 - Release Date: 1/27/04

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RE: [Fractint] Golden ratio
by Tony (Anthony) Hanmer 28 Jan '04

28 Jan '04

OK everyone, thanks for demystifying my remarks on the Golden Ratio. I'm glad to have it more fully explained, and would be the first to confess (if it weren't already obvious) that my math ability is somewhat less than my artistic ability. NOW, what do you think about the L-systems themselves?! Tony Hanmer _________________________________________________________________ Tired of spam? Get advanced junk mail protection with MSN 8. http://join.msn.com/?page=features/junkmail

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Some new tiles
by Tony (Anthony) Hanmer 27 Jan '04

27 Jan '04

The family of sets of tiles I describe below is the first of a few announcements I intend make this year in L-systems and IFS fractals, my patience with other ways of releasing my work having run out. I hope to see a renewed interest in these two types, which I see as underdeveloped and worthy of much more attention. S-Tiles There are 3 regular tiles in 2 dimensions: equilateral Triangle, Square and Hexagon. Take one side of any of these, a straight line. Distort it from this configuration in any manner which leaves it with 180-degree rotational symmetry, the same symmetry which is found in the letter S (or Z, or N). It must also be non-crossing (nc). Remake the tile using these altered lines as sides, and it will still function as a tile. I call these S-Tiles. (Does anyone have a better name?) Several examples are known already - you will find them in Benoit Mandelbrot's seminal book, "The Fractal Geometry of Nature", pp. 50-55. I include below a few of my own pieces. Paste them into a file, call it STs.l for example, save it in your Fractint directory and you can then run the fractals as type Lsystem. I have hugely expanded the family of sets as L-systems. The sets are infinite, because a line, the side of a tile, can be made as long and as convoluted as one wishes. (Fractint's capacity to produce these tiles, however, is not infinite, because it has a necessary limit on the number of characters in a line of L-systems code: 160 for versions up to the last developer's release, and 255 for the latter.) My L-systems file, STiles.l, is available zipped from http://spanky.triumf.ca/pub/fractals/params/ for those who are interested. Download and unzip it into your Fractint directory, and you're ready to explore these new tiles in Fractint; and to add more of your own. The easiest way to programme a side of any S-Tile, once you've drawn it on squared paper, is to write the set of L-system transformations ("f=f+f-ff"... etc) for the first half of the line; then reverse both the order of this line's fs and the polarity of its turns, + becomes - and - becomes +. This process could be automated to speed things up. Then, in your L-systems file, paste the 2 halves of the line (call them a and z) together, as az, one string. In your Axiom, write the required number of fs to make the tile, in different colours - e.g. a Square tile would have Axiom c9f+c10f+c12f+c14f if you used Angle 4, or c9f++c10f++c12f++c14f if you used Angle 8, etc. Then run the L-system to check that it is nc (non-crossing). The individual segments (fs) in one's side of an S-Tile need not have uniform length. Altering their lengths can increase or decrease their degree of convolutedness (which, I think, is their fractal dimension, is it not?). In some of the cases I've included in STiles.l, the Golden Ratio (phi: c. 1.6180339887499) is a limit which leads to tiles which touch themselves, and numbers slightly varying from this number lead either to not-quite-touching tiles (the goal), or to self-crossing curves. How could one automate the process of calculating fractal (Hausdorff) dimension for S-Tiles, especially for those whose segments are not uniform in length? These tiles can also be made in a vector drawing programme like CorelDraw or Illustrator, as closed curves; then filled, copied and tiled. But the number of "nodes" (segment endpoints) can quickly grow beyond such programmes' ability to handle, as I have found. More than 50000 nodes and the thing may crash. Further variations, less "orthodox", could have islands and lakes, making them into dusts - discontinuous curves, though they would still need to be tiles. Another type of variation will be the subject of a future announcement - it is a whole family of infinite sets in its own right, and even more fascinating than the whole S-Tiles family of sets, I think. S-Tiles should also work in *3* dimensions, with the 5 regular polyhedra (and with regular polytopes in all higher dimensions!), though I've yet to begin such experiments, not having the programming skills or the programme itself to do them... Anthony Hanmer Tbilisi, Republic of Georgia PS More news to follow - this is only the start. ST30016* { ; Anthony Hanmer 7/2002 Angle 6 ; nc; and 3 together make a tile Axiom c9f++c12f++c14f f=@2f@.5--f++f+@2f@.5-f--f++@2f@.5 } ST30023* { ; Anthony Hanmer 7/2002 Angle 6 ; nc; and 3 together make a tile Axiom c9f++c12f++c14f f=ff+f+f--f-f-f+f+f++f-f-ff } ST30040* { ; Anthony Hanmer 7/2002 Angle 6 ; nc; and 3 together make a tile Axiom c9f++c12f++c14f f=@2f@.5+f++f--@2f-f--f++f+f@.5++f--f-@2f@.5 } ST40001* { ; Anthony Hanmer 2000 (was T105aa, my first ST and first square ST) Angle 4; non-crossing (nc); and 4 together make a tile Axiom c9f+c10f+c12f+c14f f=ffff+fff+ff+f+f-f-ff-fff-ffff } ST40009* {; Anthony Hanmer 6/2002 (was T105aa03b) Angle 4 ; nc; and 4 together make a tile Axiom c9f+c10f+c12f+c14f f=f+@iq2f+@iq2f-@q2f-@q2f } ST40465* { ; Anthony Hanmer 7/2002 Angle 4 ; nc; and 4 together make a tile Axiom c9f+c10f+c12f+c14f f=f+f-f+f-f-f+f-f-@2f@.5+f+f-f+f+f-f+f-f } ST60020* { ; Anthony Hanmer 6/2002 Angle 6 ; nc; and 6 together make a tile Axiom c1f+c2f+c3f+c4f+c5f+c6f f=ff+f+f+ff-f-f-ff } ST60059* { ; Anthony Hanmer 6/2002 Angle 6 ; nc; and 6 together make a tile Axiom c1f+c2f+c3f+c4f+c5f+c6f f=f-f+f+@2f@.5+f+f-f-@2f@.5-f-f+f } ST60062* { ; Anthony Hanmer 6/2002 Angle 6 ; nc; and 6 together make a tile Axiom c1f+c2f+c3f+c4f+c5f+c6f f=f-ff+f+f+f+f-f-f-f-ff+f } _________________________________________________________________ MSN 8 helps eliminate e-mail viruses. 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Golden ratio
by Raymond Filiatreault 27 Jan '04

27 Jan '04

Tony Hanmer wrote: The Golden Ratio, also known as the Greek letter phi (pronounced "fee") and several other names, is indeed a fascinating number. It is approximately 1.1680339887499; or is it this number minus 1? Anyway, it is the only answer to the question, Which number satisfies *both* 1/x = x-1 and x^2 = x+1?... Wild. It is also calcualted as ((sqrt 5)-1)/2. First, the ratio is 1.61803398874989... Secondly, your two equations 1/x = x-1 and x^2 = x+1 are just variants of one another. In other words, they are identical and any solution will obviously satisfy *both*. They can also be written as: x^2-x-1=0. Solving for x yields two roots, one being the positive and referred to as the Golden ratio, the other being negative and equal to -0.61803398874989... Raymond Filiatreault _________________________________________________________________ Protect your PC - get McAfee.com VirusScan Online http://clinic.mcafee.com/clinic/ibuy/campaign.asp?cid=3963

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A couple more
by Tony (Anthony) Hanmer 27 Jan '04

27 Jan '04

Another pair of small L-systems files I have included below in their entirety are Trvar.l and TTiles.l. The former is another set of my variations on others' work - Trees, Bushes and Plants. The latter contains a few tiles I have found - some of which may be new, others not. A few of them are also mlr - multiple-layer redundant; in other words, they have several layers of the same thing on top of each other, and are in need of simplification to remove this extra unnecessary repetition. But all of them are interesting. If any of the tiles are, in fact, my rediscoveries of others' tiles, I'd like to be informed about it. Paste the files separately into a text editor and call them Trvar.l and TTiles.l; then save them into your Fractint directory and you're ready to use their contents as type Lsystem. Tony Hanmer Tbilisi, Republic of Georgia Trvar.l _README {; Anthony Hanmer 2001 angle 4; Variations on Trees, Bushes and Plants axiom f f=f } Tree01 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 4; Tree1, angle changed to 4, @ to inverse of sqrt 2 - axiom +fx; a pseudo-spacefilling tree X=@iq2[-fx]+fx } Tree01c1 {; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 4 ; Tree1, angle changed to 4, @ to inverse of sqrt 2 - axiom +fx ; a pseudo-spacefilling tree, colour version 1 X=@iq2[>1-fx]<1+fx } Tree01c2 {; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 4 ; Tree1, angle changed to 4, @ to inverse of sqrt 2 - axiom +fx ; a pseudo-spacefilling tree, colour version 2 X=@iq2[>1-fx]>1+fx } Tree02 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 12; Tree1, angle changed to 12, @ to inverse of sqrt 2 - axiom +++FX; a Levy's Curve variation X=@iq2[--FX]++FX } Tree02a { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 12; Tree1, angle changed to 12, @ to Golden Ratio - axiom +++FX; X=@.6180339887449[--FX]++FX } Tree03 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 8; Tree1, angle changed to 8, @ to inverse of sqrt 2 - axiom ++FX; a Levy's Curve variation X=@iq2[-FX]+FX } Tree03a { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 8; Tree1, angle changed to 8, @ to Golden Ratio - axiom ++FX; X=@.6180339887449[-FX]+FX } Tree04 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 8; Tree1, angle changed to 8, @ to inverse of sqrt 2 - axiom ++FX; X=@iq2[--FX]+FX } Tree04a { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 8; Tree1, angle changed to 8, @ to Golden Ratio - axiom ++FX; X=@.6180339887449[--FX]+FX } Tree05 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 8; Tree1, angle changed to 8, @ to inverse of sqrt 2 - axiom ++FX; Twindragon tree X=@iq2[---FX]+FX } Tree05a { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 8; Tree1, angle changed to 8, @ to Golden Ratio - axiom ++FX; X=@.6180339887449[---FX]+FX } Tree06 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 8; Tree1, angle changed to 8, @ to inverse of sqrt 2 - axiom ++FX; mirror image of Tree04 X=@iq2[-FX]++FX } Tree07 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 8; Tree1, angle changed to 8, @ to inverse of sqrt 2 - axiom ++FX; Twindragon tree, mirror image of Tree05 X=@iq2[-FX]+++FX } Tree08 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 8; Tree1, angle changed to 8, @ to inverse of sqrt 2 - axiom ++FX; X=@iq2[--FX]+++FX } Tree08a { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 8; Tree1, angle changed to 8, @ to Golden Ratio - axiom ++FX; X=@.6180339887449[--FX]+++FX } Tree09 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 8; Tree1, angle changed to 8, @ to inverse of sqrt 2 - axiom ++FX; mirror image of Tree08 X=@iq2[---FX]++FX } Tree10 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 4; Tree1, angle changed to 4, @ to inverse of sqrt 2 - axiom +fx; a pseudo-spacefilling... smoke? X=@iq2[-gx]+fx } Tree10c1 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 4; Tree1, angle changed to 4, @ to inverse of sqrt 2 - axiom +fx; a pseudo-spacefilling... smoke? (Colour version 1) X=@iq2[>1-gx]<1+fx } Tree10c2 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 4; Tree1, angle changed to 4, @ to inverse of sqrt 2 - axiom +fx; a pseudo-spacefilling... smoke? (Colour version 2) X=@iq2[>1-gx]>1+fx } Tree10a { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 4; Tree1, angle changed to 4, @ to Golden Ratio - axiom +fx; X=@.6180339887449[-gx]+fx } Tree11 { ; Anthony Hanmer 2001, adapted from angle 8; Tree10, angle changed to 8 - Twindragon tree axiom ++FX X=@iq2[---GX]+FX } Tree12 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 4; Tree1, angle changed to 4, @ to inverse of sqrt 2 - axiom +fx; a pseudo-spacefilling ... dust? X=@iq2[-fgx]+fx } Tree13 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 4; Tree1, angle changed to 4, @ to inverse of sqrt 2 - axiom +fx; a pseudo-spacefilling ... dust? X=@iq2[-fgx]+fgx } Tree14 { ; Anthony Hanmer 2001, adapted from angle 8; Tree12, angle changed to 8 - Twindragon tree axiom ++fx X=@iq2[---fgx]+fx } Tree15 { ; Anthony Hanmer 2001, adapted from angle 8; Tree1, angle changed to 8 - Twindragon tree axiom ++fx X=@iq2[---fgx]+fgx } Tree16 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 12; Tree1, angle changed to 12, @ to .615 axiom +++fx X=@.615[--fx--]++fx++ } Tree17 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 6; Tree1, angle changed to 6, @ to .5 axiom fx X=@.5[fx+]@2fx[+fx] } Tree18 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 6; Tree1, angle changed to 6, @ to .615 axiom fx X=@.615[fx-][fx][+fx] } Tree19 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 12; Tree1, angle changed to 12, @ to .615 axiom ++++++fx X=@.615[fx--][--fx++] } Tree20 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 4; Tree1, angle changed to 4, @ to .615 axiom fx++fx X=@.615[fx-][-fx+] } Tree21 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 4; Tree1, angle changed to 4, @ to .5 axiom fx; X=@.5+fx[-fx]@2+fx } Tree22 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 12; Tree1, angle changed to 12, @ to .615 axiom +++++fx X=@.615[gx--][--fx++] } Tree23 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 4; Tree1, angle changed to 4, @ to .5 axiom fx; X=@.5+fx[-gx]@2+fx } Tree24 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 4; Tree1, angle changed to 4, @ to .5 axiom fx; X=@.5+fx[-fx]@2+gx } Tree25 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 4; Tree1, angle changed to 4, @ to .5 axiom fx; X=@.5+gx[-fx]@2+gx } Tree26 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 12; Tree1, angle changed to 12, @ to .615 axiom ++++++fx X=@.615[fx--][--fgx++] } Tree27 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 4; Tree1, angle changed to 4, @ to .615 axiom fx X=@.615[fx-][fgx][+fx] } Tree28 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 6; Tree1, angle changed to 6, @ to .615 axiom +++fx X=@.615[fx-][-fx+] } Tree29 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 3; Tree1, angle changed to 3, @ to .615 axiom [fx]+[fx]+[fx]; X=@.615[-fx]+fx } Tree30 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 4; Tree1, angle changed to 4, @ to inverse of sqrt 2 axiom ++fx; X=@iq2fx[-fx+]@q2fx } Tree30a { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 4; Tree1, angle changed to 4, @ to inverse of sqrt 2 axiom fx-fx-fx-fx; X=@iq2fx[-fx+]@q2fx } Tree30b { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 4; Tree1, angle changed to 4, @ to inverse of sqrt 2 axiom fx++fx; X=@iq2fx[-fx+]@q2fx } Tree31 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 4; Tree1, angle changed to 4 axiom ++fx; X=fx[-fx+]fx } Tree31a { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 4; Tree1, angle changed to 4 axiom fx-fx-fx-fx; X=fx[-fx+]fx } Tree32 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 4; Tree1, angle changed to 4, @ to inverse of sqrt 2 - axiom +fx; a pseudo-spacefilling... dust? X=@iq2[-gfxg]+gfxg } Tree33 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 4; Tree1, angle changed to 4, @ to inverse of sqrt 2 - axiom +fx; a pseudo-spacefilling tree X=@iq2[-ffx]+fx } Tree33c { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 4; Tree1, angle changed to 4, @ to inverse of sqrt 2 - axiom +fx; a pseudo-spacefilling tree (colour version) X=@iq2[>1-ffx]<1+fx } Tree34 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 4; Tree1, angle changed to 4, @ to inverse of sqrt 2 - axiom +fx; a pseudo-spacefilling... dust? X=@iq2[-fgfx]+fx } Tree35 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 12; Tree1, angle changed to 12, @ to inverse of sqrt 2 - axiom +++fx; X=@iq2[--ffx]++fx } Tree36 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 12; Tree1, angle changed to 12, @ to inverse of sqrt 2 - axiom +++fx; X=@iq2[--fgfx]++fx } Tree37 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 8; Tree1, angle changed to 8, @ to inverse of sqrt 2 axiom +fx; X=@iq2[--ffx]+fx } Tree38 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 8; Tree1, angle changed to 8, @ to inverse of sqrt 2 axiom +fx; X=@iq2[--fgfx]+fx } Tree39 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 8; Tree1, angle changed to 8, @ to inverse of sqrt 2 axiom +fx; X=@iq2[-ffx]++fx } Tree40 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 8; Tree1, angle changed to 8, @ to inverse of sqrt 2 axiom +fx; X=@iq2[-fgfx]++fx } Tree50 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 6; Tree1, axiom fx; X=@iq2[--fx]+fx } Tree51 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 6; Tree1, axiom fx; X=@iq2[--fx]++fx } Tree52 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 6; Tree1, axiom fx; X=@iq2[--fx]-fx } Tree53 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 6; Tree1, axiom fx; X=@iq2[-fx]++fx[-fx] } Tree54 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 6; Tree1, axiom fx; X=@iq2[--fx]++fx[--fx] } Tree55 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 6; Tree1, axiom fx; X=@iq2[--fx][++fx]--fx } Tree56 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 6; Tree1, axiom fx; X=@.615[-fx]+@i.615fx } Tree57 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 4; Tree1, axiom +fx; X=@iq2[-fx]+@q2fx } Tree58 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 3; Tree1, axiom fx; X=@.615[-fx]+fx } Tree59 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 3; Tree1, axiom fx; X=@.615[-gx]+fx } Tree60 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 4; Tree1, axiom +x; a spacefilling tree x=f@iq2[-x!]+fx } Tree61 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 4; Tree1, axiom x; x=f@iq2[-x]!+fx } Tree62 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 4; Tree1, axiom +x; x=f@.68[+x!]+fx } Tree63 { ; Anthony Hanmer 2001, adapted from Adrian Mariano's angle 4; Tree1, axiom +x; a spacefilling tree x=f@iq2[+x]!+fx } Plant01a { ; Adrian Mariano, from the Algorithmic Beauty of Plants ; Plant-like structure, figure 1.24a p.25 ; also p.285a The Science of Fractal Images angle 4 axiom +f f=F[+F]F[-F]F } Plant01b { ; Adrian Mariano, altered by Anthony Hanmer 2001 angle 4 axiom +f f=F[+F]F[-F] } Plant01c { ; Adrian Mariano, altered by Anthony Hanmer 2001 angle 4 axiom +f f=F[+F]@iq2F@q2[-F]F } Plant01d { ; Adrian Mariano, altered by Anthony Hanmer 2001 angle 4 axiom +f f=[+F]F[-F]F } Plant01e { ; Adrian Mariano, altered by Anthony Hanmer 2001 angle 4 axiom +f f=F[+F]+F[+F]-F } Plant01f { ; Adrian Mariano, altered by Anthony Hanmer 2001 angle 4 axiom f+f+f+f f=F[+F]+[-F]-F } Plant01g { ; Adrian Mariano, altered by Anthony Hanmer 2001 angle 4 axiom +f f=F[+F]-[-F]+F } Plant01h { ; Adrian Mariano, altered by Anthony Hanmer 2001 angle 4 axiom f f=F[+F]@.5F@2[-F]F } Plant01i { ; Adrian Mariano, altered by Anthony Hanmer 2001 angle 6 axiom f f=F[+F]F[-F]F } Plant01ia { ; Adrian Mariano, altered by Anthony Hanmer 2001 angle 6 axiom [f]+[f]+[f]+[f]+[f]+[f] f=F[+F]F[-F]F } Plant01j { ; Adrian Mariano, altered by Anthony Hanmer 2001 angle 6 axiom f f=F[+F]F[-F] } Plant01ja { ; Adrian Mariano, altered by Anthony Hanmer 2001 angle 6 axiom [f]++[f]++[f] f=F[+F]F[-F] } Plant01jb { ; Adrian Mariano, altered by Anthony Hanmer 2001 angle 6 axiom [f]+[f]+[f]+[f]+[f]+[f] f=F[+F]F[-F] } Plant01k { ; Adrian Mariano, altered by Anthony Hanmer 2001 angle 6 axiom f f=F[+F]@iq2F@q2[-F]F } Plant01ka { ; Adrian Mariano, altered by Anthony Hanmer 2001 angle 6 axiom [f]+[f]+[f]+[f]+[f]+[f] f=F[+F]@iq2F@q2[-F]F } Plant01l { ; Adrian Mariano, altered by Anthony Hanmer 2001 angle 6 axiom f f=[+F]F[-F]F } Plant01m { ; Adrian Mariano, altered by Anthony Hanmer 2001 angle 6 axiom f f=F[+F]+F[+F]-F } Plant01ma { ; Adrian Mariano, altered by Anthony Hanmer 2001 angle 6 axiom [f]+[f]+[f]+[f]+[f]+[f] f=F[+F]+F[+F]-F } Plant01mb { ; Adrian Mariano, altered by Anthony Hanmer 2001 angle 6 axiom [f--f]+[f--f]+[f--f]+[f--f]+[f--f]+[f--f] f=F[+F]+F[+F]-F } Plant01n { ; Adrian Mariano, altered by Anthony Hanmer 2001 angle 6 axiom f+f+f+f+f+f f=F[+F]+[-F]-F } Plant01o { ; Adrian Mariano, altered by Anthony Hanmer 2001 angle 6 axiom f f=F[+F]-[-F]+F } Plant01p { ; Adrian Mariano, altered by Anthony Hanmer 2001 angle 6 axiom f f=F[+F]@.5F@2[-F]F } Plant01pa { ; Adrian Mariano, altered by Anthony Hanmer 2001 angle 6 axiom [f]+[f]+[f]+[f]+[f]+[f] f=F[+F]@.5F@2[-F]F } Plant02 { ; Adrian Mariano, altered by Anthony Hanmer 2001 angle 4 axiom +f f=F[+F]F[-F][F] } Plant03 { ; Adrian Mariano, altered by Anthony Hanmer 2001 angle 4 axiom f f=FF-[-F+F]+[+F-F] } Plant05 { ; Adrian Mariano, altered by Anthony Hanmer 2001 angle 4 axiom +x X=f[+X][-X]FX F=FF } Plant07 { ; Ken Philip, altered by Anthony Hanmer 2001 axiom +Z Z=ZGX[+Z][-Z] X=X[-FFF][+FFF]FX angle 4 } Plant07a { ; Ken Philip, altered by Anthony Hanmer 2001 axiom +Z Z=ZGX[+Z][-Z] X=X[-GFG][+GFG]FX angle 4 } Plant10a { ; Adapted from Adrian Mariano's Plant10, Anthony Hanmer 2001: axiom +f ; a tile f=f[+ff][-f]f[+f][-ff]f angle 4 } Plant10aa { ; Adapted from Adrian Mariano's Plant10, Anthony Hanmer 2001: axiom c9f+c10f+c12f+c14f ; a tile f=f[+ff][-f]f[+f][-ff]f angle 4 } Plant10b { ; Adapted from Adrian Mariano's Plant10, Anthony Hanmer 2001 axiom +f f=f@2[+f]@.5[-f]f[+f][-f]f angle 4 } Plant10c { ; Adapted from Adrian Mariano's Plant10, Anthony Hanmer 2001 axiom +f f=f@2[+f][-f]f[+f][-f]@.5f angle 4 } Plant10d { ; Adapted from Adrian Mariano's Plant10, Anthony Hanmer 2001 axiom +f f=f@q2[+f][-f]f[+f][-f]@iq2f angle 4 } Bush01 { ; adapted from Adrian Mariano's Bush, Anthony Hanmer 2001 Angle 4 Axiom +F F=FF-[-F+G+F]+[+F-G-F] } Bush01a { ; adapted from Adrian Mariano's Bush, Anthony Hanmer 2001 Angle 4 Axiom F+F+F+F F=FF-[-F+G+F]+[+F-G-F] } Bush01b { ; adapted from Adrian Mariano's Bush, Anthony Hanmer 2001 Angle 4 Axiom [F]+[F]+[F]+[F] F=FF-[-F+G+F]+[+F-G-F] } Bush02 { ; adapted from Adrian Mariano's Bush, Anthony Hanmer 2001 Angle 4 Axiom +F F=FF-[-F+G+]+[+F-G-] } Bush02a { ; adapted from Adrian Mariano's Bush, Anthony Hanmer 2001 Angle 4 Axiom [F]+[F]+[F]+[F] F=FF-[-F+G+]+[+F-G-] } Bush03 { ; adapted from Adrian Mariano's Bush, Anthony Hanmer 2001 Angle 4 Axiom +F F=FF+[-F-FG]-[+F+FG] } Bush03a { ; adapted from Adrian Mariano's Bush, Anthony Hanmer 2001 Angle 4 Axiom F++F F=FF+[-F-FG]-[+F+FG] } Bush03b { ; adapted from Adrian Mariano's Bush, Anthony Hanmer 2001 Angle 4 Axiom [F]++[F] F=FF+[-F-FG]-[+F+FG] } Bush04 { ; adapted from Adrian Mariano's Bush, Anthony Hanmer 2001 Angle 6 Axiom F F=FF-[-F+G+F]+[+F-G-F] } Bush05 { ; adapted from Adrian Mariano's Bush, Anthony Hanmer 2001 Angle 6 Axiom F F=FF--[-F+G+]++[+F-G-] } Bush05a { ; adapted from Adrian Mariano's Bush, Anthony Hanmer 2001 Angle 6 Axiom [F]+[F]+[F]+[F]+[F]+[F] F=FF--[-F+G+]++[+F-G-] } Bush06 { ; adapted from Adrian Mariano's Bush, Anthony Hanmer 2001 Angle 6 Axiom F F=FF-[-F+G+]+[+F-G-] } Bush06a { ; adapted from Adrian Mariano's Bush, Anthony Hanmer 2001 Angle 6 Axiom F+++F F=FF-[-F+G+]+[+F-G-] } Bush06b { ; adapted from Adrian Mariano's Bush, Anthony Hanmer 2001 Angle 6 Axiom F+F+F+F+F+F F=FF-[-F+G+]+[+F-G-] } Bush06c { ; adapted from Adrian Mariano's Bush, Anthony Hanmer 2001 Angle 6 Axiom [F]++[F]++[F] F=FF-[-F+G+]+[+F-G-] } Bush06d { ; adapted from Adrian Mariano's Bush, Anthony Hanmer 2001 Angle 6 Axiom [F]+[F]+[F]+[F]+[F]+[F] F=FF-[-F+G+]+[+F-G-] } Bush07 { ; adapted from Adrian Mariano's Bush, Anthony Hanmer 2001 Angle 6 Axiom F F=FF--[-F+G+F]++[+F-G-F] } Bush07a { ; adapted from Adrian Mariano's Bush, Anthony Hanmer 2001 Angle 6 Axiom [F]++[F]++[F] F=FF--[-F+G+F]++[+F-G-F] } ____________________________ TTiles.l _README {; Anthony Hanmer 2000-2002 Angle 4; Miscellaneous tiles, some of them perhaps not new. Axiom f f=f } ADH0794 { ; Anthony Hanmer 2000 Angle 6 ; a tile Axiom f f=+@.5ff+++ff++@2g } ADH01782 { ; Anthony Hanmer 2000 Angle 4 ; DC type Axiom f f=ff++f+f+f } adh6280 { ; Anthony Hanmer 2001 Angle 3 ; a tile; rounding needed Axiom f ;Axiom c9f+c12f+c14f; 3 colours ;Axiom c32[f]+c35[f]+c39[f]+c42[f]+c44[f]+c2[f]; 6-coloured star f=f+f-f-f+f+f-f ;f=>1f+f-f-f+f+f-<1f; colour 1 } adh6543 { ; Anthony Hanmer 2001 Angle 4 ; a new tile! Axiom f ; (though massively layer-redundant, or mlr) ;Axiom c9f|c12f f=+!ff|ff-!@2f@.5 ;f=+!>1ff|ff-!@2<1f@.5; colour 1 ;Axiom x ; (6543 using x instead of f) ;x=+!fx|fx-!@2f@.5 ; Rhombic tile of 1:2 bricks } adh6544 { ; Anthony Hanmer 2001 Angle 8 ; The new tile's Angle can be changed Axiom f ; (mlr) f=+!ff|ff---!@2f@.5 } adh6545 { ; Anthony Hanmer 2001 Angle 8 ; The new tile's Angle can be changed Axiom f ; (mlr) f=+++!ff|ff-!@2f@.5 } adh6672 { ; Anthony Hanmer 2001 Angle 4 ; a tile Axiom +x x=f[@.5x]+![@.5x]+!+!f[@.5x]-![@.5x] ;x=>1f[@.5x]+![@.5x]+!+!f[@.5x]-![@.5<1x]; colour 1 } adh6748 { ; Anthony Hanmer 2001 Angle 4 ; tile w/td"vines", sides ratio 1:GR Axiom x x=f+![@.6180339887499x]+[@.6180339887499x]|[@.6180339887499x] ;x=>1f+![@.6180339887499x]+[@.6180339887499x]|[@.6180339887499<1x]; colour 1 } adh8320 { ; Anthony Hanmer 6/2002 Angle 3 ; nice overlapping hex tile Axiom f f=f+@2f@.5-f ;f=>1f+@2f@.5-<1f; colour 1 } adh8735a { ; Anthony Hanmer 7/2002 Angle 6 ; a hexagonal (tile) echo of 8735 Axiom f f=f+f|@2f@.5|f-f ; Hausdorff dimension: log(5)/log() = } adh9622 { ; Anthony Hanmer 19/10/2002 Angle 6 ; I BELIEVE this is a tile... Axiom f ; but it's hard to prove. f=f++f--g++f|f--g++f+g g=gg } T325 { ; Anthony Hanmer 2000 Angle 4 ; DC type Axiom f;+f+f+f ;Axiom c9f-c10f-c12f-c14f; colour 1 ;Axiom c09f-c12f-c09f-c12f--c14f+f+f+f; colour 2 f=f-ff++f-f } _________________________________________________________________ The new MSN 8: advanced junk mail protection and 2 months FREE* http://join.msn.com/?page=features/junkmail

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FOTD 27-01-04 (Bouquet of Numbers [8])
by Jim Muth 27 Jan '04

27 Jan '04

FOTD -- January 27, 2004 (Rating 8) Fractal visionaries and enthusiasts: After yesterday's exciting adventure in the world of Z^1.003, I decided to subtract Z^(1.003) from Z^(-1.003) and explore the fractal world created by this combination. Before starting, I had to decide on the escape radius, which has a significant effect on fractals in this range. I chose the escape radius of 250 entirely at random. Apparently, I chose well. The image I found rates an 8 and has an overall value of 43. The resulting parent fractal is an almost-symmetrical Mandeloid rotated 90 degrees. Perhaps I should describe the parent as part of a Mandeloid, for the northern area of the Mandeloid is obliterated by the blue disk that usually appears at the origin of fractals with negative exponents of Z, and is likely an artifact. It's no problem however, because today's scene is located in the East Valley area, which lies on the south side of the Mandeloid. Much of the flowery effect resulted from rendering the scene with the outside set to 'summ' rather than the usual 'iter'. The name "Bouquet of Numbers" came to me as I sat in wonder that all this came from such a simple beginning. The render time of 18 minutes is bearable, but a far better way of viewing the image is to download it from Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With the yard buried 20cm deep in snow and ice, and the tempera- ture lurking around 19F -7C, the fractal cats passed an unevent- ful day Monday curled by the nearest source of heat. Today is starting with freezing drizzle, so I predict another uneventful day for the cats. For me, the work is pretty much caught up. Combined with the abysmal outside conditions, this should give me plenty time to ensconce myself indoors and find another good fractal. If I do, the fractal will appear as tomorrow's FOTD. Until then, take care, and beware of extrasensory fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Bouquet_of_Numbers { ; time=0:18:46.52--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+0.00045100966909858/-0.356152672378903\ 30/6.50686e+009/1/90/3.88578058618804789e-016 params=-1/1.003/1/-1.003/0/150/0/0 float=y maxiter=3000 inside=0 outside=summ periodicity=10 colors=000fbZfb_fc_fc`fd`fe`feaffaffbfgbfgcfhcficf\ idfjdfjefkefkedhfcffbdgabg`_h_YhZWhYUiXRiWPjVNjULj\ TIkSGkRElQClR8kPAlOBlNDmMEmLFnJHnIIoHJoGLpFMpDNpCP\ qBQqARr9Tr7Us6Vs5Xt4Yt0_z2Zw3Zt4Zq5Zn6Zk8Zh9ZeAZbB\ Y`UYYUYVXZSX_P_`M`aJcbGccEhbGh`Ic_KcZMZYNZXPXVRXVT\ UTVUUFUUOUSWSIdQBo39l48i47f55c64`52Y63Z74_85`96`A7\ aA8bB9bCAcDAdEBdECeFDfGEfHFgIGhIHiJIiKIjLJkMKlMLnN\ MpONqPOsQPuSQxRPvQPtPPsOOqNOpMOnMNlLNlKNkJMkIMjHMj\ HLiGLhFLhEKgDKgCKfDHdCKfBNgAQh9Ti9Wk8Zl7am6dn3gq6f\ o8fnBemDelGekIdiLdhNdgQcfSceUcdXbbZbaaa`ca_faZh`Xk\ `Wm`Vp_Ur_Tt_SvaRxbRzfR000000000000HDHHJEHSBH_8Hf5\ Hn2Ld6PZ9TWDXWG`TKdQNhORlLUpIYsG`tIatKatLatNbtObtQ\ btRctTctUctWduXduZdu_euaeubeudfuefugfuhgujgukgvhev\ fdvdcwbbw_awY_xWZxUYxRXyPWyNUyLTzISzGRzEQzCPyERyGS\ yHTxJUxLWxMXxOYwQZwR`wTawUbvWcvYdvZfu`gubhuciuektg\ luinukovmqtmqsmqrnrqnrmhe } 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 } END 20.0 PAR-FORMULA FILE==================================

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Golden Ratio and related plants
by Tony (Anthony) Hanmer 27 Jan '04

27 Jan '04

The Golden Ratio, also known as the Greek letter phi (pronounced "fee") and several other names, is indeed a fascinating number. It is approximately 1.1680339887499; or is it this number minus 1? Anyway, it is the only answer to the question, Which number satisfies *both* 1/x = x-1 and x^2 = x+1?... Wild. It is also calcualted as ((sqrt 5)-1)/2. It appears in numerous surprising places in nature as well, such as angles of packing of sunflower seeds and ratios of flower petals in many species. I have used the GR in a series of L-systems, where in many cases it acts as a limit, allowing growth to approach a certain point but not overlap. At http://spanky.triumf.ca/pub/fractals/params/ There is a file, gr_iq2_pl.zip, containing 2 files - grpl.l and griq2pl.l The first of these uses the GR, the second the average of the GR and the inverse of the square root of 2. Some examples appear below. Paste them into a text editor, call the file griq2.l, put it into your Fractint directory and it'll be ready to use as type Lsystem. Unzip these files into your Fractint directory and they're ready to be used as type Lsystem. Enjoy. And please let me know what you think or if you have any questions. This is also the place to mention some ideas about colouring L-systems. One way to really jazz up an otherwise flat L-system can be the following type of colouring variation: Before the first f, put >1, making it >1f Before the last f, put <1, making it <1f Other combinations are possible, such as <1/>1, or if there are 4 fs, >1f >1f <1f <1f >1f <1f >1f <1f >1f <1f <1f >1f I use this a few places in the above files, and much alsewhere also. Try it for yourself. I have coloured versions of many old spacefilling curves, the Dragon Curve and TwinDragon, etc. Tony Hanmer Tbilisi, Republic of Georgia pl03-- { ; Anthony Hanmer 2001 Angle 3; Golden Ratio plant series Axiom x x=f[+!@.6180339887499x-x] } pl03a { ; Anthony Hanmer 2001 Angle 3; Golden Ratio plant series Axiom x x=f[+@.6180339887499x!-x]! } pl04+ { ; Anthony Hanmer 2001 Angle 4; Golden Ratio plant series Axiom x x=f[+@.6180339887499x!+x] } pl04+++ { ; Anthony Hanmer 2001 Angle 4; Golden Ratio plant series Axiom x x=f[+!@.6180339887499x!+x] } pl04b { ; Anthony Hanmer 2001 Angle 4; Golden Ratio plant series Axiom x x=f[+@.6180339887499x!-x]! } pl05++ { ; Anthony Hanmer 2001 Angle 5; Golden Ratio plant series Axiom x x=f[+!@.6180339887499x+x] } pl06- { ; Anthony Hanmer 2001 Angle 6; Golden Ratio plant series Axiom x x=f[+@.6180339887499x!-x] } pl06+ { ; Anthony Hanmer 2001 Angle 6; Golden Ratio plant series Axiom x x=f[+@.6180339887499x!+x] } pl08+++ { ; Anthony Hanmer 2001 Angle 8; Golden Ratio plant series Axiom x x=f[+!@.6180339887499x!+x] } pl08-c1 {; Anthony Hanmer 2001 Angle 8; Golden Ratio plant series Axiom x; colour 1 x=f[+@.6180339887499>1x!-x] } pl08e { ; Anthony Hanmer 2001 Angle 8; Golden Ratio plant series Axiom x x=f[+@.6180339887499x!-x!-@.6180339887499x] } pl12a { ; Anthony Hanmer 2001 Angle 12; Golden Ratio plant series Axiom x x=f[+@.6180339887499x!+++++x] } pl16- { ; Anthony Hanmer 2001 Angle 16; Golden Ratio plant series Axiom x x=f[+@.6180339887499x!-x] } pl16+++ { ; Anthony Hanmer 2001 Angle 16; Golden Ratio plant series Axiom x x=f[+!@.6180339887499x!+x] } pl24+ { ; Anthony Hanmer 2001 Angle 24; Golden Ratio plant series Axiom x x=f[+@.6180339887499x!+x] } pl24b { ; Anthony Hanmer 2001 Angle 24; Golden Ratio plant series Axiom x x=f[+@.6180339887499x+x+x!+@.6180339887499x+x+x]! } _________________________________________________________________ The new MSN 8: smart spam protection and 2 months FREE* http://join.msn.com/?page=features/junkmail

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Derivations
by Tony (Anthony) Hanmer 27 Jan '04

27 Jan '04

The file derivations.zip at http://spanky.triumf.ca/pub/fractals/params/ contains the following L-systems files: alfovar.l feather.l leafvar.l m09vars.l schnvar.l t034ifs!.l These are some of my early variations on the L-systems of others. As I began exploring the amazing world of L-systems programming, this was a great way for me to play and to learn. I appreciate the opportunity to build on other people's hard work and still produce something new, recognising that I am only altering an existing L-system. (Some examples appear below. Paste them into a text editor, call the file deriv.l, put it into your Fractint directory and it'll be ready to use as type Lsystem.) I also wish to thank especially William McWorter and Morgan Owens for some very useful correspondence over the last few years which has helped me with some key questions usually relating to L-systems. I STILL have lots of blank spots in my understanding, but that's not your fault! THANK YOU VERY MUCH. Tony Hanmer Tbilisi, Republic of Georgia Alfonseca029 { ; Manuel Alfonseca rendered for fractint Angle 4 ; altered by Anthony Hanmer 2001 Axiom +A A=f-[A+A]+f[+fA]A f=ff } Alfonseca097 { ; Manuel Alfonseca rendered for fractint Angle 12 ; altered by Anthony Hanmer 2001 Axiom A A=f-[A+A]+!f[+!fA]-A f=ff } Alfonseca120 { ; Manuel Alfonseca rendered for fractint Angle 16 ; altered by Anthony Hanmer 2001 Axiom A A=f-[A+A]+f[+fA]-!A f=ff } _________________________________________________________________ Tired of spam? Get advanced junk mail protection with MSN 8. http://join.msn.com/?page=features/junkmail

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FOTD 26-01-04 (Spiral Mesa [8])
by Jim Muth 26 Jan '04

26 Jan '04

FOTD -- January 26, 2004 (Rating 8) Fractal visionaries and enthusiasts: In the discussion of the "Whirling Devilish" fractal of two days ago I remarked about the straight edge cutting through the upper right portion of the image. I commented that some very unusual chaos lies in this area but that the exploration there is too slow to be practical. Well, for today's image I have turned impractical and wandered into the chaos along the straight-edge. Today's FOTD is what I found there. I have rarely seen an image with such contrasting parts, the dull reddish rocky lower part contrasting as starkly as it does with the ethereal blue celestial spiral filling the upper part. The lower part of the picture reminds me of one of those mesas found in the southwest desert area of the U.S. The upper part reminds me of nothing other than a fractal spiral. Combining the two impressions, I named the image "Spiral Mesa". I feel that the rating of an 8 is justified, though the extreme slow- ness holds the overall value to a lowly 4. Perhaps the most incredible thing about the image is that it is produced by Z^1.003. The graph of this expression is basically a straight line, and linear expressions do not make fractals. It is only at very large values of Z that the slight curve in the graph becomes noticeable, which is why a maxiter of 20000 is necessary to reveal the chaos. An unfortunate effect of the high maxiter is the 3-hour render time. The wait can be eliminated however by downloading the completed GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> I sent the image file to Paul several hours ago, so the image should be posted shortly after he receives this discussion. As a matter of interest, I made a 0.65-degree change in the rotation of the image since I sent it. This was done so that the border between sky and mesa would be level. To see a perfectly straight horizon, run the parameter file; to see the image without a wait of several hours, download it. The only difference is in the orientation, which is barely noticeable. Thickening clouds and cold temperatures prevailed all day here at Fractal Central on Sunday. The high temperature of 18F -8C and lack of sun kept all thoughts of outdoors from the minds of the fractal cats. They were quite content to lie by the heat source and occasionally ask for food. This morning we have 6in 15cm of fresh snow on the ground and a temperature of 17F -8C, which makes the outdoor conditions worse. The forecast is for freezing rain, sleet and more snow. I feel sorry for the duo. There is no reason to feel sorry for myself however. The work is caught up, leaving me little to do but sweep the powdery snow and explore the world of fractals. Until next time, take care, and don't forget to remember. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Spiral_Mesa { ; time=3:08:09.19--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=+0.84105158773950410/-0.082216007167982\ 33/10307.65/1/-176.85/6.14521628028441569e-012 params=1.003/0/1040/1500 float=y maxiter=20000 inside=255 logmap=4824 periodicity=10 colors=000_00ODNQCMPBLT9JU8IV7HX5GY4FX2FZ3EZ4D_4D_\ 5C`6BW6BY7AZ8A_89a98bA8dA7eB7bC6hC5eD5kE4hF3lE4gR5\ lE6gT7kE8aD9kDAfDBkDCjQDjDEeOFjCG_CHiCIiRJiCKdULhU\ McBNhBOcBPhBQbCPgDPgPPgPOgQOgUObUOgUNbUNgUNgYNgUMg\ NMgNMYOMgPLgQLgRLYSLgTKgTKgUKgVKgWJhXJiYJg0EkYJa1N\ qYSdJWvY`wUexYddIcxdbyAayk`yo_yrZrnUkkQdhMYeIRbEK_\ ALZCMYEMYFNXHNWIOWKOVLPVNPUPQTQQTSRSTRSVSRWTQYTQ_U\ P`UPbVOcVNeWNfWMhXMjXLkYKmYKnZJpZJq`KpaLpbMpdNoeOo\ fPohQoiRnjRnlSnmTmnUmpVmqWmrXltYluZlvZltYmrYmqXmoX\ mmXmlWmjWmhWmgVmeVmdUmbUm`Um_TmYTmWTnVSnTSnRSnQRnO\ RnNQnLQnJQnIPnGPnEPnDOnBOnAOnEQpIRqJQtLSuMTvNVwOWx\ PXyRZzS_zTazUbzVczXezYgzZiz_kz`mzbozcpzdqzerzfszht\ ziuzjvzkwzlwzkwzjvziuzhtzgszfrzeqzdpzcozbnzamz`lz`\ kz_jzZizYgzXezWczVazU_zTYzSWzRUzQUzPUzQUzRUzSUzTUz\ UUzVUzWUzTUzQUzNVzLWzI_zFdzDhzAlz7pz5tzCuzIvzOwzVw\ z`xzfyznzzlyzjxzhwzfvzemz } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(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 } END 20.0 PAR-FORMULA FILE==================================

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Graphics card for Fractint
by fracwood＠argonet.co.uk 26 Jan '04

26 Jan '04

Fractaliers My long used 32MB Matrox millenium G400 graphics card which has supported my 1600x1200 use of Fractint for many years failed this week and in my haste to get back computer function I purchased an Nvidia GForce Max 400( not much choice) card inexpensively from a local computer store. I was surprised to find that not only would this card nor run Fractint but it would not allow any DOS programs to be run. Under Windows 98SE on my 1Ghz Athlon Thunderbird PC it does support all the modes allowed by the monitor upto 1600x1200. After opening DOS from from the Windows Shutdown menu and attempted to run Fractint or a smaller DOS appliication the message that is displayed indicates there is not enough memmory. Attempts to run DOS apps. from Windows similary indicate there is not enough memory. Clearly with 768 MB RAM and no other applications this message means something else. Presumably since the DOS MEM /c/p command shows 455 K of usable memory the problem is that the driver software for the Nvidia card does not load any DOS drivers. Does anyone know if there are DOS drivers for this card and if not what alternative choice of inexpensive card is now available( does the Matrox G550 support Fractint?) .The Matrox G400 seems to be no longer available. Ian Entwistle --

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Re: [Fractdev] No bailout in bjax formula?
by Edwin 26 Jan '04

26 Jan '04

On Sun, 2004-01-18 at 10:13, Paul N. Lee wrote: > Edwin wrote: > > > > Looking at the fractint.frm which comes with > > xfractint 3.10, the "bjax" formula is: > > > > Have you tried using the later versions instead of the very old 3.10 ?? Good idea. I downloaded the latest-and-greatest 20.3 just now. BTW freshmeat.net still links to 3.10 as the latest version -might be worth updating that. This version doesn't have any .frm files included - is that deliberate? Copying fractint.frm from the previous version, I get the same results as before. Following Jonathan's suggestion, I get something (if not anything all that interesting) if I set the inside coloring method. Thanks, -- Edwin

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On a Jim Muth-SherLok Merfy-Osher Doctorow Debate?
by mdoctorow＠comcast.net 26 Jan '04

26 Jan '04

>From Osher Doctorow Ph.D. In replying to a member of Fractint who was interested in my Deformation and other postings, I also happened to reply to Jim Muth's posting that included comments on Precognition. SherLok Merfy then replied to my reply which latter reinterpreted Precognition as Telepathy and Clair- voyance in the part that referred to Jim Muth's posting, although Merfy apparently didn't include his opinions if any on Deformation mathematics and physics regarding fractals. The main thrust of my Deformation and other postings has had nothing to do with Precognition, Telepathy, clairvoyance, and what I mentioned in my last Deformation posting was that in effect I wouldn't submit any more Deformation postings unless other member(s) were interested as a courtesy to members of Fractint. This is what mainly interests me, not Precognition, Telepathy, or Clairvoyance. Having said all that, I did praise Jim Muth in my reply for having the courage to go against the Mainstream by indicating his interest in Precognition. I still think that he is quite courageous. SherLok Merfy's reply to my reply contains both excellent ideas on unlikely knowledge and senses that are often neglected by science and some opinions that I'm not in agreement with. To save space, I'll discuss those opinions of his that I'm not in agreement with, and readers can read his reply if they want to for his excellent ideas. Merfy indicates that a lot of self-professed clairvoyants are mental patients which says nothing about probability of fraud (almost quoting him word for word) and indicates that no one has been able to demonstrate direct image transmission from mind to mind. He is technically correct, but unfortunately there is a world of difference between the "letter of science" and the "spirit of science" or in other words the "deeper ideas of science". For those who don't know, this terminology comes from the expression "the letter of the law versus the spirit of the law," which you might want to look up on the internet if you haven't seen it before. My wife Marleen J. Doctorow Ph.D. is a licensed clinical psychologist with the State of California and has been in practice for several decades (we've been married almost 4 decades - perhaps a record for many professionals in the 50% or so divorce rate fad nation). She is one of the best psychologists in California. I don't think that, being married to her for almost 4 decades, it is very likely that I fall under the category of "mental patients", so it isn't necessarily true that somebody who thinks that Telepathy and Clairvoyance may or probably do exist is a mental patient. I am, however, a Nonconform- ist, which in the modern world is close to having the negative interpretation of being a mental patient - not that Merfy claimed that I'm a mental patient. Mental patients actually fall into two very important categories (and even more than two, but these two are important): A. Paranoid, B. Depressive. In simple language, using the psychoanalysis of Melanie Klein, the Paranoid position is Anger/Hatred Against Others, while the Depressive position is Anger/Hatred Against Oneself. Kleinian psycho- analysis, one of the most respected branches of psychoanalysis, has found that Depressives can usually be cured if they're treated early enough, while Paranoids can't because they hate the Psychiatrist and/ or Psychologist. Contrary to common belief, Paranoia and Depression aren't limited to mental patients in hospitals or doctor's offices - they range in "degree" from character disorders that are quite common both in and out of the academic world to neuroses that are often treated in an outpatient way to psychoses which usually require inpatient treatment in hospitals (although hospitals have their own problems due to overcrowding and so, and hospitalization is often far from an ideal solution other than preventing the psychotic from injuring anybody including himself/herself). So even if many self-professed Clairvoyants or Telepaths are mental patients, it's also true that many educated people are mental patients with or without belief in Clairvoyance or Telepathy, while many less educated people should have treatment but don't have the education to realize it. In fact, an amusing thing about the word "Normal" in comparing oneself with "Abnormal" mental patients is that according to clinical psychologists and psychiatrists, most people need some type of psychological or psychiatric treatment. You might like to look up "Character Disorders" on the internet as keywords to see some perhaps familiar examples of people who need treatment, including some professors and students who "keep on trucking" without being much interested in where they're heading. I don't think that human beings have much if any Telepathy or Clair- voyance, and certainly there's no evidence that they exert control over it or that Telepathy or Clairvoyance exert control over human beings. However, I think that somebody who thinks that it exists or might exist is a Nonconformist, and not a harmful Nonconformist such as a rapist or murderer. It might even help us in the rare event that humanity ever contacts a species in outer space which does have senses beyond human senses - perhaps senses similar in some ways to Telepathy or Clairvoyance. That is to say, it might help us in space exploration if we consider the possibility and the scenarios in which other possible species have very different senses and abilities from our own. Where Telepathy and Clairvoyance beliefs become dangerous is if one believes that "a dog is controlling me," or "somebody else's mind is controlling me," or "the devil made me do it," etc. Educated people do not tend to believe this, and seem to believe it less the more educated they are, which is fortunate for all of us. Occasionally a "semi-educated" person with considerable knowledge in one narrow field but little in other fields goes "off his/her rocker", though, and believes that he/she is controlled by or controls others. Bin Laden is possibly an example among others. Osher Doctorow

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FOTD 25-01-04 (The Best Dressed [6])
by Jim Muth 25 Jan '04

25 Jan '04

FOTD -- January 25, 2004 (Rating 6) Fractal visionaries and enthusiasts: The number one mystery of the day is why fractals exist. The number two mystery is why anyone would open an e-mail with a subject line such as 'blnfus fgoiun sheub ksnfiyve'. And the number three mystery is why so many of my FOTD fractals rate a 6. Today's image rates a 6. There is nothing wrong with a rating of 6 -- it's the rating I give to the greatest percen- tage of my FOTD's -- kind of like getting a 'B' grade in school. But what I want is a series of un-inflated A's and A+'s. The most frequent FOTD rating is a 6, which is a slightly-above- average fractal. Admittedly, this situation is a bit contradic- tory. How can an above-average rating be considered a group average? Well, if 90 percent of the kids in the local school can be far enough above average to be on the honor roll, why not 90 percent of the FOTD fractals? :-) Combined with a render time of 7-3/4 minutes, today's image has an overall worth of 80. It is a scene in the fractal created by combining 0.25 negative parts of Z^(-5.1) with one negative part of Z^(-1.5) and adding (1/C). This parent fractal is one of the typical amorphous things crea- ted by negative powers of Z. It consists of a large irregular bay with a prominent bud on the southwest shore. The southern valley leading to this bay is split into two sections, which made it unusual enough for me to examine closer. The closer examination proved fruitful. The area proved to be rich with midgets of a new variety, strangely similar yet strangely different. Today's image is a sample of what lies in this newly-discovered part of the fractal multiverse. I named the image "The Best Dressed". Whether it is actually best-dressed or not is up to the viewer to decide. But before making such a decision, one must view the object in question, and the way to view the object is to run the included parameter file or download the completed GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Light fluffy snow fell until midday here at Fractal Central on Saturday. When it ended, 5-cm of fluffy snow was on the ground and the fractal cats were completely unhappy. The temperature of 25F -4C would have been too cold for their ears even if the ground had been bare. Today is even colder, the temperature is 14F -10C, the snow is still there, and much more snow is coming. I have yet to break the bad news to the not-so-dynamic duo. As for me, I'm ready to have a relaxing day doing as little as possible. I might find a great fractal or two in between spells of relaxation. And in 24 hours I will return with the best fractal that I find. Until then, take care, and the fact that we can give no reason for fractal existence does not mean that no reason exists. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Best_Dressed { ; time=0:07:48.46--SF5 on a p200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=-0.13405699332489620/-2.142627954268001\ 00/1428134/1/-75/-5.16187510977983433e-007 params=-1/-1.5/-0.25/-5.1/0/0/0/0 float=y maxiter=1000 inside=0 logmap=149 periodicity=10 colors=000000000000gdZid`kbambbo`dq`eq_fq`hp`ho`kn\ `klankanjapiargbsfbtebvdbwactZcrWcrTcmQcoOciLcjIcd\ FcfCc`AcZA7_99d9Bh9Dl9Fp9GtALtBQtBUuCZsCcqDgoDlnEq\ mEumwIDzXEzkFxrGweDw`AwP7oTIgWT_ZcTanRZmQWlOTkNRkL\ OjKLiJJiMLhPNhSPgVRgYSf`UfcWffYei_el`dobdrhcuicxrc\ vo`ulYsiVrfSpcPoaMm`Jl_GaSSRLbGDn66y55w55v45u44t34\ r34q33p23o23m12l12k12j97nGBqNFtMJsMMsMQrLTrLXqL_qK\ bpKfpKioJmoJpnJsnMohPlbSiXVeRYbL`_FbX9aVDaUGaSJaRN\ aPQ`OT`MX`L_`Jb`IeaJbbJ`cJZdJXeJVfJTgJQhJOiJMjJKkJ\ IlJGmKElPDlUDlZClcCkhBkmBkrAkrAkwAjjCiiEhgGhfIgeKf\ cMfbOe`Qd_SdZTYUORPJKKEDF96A4060h5JdBHaHFZMDWSBTYA\ Qb8Nh6Kn4Hs3Ip7ImAIkDJhHJfKJcNKaRKZUKXXLU`LScLPfLN\ iOPjRRjUTjXUkZWkaYkdZlg`libllcmoemrgmthmsdlsakrZkr\ WjqTiqQiqMhqJgsGguDgwAix7ky5mz4oz3qz2rz1sz0tz2uz4v\ z6wz7xz9yzBzzCzzEzzGzzIzzJzzLzzNzzOzzPzzPzzPzzPzzP\ zzPzzPzzPzzPzzPzzPzzPzzPz } 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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 24-01-04 (Whirling Devilish [6])
by Jim Muth 24 Jan '04

24 Jan '04

FOTD -- January 24, 2004 (Rating 6) Fractal visionaries and enthusiasts: In the most recent FOTD, the Z^1.003+C fractal that appeared two days ago, I mentioned that the large Mandeloid filling the frame has a tiny area of chaos on its northeast shore, but that the iteration count in this chaotic area is too high for exploring to be practical. For today's FOTD, I accomplished the impracti- cal. The image I found takes over 4 hours to render. Today's image is a scene in this narrow area of chaos, which appears to consist entirely of discontinuities. The unbroken features themselves, if such things exist, consist only of equal-iteration bands with smoothly curving boundaries. It is the way these boundaries are broken up that makes the image. The image shows a series of incomplete spirals with exaggerated colors -- the kind of thing that might be expected. But behind the spirals lies an 'inside' area with a perfectly straight edge, and this edge cuts uninterrupted across all the disconti- nuities that would normally be expected to disrupt it. A few thumbnail excursions into the detail along this straight edge have shown that the chaos there is totally unorganized, with areas having totally differing characteristics lying side-by- side. (I might explore this area in the near future.) I named the today's image "Whirling Devilish", a play on words that takes note of its prominent spirals. The over-exaggerated color palette permits a rating of no higher than a 6, which, combined with the 244-minute render time, gives an overall value of a pathetic 2.4. Wise fractalists will find a far better value by downloading the finished image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> I e-mailed the image to Paul several hours ago, so there should be no unusual wait for it to be rendered and posted. Friday was far too cold here at Fractal Central for dignified cats to be outdoors. The temperature never rose beyond 19F -7C, and the wind blew at a brisk pace all afternoon. The dynamic duo satisfied themselves curled by the radiator, catching up on sleep. This morning the ground is covered with about 3cm of powdery snow, and it is as cold as yesterday. It's no mystery how the cats will pass the day. I hope to pass the day uneventfully. I'll start by sweeping the sidewalk, and then . . . . Until next time, take care, and who knows what fractals lurk in the world of numbers? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Whirling_Devilish { ; time=4:04:39.54--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=+0.84148491609888050/-0.080629287046106\ 61/527.1442/1/117.5/-5.21221954485895367e-013 params=1.003/0/1040/1500 float=y maxiter=60000 inside=0 logmap=-4386 periodicity=10 colors=000L0HL0IM0IM0JN0JN0KO0KO0LP0LP0MQ0MQ0NR0NR\ 0OS0OS0PT0PT0QU0QU0RV1RV2SW3SW4TW5TW6UW7UW6UV6SU6R\ T6PR6OQ6MP6LO6JM6HL6GK6EJ6DH6BG6AF68A48E67I87M97QB\ 7UD6YE6cG6iI6mJ6qJ5nJ5kJ4iJ4gJ3dJ3aJ2ZJ2WJ1VJ1XO3Z\ S4`W5c_6ec7hg8jk9moAqtAosBmsCkrDirDgqEeqFcpFapG_pH\ YqIWqIUrJSrKPtLRtKSuKTvKUuKWtJXsJYrJZqJ_pJaoIbnIcm\ IdmIfmHgmHhmHimHjmHlmGmmGnmGomGqmFrmFsmFtmFumFvnHw\ oJxpLyqMzrOzsQztSzuTzvVzwXzxZzy_zzczzgzzlzzkzzjzzi\ zzhzzgzzfzzezzdzzczzbzzazz`zz_zzZzzYzzZzzXzzWzzVzz\ TzzSzzRzzPzzOzzNzzMzzKzzJzzIzzGzzFzzEzzDzzBzzAzz9z\ z7zz6zz5zz5zz4zz4zz4zz3zz3zz3zz3zz2zz2zz2zz2zz1zz1\ zz1zz1zz0zz0zz0zz0zz3zz6zz8zzBzzDzzGzzIzzLzzOzzQzz\ TzzVzzYzz_zzbzzezzgzzjzzlzzozzqzztzzwzzvzzuzzuzztz\ zszzszzrzzqzzqzzpzzozzozznzzmzzmzzlzzkzzkzzjzzizzi\ zzgzzezzdzzbzz`zz_zz`zzazzbzzbzzczzdzzdzzezzfzzfzz\ gzzhzznzzmzzlzzjzzizzgzzf } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(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 } END 20.0 PAR-FORMULA FILE==================================

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No FOTD for January 23!
by Jim Muth 23 Jan '04

23 Jan '04

Fractal fans: Due to an unexpected work back-up here at F.C., there will br no FOTD for today. The problem is strictly temporary, and the FOTD will return on schedule in 24 hours. Jim M.

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New location for the -UPDATED- OrgForm Compilation
by Paul N. Lee 23 Jan '04

23 Jan '04

Greetings, George Martin did a wonderful job in putting the ORGFORM compilation together way back when, but he last made changes to it back in October of 1999. And that is the same copy which still exists on Noel Giffin's Spanky server (along with a few other sites). As some of you should be aware of by now, I have been keeping the old ORGFORM collection as up-to-date as I possibly can. And all of those new changes made over the last several years have been available as a download from my website. Well, the collection is now over twice the size it once was (or still is at some places), and I have created a specific location where it can always be accessed. The new URL is as follows: http://home.att.net/~Paul.N.Lee/OrgForm.html The old location will only remain through this weekend, after that all future updates may be obtained from the above URL. So those that may have links to the old site should make note of this and modify any bookmarks and/or web listings. Thank you. Sincerely, P.N.L. ------------------------------------------------- http://home.att.net/~Paul.N.Lee/PNL_Fractals.html http://www.Nahee.com/Fractals/

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Documentation for a new 'official release' of Fractint
by Hal Lane 22 Jan '04

22 Jan '04

############################################################# > I agree that the program itself [Fractint V20.03] is stable and worthy of > release (with perhaps just a little bug fixing). But the > documentation has gotten way out of date > Tim I also agree that in an 'official release' the documentation must match the program. I started updating the V20.0 docs when I occasionally learned of something that later versions of Fractint did beyond V20.0. However, I'm concerned that my merely editing the distributed docs (which now include page numbers which are no longer at the top of the pages) doesn't create anything useful that can be merged into an 'official release' of V20.03.0 docs. My copy of the docs can still be viewed in an editor but can no longer be printed correctly. Has anyone else done any updates to their local copy of the docs or collected update information that could be included in a up-to-date version of the documentation? <---<< The demo files also run extremely rapidly on my 400MHz machine. I also suspect that they are not doing some things correctly but I don't have any way to know if their results are correct or not. I feel that a name change to something like Fractflo is likely to be confusing to many non-technical users. Having a consistent name for the program is more important that being technically accurate about the program's method of calculation. The days when the 'integerness' of Fractint was critically important have passed into nostalgia (at least for me). - Hal Lane ######################### # hallane(a)earthlink.net # ######################### ############################################################# --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.564 / Virus Database: 356 - Release Date: 1/19/04

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FOTD 22-01-04 (An Old Smoothie [4])
by Jim Muth 22 Jan '04

22 Jan '04

FOTD -- January 22, 2004 (Rating 4) Fractal visionaries and enthusiasts: The magnitude of today's image is around 0.3, which is probably the lowest magnitude image ever to appear as an FOTD. The very low magnitude is necessary because the size of the fractal is many times the size of the classic M-set. In fact, I wonder whether to call today's image a fractal at all. There appears to be little of interest in the single large squashed bay with its single large squashed bud. True, an area of chaos does exist on the northeast shore, but this area is quite slow to explore, and hardly worth the effort. I present today's image mainly as a curiosity, to show what exists even in fractals (if such things are fractals) with a generating formula so close to unity, when the maxiter is raised to a value as high as the 50000 of today's image. While searching for a name for the image, titles such as 'Unibud', 'Squashed', 'Schmoo', 'Tubby', etc., went through my head. I finally noticed a certain feeling of relaxation about the image, and decided on the name "An Old Smoothie". The extreme maxiter and large expanse of 'inside' points makes the image a relatively slow one to generate. Combined with the rating of 4, which is all I could honestly give the image, this render time results in an overall value of 18. But don't take these values too seriously yet. The current system gives too much importance to the render time. I will soon develop a more appropriate way of deciding the overall value of the FOTD images. Most likely, I will divide the rating by the square root of the minutes required to render the image, and multiply the result by 100, which would give today's image a value of 85. We'll see what I come up with. As always, the finished GIF image is available at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Another very cold day on Wednesday, with a high temperature of 28F -2C here at Fractal Central, kept the fractal cats indoors all afternoon. Their mood was one of surprising acceptance however, and only a small bit of tuna was needed to keep them happy. Today is starting cloudy but not so cold. The cats are already thinking of a romp in the yard. I have about the average amount of work to finish before I can call it a day. Until next FOTD, take care and smooth out those rough edges. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ An_Old_Smoothie { ; time=0:22:28.03--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor center-mag=-0.771347/0.955451/0.2969827/1/67.5/3.8\ 8578058618805e-016 params=1.003/0/1040/1500 float=y maxiter=50000 inside=0 logmap=-350 periodicity=10 colors=000`Am`Al`Ak`Aj`Ai`Ah`Ag`Af`Ae`Ad`Ac`Ab`Aa`\ A``B_`CZ`DY`EX`FW`GV`HU`IT`JS`KR`LQ`MP`NO`ON`PM_QL\ _RKZSJZTIYUHYVJXXMX_OWbQVeTUhVUkXTn_SqaRtcRweUudWr\ cZqc`nbcmbejahiajg`me`oc_rb_t`Zv_ZsaYqbYodXmeXjfWh\ hWfiVdjValU_mUYoTWpTTqSRsSUtRcuRmlUwdXzX_zObzGez8h\ z0jz2iz3iz4iz5hz7hz8hz9gzAgzCgzDfzEfzFfzGfze0zf7zf\ DzfKzgQzgXzgbzf`zeZzdXzdVzcTzbRzbQzaOz`Mz_Kz_IzZGz\ YEzYDz0yz7szEnzLizSczZZzeUzkPzlOzmOznOzoOzpOzqOzqN\ zrNzsNztNzuNzvNzvNzhTzVZzIdzKezMezNezPezQezSezTfzV\ fzWfzYfzZfz`fzafz_czZ`zYYzXVzVSzUPzTMzSJzQGzPDzOAz\ N7zM5zO8zQAzSCzTEzVGzXJzZLz_NzaPzcRzeUzfWzhYzj_zla\ zmczkfzjhzijzglzfozeqzcszbuzawzZuzXtzUrzNXzVTzSTzQ\ TzOTzHVzMTzQRzUPzYOzbMzfKzjIzvBzrEznHzkJzgMzdOz`Rz\ VSzYTz`TzcTzeTzgSziRzjQzlPzmOzoNzlcznVzpMzaMzJLzOM\ z31zGCzSMzdWzpdzpezoizomznqznuzszznxzjvzftzbrzUgzW\ pzZqzarzdszgszfnzfjzfezfa } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(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 } END 20.0 PAR-FORMULA FILE==================================

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Fractint as a background process
by Vortex Swirling 22 Jan '04

22 Jan '04

Excellent. Thanks for the tip. I still had the disk video modes in my cfg so I tried it. The Fractint Dos box then remains active in XP and in fact can be restored to a window so you can see the course of the calculation. --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.564 / Virus Database: 356 - Release Date: 1/19/2004

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Zoom into Jim Muth's Jan 18, '04 Fractal of the Day.
by Hal Lane 22 Jan '04

22 Jan '04

################################################################## Here is a zoom into Jim Muth's Jan 18, '04 Fractal of the Day. It has the Leather Gem color map obtained from one of the Fractint Art Contest images. The color map has been rotated for best effect. Although I am using Fractint Version 20.03.0 I'm pretty sure that earlier versions can be used to create this image. START 20.03 PAR-FORMULA FILE================================ The_Wheel_of_Life2 { ; time=19:12--SF3 on a P II 400 ; Fractal of the Day Jan 18, '04 zoomed ; with rotated Leather Gem color map ; - Hal Lane 04/01/19 reset=2003 type=formula formulafile=pastengo.par formulaname=mandelbrotbc1 function=floor passes=1 center-mag=+1.74225596554302200/-0.00475135722486870\ /1.010771e+008/1/-24.9999998026450712/7.054525103911\ 13563e-006 params=2.003/0/1040/0 float=y maxiter=1500 inside=0 outside=fmod periodicity=10 sound=off colors=000XkG<3>hoAkp8nq6<2>wt1<6>Zf8Vd9SbA<3>DVF<4>\ CPCCNBCMA<2>BI9BH8BH8<3>AE79D6DE6<3>UI9YJAaLBeMCgODj\ QF<9>tgGuiGvjG<2>ypGzrFzrK<3>yufxukxvqwww<3>rhh`F0`F\ 0<5>UA0T90S80R80Q70P60<3>L30K30J20I10I10<16>UB2UB2VC\ 2<3>YE3<3>Q82O61M41<3>Q71R81S91fM5<3>iO5jP5kQ6<9>UB3\ S92Q82<3>I10931A00<3>VK0_P0dU0<3>zm0<3>zb0z_0zX0zU0<\ 3>`F0UC0O80H40<2>A4773A73C<3>56K47M48O39Q2AS<8>9QaAS\ bATc<3>E`hFbiGdi<3>JklKmmJkj<7>CURBSOAQM<3>6GB5E86G9\ <9>EWHFYIGZJ<2>JdMKfNLhM<2>UkH } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(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 } END 20.03 PAR-FORMULA FILE================================== - Hal Lane ######################### # hallane(a)earthlink.net # ######################### --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.564 / Virus Database: 356 - Release Date: 1/19/04

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FOTD 21-01-04 (What the . . . [5])
by Jim Muth 21 Jan '04

21 Jan '04

FOTD -- January 21, 2004 (Rating 5) Fractal visionaries and enthusiasts: For today's FOTD I tried the trick of the past two days on the quartic Mandeloid. This trick worked quite well on the quadratic and cubic Mandeloids, leading to some very inter- esting images, but it produced only near-total chaos when I applied it to the quartic Mandeloid. A quick glance at today's image shows a scene that has no business being in a fractal with a formula of Z^(4.003)+C. The image is totally disorganized. Where is the 4,16,64... symmetry that should be there? What are all the discontinuities doing in the picture? Forget about unimportant things like the meaning of existence; these fractal mysteries are the questions that need to be answered. When I saw the image, I thought, "What the...", and the name stuck. Unfortunately, we will have no third consecutive 8-rated FOTD. Today's image rates only a 5, which gives an overall value of 53 when combined with the render time of 9-1/2 minutes. The value may be increased by downloading the finished GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Another very cold day Tuesday here at Fractal Central kept the cats safely ensconced indoors. The high temperature reached only 28F -2C, which was far too cold for their sensitive ears. But they had a pleasant day anyway, resting by the heat. Today is another repeat. Somehow the cats will survive. The work for me is rather heavy today, so I had best get back on it. Until next time and next FOTD, take care, and don't get spammed -- it's no treet. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ What_the---- { ; time=0:09:30.07--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-0.47577616215156650/-0.003703526351880\ 48/2.714026e+007 params=4.003/0/1040/0 float=y maxiter=1800 inside=0 logmap=163 periodicity=10 colors=222Q22T22V22X24Y26_27a29c2Bf2Bd2Dg2Ef2Gh2Ih\ 2Je2Lh2Nh2Pk2Pl2Po2Pq2Ps2Pu2Pv2Px7PxEPxLPxVLxaGxhB\ xo6xx2xx2xx2xx2xx2xx2xx2xx2xx2xu2xs2xo2xn2xj2xh2xd\ 2xc2xa4xY7xX9xTDxQExNIxLJxINxGPxEQxN_xXhxdoxnxxxxx\ sxxoxxlxxhxxdxxaxxYxxVxxQxxNxxJxxGuxDux9sx6sx2rx2r\ x4sx9urExlJxfPxaVwX_wQcwLfwGfwBcw7Xw7PwBGwG9wJ2wP2\ wT2wY2wa2w_2w_2w_2w_2w_2wY4wY9wYEwYJwYNwcJwfGwjDwn\ 9wr7wu4wx2wx2wx2wx2wx2wx2wx2wx2wx2wx9wxIwrQwj_wdhw\ _jwXlwTjwPhwLdwJcwG_wDYw9Vw6Tw4Pw2Lx2Jx2Gx2Ex2Bx29\ x26x24x22x22x22x24x26w27w29w2Bw2Dw2Gw2Iw2Jw2Lw6Nw9\ PwBQwEVwGXwJYwL_wPawQcwVdwXfwQfwVfwXfwYfw_fwafwcfw\ dfwffwhfwjfvlfunftofsrfrsfqufpxfoxfoxfrxfuxfxxfxxf\ xxfxxfxxfxxfxxfxxfxxfxxfxxfxxfxxgxxgxxhxxhxxixxixx\ jxxjxxkxxkxxlxxlxxmxxmxxmxxmxxmxxmxxmxxmxxmxxmxxmx\ xmxxmxxmxxmxxmxxmxxmxxmxxmxxmxxmxxmxxmxxmxxmxxmxxm\ xxmxxmxxmxxmxxmxxmxxmxxmx } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 14-01-04 (The Unseen Squid [5])
by Jim Muth 21 Jan '04

21 Jan '04

FOTD -- January 14, 2004 (Rating 5) Fractal visionaries and enthusiasts: When I stepped back to view today's image from a distance, I was immediately reminded of an undersea scene, where a squid or octopus has been threatened and has released a cloud of black ink to conceal its escape. Since I saw no actual squid in the image, I named it "The Unseen Squid". (I doubt that a Mandel- brot 'molecule' could pass for a squid.) All in all, it's a very traditional fractal, created with the MandelbrotMix2 formula and rendered with the outside set to 'iter' and the inside set to zero. The image has the appearance of being very close to the escape radius, but this appearance is the actual nature of the fractal at this particular point. Increasing the bailout by entering a large number as the imag(p3) parameter has very little effect on the image. A large bailout radius will not evaporate the image because its formula contains a positive power of Z. When rating the image, I studied it for several minutes, trying to find a reason to rate it at a 6. I found nothing in it worth more than a rating of a very-average 5. Combined with a render time of 11-1/2 minutes, this gives an overall value of 43. This value can be raised considerably by letting Paul render the image and downloading the finished product from his web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The temperature reached 48F 9C here at Fractal Central Tuesday afternoon, though the clouds, which came and went, kept conditions from being ideal. The fractal cats had as good a day as possible in the yard, considering the less-than-ideal weather. This morning is much colder, and a snowfall is moving in. The cats' moods will suffer, I fear. My day will be adequate once I finish the waiting work. And an adequate day is about the most one can ask for. Tomorrow, I will return with another fractal of a quality yet to be deter- mined. Until then, take care, and have faith in fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Unseen_Squid { ; time=0:11:34.70--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+1.68407403939392000/+12.56396673625027\ 000/48065.35/1/49.9999999999923546/-6.064168889263\ 75464e-010 params=-0.3/-1.5/1/1.5/0/0/0/0 float=y maxiter=1500 inside=0 logmap=181 periodicity=10 colors=000HZ_F_ZE`YCaXBaWGbXKcXOdXTdXXeY`fYegYigYm\ hZriZvjZzjZngVcdRTaNIZJ7WFAXECXDEYDGYCIYCKZBMZAO_A\ Q_9S_9OXELVIITMFRRCPV9NZqxunurksoiqlfnjdlgajd_hbbe\ debeh_fjXgmUhpRirOjrTiqXiWimUfjScgR`ePYbNV_LSYKPVI\ MSGJQEGNDDKBAI97F74C61A55D49G4CI4HN4LR4PW4T_4Xd4`h\ 4dm4hq4lv4pz7Xo9DdLANX86Z88_8A`8Ba8Dc8Ed8Ge8Hf8Jh8\ Ki8Mj8Nk8Pl8QmARmCSnDSnFToHUoIUpKVpMWpNWmMTkLQiKNf\ JKdIIbHF_GCYF9WE6UD4TF7TGATHCTIFSKISLKSMNSNPRPSRQV\ RRXRS_QUbQVdQWgQXiTZkV_lXamZbn`cobepdfqfgriiskjtml\ uomvqnwspxuqywrznpyeoxYnwPlvGku8jtAisBisCisDisEisF\ isGirHirIirJirKirLirMirNdpO`oPWmPSlQOkRJiRFhSAfT6e\ T2dNNjIfpDzuCvrCrpCnnCjlBfjBbhBZfBVdARbAN`AJZAFXAB\ VNLWZVXjdYvnYtm`rlcpkenjhlijjhmhgoffreftggshhriirk\ iqljqmkpnkpploqmnrnntnmuomvplwplpkejgZdcTZ_MTWGVXH\ XYHYZH__Ia`IcaJebJfcJhdKjeKlfLngLybbwc_vdXteVseSqf\ QpgNTUhRVgPVeOWdMXcKYbJZa } 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 } END 20.0 PAR-FORMULA FILE==================================

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Fractint as a background process?
by Vortex Swirling 21 Jan '04

21 Jan '04

Is there anyway to run Fractint as a background process in XP? That is, when I minimize fractint, is there any way to make it not pause until I maximize it again? --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.563 / Virus Database: 355 - Release Date: 1/17/2004

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Re: [Fractint] Fractint as a background process?
by nick.grasso＠hrads.com 21 Jan '04

21 Jan '04

Vortex Swirling wrote: >>>Is there anyway to run Fractint as a background process in XP? That is, when I minimize fractint, is there any way to make it not pause until I maximize it again?<<< You are lucky that it runs in XP at all. I can run it in XP, but only at 320x200 or 360x480. Different people have reported better luck with different video cards, but the only way I know to do what you want is to run Virtual PC. Microsoft recently bought Virtual PC from Connectix and just released 'Microsoft Virtual PC 2004' (http://www.microsoft.com/windowsxp/virtualpc/) I am running the last Connectix version and I don't know what Microsoft has changed. Anyway, Virtual PC emulates hardware in software (using DirectX) therefore allowing you to run other operating systems on top of Windows, e.g. DOS, OS/2, Linux, etc. I can run Fractint, as well as several DOS games, in a window or full screen on XP. There are 2 problems with it however. First, fractint runs quite a bit slower than in native DOS. Second, Virtual PC is expensive, about $120.00, although you can download a fully functional 45 day free trial. Actually, they lowered the price - Connectix charged $200. Nick

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FOTD 20-01-04 (The Cubic Trinity [8])
by Jim Muth 20 Jan '04

20 Jan '04

FOTD -- January 20, 2004 (Rating 8) Fractal visionaries and enthusiasts: Today's image is the second consecutive one to rate an 8, though its slower render time cuts its overall value to 59. I did need to take a slightly liberal view of the image to reach that rating however, but it is still an unusually interesting sample of a midget in an almost-cubic fractal. The name I chose for the image, "The Cubic Trinity", has nothing to do with religious belief. It merely reflects the fact that, in the image, everything comes in powers of 3. While yesterday's FOTD image examines the negative real axis of the Z^(2.003)+C Mandeloid as it appears 1040 levels up the spiral, today's image looks at the negative real axis of the Z^(3.003)+C figure at the same level. Not unexpectedly, much of the same type of detail appears. We have the same features resembling skeletal hands, and the same barely noticeable lack of symmetry. The breaks that do appear are arranged symmetrically around the midget so that they become a regular part of the pattern. Indeed, it takes a bit of searching to find the places where the symmetry breaks, but a careful search will reveal that all corners of the midget's basin are not quite identical. The render time of 13 minutes is slow for an image that might be a bit exaggerated. That wait may be eliminated by downloading the finished GIF file from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With the temperature hovering around 25F -4C all afternoon, the day was far too cold for the delicate whiskers and paws of the fractal cats. They tested the outdoors only a few minutes before deciding that warmth was better than adventure. A bit of tuna kept them happy. Today is starting sunny and just as cold. The cats will likely have a similar day. I have a bit of work to finish before starting the search for the next fractal, but I can finish that work with the speed of a photon. I also have an urge to treat myself to some junk food at the golden arches 1/2 mile down the road. If I survive, I'll return in 24 hours with the next FOTD image. Could we possibly have three consecutive images that rate an 8? Check back here in 24 hours to find out. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Cubic_Trinity { ; time=0:13:28.73--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=mandelbrotbc1 function=floor passes=1 center-mag=-1.08945153107755200/-0.010540023154615\ 56/4.734514e+012/0.9997/-170.7/0.200745373042978764 params=3.003/0/1040/0 float=y maxiter=2100 inside=0 logmap=355 periodicity=10 colors=000EEKCDJGHMJLPNPRQTUUXWX`Z`d`chchmfmskryou\ uuwwwXuTSmONhIHcCCZ67U1UY6p`AmYFjVJgTNdQRaOVZL_WIc\ TGgQDkNBoQEpTHpWKpYMp`PpcSpeUpdTmdTkdTicTfcTdcSbbS\ `bSYbSWaSUaRSaRP`RN`RL`RJaPKbOLcMMcLNdKOeIPeHQfFRg\ ESgDThBUiAVi9WiCUkETmGSoIRqKPsMOuPNwRMwUKwWJwZIw`H\ wcFweEwhDwjCweLw_UzQbtHZnGWiFScDPZCMTBIOAFI8CD7876\ 585287688A8AD8BH8DL8EO8GS8HW8JZ8Kb8Mf8NiELeKKbQIZW\ HWaGT_EUZDVYBVWAWV9WU7XT6XR5YQ3YP2ZO1ZP6WQAURERSIP\ TMMUQKVUHWYFXaCYeAZi7Zm5X3lV4hU4eT5bS5_Q5XP6UO6RN6\ OL7LK7IJ8FI8CG89F96E93D90GA2IA4KA5NA7PA9RAAUBCWBEY\ BF`BHbBJdBK`EIYHGUJERMDOOBKR9HT7EW6AY4lr2fj13Z33W5\ 3T72Q92NB2KC2HE1EG1BI18K15L27M39M4AM5CM6EM7FM8HN9I\ NAKNBMNCNNDPNDQNGRPJSRMTTPUVSVXVWZYW``XbcYdfZfi_hl\ `jo`libecd_YfUThONjIHlCCm6Dn9DnCDnFDnHEoKEoNEoPEoS\ FqVFsXFu_FwbFxdJz`MzXQzTTzPXzL_zHczDfz9azNYz`Uznbz\ `kzOszBczJQzQNzPLzNJzMGzL } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(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 } END 20.0 PAR-FORMULA FILE==================================

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Some More on Deformation and Reply to Guy Marson
by mdoctorow＠comcast.net 20 Jan '04

20 Jan '04

>From Osher Doctorow Ph.D. mdoctorow(a)comcast.net In reply to Guy Marson, who asked what if one is depressed over being paranoid, it's an interesting idea but doesn't usually occur in that way (that is to say, being depressed over being paranoid) because it would require the paranoid person to be by definition angry at himself/ herself predominately in those circumstances. A Paranoid person is predominately angry at others. It is theoretically possible, I do admit, for one to be exactly at the borderline of being equally angry at others and oneself, perhaps occasionally - for example, if one does poorly in an exam or a course, one could "kick oneself" as well as the "course" or (God forbid) the teacher. I suspect that in such a case one wouldn't be likely to make a vendetta against the teacher since one would realize one's own part in the poor performance in the course. Regarding Deformation, I proved yesterday on sci.stat.math that: 1) P(A-->B) - P(B-->A) = P(B) - P(A) < = P(B/A) - P(A/B) if and only if A and B are statistically positive quadrant dependent, that is to say P(AB) > = P(A) times P(B). Let me translate this into English (those who want to know the technicalities I'll briefly discuss at the end). Inequality (1) says the the Rare Event difference in the probable influence of A on B and the probable influence of B on A reduces to the probability of B minus the probability of A and this in turn is less than or equal to the Fairly Frequent Event Conditional (Bayesian) probability of B given A minus the Conditional probability of A given B provided that A and B probably increase together rather than being unrelated or going in opposite directions. This in turn describes an "avalanch" in probable influence somewhat similar to the way in which Rasputin's influence over Tsar Nicholas II and his wife Alexandra in Russia resulted largely in their unpopularity and ultimately largely in the Russian (Bolshevik) Revolution. The discrepancy in Rare Event probable influence, when it increases much, triggers a discrepancy in Fairly Frequent Event analogs or "given" type probabilities. They aren't pure analogs because "given" isn't the same idea as influence, but they're the closest that Conditional Probability comes to formulating probable influence. For those interested in the math, P(B/A) = P(AB)/P(A) for P(A) not 0, and P(A-->B) = 1 + P(AB) - P(A). To prove the inequality very fast and easily, notice that algebraically P(B/A) - P(A/B) = [P(B) - P(A)] times P(AB)/(P(A)P(B))! Osher Doctorow

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RE: [Fractint] Fractint version 20.3
by Tony (Anthony) Hanmer 20 Jan '04

20 Jan '04

Jonathan, Thank you very much for including the L-system line limit increase in your new Fractint release! Maybe there are hardly any people out there still tinkering with L-systems in Fractint... but I will have a major announcement or two to make this year. I'm just waiting for magazine interest first. Tony Hanmer Tbilisi, Republic of Georgia _________________________________________________________________ Add photos to your messages with MSN 8. Get 2 months FREE*. http://join.msn.com/?page=features/featuredemail

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Re: [Fractdev] No bailout in bjax formula?
by Jonathan Osuch 20 Jan '04

20 Jan '04

On Saturday 17 January 2004 11:40 pm, Edwin wrote: > Looking at the fractint.frm which comes with xfractint 3.10, the "bjax" > formula is: > > Bjax {; > z=c=2/pixel: > z =(1/((z^(real(p1)))*(c^(real(p2))))*c) + c > } > > This looks like it's missing a bailout condition. Does fractint supply a > default bailout function if the user doesn't give one? > > When I render it I get a blank screen. However even if I add |z| < 4 at > the end, it still doesn't display anything, so I'm a bit confused. Yes, it is missing a bailout condition. No, a bailout function is not automatically supplied. The iteration continues until the maximum iteration count is reached. This means you need to play with the inside= options to get an image (all points are inside the set). You can verify this by setting inside=maxiter and then calling up the palette editor after the image is generated (this will be possible if you are using Xfractint version 20.3, although editting the palette is still essentially broken). There are a lot of formulae that produce a blank screen at the default settings. This formula was probably written while using the integer math (not available in Xfractint). Because of the reduced dynamic range, the integer math artifacts produce more interesting images. Jonathan

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FOTD 19-01-04 (Quadropod [8])
by Jim Muth 19 Jan '04

19 Jan '04

FOTD -- January 19, 2004 (Rating 8) Fractal visionaries and enthusiasts: Today's FOTD is the second one I have found with the newly released Fractint version 20.3. Other than a few minor glitches in the evolver and view-window, which have been corrected, I have noticed no difference in the program performance. Of course, some of the changes involve features I rarely use. In yesterday's FOTD we examined stem area of the Z^(2.003)+C Mandeloid as it appears 1040 levels up the logarithmic hyper- spiral. Today we turn our attention to the west, and examine the 'East Valley' area of the Mandeloid. Unlike the main stem, which simply breaks into infinite bits and pieces, the East Valley area smears out into a broad flat wedge with jagged edges. Today's image is located in a narrow band of chaos on the southern edge of the wedge. I named the image "Quadropod". It reminds me of some fantastic animal with four translucent arms. Perhaps I should have named it 'Study', since I spent so much time studying the background colors and trying to create a smoothly blended gradient with no visible bands, a challenging task in GIF format with its meager 256 colors. Though the result is not perfect, I feel I came close enough to the goal of perfect smoothness to rate the image at an honest 8, which, combined with the render time of just under 11 minutes, gives an overall value of 73. (To find the overall value, the image rating is multiplied by 100 and the result divided by the render time in minutes, making the render time like the money one must pay to buy an item. The shorter the render time, the more value for the money spent.) As always, the render time may be eliminated entirely by down- loading the finished image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The cold rain continued most all day Sunday here at Fractal Central, changing to a few snowflakes just before ending around sunset. The high temperature never made it above 36F 2C, which is far too chilly for the cats' fractal ears. The duo spent the day sleeping by the heat. Today is starting sunny, but it is very cold again. We'll see how the cats make out. My day looks as though it will be notably average. Hopefully, the fractal I find this evening will be notably above average. Until the next FOTD appears, take care and be forever fractalish. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Quadropod { ; time=0:10:57.62--SF5 on a p200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-0.25242073906725380/-0.005654551455851\ 47/2.66834e+010/1/145/-0.00262791307117529738 params=2.003/0/1040/0 float=y maxiter=2700 inside=0 logmap=309 periodicity=10 colors=000vwmuwmtwmswnrwnqwnpwnowonwomwolwpkwpjwpi\ wphwqgwqfwqewqdwrcwrbwr`ws_wrZwsYwsXwtWwtVwtUwtVws\ VwsWwrWwrXwqXwqYwqYwpZwpZwp_wp_wp`wp`wpbwpcwpdwpew\ pgwphwpiwpjwplwpmwonwnowmpwllhQiePfbPc_OaWOZTNWQNT\ NLSKLRGKQDKPAJO7IN4HM7IL9JKBKMELOGMQIMSLNUNOUPPUSQ\ UURWWRZXSaYTe_UhaVkcWmeWlgXlhYlgYlgZlgZlf_lf_le`le\ `lealdaldckcdkcfkcgkbikbjkalkamkaok`pk`rk_qk_qk_pj\ `mj`lj`kj`jjaijahjagjafjbejbdjbcjbbjcajc`jc_jcZjdY\ jdXjdWjdVjeUjeTjeSjeQjeOlcMmbKm`ImZGmYEmOKhPTcQVZR\ XUSVPTUKUUKUUPUTTVTXZTaaSeeSiiSnlRrpRvtRzwRxuQvtPt\ rOrqNpoNonMmmLkkKijKghJfgIdfHbdG`cGZaFX`EW_DUYDSXC\ QVBOUANTAPSCRSESSGUSIVSKXSLYRN_RP`RRbRTcRVeRWgQYhQ\ _jQakQcmQenQfpShqUjsWltYnv_pwaqrcomemigkdii`kgWmeS\ ocNqaJs_EuYAwW9xV9yV9zV9zU9zU9zU9zU8zT8zT8zT8zT8zS\ 8zS8zS8zSAzRCzPEzNGzLIzNUzPezRdzTdzVdzXdzZdz`dzbcz\ dczfczhczjczlcznczpczpczp } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(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 } END 20.0 PAR-FORMULA FILE==================================

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Zoom into Jim Muth's Jan 18, '04 Fractal of the Day
by Hal Lane 19 Jan '04

19 Jan '04

################################################################## Here is a zoom into Jim Muth's Jan 18, '04 Fractal of the Day. It has the Leather Gem color map obtained from one of the Fractint Art Contest images. The color map has been rotated for best effect. Although I am using Fractint Version 20.03.0 I'm pretty sure that earlier versions can be used to create this image. START 20.03 PAR-FORMULA FILE================================ The_Wheel_of_Life2 { ; time=19:12--SF3 on a P II 400 ; Fractal of the Day Jan 18, '04 zoomed ; with rotated Leather Gem color map ; - Hal Lane 04/01/19 reset=2003 type=formula formulafile=pastengo.par formulaname=mandelbrotbc1 function=floor passes=1 center-mag=+1.74225596554302200/-0.00475135722486870\ /1.010771e+008/1/-24.9999998026450712/7.054525103911\ 13563e-006 params=2.003/0/1040/0 float=y maxiter=1500 inside=0 outside=fmod periodicity=10 sound=off colors=000XkG<3>hoAkp8nq6<2>wt1<6>Zf8Vd9SbA<3>DVF<4>\ CPCCNBCMA<2>BI9BH8BH8<3>AE79D6DE6<3>UI9YJAaLBeMCgODj\ QF<9>tgGuiGvjG<2>ypGzrFzrK<3>yufxukxvqwww<3>rhh`F0`F\ 0<5>UA0T90S80R80Q70P60<3>L30K30J20I10I10<16>UB2UB2VC\ 2<3>YE3<3>Q82O61M41<3>Q71R81S91fM5<3>iO5jP5kQ6<9>UB3\ S92Q82<3>I10931A00<3>VK0_P0dU0<3>zm0<3>zb0z_0zX0zU0<\ 3>`F0UC0O80H40<2>A4773A73C<3>56K47M48O39Q2AS<8>9QaAS\ bATc<3>E`hFbiGdi<3>JklKmmJkj<7>CURBSOAQM<3>6GB5E86G9\ <9>EWHFYIGZJ<2>JdMKfNLhM<2>UkH } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(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 } END 20.03 PAR-FORMULA FILE================================== - Hal Lane ######################### # hallane(a)earthlink.net # ######################### ################################################################## --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.562 / Virus Database: 354 - Release Date: 1/16/04

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Graphics card for Fractint
by Vortex Swirling 19 Jan '04

19 Jan '04

Ian, I put in "Maxtrox G400" into Ebay and found 38 hits. Many of them at a "buy it now" price of 20-25 dollars for a 32 MB card. I don't know if they are exact matches for the card you had but its worth a look. --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.563 / Virus Database: 355 - Release Date: 1/17/2004

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FOTD 18-01-04 (The Wheel of Life [7])
by Jim Muth 18 Jan '04

18 Jan '04

FOTD -- January 18, 2004 (Rating 7) Fractal visionaries and enthusiasts: Today's image is a scene in the Z^(2.003)+C Mandeloid. This is the same fractal that holds the curious Julia rectangle that I sometimes use as an interesting FOTD object. But that rectangle exists at the ground level of the formula, which can be seen by setting the real(p1) parameter of today's MandelbrotBC1 formula to 2.003, and the real(p2) parameter to 3.14159... The actual parent fractal of today's image lies 1040 levels up the logarithmic hyper-spiral. Such an extreme height is necessary because the exponent of Z is so close to an integer value. This closeness causes the parent fractal to rotate and change very slowly as the value of real(p2) is raised. At a height of 1040, the parent fractal is rotated 180 degrees, a position that has the main stem, which has split into infi- nite flinders, facing east, and the East Valley, which has become smeared out, facing west. Interesting things happen at both locations. Today, we examine the things that happen on the east-facing main stem. I have chosen to explore the area immediately behind the large midget. In this area, we find what looks like a grid of railroad tracks, with midgets located where the switches would lie. Today's scene is located in the basin of attraction of a larger midget, which in turn is located in the basin of the largest midget on the main stem. And BTW, this large midget has been transformed into something that must be seen to be believed. To liven the image I have rendered it with the outside set to 'fmod' and the proximity set to the default 0.01. When editing the parameter file, I entered the proximity value by hand, though I doubt that this was necessary. While searching for a name, I was thinking of the mysteries of existence, which probably inspired the name "The Wheel of Life". The name is justified by the filimentary circular features surrounding the central midget. The rating of 7 combined with the render time of just under 4 minutes gives an overall value of 183. A good way to increase this value is to download the completed GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Saturday was cloudy and chilly here at Fractal Central, with a high temperature of only freezing. The snow held off until nightfall, giving the duo of cats ample time to wander the yard in search of adventure. They found none, and peacefully retired to their beds at the end of the day. Today is starting most un- pleasant, with an inch of slush on the ground and a cold rain falling. It's a good thing I have tuna in stock. My precognition now tells me that in 24 hours I will return with the next FOTD. So until then, take care, and either see the light or remain in the dark. The challenge is how to recognize the actual light. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Wheel_of_Life { ; time=0:03:15.46--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=+1.74225596554302200/-0.004751357224868\ 70/3.656832e+007/1/-25/7.36727087773808575e-006 params=2.003/0/1040/0 float=y maxiter=1500 inside=0 outside=fmod proximity=0.01 periodicity=10 colors=000RgaMjdGmfAph5rjBniHkiNghTdhZ`gdYgca`beVb\ iOamIapCSSqUUnWVkYXi_Yfa_dc`adb_fcXheVjfSlhQniNojL\ ebKXVJNNIEGHJNVNUhR`vTauVatXbsZbr`cqEOVEMWELYEKZOJ\ ZYIZfHZ`SXVbVQmTaiYlfawcevbfvbgvbhuahuaiuajuajt`kt\ `lt`lt`ms_ns_ns_os_prZprZqrZrrZrsXosVlsTisRfsPcsN`\ tMYtKVtIStGQtENtCKuBHu9Eu7Bu58u35u12u00p84kF7gMAbT\ DY_GUfJWcLY`M_ZNaWPcUQeRRfPShMUjJVlHWnEYpCZr9_s7`r\ AbrCcrEdrGerIfrKgrMhrOirQjrSkrUlrWmrYnr_oraprcqrer\ rgsnfpkenhdkecibbf_adX`aU__QZYNYVKXTHWQEVOBUL8TJ5T\ H7YL9aPBeTCiXEm`GqdHuhNqcTn_YkVchRidNnaItZEyWAuXEq\ YHmYKiZNe_Ra_UY`XU`_QacMbfIciEclAbo9am9_k9Yi9Wg8Ue\ 8Sc8Qa8O_7MZ7KX7IV7GT6ER6CP6AN68L66K78N8AP9CRAETBG\ WCIYCK_DMaEOcFQfGShHUjHWlIYnJ_qKasLcuMewMgyNhvOitO\ jrPkpQlnQllRmjSngSoeTpcTpaUq_VrYVsWWtTXuRXuPYvNZwL\ ZxJ_yH_yFbxLdxQgxViw_lwdnwiounjrhdmbZhXTcRNZLHUFBP\ 9AU88Z77d7sURmXTg_VbbYXd_ } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(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 } END 20.0 PAR-FORMULA FILE==================================

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ATI 9700 with Catalyst 3.10 using VESA modes in Fractint
by Vortex Swirling 18 Jan '04

18 Jan '04

I have been using Catalyst 3.08 drivers for my ATI 9700 AIW graphics card under XP. I could use fractint but whenever I'd exit I'd have to reset the display properties resolution to fix my corrupted screen back in XP. This weekend I updated to Catalyst 3.10 drivers and now when I exit fractint after using VESA mode drivers the XP screen is not corrupted on exit. --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.563 / Virus Database: 355 - Release Date: 1/17/2004

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[Fractint] On Bill Jemison's Reply and Jim Muth's Precognition Comments
by mdoctorow＠comcast.net 18 Jan '04

18 Jan '04

>From Osher Doctorow Ph.D. I want to thank Bill Jemison for his interest in my postings, and to assure him and other readers that I will try to not over-bombard Fractint with posts far disproportionate to the number of people who are interested. Also, I will try to make postings usually intuitively clear for non-experts in the field(s). On Jim Muth's Precognition comments of Jan. 17, I think that it is an excellent sign of Creative Genius that he is courageous enough to discuss Non-Mainstream ideas. My own opinion is that what some people interpret as Precognition is probably more Telepathy or Clairvoyance (respectively receiving auditory versus visual mental images in one's mind which originate from others' minds). Jim, I would guess, picked up the plotters' thoughts, and I'd suggest trying to compare his location on 9-11 or 9-10 with those of the plotters or else those of people or agencies who might have had an indirect connection to the plotters via (a) support or (b) surveillance. It is even conceivable that Jim picked up NYPD's surveillance of somebody indirectly involved in 9-11 or (crazy as it may sound) even somebody who could explain the anthrax attacks and the deaths of the Vietnamese immigrant in the Bronx and the older woman in Connecticut who died from anthrax poisoning. We run into the difficulty with Telepathy and Clairvoyance that I have run into with Non-Mainstream ideas in Mainstream Mathematics and Physics and other sciences/professions, namely, people who don't experience certain things are very unlikely to believe them. This is especially a difficulty in teaching. I try to teach my college classes in Mathematics with emphasis on most students rather than "exceptionally bright" students partly for this reason. The exceptions often have experienced Mathematics from parents who are teachers, engineers, physicists, and so on, but the majority of students usually have parents who weren't taught well and didn't learn much in mathematics. This disagrees with the way in which most Research Universities teach mathematics, and also with the way in which many Teaching Universities or their faculty teach mathematics. Fractals probably relate to Telepathy and Clairvoyance, in my opinion, through their self-similar Expansion-Contraction property, since I think that Consciousness-Perception-Memory also have (wavelike or field-like) Expansion-Contraction properties. When we awaken, our perceptions and Consciousness and Memory subjectively expands and probably also do objectively via various instruments that can monitor brain activity. When we go to sleep, there is a subjective and probably objective contraction in Consciousness and Perceptions and Memory although during sleep various cycles like REM are known to involve differing degrees of dreaming and so on. Osher Doctorow

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FOTD 17-01-04 (Iterative Toytown [7])
by Jim Muth 18 Jan '04

18 Jan '04

FOTD -- January 17, 2004 (Rating 7) Fractal visionaries and enthusiasts: In yesterday's discussion I wrote about precognition. When I wrote it, I was undecided whether to say that I believe in precognition or to claim that I know it exists. I ended up stating that, because of personal experiences, I am convinced that the ability to foresee future events does exist. This is one step short of saying that I *know* it exists. In order to claim that precognition *does* exist as a proven fact, I would need to display the ability to do things like predicting winning lottery numbers at will, an ability I do not have. I would have been more accurate if I had stated that I am convinced that, on rare occasions, we receive hints of great (and not-so-great) events which have not yet happened. The point in question is whether these hints are actual information from the future, which has somehow moved backward in time and worked its way into our awareness, or whether we merely give undue attention to real events that happen by chance to resemble fantasies we have recently experienced. After considering my own experiences on the seven nights of September 4 to September 10, 2001, I have decided that somehow, information of what would happen on the morning of 9-11 did somehow enter my awareness on those earlier nights. I have no idea of a mechanism through which this might have happened. The important thing is that, because of my experience, I am convinced that our relation to the four-dimensional space-time world around us is far more intimate than the "I'm in here and the world is out there" relation presented by our senses. I am not yet ready to take seriously the pseudo-mystical phrase 'become one with...', but I am now convinced that the hard skeptics, while keeping a thread of reason in a world drowning in nonsense, are still missing something big. And I would not be surprised if fractals were somehow involved. Today's image is a scene in the fractal that results when Z^(-2.5) is subtracted from (1/Z) and (1/C) is added. This parent fractal is a double-lobed thing with X-axis symmetry, consisting of a central area of chaos with a zig-zag filament arching out to the east. Today's scene is located in the vicinity of a larger midget on this filament. The image has been rendered with the outside set to 'tdis'. I named it "Iterative Toytown" for no good reason. The name merely reflects the frame of mind I was in when I thought of it. I have inserted the mathtolerance entry into the parameter file because of the high magnitude of the image, which might cause the image to render at the wrong magnitude if the resolution were increased beyond 640x480. After careful thought, I rated the image at a 7, which is above FOTD average and, combined with a render time of 5 minutes, gives the image an overall value of 140. The value can be raised to 700 or so by eliminating the wait for the image to render. This can be done by letting Paul render the image and by then downloading it from his web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The Friday weather was cold here at Fractal Central, but with a temperature of 28F -2C and lighter winds, it was not as cold as recent days. The fractal cats must have agreed. They spent over an hour in the yard, investigating the things they had not checked in several days. When the day ended, they settled comfortably for a peaceful evening. I have only a small bit of work to finish before today will be totally free. What will be done with that free time however remains to be determined. Regardless of what happens, I'll be back in 24 hours with another fractal. Until next time, take care, and be assured that the future will come to pass. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Iterative_Toytown { ; time=0:04:59.40--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+3.093845088968933/+0.4908436478215898/\ 1.234142e+012/1/70.01/-0.0191153986490802952 params=1/-1/-1/-2.5/0/0 float=y mathtolerance=/1 maxiter=1200 inside=0 outside=tdis periodicity=10 colors=000VVPkLgxBywDssFnoHhjJcfLYbNTZPNURIQTCMV7I\ X2LU5OR7RO9UMCXJE_GGbDIeBLh8Nk5Pn3R8FsEHpJImOJkTKh\ YMebNcgO`lPYqQWMMYPQURURTYNVaKXeHZiD`mAbq7dsEetKfv\ QgwWhxaGbTIZQKWOMTMNQKPNIRJFTGDUDBWA9Y77Z45Z89ZBCZ\ FFZIIZMLZPOZTRZWUZ_XZb_ZfbZieYfcYdaYa`Y_ZYXXYVWXSU\ XQSXNRXLPXINXGMWFKWEJWEHWDGVCEVCDVBCVAAVA9U97U86U8\ 4U73U72ZA8bDDfGIkJNoLTsOYxRbxUgxWlxUixSfxQcuOarMZp\ KWmITjGRhEOeCLbAI`8GY6DV4AT38S3PR3eQ3vP6rO8oNBlMDh\ MFeLIbKKZJNWIPTIRPHUMGWJFZFE`CEb9DaBDaDC`FC`HC_JB_\ LB_NBZPAZRAYTAYV9XX9XZ9X_AVYAUWBSUBRSBPQCOOCMMCLKE\ JIEIGFHFILALPFNTLRXQT`VWcVZgV`kVboWesZgwciycjwcjtc\ jqajo_klXjiUjfUidUkaUlZUmWUnTUpQQpOLnNKlNKjNKiNKgM\ JeMJdMJbMJ`MJZLIYLIWLIULITLIXQF_UDbYBea9he7ki5nm3g\ o8`qDUrINtNGuSKpTOlURhVVcVZ_WaWXeRYiNYlJZpE_tA`w6`\ p5gi4nb3udFdeROfb8ecCdcFdcJccMbdPbdTadWadZ`eb_ee_e\ iZelYfoYfsXfvXfyLkNPeOS_P } 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 } END 20.0 PAR-FORMULA FILE==================================

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Re: Quantum Fractals?
by JackOTradez 17 Jan '04

17 Jan '04

Hey Dr. Osh: You makin' more of this then there iz ! - fractals are cool images and seriously trippy animationz. Also they are the visual depiction of the chaotic Universe we all be thrown into - but make no more of it then that! Take a break. Give it a rest. Try skydiving or SCUBA. JoTz

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Are Fractals (Quantum) Deformations?
by Bill Jemison 17 Jan '04

17 Jan '04

I am interested...don't understand much, but am interested, as I have been in all your posts. Bill

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Re: Are Fractals (Quantum) Deformations?
by mdoctorow＠comcast.net 17 Jan '04

17 Jan '04

>From Osher Doctorow Ph.D. I meant to say, in paragraph 9 (on the Calculus) that after Calculus was discovered Mathematics and Physics and several other Sciences changed very much. Then comes: "They changed fundamentally," which sentence was left dangling in the paragaph beginning "Before getting to Fractals,". Osher Doctorow

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Are Fractals (Quantum) Deformations?
by mdoctorow＠comcast.net 17 Jan '04

17 Jan '04

>From Osher Doctorow Ph.D. I'm going to introduce a question and a theory - although the theory is still being developed in the early stages. If readers aren't interested in this first post, I'll take the question and theory else- where. QUESTION. Are fractals Deformations, and if so, are they in particular Quantum Deformations? The Theory involved is Deformation Theory. If you look under the key- word Deformation on the internet, you'll find hundreds of articles in many different fields and disciplines and quite a few definitions of Deformation that seem to have nothing in common. My interest is to unify these different theories but in a Simple way and an Intuitive way that doesn't require years of study but applies almost directly to fields like Fractals. Deformation intuitively is "change". Unlike the concept of the "infinitesimal" in calculus, which is a "very small change," a Deforma- tion can be large or small or intermediate, but it is specified in some way both globally and locally. Deformations have revolutionized Quantum Theory and Mathematics, and for example Quantization in Quantum Theory is presently of two main types: Deformation Quantization and Geometric Quantization (look them up as keywords on the internet). The simplest example of Deformation is probably also one of the most fundamental in mathematics and physics: Non-Euclidean Geometry (NEG for short here). NEG is the Geometry of curved ("bent") space while Euclidean Geometry (EG for short here) is the Geometry of flat space. So we get from Eucidean Geometry to Non-Euclidean Geometry by the very Simple and Intuitive idea of Bending or Curving something. What's so great about that? Well, Non-Euclidean Geometry was discovered in the 1800s by Gauss, Riemann, Lobachewski, and Bolyai, and both Mathematics and Physics were fundamentally changed afterward. Physics used NEG as the basic tool (in what is called tensor formulation) for General Relativity of Einstein, and General Relativity is in turn involved either in classical or modified forms in Quantum Gravity and Superstring and other Quantum-Related research. Before getting to Fractals, I'll give one more example of "what's so great about that". "Very small" Deformations were discovered as "Infinitesimals" by Sir Isaac Newton and Leibniz in the 1600s, although they actually built upon pioneering work of Pierre De Fermat of 1600s France and Archimedes of later Ancient Greece. In other words, they are the essence of Calculus. Mathematics and Physics and other Sciences were not the same after Calculus. They changed fundamentally. Yet, like Non-Euclidean Geometry, Calculus was a type of Deformation, both very Simple and very Intuitive when formulated as Deformations (not so simple when presented in complicated textbooks designed for Math or Physics majors who have mastered many prerequisite courses). Most of us, I think, have an intuition that Fractals and Chaos are as Revolutionary as anything around, so a "natural" choice is to ask whether they can be regarded as Deformations of anything. Fractals change the shapes of objects by Self-Similar Contractions. In simple language, the original shape of a "large" object is shrunken into many smaller copies of that object, and that is the Change involved. The new, smaller objects are similar to the origin ones. Everywhere you look, so to speak, there are smaller copies of the original object - smaller and smaller on smaller and smaller scales. In Computer and Mathematics language, the way in which the original object changes is kept track of and specified by Iteration and repetition of the previous operation (the opera- tion often called Composition in Mathematics). What could "Deformation" give FractInt that current methods don't give? In my opinion, it will probably eventually yield Quantum Fractals and Quantum Knowledge-Information from a different route than current Quantum Computer and Quantum Information theories. That route, as I indicated above, is through Deformation Quantization among other methods. But as important as that, it will probably enable us to understand the relation- ship between "shrinking" large objects on the human scale and the nature of the apparently very diferent microscopic Quantum world where waves or fields and particles have a curiously different nature. If no reader is interested, I'll take this thread elsewhere, and I'll have no hard feelings since I won't give up my interests. Hopefully, readers won't have hard feelings about being disturbed from their other interests in this posting. Incidentally, nobody has to make a "major" contribution to be interested - just indicate that it interests you. Osher Doctorow

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Fractint version 20.3
by Jonathan Osuch 17 Jan '04

17 Jan '04

Fractint version 20.3, both DOS and Linux, is now available at www.fractint.org. Note that this is the float only version. What's new: Incremented the version number to accommodate backwards compatibility for the inside=atan and outside=atan options. Fixed inside=atan and outside=atan to use the full color palette instead of limiting to 180 colors. Added Charlie Chernohorsky's virtual screen zoombox fix. Added Gerald Dobiasovsky's fixes for the demo key files needed because of menu prompt changes and pan/zoom size changes. Fixed evolver parameter entry. Fixed hypercomplex fractal type to turn off symmetry when a cj parameter is used. Fixed the plasma type to show the value of the parameter that is actually used in the image generation. Fixed the plasma type so that a parameter file uses the colors included in the parameter entry instead of the default colors. Revised the plasma type prompt to reflect the values that can actually be used. Increased the Lsystem line length from 160 characters to 255 characters. Fixed the browser so that it recognized the fractal type stored in images. Fixed the Xfractint FPUcplxdiv and FPUcplxlog routines in fpu087.c to match the Fractint assembler code. Modified the Xfractint resume code to remove the Xfractint specific sections since they are no longer needed (gcc macros match MSC macros). Jonathan

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FOTD 16-01-04 (Into the Fray [7])
by Jim Muth 16 Jan '04

16 Jan '04

FOTD -- January 16, 2004 (Rating 7) Fractal visionaries and enthusiasts: As I have often stated in the past, I enjoy reading "Skeptical Inquirer" magazine, a publication devoted to debunking claims of the paranormal and promoting the materialistic philosophies. But after reading this magazine for 15 or so years, I still believe that some paranormal things do exist, and I still am not a materialist. This could be because the magazine articles are ineffective or because I am slow to see the truth. This incon- sistency has long been a puzzle to me, but the mystery has now been solved. There is an article in the latest issue, which tackles the question of why skeptics have such a hard time debating with believers. It claims that believers have so many mistaken ideas about using reason that they are nearly impossible for skeptics to argue with. Believers fall into new reasoning fallacies faster than skeptics can set them straight, and as a result, the skeptics soon give up in disgust. In other words, skeptics are right, but believers are too confused to recognize it. Now I know why I am convinced that precognition is a true ability of man. I am too confused to know that it logically cannot exist and I therefore could not possibly have experienced it, which I have a very clear memory of having done. But slow-wittedness has its good features. Fractals do not exist either. But I am unaware of this fact, and I find fractals everywhere. I have been finding them in fact just about as long as I have been reading "Skeptical Inquirer" magazine. Today's fractal is a typical example. There is little of interest in the Z^(1.5)+C Mandeloid, but, being unaware of this, I continue searching. By using the 'tdis' option on the outside parts of the parent fractal, I have now found another midget in Z^(1.5)+C worth a 7, this one with an overall value of 102. I named the image "Into the Fray". The image has a certain feeling of a boisterous melee about it, which inspired the name. And reading that magazine article put me in just the right mood to apply the name. I could just as easily have seen peaceful garden terraces in the image, but we will never know what type of names I might have chosen if I had found today's image on a different day. I guess it is up to the individual viewer to decide whether the image is violent or peaceful. The image may be seen either by running the parameter file and waiting 6 minutes or by download- ing the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and seeing it at once. Though it was cold Thursday here at Fractal Central, it was not as cold as forecast. With a high temperature of 27F -3C and occasional sun, it was bearable enough for the dynamic duo to enjoy 15 minutes in the yard. This was time enough for them to do the things that needed to be done. Today is starting the same. My own work is moderate to heavy, so I had best get started, or else be in danger of falling behind and believing aliens from outer space are among us. Until the next FOTD, which will appear in 24 hours, take care, and please direct any non- fractal comments about skepticism to the philofractal list. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Into_the_Fray { ; time=0:06:53.04--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=+0.11122362069284430/+0.715289864598950\ 50/188093.8/1/87.5/8.61523595518942642e-010 params=1.5/0/-2/0 float=y maxiter=32767 inside=0 outside=tdis periodicity=10 colors=000OYSTSOYMJaGFfAAj46iA9hFChKFgQIgVLf_OfdRe\ jUeoXdt_dyb_t_WpYSlWOgTKcRG_PCWNIZUO``TcgZencgtKmm\ 0sf4sc8saCs_GsYKsWOsUSsRWsP_sNcsLgsJksHirKgqNeqPcp\ SaoV_oXYn_XmbVmdTlgRkjPklNjoLirKitPboUXkYQgbKcfD_k\ 7Wo1Sn2Rn3Rm4Rm5Rm6Rl7Rl8Qk9QkAQkBQjCQjDQjDQoRItcA\ yp2if4VX5GN71E85GB8IDCJFFLIJMKMOMQPOTRRXST_UVcVXfX\ _jYam_cp`eqcfqefqhgqjgqlhqohqqiqtiqvjqxjtVRw17u2Ct\ 3Hs4Mr5Rq6Wp7`o8en9jmAnjDmhGmeJmcMlaPlZSlXVkVYkS`k\ QcjNfjLijJliGoiEriCuiDpgDleDhcDdaE`_EXYETWEOUEKSFG\ QFCOF8MF4KF0IG2LH3NI4PJ5SK7UL8WM9ZNA`OCbPDeQEgRFiR\ GkTIgVJdWL`YMYZOU`PRaQOcSKeTHfVDhWAiY6kZ3l_0gW0cS0\ ZO0VL0RH0MD0I90E60E52E44E45E37E39E2AE2CE1EE1FKDJQP\ NW_QakUfvXYhYPVYGHYILWJPVLTUMXTN`SPdRQhQRlPUjRWhSY\ fT_dUbbVd`WfZYhXZkVzmTzoRzqQzpVzoZznczmgillklzlzzz\ zzhonfzzdplbqlark_rkYsjWtiUuiTuhRvgPwgNxfLxfKtl_qq\ nnmmljmifmgcmBmeAoeFi`KcX } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(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 } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] FOTD 15-01-04 (Fractal Fossil [7])
by Jim Muth 16 Jan '04

16 Jan '04

At 12:14 PM 1/15/04 -0700, you wrote: >On Thu, 15 Jan 2004, Jim Muth wrote: >(...) >> with the reminder that the 11-minute wait for today's parameter >(...) >> maxiter=12000 bailout=9 inside=0 periodicity=10 > > Come on, man. The bailout _might_ be reasonable, but how many >points escape after 255 iterations? The bailout=9 entry should have been edited out of the parameter file. It appears only because I have it entered that way in my sstools.ini file. It has no effect on the resulting image however, the actual bailout of which, as specified in the generating formula, is imag(p2)+100 or 100. As for the 255 iterations, where did you find this entry? The maxiter of the image is 12000. Jim M.

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Frenzy! luminance=atan chrominance=palette
by SherLok Merfy 16 Jan '04

16 Jan '04

http://ecn.ab.ca/~brewhaha/img/Frenzy.png Okay...you won't find those settings in fractint, but that's how you might write it. Either that or outside=iaTan (iterated atan), and he looks kind of serious for a mascot (maybe he's working in Irak), plus the colours are so loud that you might miss the impression that he wore a tuxedo. Maybe it's more like a duck than a penguin, but it's gotta be a bird! The image I jenerated was actually post-processed with Paint-Shop-Pro (it might actually be nifty to make fractint ignore lines with either more or less than three numbers on them, so that it could share palettes with PSP, BTW). Um...you know what...maybe FRACTINT does that already. In any case, I took identical views of the same formula, but with different settings for outside. Then, I used PSP to replace the default map with a graymap, (loaded a palette with indexes maintained. Then I took the image from "BrainH" parameters (it looks black on my screen, but look at the numbers on the palette manager) and made the BrainV imaje into a mask for it. Then I unloaded the brainV imaje, because PSP doesn't seem to do live masking. Then I raised the luminance of this masked image three times. Aside from choosing PNG format, which is the king of lossless compression (equivalent in size to a JPEG with about 90% quality in this case), that's all there was to it. You can adapt this process to making logos in many other pixel editors. (What remains is for me to pipe the comments from the source images into a PNG for the web). The downloadable is currently (and likely not permanently) about 600k, because it's set for landscape printing at 200dpi with quarter inch margins, because I went to the print shop with it. The laser printer there is good for 600dpi, but I didn't feel like dealing with commands that always require parameters today, so I stuck with Win 3.1, which can't see over 64meg of RAM (SXMS), and PSP which apparently can't see THAT much, despite Window's claim that I hav over 200meg of virtual memory. The space required for 200dpi and 24bits is fairly close to the space required for 600dpi and 3bits (8*10.5*200^2 works out to one nineth of the surface area at 600dpi, but eight times as many bits per pixel or a little less depending on whether there can be more than one colour on a pixel), so the colours came out very nicely, minus the edges weren't as sharp as they could be, plus the ink isn't as sensitive as with a bubble-jet, plus you can't tell how high the print head is. So, it was worth 75 cents and maybe this two bits. Frenzy {; Where went the neg function? z = pixel, s=-fn1(fn2(pixel)): z = z * s + z s = s/z + pixel |z| <= 8 } BrainV { ; Luminance. ; Version 2002 Patchlevel 5 ; How many times will you tell me that? ; 1/5 speed with intejers on PII. reset=2002 type=formula formulafile=fractint.frm formulaname=frenzy function=ident/conj passes=1 center-mag=0.496851/0.00495108/0.5604486/1.4649/90/-1.2337353361147052\ 1e-014 float=y maxiter=255 outside=atan inside=0 } BrainH { ; Chrominance. ; Version 2002 Patchlevel 5 ; Version 2002 Patchlevel 5 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=fractint.frm formulaname=frenzy function=ident/conj passes=1 center-mag=0.496851/0.00495108/0.5604486/1.4649/90/-1.2337353361147052\ 1e-014 float=y maxiter=255 inside=0 colors=050505502500055520025550005490205050505502500055520025550005490\ 2050505055025000555200255500054902050505055025000555200255500054902050\ 5050550250005552002555000549020505050550250005552002555000549020505050\ 5502500055520025550005490205050505502500055520025550005490205050505502\ 5000555200255500054902050505055025000555200255500054902050505055025000\ 5552002555000549020505050550250005552002555000549020505050550250005552\ 0025550005490205050505502500055520025550005490205050505502500055520025\ 5500054902050505055025000555200255500054902050505055025000555200255500\ 0549020505050550250005552002555000549020505050550250005552002555000549\ 0205050505502500055520025550005490205050505502500055520025550005490205\ 0505055025000555200255500054902050505055025000555200255500054902050505\ 05502 }

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Re: [Fractint] FOTD 15-01-04 (Fractal Fossil [7])
by Noel Giffin 15 Jan '04

15 Jan '04

SherLok Merfy wrote: > On Thu, 15 Jan 2004, Jim Muth wrote: > (...) >> with the reminder that the 11-minute wait for today's parameter > (...) >> maxiter=12000 bailout=9 inside=0 periodicity=1 > > Come on, man. The bailout _might_ be reasonable, but how many > points escape after 255 iterations? I can't speak for this particular image, but several years ago, (before I had a family and I still had lot's of spare time), I created a mandelbrot fractal image where every pixel in a 1024x768 image iterated a minimum of 83,693 times with a max iter set to 2 million. It is hard to imagine an array of adjacent points iterating that many times before diverging into a unique and beautiful image but the proof is before you. http://spanky.triumf.ca/www/fractint/hi-iter.html Cheers, Noel

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FOTD 15-01-04 (Fractal Fossil [7])
by Jim Muth 15 Jan '04

15 Jan '04

FOTD -- January 15, 2004 (Rating 7) Fractal visionaries and enthusiasts: As I mentioned in the FOTD of January 13, I have long been searching for a great midget in a Mandeloid fractal with an exponent of Z between 1 and 2. The midget illustrated in today's image might not be great, but it is at least above average. The rating of a 7 might be a bit generous, but regardless, it is still one of the best midgets I have yet found in such a low-order Mandeloid. The overall value comes in at a 61. The exact exponent of Z in today's image is 1.5, which has been calculated 1.5 levels down the logarithmic hyper-spiral. The parent fractal appears as a reasonably normal Mandeloid rotated 180 degrees. On the north shore of the large western bay lies a tiny rudimentary bud, with a curious half-developed valley on its inside top shore. The shoreline of this valley is lined with areas of near total chaos, cut-off bits of which extend some distance inland. Today's scene lies in one of these cut-off inland islands of chaos. As is typical of all fractals with fractional exponents of Z, today's image is filled with discontinuities. The discontinui- ties are in fact the substance that composes the image. These breaks are a nuisance, but they also show the way to midgets. When one is searching for quadratic midgets, the signposts are areas where the features are arranged roughly symmetrically around a point. When the object of the search is a midget of a lower order, the breaks in continuity serve as the signposts. The breaks usually converge on midgets which otherwise would be nearly impossible to find. I named the image "Fractal Fossil". The name came to me when I started wondering how long this particular scene existed before I discovered it. It certainly existed billions of years, but did it exist before the 'big bang'? As far as that goes, did the 'big bang' actually happen, or is it just a creation myth without an outside creator, carefully designed to fit into our scientific world-view? While pondering the imponderable, I will end today's discussion with the reminder that the 11-minute wait for today's parameter file to run can be avoided by downloading the finished GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The snow held off until after dark on Wednesday here at Fractal Central, but with a temperature of 23F -5C and brisk winds, the outdoor conditions were too harsh for the dynamic duo to venture forth. They spent the day indoors, sleeping and eating. Today is starting with a fresh inch of snow and falling temperatures. The cats will likely have another indoor day. With about 4 hours work to finish, I will likely have an indoor day also. And in 24 hours, I shall return with the next FOTD fractal. Until then, take care, and remain fractally oriented. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Fossil { ; time=0:11:27.07--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=+0.04526308974509857/+0.771631709693025\ 60/698846.7 params=1.5/0/-1.5/0 float=y maxiter=12000 bailout=9 inside=0 periodicity=10 colors=000DIMEDHF9CG479vwBghDTVFEGgTubOkZJbUEUQ9KL\ 4BdkYciWbgVaeU`cT_bSZ`QYZPXXOXWNWUMVSKUQJTOIXL_`QX\ cUTgUQjUNnUKqUHsUErUIqULpUOoUSoUVnUYnU`mUcmUfmUimU\ gkUjjWgiXdhXbgW_fUYfRVfNTfJQeFOeCLe8Je4Ge1Ed3Hc4Kb\ 5Ma7P`8R_9UZBXYCZXDaVFcVGfUHhVLiWPiWSjXWjX_jYbkYfk\ ZjkZml_ql_tm_um_um_vm_vm_wn_xp_yr_zv_zzQkcGZc6Nc5P\ `5QZ5RW5SU5TR5UP5VN4XK4YI4ZF4_D4`A4a84b67Z79V8BS8D\ O9GK9IHAKDAM9BO6BUBGZFKcJPhOTmSYrWaiS_`PYTLXKIVBET\ 3BS4FR5JQ6NP6RO7UN8YM8cM9gLPkKUnJZqIcsHcvHcqFFkEGe\ CH_BJU9KO8LI6MK5NK4LK3JK2`naXiUTcNPWGLU9JYPIUMIRKI\ OIILGIIEHFCHCAH98H66H34y0Zw0Xu0Ws0Vq0Tp0Sn0Rl0Pj0O\ h0Ng0Le0Kc0Ja0H_0GZ0FX0DV0CT0BR09Q08O07M05K04I03eZ\ 8XN6PB4gGLIqMHnLHkKHiJHfIHdHHaGbLcbMbbNacOacP`cQcc\ RfcSjdTndUrdVvdWzdWWcUVbTUaST`RS`QR_PQZOPYNOXMNXM3\ XLMWKLVJKUIJTHITGHSEGRDFQCEZBDPACO9BN8AM79L68L57K4\ 6J35I24H137dl9_fAVaBRXCMS } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 13-01-04 (Hope Springs Eternal [4])
by Jim Muth 13 Jan '04

13 Jan '04

FOTD -- January 13, 2004 (Rating 4) Fractal visionaries and enthusiasts: As they say, hope springs eternal. And that is what happened to me yesterday as I was deciding which part of Fractal Land to explore. Moved by eternal hope, I finally decided on a different part of the same fractal that held the 'half- elephant' image which appeared on January 11. I constantly hope to find a truly outstanding midget in the Mandeloids with exponents between 1 and 2; I never have found one. But hope springs eternal, and I keep trying, apparently unable to learn from the years of coming up short. Today's image shows a very typical midget in the Z^(1.5)+C Mandeloid. As is true with almost all other midgets in this range, the area is far too broken and chaotic to make an impressive image. Maybe the truly great scenes are there, hiding somewhere in some remote corner of the parent fractal, but somehow I doubt it. But, being a hopeful fellow, I will continue searching for something that I know might not exist. Any unusual scenes I come upon in my search will appear as a FOTD. Most scenes will vanish into the limbo reserved for deleted fractal images. In all honesty, I could rate today's image no higher than a 4, which, combined with the render time of just under 12 minutes, gives an overall value of 33. There are two ways to see the image: first, by running the included parameter file; second, by downloading the completed GIF image from Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The dynamic duo of fractal cats had one of their best days in quite a while here at Fractal Central on Monday. When the temperature reached 46F 8C shortly after noon, they paraded to the door and asked in unison to go out. They looked almost like kittens as they romped in the dead grass and played hide-and-go- seek in the holly thicket. When evening came they were ready to come indoors to eat and sleep. Today looks like a repeat, but another cold wave is on the way, and due to arrive toward eve- ning. Hopefully, the duo will finish romping before the cold air arrives. And also hopefully, my work will be finished before the duo ends their romp. Until next time, take care, and when, if ever, will the new anti-spam law start working? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ HopeSpringsEternal { ; time=0:11:57.49--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-0.81193569327624530/+0.514042346538518\ 10/4.870091e+007/1/25/1.19288052269350686e-007 params=1.5/0/1.5/0 float=y maxiter=1800 inside=0 logmap=326 periodicity=10 colors=000g70m60a70e90`90ZA0fC1fC3dD4cD6aF7`G9_GAX\ ICVJDTJFSLFQLGPMIMOJLOLJPMIQOGQPFSQCSS9TT4VV0VX0XY\ 0XY0VX0TV0TT0SS0SQ0QP0QO1PM3PL4OJ6OI7MG7MG9LFAJDCJ\ CDIAFI9GG7IG6JF4LF3MD1OD0PC0PC0SA6VADYAL`AQcAYf9di\ 9ll9ro9yr9zu9zsDzsGzrJzrMzpPzpTzpXzo_zoazmdzmizllz\ lozlrzjuzjyzizzizzgzzgzzgzzczz`zzYzzTzvQzrOzmLziGy\ dDx`AvX7sS3rO0pJ0oF0mC0oD0oD0oD0oD0oD0oD0oD1oD1oD3\ pD3pD4pD4pD6pD6pD7pD7pD9pD9pDArDArDCrDCrDDrDDrDFrD\ FrDGrDGrDIoFImFJlFJjGLiGLgGMfIMdIOcIOaIO_JPYJPXJQV\ LQTLSSLSQMTPMTOMTMMYDX`4fc0pa1ma7j`Dg`Jd_Pa_V_Y_XY\ dTXjQXpOVvLVzITzFTzC`zAgzAmz9uz9zz9yzAyzAyzAyxCyvC\ ysCyrCyoDymDyjDyiFyfFydFyaFy`GyYGyXGyTGySIyPIyOIyL\ JyJJyGJyFJyCLyALy7Ly6Lv7Ms7Op9Om9PjAQiAQfCScCT`DTY\ DVVFXTFXQGYOG_LI_II`FJaDJagScz`dzafzafzagzagzaizci\ zdjzfjzglzilzjmzlmzmozoozppzrpzsryuryvsxxsxyuvzuvz\ vuzvuzxszxszyrzyrzzpzzpzz } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 12-01-04 (Into the Crucible [7])
by Jim Muth 12 Jan '04

12 Jan '04

FOTD -- January 12, 2004 (Rating 7) Fractal visionaries and enthusiasts: Every once in a while one must vent a little frustration. In my e-mailbox this morning I found at least a dozen letters telling me how to get a bigger pole, or a heavier or longer or bulkier pole, etc. Why would anyone want to sell me a new pole? I don't need a bigger pole. The pole standing in the corner of the fractal yard has been faithfully supporting the wires for at least 40 years. It is 10 meters tall, 30 cm thick, and still in perfect condition. The market for poles must be very limited. Those spammers should wise up and try to sell a product that people actually want. The fractal for today is far less confusing. It is a scene in the fractal that results when 8.3 parts of Z^(-3.8) are subtrac- ted from 9.8 parts of Z^(-1.5) and (1/C) is added. To compli- cate things, the fractal has been evaporated and rendered with the 'bof61' inside fill. Fractal evaporation is achieved by raising the escape radius of fractals with negative exponents of Z to a value large enough so that all points are trapped. I named the image "Into the Crucible". With its clashing colors that are almost painful to look at, it reminds me of looking down into a crucible of molten steel. The rating of a 7 seems appropriate -- at least by my fractal standards. Those with different standards may rate the image differently. Combined with the reasonable render time of 3-1/2 minutes, the image has an overall value of 200. Those who prefer their fractals ready-to-go may pick up the finished GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> It was warmer here at Fractal Central on Sunday, and the sun was shining most of the day, but the temperature of 28F -2C was warmer only by comparison to the day before, and the fractal cats compared the temperature to a day in midsummer. They decided to remain indoors all afternoon, thinking of what might have been. Today is starting even warmer -- it's actually above freezing. But it is cloudy. We shall see what the duo makes of this. And I must decide what to make of the work on the shelf beside me. Most likely, I'll work on it until it is finished. And when it is finished, I will enter fractal-land to see what has happened since last I ventured there. Whatever I find will appear as the FOTD for tomorrow. Until then, take care, and remember the children. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Into_the_Crucible { ; time=0:03:31.41--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.93333741621415410/-1.559243860808650\ 00/3009538/1/-117.5/7.47725191418274759e-006 params=9.8/-1.5/-8.3/-3.8/0/1e+100 float=y maxiter=1200 inside=bof61 periodicity=10 colors=000mHKiLIePHaTGj0uU`EIn2QcDXTOdIZj4hu0jlCjm\ FknJloNmoQmbLUQGA000OH7RI9UIAWIBZID`IEcIFfIHhJIkMJ\ mPLpSMsVNuYPx`QzcRwIPuHNrGMpFKmEJkDHhCGfBEcACa9BZ8\ 9X78U66S55U79V8DWAGXBKYDNZER_GVaHYbJacKddMheNlfPog\ QshRvjQskQqlQnmPlnPipPgqPdrObsO_tOYvOVwNTxNQyNOzNM\ xRNwVOuZPtbQrfRqjSonTnrUmuUirXepZan`YlbUieQggMeiIc\ kEUiALg7Cf7dBAgGCiLFlQHnV8xeJpZUiSdbLoWEzP7nUHcYRO\ NMTa_YtpXplXmiWjeWfbVcZV`WVYTYZ_`_ec`kfaqaNZX9H_GM\ aMQdSUfYYhcakiemoioumlrcipVfmLckCXa0`i3dq6hy8evCbt\ F_rIYpLchTha_e_ZbYZ_WYYUYVSXSQXPOWNMWcJitGwrFqpEkn\ EemD_kDUiCOkBAhCJfCScC`aCi_CqZBpYBoXAnXAmWAlV9kU9j\ U9jXSn_iqZekYaeYZ_XVUjDTXSO8`LJeKVq0TiKRacQUvSXrU_\ nVakXdg9gnYfdRbfKZh4CwEWiRo_OnWLnTImQGmNDmJAlG7lDb\ Rc5lABkCGjEMiFRhHXgIafKm8TffLeeIdeFdeCce9be6be3Z_A\ VVHRQONLVJFaFAhB5o70v68o5Gh1I`4Nb7RdAVfDZhGbjJflMj\ nJvwOnpTgjY`cOThbUYzbUqUO } 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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 06-01-04 (Rich Field Fractal [8])
by Jim Muth 12 Jan '04

12 Jan '04

FOTD -- January 06, 2004 (Rating 8) Fractal visionaries and enthusiasts: Way back when I was a curious young boy, (I'm now a curious old boy!), I wanted more than anything else, a telescope. I wanted to see with my own eyes all those stars and nebulae of outer space that I had seen only in pictures in the popular astronomy books I was reading at the time. So I began worrying my father to give me the most powerful telescope available. I wanted something like a 2000 power telescope. I thought that the higher the magnification, the more stars and nebulae it would show. When I finally got my telescope, I was a bit disappointed. Instead of the 2000 power monster that I wanted, my father gave me a 40 power rich-field telescope. But he explained how telescopes work, how empty magnification is helpful when observing the planets, but basically useless when one wants to observe fields of stars and faintly glowing clouds of interstellar gas. He told me that those brilliant pictures in my books were time exposures on sensitive photographic plates, and that I would never see the nebulae with my eyes as clearly and brilliantly as they were illustrated in the books. A bit disappointed at first, I overcame my disappointment the first dark night in the yard, when my father directed the telescope toward the Beehive cluster. I used my telescope every clear moonless night after that for several years. I named today's image "Rich Field Fractal". It fills the screen with such detail that I can almost see myself at the eyepiece of that old telescope, which BTW is still packed away in a closet. The image itself is an 'evaporated' one, as ephemeral as those deep-space nebulae I gazed at in wonder those many years ago. The generating formula continues the theme of the past few days by combining various portions of Z^(-1.3) and Z^(-3.1). I then added (1/C) instead of plain C because (1/C) turns a fractal inside out, and fractals with negative exponents are already inside out. Turning them inside out a second time makes normal fractals out of them. And we all like things to be normal. As I said above, the image has been 'evaporated'. Evaporation works only on fractals with negative exponents of Z. When I find an interesting 'normal' scene in such a fractal, I usually 'evaporate' it by raising the escape radius to 10^100, (or one- googol). Sometimes the evaporated version is better, sometimes not. In today's case, it is a close call, but the 'evaporated' version is a bit better. I rated the scene at an 8, a rating that helps make up for the half-hour wait while it renders from the included parameter file. But a half-hour is still a half-hour, and those with more important things to do can save time by downloading the completed GIF image from paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> It rained most all day Monday here at Fractal Central, and the temperature never rose above 45F 7C. The cats did not like it, but, compared to some of their past bad moods, their moods were acceptable. I gave them a treat of tuna just as a reward. The sun has appeared this morning, but a cold wind has sprung up. We'll see what the dynamic duo thinks of this. I have about the normal amount of obligatory work to finish before I engage in fun. The next FOTD will appear in 24 hours. Until then, take care, and live a peaceful life. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Rich_Field_Fractal { ; time=0:28:56.14--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+2.13380830806844900/+0.950227584052971\ 10/2264450/1/-12.5/1.19070429488443708e-008 params=-1.3/-3.1/-3.1/-1.3/0/1e+100/0/0 float=y maxiter=2500 inside=bof61 periodicity=10 colors=000a4k`5jZ5iX6hW7gU8fS8eR9dPAcNAbMBaKC`ID_H\ DZFEYDFXCFWFKUIPSLUQOYORbMUgKXkI_pGbuEdyCftFgoHhkK\ ifMjbOlYRmTTnPWoKYpG_mWcjZjW`lXefYj`YoVZtPZyJ`uIbq\ IcnIejIffHhcHi_HkWHlTHhQKdON`MPXJSUHUQFXMC_IAaE8dB\ 6fGA`LEVPIPUMJYPE_NG`MHaLIcKJdJKeHLgGMhFOiEPkDQlBR\ mASo9Tp8Uq7VoF_nMdmUil`nkgrghpdin`ilYjjVjhRkfOkdKl\ bHl`EmZAmX7nV4nTRnkQojQpjQpjQqjQrjQrjPsjPtjPtjPuiP\ uiPviOwiOwiOxiOyiOyiOziOziTwdYt`aqXfnTjkPohLsfHuiH\ vlHtjGsiFrgFqfEpdDocDmaCl`BkZBjYAiX9hV9gU8fS7eR7dP\ 6cO5bM5aL4`K4_J6ZJ8YJAXJCWJDVJFUJHTJJSJKRJMPJOMJQL\ JSKJTJJVIJXHJZGJ_FL`FN`EP`ER`DT`DU`CW`CY`B_`Ba`Ac`\ Ada9fa9ha8ja8la7na7oa6qa6sa5ua5wa5xa5zmUzzczzezzgz\ zmzzmzzTjXOkbJkgHn`FqVDsPBvJ9xDAuFAsGAqHAoIAmJAkKA\ iMAgNAeOAcPA`QAZRAXSAVUATVARWAPXANYALZAJ_BMYBOXCQW\ CTVCVUDXTD_SEaQEcPEfOFhNFjMGmLGoKGqJHrIHrIHrIIrIIr\ HIrHJrHj2oj0qh1of2ne3mc3l } 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 } END 20.0 PAR-FORMULA FILE==================================

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[Fwd: Error in bjax formula?]
by Edwin 12 Jan '04

12 Jan '04

Hi, Looking at the fractint.frm which comes with xfractint 3.10, the "bjax" formula is: Bjax {; z=c=2/pixel: z =(1/((z^(real(p1)))*(c^(real(p2))))*c) + c } This looks like it's missing a bailout condition. Does fractint supply a default bailout function if the user doesn't give one? When I render it I get a blank screen. However even if I add |z| < 4 at the end, it still doesn't display anything, so I'm a bit confused. Regards, -- Edwin

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FOTD 11-01-04 (Half an Elephant [6])
by Jim Muth 11 Jan '04

11 Jan '04

FOTD -- January 11, 2004 (Rating 6) Fractal visionaries and enthusiasts: In the East Valley area of the Mandelbrot set there lives a herd of elephants. Each elephant stands astride its personal bud, guarding that bud from anything that might threaten it. In the cubic M-set two elephants guard each double bud. In the quartic set, there are three elephants per triple bud. And so it contin- ues into infinity, the elephants eventually merging into a haze of undifferentiated elephant stuff. But what of the Z^(1.5)+C Mandeloid? In this set, the same trend continues. Half an elephant stands guarding each half-bud. I have no idea what happens to the ele- phants' rear ends, but the front parts are there, complete with curled trunks. It took the MandelbrotBC1 formula to show a level of the parent fractal where these half-elephants are not broken beyond recogni- tion. Luckily, that level was found only 1.5 turns up the log- arithmic hyper-spiral. I named the image "Half an Elephant", most likely because half an elephant is better than none. Of course, a half-elephant is not as good as a whole elephant, but that's another story. When the time to do the rating arrived, I pondered the image and decided on a rating of 6, which combined with the render time of 10.67 minutes gives an overall value of 56. The GIF image is available for near-instant download on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather Saturday here at Fractal Central was very cold. All day, my digital thermometer hung around 10F -12C, which kept the cat duo confined very securely to the sources of heat. They needed only one minute on the porch to convince them that the outdoors was uninhabitable. In the evening, I presented them with a treat of tuna, which lifted their sullen spirits. Today, the regular work is pretty much caught up, but the fractal lady is thinking of a trip to look at 'antiques', (IMO, discarded junk), so I guess I'll tag along. But I'll be back in plenty time to find the next FOTD fractal. Until that next fractal appears, take care, and look for the other half. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Half_an_Elephant { ; time=0:10:40.43--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor center-mag=+0.15911535849239720/-0.002404932214412\ 98/1541.738/1/22.5/4.45664338766249557e-013 params=1.5/0/1.5/0 float=y maxiter=15000 inside=255 logmap=39 periodicity=10 colors=000R9YS9YS9ZT9ZU9_V9_V9`W9`X9aY9aY9bZ9b_9c`\ 9c`9da9db9ec9ec9fd9fe9gf9gg7gg8gf9geAgdBgcBgcCgbDg\ aEg`Ff_Ff_GfZHfYIfXJfWJfVKfVLfUMeTNeSNeROeRPeQQePR\ eOReNSeMTdMUdLVdKVdJWdIXdIYdHZdGZdF_cE`cDacDbcCbcB\ ccAdc9ec9ecAdbAcbAcaAbaAa`Aa`A`_B`_B_ZBZZBZYBYYBYX\ BXXBWWCWWCVVCVVCUUCTUCTTCSTCSTDRSDQSDQRDPRDOQDOQDN\ PENPEMOELOELNEKNEKMEJMEILFILFHKFHKFGJFFJFFIFEIFEIF\ EIFEImSNoQPqNRpOQoPPnQPmROlSOkSNjTNiUMhVLgWLfWKeXK\ dYJcZJb_Ib_Ia`H`aG_bGZcFYdFXdEWeEVfDUgCThCShBRiBQj\ APkAOl9Mk7Nl8Ol9Ol9PlAQmBQmBRmCSmDSmDTnETnFUnFVnGV\ oHWoHXoIXoJYoJYpKZpL_pL_pM`pMaqNaqObqOcqPcrQdrQdrR\ erSfrSfsTgsUhsUhsVitWitWjtXktYktYluZmu_mu_nu`ovZpu\ `qtbrtcssetsfurhvriwpfxocymazlZzkWziUzhRzgOzeMzgJz\ iIzkHzmHzoGzqGzsGzuFzwFzxFzyEzzEzzDzzDzzDzzCzzCzzC\ zzBzzBzzAzzLzzMzzNzzOzzOzzPzzQzzQzzRzzSzzTzzTzzUzz\ VzzUzzVzzVzzWzzWzzXzzXPPm } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(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 } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] FOTD 09-01-04 (Fractal Ribbons [6])
by Guy Marson 11 Jan '04

11 Jan '04

At 01:29 11/01/2004 -0700, you wrote: >On Fri, 9 Jan 2004, Jim Muth wrote: > ... >number for a constant inside or outside colour would go). > ... > Like I implied, the problem isn't as fundamental as the atan >function itself. If you're bent on identical output for the same .par >file, then you can set the default max_colors to historical values. > Hi fractinters, here are a few examples on how to find the pretty rare midgets with "inside=atan": atan-a0, b0, c0 and d0 pars are starting pics with low magnification and low maxiter (80 or 160). Zoom-in until points of intersecting colours a visible.. (atan-a1, b1, c1, d1). Then one can double the maxiter while zooming into the pic, double maxiter again, and still zooming-in onto points of intersection.. and so on.. meanwhile on can change to "logmap=yes" .. (the final midget is +/- in the centre..) have fun.. cheers, Guy ****** atan-a0 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-0.758205/0.076935/1 params=0/0 float=y maxiter=80 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-a1 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-0.75820548276543810/+0.07693499922059592/100 params=0/0 float=y maxiter=80 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-a2 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-0.75820548276543810/+0.07693499922059592/4000 params=0/0 float=y maxiter=80 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-a3 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-0.75820548276543810/+0.07693499922059592/160000 params=0/0 float=y maxiter=160 inside=atan logmap=yes periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-a4 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-0.75820548276543810/+0.07693499922059592/3500000 params=0/0 float=y maxiter=160 inside=atan logmap=yes periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-a5 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-0.75820548276543810/+0.07693499922059592/7.014636e+007 params=0/0 float=y maxiter=2560 inside=atan logmap=yes periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-b0 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-1.75122/0/0.6666667 params=0/0 float=y maxiter=100 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-b1 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-1.74967/-9.77836e-007/10 params=0/0 float=y maxiter=80 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-b2 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-1.74967399804496800/-0.00000097783572361/200 params=0/0 float=y maxiter=80 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-b3 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-1.74967282502444000/-0.00000058670143418/163934.4 params=0/0 float=y maxiter=80 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-b4 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-1.74967152290777700/+0.00000000000000000/200000 params=0/0 float=y maxiter=80 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-b5 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-1.74967152290777700/+0.00000000000000000/7.5e+010 params=0/0 float=y maxiter=2560 inside=atan logmap=yes periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-c0 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=0.251563/0/0.666 params=0/0 float=y maxiter=80 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-c1 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=+0.25156256516781210/+0.00000000000000000/3000 params=0/0 float=y maxiter=80 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-c2 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=+0.25166857146736680/+0.00009995654063451/60000 params=0/0 float=y maxiter=80 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-c3 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=+0.25166949902248790/+0.00010019991308127/60000 params=0/0 float=y maxiter=160 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-c4 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=+0.25166949349197440/+0.00010020051434159/4000000 params=0/0 float=y maxiter=160 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-c5 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=+0.25166949349197440/+0.00010020051434159/2e+009 params=0/0 float=y maxiter=2560 inside=atan logmap=yes periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-d0 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-0.750518/-0.0200659/0.66666 params=0/0 float=y maxiter=160 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-d1 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-0.75051765447904200/-0.02006592913197069/1000 params=0/0 float=y maxiter=160 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-d2 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-0.75051765447904200/-0.02006592913197069/1000000 params=0/0 float=y maxiter=1280 inside=atan logmap=yes periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-d3 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-0.75051765447904200/-0.02006592913197069/3e+007 params=0/0 float=y maxiter=1280 inside=atan logmap=yes periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-d4 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-0.75051765447904200/-0.02006592913197069/2.503263e+009 params=0/0 float=y maxiter=2560 inside=atan logmap=yes periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-d5 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-0.75051765447904200/-0.02006592913197069/2.500003e+012 params=0/0 float=y maxiter=40960 inside=atan logmap=yes periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 }

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FOTD 09-01-04 (Fractal Ribbons [6])
by Jim Muth 11 Jan '04

11 Jan '04

FOTD -- January 09, 2004 (Rating 6) Fractal visionaries and enthusiasts: With today's image we return to fractal normalcy -- a rating of 6. The illustrated scene lies in the same parent that produced yesterday's image, and once again, one of the more exotic 'outside' options was used, this time the 'atan' option. I read somewhere recently, probably in a letter on the list, that the Fractint 'atan' function has an error somewhere in it. If so, it's a bit late now to correct it, since if this were done, images such as today's, which use the incorrect version, would no longer work. Of course, we could always save the incorrect version by giving it a new name, as was done with the 'cosxx' function. Or even better, we could give the correct version a different name. Today's image reminds me of the type of image that was so popular around 10 years ago, and resembled curled satin ribbons. I named the image "Fractal Ribbons" because of this resemblance. I rated it a 6 because, at least by my standards, it is a bit above average. I cannot say why I am staying with this particular parent fractal, which is giving me such a hard time. Maybe I want to prove that potential glory lies in every fractal, even the most humble. Well, I'll stay with the same fractal another couple days. If I find nothing in it by then worth a rating of 8, I'll give it up and move on. Today's image renders in only 4 minutes, making it a reasonable value for the time spent. Hmmm, maybe I'll start giving my FOTD images a 'value' rating. I could take the present 0-to-10 rating, divide it by the minutes needed to render the image, and multiply the result by 100. This would make today's image worth 150 value points. We'll see . . . The best value of all however is still downloading the completed GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> which can be done in a minute or so. The temperature reached 34F 1C here at Fractal central on Thurs- day, but clouds moved in by midday, making things too chilly for the sensitive whiskers of the fractal cats, who passed the after- noon curled by the radiator, sleeping peacefully. A bit of tuna in the evening made their day complete. This morning is start- ing cloudy and cold again, with a few flakes of snow in the air, and even colder air due by this evening. The fractal cats will not be happy about this. For me, today will be another forgettable day -- that is unless I find a fractal that rates an honest 10. Check back here in 24 hours to see if I succeed, but don't be surprised if I fail. Fractals that rate a 10 are as rare as dodo birds. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Ribbons { ; time=0:04:07.60--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=-0.61045250190546770/-0.011003094073171\ 64/2128.036/1/-142.5/-5.97177099437296022e-011 params=1.2/-2.1/-2.1/-1.2/0/50/0/0 float=y maxiter=1200 inside=255 outside=atan periodicity=10 colors=000NjAMiALhAKgAJfAKeAKdAKcALbBLaCL`DM_OMZFM\ ZGNYHNYINXJNXKOXLOWQOWQPWRPWSPWTQWUQWVQWWRWYRW_RWa\ RWcSWdSWeSWfTWgTWhTWiUWjUWkUWlVWmVWnVWnVWoWWoWWpWW\ pWWqWWrWWsWWtWWuWXsWXtWXtWXuWXvWXwWYvWYwWYwWYxWYxX\ XyWXxWXwVWvVWuUVtUUsTTrTTqSSpSRoRRnRQmQPlQOkPOjPNi\ OMhOLgOLfNKeMJdMJcLIbLGaKG`KG_JFZJEYIEXIDWHDVHCUGC\ TGBSFARF9QE9PE8OD7ND7MC6LC5KB4JB4IA3HA2G81F92EA2DB\ 2CC3BD3BE3AF3AG49H49I48J48K57L57M56N65O65P64Q64R73\ S73T72U72V81W81X80X80ZA2_B3`D4aE5bG6cH7dJ9eKAfMBgN\ ChPDiQEkSGlTHmVInWJoYKpZLq`NraOscPtdQufRvgSufRtfQt\ fQsfPrfPrfOqeNpeNpeMoeMneLneKmdKmdJldJkdIkdHjdHicG\ icGhcFgcEgcEfdDie5lf9ogDrhFrhGrhHrhHrhIrhJrgJrgKrg\ LrgLrgMrfNrfNrfOrfPrfPreQreRreRreSreSreTrdUrdUrdVr\ dWrdWrcXrcYrcYrcZrc_rb_rb`rbarbarbbv`crbbocbldbheb\ efbbgb_hbYi_WjYUkWSlUQmRPnPNoNLpLJqIHrGFsEEtCCu9Av\ 7XwKWwJVwIUwHSwGRwFQwFzzz } 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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 10-01-04 (The Last Try [5])
by Jim Muth 10 Jan '04

10 Jan '04

FOTD -- January 10, 2004 (Rating 5) Fractal visionaries and enthusiasts: Against my better judgement, I tried one more time to find a quality image in the parent fractal I have been exploring for the past several days. Once again I came up short. With a rating of an average 5, today's image is not bad, but it is not good either. This will be my final venture into this particular fractal. To emphasize this point, I have named today's image "The Last Try". The image is a harlequin kind of a thing -- patches of brilliant but unorganized color and apparently random shapes surrounding the usual central midget. The image was rendered in the traditional manner, with the inside set to 'zero' and the outside set to 'iter'. Some of the other options do as good a job of rendering the scene, but I used the traditional method because I wanted to emphasize how this particular area of this particular fractal 'really' looks. Of course, when working with fractals, the word 'really' is relative. Fractals are actually nothing more than numbers -- total abstractions. It is what we do with those numbers to make them register on our senses that creates the 'reality'. The numbers can be used to create sounds as easily as images. The numbers could also be used to create tactile impressions. It is harder to imagine how one might turn a fractal formula into something that can be tasted or smelled, but stranger things have happened. Today's image renders in 26 minutes. This, combined with the rating of 5, gives a total fractal value of 19. The image may be seen by running the included parameter file or by downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Those who wish to feel, taste or smell the numbers will need to invent an appropriate means of doing so. With a temperature of 28F -2C, Friday was too cold for the cats' whiskers. They seemed quite happy to spend the day sleeping by the heat. This morning the temperature is 3F -16C, and though the sun has appeared, this kind of cold is far too severe for sensitive cats to be outdoors. They will certainly be satisfied with another day by the radiator and a dab or two of tuna. I have enough work waiting to keep me busy for a good part of the day. When the work is finished, I'll have time to find a fractal in a different fractal world. In 24 hours I'll return with the fractal I find. Until then, take care, and if in the southern hemisphere, keep cool. Otherwise, keep warm. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Last_Try { ; time=0:26:04.66--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.51767124083257100/+0.951548168001671\ 90/2041548/1/-27.5/2.17169040875320185e-008 params=1.2/-2.1/-2.1/-1.2/0/525 float=y maxiter=2700 inside=0 logmap=300 periodicity=10 colors=0000J00F00F00A005005001000000100A00F00J00F0\ 0A01A0550A10A10F00J00O00U00U00Z00c00h00l00l00q00v0\ 0z00z00z00h00O001100F00O00c00q00z00zz00z00z00z00z0\ 0z00z00z00z00z10z50zA0zF0zJ0zO0zU0zZ0zc0zc0zl0zq0z\ v0zz0zz0zz5zzFzzUqzclzlhzvczzZzzOzzJzzFzzAzz1zz0zz\ 0zz0zz0zzlzzzOzz0zz0zzOzzqzzzzzzzzzzzzzzzzzzzzzzzz\ zzzqzzhzzUzzJzz5zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zq0z\ O0z10z00z00z00z00z00z00z00z00z00v00l00h00Z00U00J00\ F00500100000000100A00O00Z00l00v00z00z00z00z00z00z0\ 0z00z00z00z00z00z00z00z00z00z00z01z05z0Az0Fz0Jz0Uz\ 0Zz0cv0hv0qv0vq0zq0zq0zq0zl0zl0zl0zl0zl0zl0zl0zl0z\ F0z00q00l00zl1UlAOlJFlUAlc1ll0lv0lz0cv0Zv0Uv1Ov5Jv\ AFqFAqJ5qO1qU0qZ0lc0lh0ll0lq0lv0hz0hz0hz0hz0hz0cz0\ cz0cz0cz0cz0Zz0Zz0Zz0Zz0Zz0Zz0hz0hz0lz0qz1vzAzzJzz\ Uzzczzlzzvzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 07-01-04 (Total Failure [2])
by Jim Muth 09 Jan '04

09 Jan '04

FOTD -- January 07, 2004 (Rating 2) Fractal visionaries and enthusiasts: Today's image rates a horrendous 2. It is one of the lowest rated images ever to have made the status of FOTD. And to make things worse, it takes almost an hour to render. Normally, this image would have been an instant victim of the delete key, but I included it among the honored FOTD fractals for two reasons: first, I wanted to demonstrate what, IMO, makes a fractal image bad; second, I had a bad day at the fractal keyboard. (Those who work with fractals have bad days, just like those who work with everything else.) The image is an 'evaporated' one in the parent fractal that results when some Z^(-1.2) is subtracted from some Z^(-2.1) and (1/C) is added. This parent fractal has within it far more potential than would be guessed by glancing at today's image. To prove the point, tomorrow's image will be another scene in this same parent fractal, and I guarantee the image will have a higher rating. I will not dwell at length on the deficiencies of today's image. The image speaks, (or does not speak), for itself. The ring- like features hold some promise, but the muddy, unorganized colors spoil anything that the rings might hint at. I guess the best thing to do with today's image is to consider it a reminder that the many FOTD images which rate a 6 are indeed a little above average. I gave little thought to naming the image, finally deciding on the discouraging name "Total Failure". Few will want to devote nearly an hour of computer time to rendering the failed fractal, but Paul is one of the few, and the completed GIF image will be available for download on his web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> as soon as he can get it posted. The temperature on Tuesday here at Fractal Central reached no higher than 36F 2C, and to make things worse, a snow squall struck at 2:30 pm, just as the cats were starting to enjoy their time in the yard. The sudden snow and burst of wind sent them scurrying to be let inside. The snow moved out within 20 minutes, leaving a dusting on the grass, and the sun returned, but by then the duo were safely settled by their radiator, where they spent the rest of the afternoon sleeping. This morning is starting sunny but windy and very cold, with a temperature of 18F -8C. These are not the conditions to make sensitive cats happy, so I guess we'll have to wait and see how the day goes for them. For me it looks like a fairly routine day. Until next time and a better fractal, take care, and if the truth were known . . . Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Total_Failure { ; time=0:50:11.74--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=-1.12301102275173500/+1.063120905547293\ 00/4820.856/1/125/3.20222112715207174e-011 params=1.2/-2.1/-2.1/-1.2/0/1e+100/0/0 float=y maxiter=1500 inside=bof61 periodicity=10 colors=000kNTlMRlKQmIOmHNnXLnDKoCIoAHp8FH`fFagCciA\ ek7gm2lt5hn8eiAbdD__FXVIUPLRKNOFQLAQK0SI5UH9WFDYEH\ _CLdBPc9Tk9We8Xb7X_6YW6YT5ZQ4ZM3_J3_G2`C1`90a1n560\ aC4dH8fMBhRFkWJm`MoeQrjUtjuxoXvu8vt9ut9ttAstArtBqt\ BptCotCnsDmsDlsEksEjsFisFhsGgyDcsGfmIihKlbMoYOrSQu\ NSwPVsQYpR`lSciTfeUibVlZWoWYjXZfX`bYaZYcUZdQZfM_gI\ _n7UhE_bKdXRjRXoMbtPcsRdsUerWfrYfr`gqbhqeipgjpijpl\ konloqmnsnnxqsunnrljoiflgbjeZgbVd`RaYNZWJSY3XUF`QR\ dNahJmlGxkFvkEtkDrkCqkBojAmj9kj8jj7hj6fh3hj5ek7cl9\ amB_nDYpFWqHUrJSsLQtNOuOMvQNvSOvUPvVPvXQvZRv`SvaSv\ cTveUvgVvhVweWwbXw_YwXZwV_xS`xPaxMbxJcxHdrLemPehTf\ cKfZ`gUdgPhhKlhFpiAti8sb7sX6sQ4rK3rD2r76p69o6Dn5Gl\ 5Kk4Nj4Qi3Ug3Xf2`e2cc1gb1ja0w`0ja1mb1ec1cZ1`d2Ze2X\ f2Ug2Sh2Ph3Ni3Kj3Ik3Gk3Hf6Hb9HZCIUFIQIIMLEJLIIOMIQ\ PITTIVWIY_I_bIbfIdmIfaNhURjMVlEZnCIw6boCalI`jO_hTZ\ eZYcdXahYaiW_iUZjSXjRWkPU } 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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 08-01-04 (A Little Bit More [4])
by Jim Muth 08 Jan '04

08 Jan '04

FOTD -- January 08, 2004 (Rating 4) Fractal visionaries and enthusiasts: For today, I promised a better fractal from the same formula that created yesterday's image. Well, a fractal that rates a 4 is better than one that rates a 2, but I had hoped for something a little more better. Maybe the parent fractal really is nearly worthless, or maybe I simply failed to search far enough. For today's rendering, the outside has been set to 'fmod', with a proximity value of 2. This is somewhat of a program feature, rather than a pure illustration of what exists in the formula graph at that location. The fact that I needed to resort to it is a sign that the basic fractal is not all that impressive. I named today's image "A Little Bit More" because it is a little bit better than yesterday's. Another good feature is the render time, which is only 5 minutes -- marginally worth the effort. Hopefully, tomorrow will bring a better image. I should hope for an image that rates at least a 6, my run-of-the-mill rating. The completed GIF image of today's fractal may be downloaded from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The cold kept the cats indoors here at Fractal Central on Wednesday. Not appreciating the outdoor temperature in the mid 20'sF, (around -4C), the cats barely thought of going out. They passed the day instead by catching up on their sleep. Today is starting about the same. I expect the duo will have a similar day. My day includes work, which I had best get started on. Until next FOTD, take care, and have you tried the fractal weight-loss program? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Little_Bit_More { ; time=0:05:23.84--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+0.38849806591214900/+3.327863228966088\ 00/3866.667/1/-122.5/-5.61300450563351205e-011 params=1.2/-2.1/-2.1/-1.2/0/50/0/0 float=y maxiter=1200 inside=0 proximity=2 outside=fmod logmap=yes periodicity=10 colors=000wTjuRgsPeqNcmM`iMYfMVbMSZLPWKMSJJOIGLMEO\ QDQUCSXCV`BXdBZgAak9co9er8hv8jz7lz7pz8sz9vzAyzBzzC\ zzDzzHuwLpsPkoTflXah`XddS`hNXlJUpZSenRWzQMzTNxWOuZ\ PraQodRlgSeiWcfY`c_Z`aWYcTVeRSgOPiMMkONZQOMPPNPPNP\ QOPQOORPORPOSQOSQZXQh`QsdQzhQziPzjOxjNwkMukLtlKrlJ\ qmIonHnnGloFkoEipDhpCioDjnEkmFllFmkGnjHoiIpiIqhJrg\ KsfLteLudMvcNvcNudOuePufQugRtgRthStiTtjUtkVskVslWs\ mXsnYsnYtjZtfZtbZtZZuV_uR_uN_uJ_wLaxMbzNczOezPfzQg\ qMeeJdUFcICbMD`PD_SEYWEXZFWaFUeGThGRkHQoHPrINuIMyJ\ KzJJzJIpTPbbWOlbAuiVobniWzdQz`TtXWmTZfPa_LdTHfYGdb\ GcgGalG`qF_vFYzFXzFWzHVyIVvJUtKUqLTnMTkNSiOSfPRcQR\ `RQZSQYURXVSXWTWXUVYVVZWU_XT`YTaZSb_Rc`RdaQebPfcPg\ dUzGWzIXzKYzMZzN`zPaxRbwScuUdsWfrYgpZho`imbjlckndk\ odlpelqelrfmsfmugnvgnwhnxhoyioziozisxhvugzrfzoezle\ xhbpd_haX`YUUVRaTGhR6th7zy8xs7pm7hg7`a6TW6LR6RSCXT\ IaUOgVUmW_rXexYkzZqzXnyVl } 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 } END 20.0 PAR-FORMULA FILE==================================

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Plotting the Julia set only - not the filled Julia set
by Jonathan Marshall 07 Jan '04

07 Jan '04

Hi all, I'm a mathematics PhD student whose research involves Functional Differential equations, whose solutions can be analytically continued through iterating a functional argument - thus, they obtain solutions within a component of the Fatou set. The Julia set forms a natural boundary for these solutions. For my Thesis, I am wanting to generate images of just the Julia set, without anything from the Fatou set drawn - these can be in monochrome, the Julia set in Black, and all Fatou components in white. This is fairly easily done in the case where all the Fatou components are attractive basins, and I believe that FractInt can handle this case by adding in the search for attracting orbits. The tricky cases are where neutral fixed points are involved. Siegel disks in particular. Can Fractint detect and eliminate any pixels inside a Siegel disk? If so, how? A few images from the quadratic case would probably suffice, although it would be nice if it could handle more arbitrary rational functions. Any info would be appreciated - if Fractint can't do it, then I'll code up my own routine (though it'll be specific to particular cases if I do that). Cheers, Jonathan

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FOTD 05-01-04 (Octo-Something [4])
by Jim Muth 05 Jan '04

05 Jan '04

FOTD -- January 05, 2003 (Rating 4) Fractal visionaries and enthusiasts: With today's image I make one of my rare departures from fractal purity. Instead of showing an interesting scene rendered in the normal manner, the image shows a rather ordinary scene rendered in an unusual manner. Instead of consisting of equal iteration bands, the image was created by rendering it with the outside set to 'atan'. Instead of spending my fractal time searching for a scene, I spent it in fine tuning the color palette for the smoothest possible effect. The net result rates a 4, which is somewhat below average, and shows that, at least to me, an undistorted presentation of a fractal discovery is more important than pseudo-artistic fractal 'creativity'. I named the image "Octo-Something". An early version of the image had eight 'somethings' lying somewhere in it. But whatever it was that inspired the name has long since been lost. In the image, the perennial midget is offset to the right, and has little of the usual symmetry surrounding it. The lack of symmetry is partly due to the nature of the area and partly due to the unusually low magnitude. This low magnitude has one great benefit however -- it makes the image a very fast one. The 45-second render time is a welcome relief from the 1-1/2 hour wait that was necessary to see yesterday's image. The parent fractal, which was created by combining negative portions of Z^(-1.9) and Z^(-9.1) and adding (1/C), is a shapeless thing with three large bays and many smaller coves. Today's image is located in an unlikely area that I happened to zoom into by chance. It will probably take longer to download the image than to render it from the included parameter file, but those who choose to download will not be disappointed. The completed image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Though Sunday promised to be pleasant here at Fractal Central, the promise was not fulfilled. Instead of the forecasted sun and temperature close to 70F 21C, we had heavy clouds and a temperature of 46F 8C. The cats tried the yard only a few minutes before deciding that a day indoors would be more com- fortable. The traditional tuna treat restored their spirits. Today is starting even worse -- it is raining. Check back in 24 hours to see how the cats adapt, and when you do, you might even enjoy a better fractal. Until then, take care, and keep discour- agement at bay. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Octo-Something { ; time=0:00:45.53--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.99960116589275130/-0.228694138466237\ 50/117.874/1/50/-6.99683366800485373e-012 params=-1.9/-9.1/-9.1/-1.9/0/0 float=y maxiter=1800 inside=0 outside=atan periodicity=10 colors=000Ae`9gY9iW9kU9mR9oP9qN9rL8tI8vG8xEAzBhz9m\ z7hz5cz6Cz6Ex6Gv7It7Kr7Mo7Om8Pk8Ri8Tg9Ve9Xb9Z`9`ZA\ bXAcVAeTBgQBiOBkMBmKCoICqGCrFFrEClDAfC8`C6VB4PA2JA\ 0OB5TC9XCEaDIfENjERoFWsF_rGZrGZrGZqGZqGZqGZpGYpGYp\ GYoGYoHYoHYnHXnHXnHXmHXmHXmHXlHWlHWlIWkIWkIWkIWjIV\ jIVjIViIViIViIViGWiIVhKVhMVgNVfPVeRVdTVdUVcWUbYUa_\ Ua`U`bU_dUZfUYiTZgU_fV`eVadWbcWbbXcaXd`Ye_ZfZZfY_g\ X_hW`iV`jUajTbkSblRcmQcnOdoMdpNeqOfrPgsQitRkrSmpTo\ nUqlVojWmhXkfYidZgb_e``cZaaXb_VcYTcWRbUPaSN`QL_PJY\ OHXNFWLDVKBUJASI8RG7QF5PE3NC4OD5PD5QD6RD7SE7TF8UG9\ VH9WIAXJBYKBZLC_MD`NDaOEbPFcQGdRHeSIfUJgXKhZKhaNfV\ PdURbTU`SWZRYXQ`VPbTOdQNfOMeOLdPKcQJbRKaSLaTM`UO_V\ PZWQYXRYYTXZUW_VV`XUaYUbZTc_SdaRebQfcQgePhfOigNjhM\ kjMlkLmlKnnJooIppMquIpqEpmAoi6oe2ob8mZElWKkTPjQVhN\ `gKffHkeElfGlfImfJmfLmfMnfOnfPnfRofSofUofVpfXpfYpf\ _qf`qfbujbqfcmccj`cfXccUd } 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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 04-01-04 (Arachnid [6])
by Jim Muth 04 Jan '04

04 Jan '04

FOTD -- January 04, 2004 (Rating 6) Fractal visionaries and enthusiasts: Last evening I heard an item on one of the local news outlets that caused me to stop and wonder. The news item claimed that, with 500 or so homicides in 2003, Chicago had the highest murder rate in the nation, while here in Baltimore, we had only 300 or so homicides, making us only 60-percent as violent. It sounds good until one realizes that the population of Chicago is around 3,000,000, while the population of Baltimore is close to 600,000. My calculations tell me that this gives Baltimore a homicide rate 6 times that of Chicago. I wonder whether this was local Chamber of Commerce propaganda or whether the news reporters actually did not know any better. When this kind of stuff starts annoying me, I turn to fractals for distraction, and in this case, I was distracted by today's image, which like yesterday's, is an evaporated one consisting only of 'bof61' inside fill. The image is a scene in the ghost of the fractal that results when various portions of Z^(-1.8) and Z^(-8.1) are mixed and (1/C) is added, then the whole thing is evaporated by raising the escape radius to one-googol. I named the image "Arachnid". I gave it this name when the dark filaments surrounding the ever-present central midget reminded me of a spider's web in front of a carnival-like display of colors. I rated the image at a 6, since IMO it's not really that great. Another drawback is the render time, which on my machine is over 1-1/2 hours, making a download of the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> the far better choice. But before rushing for the download, give Paul an hour or so to render and post the image. Saturday was warm or chilly, depending on which side of town one was located. Here on the northeast side, the temperature reached 52F 11C, which was mild enough to keep the cats happy; but a few miles to the south, the temperature reached 70F 21C, which would have made them ecstatic. As it was, the duo spent several hours in the yard, meditating and enjoying their senior years. My day went fair enough. Hopefully, today will be just as fair. Until next FOTD, take care, and stay fairly well. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Arachnid { ; time=1:36:43.82--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+1.12455703364229600/+0.172257651110892\ 40/1.987188e+009/1/-120/-0.000760825470566633966 params=1.8/-8.1/8.1/-1.8/0/1e+100/0/0 float=y maxiter=3600 inside=bof61 periodicity=10 colors=000CaZC_YDZYDYXDWWEVWETVESUFRUFPTFOSGNSGLRG\ KQCFPGJQJNRMQSPUSSYTV`UZdVahVdkWgoXjsYpx_mvYkuWitV\ fsTdrRbpQ_oOYnNWmLTlzRjIPiGMhEKgDIfBFdADc8Bb68a56`\ 34hzFc4Qg5Wn7_k6ci5gg4jd4nb3r`2uZ2vczveCviHvlMwpRw\ sWww`wzduxcsvbquaqR0nr_lpZjnYimXgkWejVchUbfT`eSZcR\ pflYbREb1F_6GXAHVEHSJIPNJNRJKVKH_LFcMCgM9lN7pO4taP\ IO2xQCnRLeSUXUcOVlFWu6ToAQiDNdGKZJHTMEOPDPODPNCPMC\ PMCPLBPKBPKAPJAPIAPIBRHCSGDTGEUFFVFGXEHYEIZDJ_DK`C\ Gj6LaCPUHTMNXES`6XcHTfRQi`NljKotHisIdrJ_qJVqKQpKLo\ LGoLGoMGoMIkLJhLLeLMbKN_KPXKQUKRRJTOJULJVIIXFIYCIZ\ 9IWDOTGTQJZNMcKQhHTnEWsCZxJXwQVvXTvcRujPtpOtkLufJu\ aGuXEvSCvN9vI7wD4w82w40w7Ct9OrBZpDjnFulIpjKlhNggPc\ eSZdUVbXQaZM_aHZcDXe9W`BXWDYRFYMHZHJ_CK_GOZJRZMUZP\ XZT_ZWbZZfZaiZelZhoZkrZnuZkq`hnafjbcgcaddZ`eWYfUUg\ RRhPOiMKjJHkHDlEAmC7nBBjBEgBHcBK`BNXBQUBTRAWNAZKAa\ GAdDAjcAibAgaBfaBe`Bc_Cb_ } 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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 02-01-04 (Just For Fun [6])
by Jim Muth 04 Jan '04

04 Jan '04

FOTD -- January 02, 2003 (Rating 6) Fractal visionaries and enthusiasts: Fractals are for fun. True, they have other uses, and perhaps deep meanings that we are yet to fathom. They might even be a mathematical manifestation of God, but above all else, fractals are fun. And today's fractal is total fun. I was in a fun mood when I found it, and with its gaudy colors, the image looks like pure fun. The image is actually a scene in the fractal that results when various portions of Z^(-1.6) and Z^(-6.1) are combined and (1/C) is added. The formula, like the last two, is whimsical. (Most likely, tomorrow's FOTD will be a play on the fractions 1.7 and 7.1.) The parent fractal of today's image is a Mandeloid with four main bays, the easternmost of which appears the most critical, with lots of Mandel-buds and filaments that terminate in rings. Several disconnected features lie a small distance to the west and north of the main Mandeloid, but these play no part in today's FOTD. The midget in today's image is located near the point where the filament of an eastern bud intersects its terminal ring. To add a bit of 'zip' to the scene, I rendered it with the outside set to 'tdis'. Then I named the whole thing "Just For Fun", which, after all, is what fractals are the best at. The rating of a 6 is boringly average, though the render time of 3 minutes is thankfully short. And the image may be seen even faster by downloading it from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Once we got our act together here at Fractal Central on Thursday, the day went very well. There was lots of sun and the temperature reached 50F 10C, just mild enough to keep the cats happy during their afternoon in the holly thicket. In the evening, and against my better instincts, I went to a New Year's dinner at the home of the Fractal Lady's brother -- the second outing in 24 hours. I would rather have spent the evening in search of fractals, but all went well and now, when someone tells me to 'get a life', I can reply that I have one. But today is starting rainy, the dinners are past, and the cats already look sullen. Check back in 24 hours to see how things turn out. Until tomorrow take care, and if searching for fractals is not 'having a life', then what is? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Just_For_Fun { ; time=0:03:00.43--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.62834596524853100/+0.561897474119188\ 30/32042.8/1/-35/-1.25182780807975291e-011 params=1.6/-6.1/6.1/-1.6/0/0 float=y maxiter=1000 inside=0 outside=tdis logmap=yes periodicity=10 colors=000zzNp`QndSlhVjkYho_fsbevdcsbbqa`o`_l_YjZX\ hYVfXUcWSaVR_TPYSOVRMTQLRPJPOIMNGKMFILABLCEKEGKFJK\ HLKJOKKQKMTKOVKPYKR_KTbKVfGUeIUdKUcMUbOUaPU`RU_TUZ\ VXVOVXSUYWT__S`bRafQcjPdnOeqNguMhvLivNhvPgvRfvTeuV\ dsXcqYbp_ana`lc_keZigYghXfjWdlVbnUapT_rSYzT`vSZsRX\ pRVlQTiQRfPPbPN_OMXNKTNIQMGNMEJLCGLADK89I4AK7BL9CM\ BDOEEPGFQIGSKHTNIUPJWRKXTLYWM_YN`_OaaPcdQdfRehRfhQ\ ghPhhOgfRfaUdZWbW_`VbZSdXJfVIiTHkRGnPFqNErLEoKDkKD\ hKCdKC`KCYKBUKBQJBNJAJJAFJACJ98J94K65J96IC6IF7HH7H\ K8GN9GQ9FSAFVAEYBE_CDbCCeDChDBjEBmFApFAtGFwGKxHPyH\ TzJXzL`zNLkONjPOhPPfQQeQRcQSbRT`RUZRVYSWWSXVTYTTZS\ T_QU`OUaNUbLVcKVdIgpMVdHJUC3H87J7AL7EN7HP7LR7OT7SV\ 7VX7ZZ7a`7eb7hd7lf7oh7sj7vk7wfBwbEwZHwVLxQOxMRxIVx\ EYxA`vC_tE_rFZpHZoIZmKYkMYiNYgPXfQXdSWbTW`VWZXVYYV\ W_VU`USbURcUPfQMiMKlIHoEFrBIqCKqDMqDPpERpETpFVoGYo\ G_oHanHcnIfnJhmJjmKvQItUK } 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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 01-01-04 (Happy New Fractalss [9])
by Jim Muth 03 Jan '04

03 Jan '04

FOTD -- January 01, 2004 (Rating 7) Fractal visionaries and enthusiasts: Due to an unplanned busy night, today's discussion is not only late, it is very short and to the point. I named the fractal "Happy New Fractals" because it is the first in a year-long series of hopefully superior images. The generating formula combines portions of Z^(-5.1) and Z^(-1.5), and adds (1/C). The resulting fractal consists of the usual indescribable Mandeloid, with a separate area of chaos lying just southwest of the main fractal unit. Today's scene lies in this separate area of chaos. Most of the effect was achieved by rendering the image with the outside set to 'tdis' and the inside set to 'fmod'. The rating of an above-average 7 makes the 3-minute render time worth the effort. The image can also be seen by downloading it from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The last day of the year passed uneventfully here at Fractal Central. With lots of sun and a temperature of 54F 12C, the day was pleasant enough for the cats to enjoy almost two hours in the wild outdoors of the yard. When midnight came and people began setting off fireworks, they cats took shelter in their closet in the spare room, where they were still sleeping when the night ended. Today is the first day of another year, and it is starting the same as yesterday. I expect the cats will be acceptably happy. I will be unable to comment on my happiness until 8784 hours have passed. So check back then to see how the year goes. Luckily, the next FOTD will appear far before then. It will appear in 18 hours in fact. Until then, take care and happy recovery. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Happy_New_Fractals { ; time=0:03:25.14--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=-2.466097773964582/-1.765694766786944/4\ 37507.9/1/22.5/-4.23133679e-007 float=y params=1.5\ /-5.1/5.1/-1.5/0/0/0/0 maxiter=1000 inside=fmod proximity=0.7 outside=tdis periodicity=10 colors=000U73V84W94XA5ZC5_D6`E6aF7cH7dI8eJ8fK9gLAi\ NAjOBkPBlQCnSCoTDpUDqVErWEi`KadQUiWLmaDrg5vm7sm8qm\ 9omBlmCjmDhmFemGcmHamJ_mKXmLVmNTmOQmPOmRMmSKmTHmVF\ mWDmXAmZ8m_6m`4ma6ka7ia9gaAebBcbDabE_bFYbHWcIUcKSc\ LQcMOcOMdPKdQIdSGdTEdVCeWAeX8eZ6e_4e`3eWEeSOeNZeJh\ fLggMfgNehOeiPdiQcjRcjTbkUalV`lW`mX_nYZi00o`YoaXpb\ WqcWqdVreUT00V88XFEZ17`26a26b36c35d35e45f44g44h54i\ 54i53l63m63n62o72p72q71r81s81t81uB3uD4uF5uI7uK8uM9\ uPBuRCuTDuVEuYGu_HuaIudKufLuhMujNumPuoQuqRutTuvUux\ VuzWgyVVyVIxV5xV6tV6pV7lV7hV7dV8aV8YV8UV9QV9MV9JVC\ IUEITGISIISNTNSbIXlDav8`qD`mI`iN`eS`aW`Y``Ue`Qj`Mn\ XDwTKoQRhNY`KdUHkMEqFMjLTdR_ZXfTbmNg_`mMms9zy8vt7s\ p6pl5lh4id3f`2dY8c_EbaKacP`eV_h`ZjfYlkXnhXofXogWlh\ VjiUgjTekSbkR`lNXmKUmHRnDNnAKo7Ho4En9ImEMlIQlNTkRX\ jW`j_c4ci3RV1DFfjufiufhuePXe68c5Ab5Ca5E`5G_5IZ5KY5\ MX5O`GYdRfhao0bl7_mEYmLVm } 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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 03-01-04 (Iterative Wreaths [7])
by Jim Muth 03 Jan '04

03 Jan '04

FOTD -- January 03, 2003 (Rating 7) Fractal visionaries and enthusiasts: Today's fractal continues the theme of the past 3 fractals. We combine portions of Z^(-1.7) and Z^(-1.7), and add (1/C) to get a many-bayed parent Mandeloid with a separate ring of chaos lying some distance to the north. Today's scene lies in this outlying ring of chaos rather than in the main body of the fractal itself. But today's image is an 'evaporated' one, in which all 'outside' parts have shrunk until they vanished, so speaking of bays and outlying areas of chaos makes little sense. The escape radius has been raised so high that the parent fractal has been reduced to a sea of trapped points. Luckily, these points do interes- ting things in their confinement, which can be revealed by rendering the scene with the inside set to 'bof61'. The trapped points that make up today's image remind me of a seasonal wreath. I named the image "Iterative Wreaths", needing no reason at all for using the plural. The rating of 7 is high enough to justify the brief 2 minutes required to render the image from the included parameter file. The image may also be seen by downloading it from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Friday was another routine day here at Fractal Central, both with the weather and the activity of the fractal cats. The pleasant winter sun and temperature of 54F 12C was just enough to give the cats a couple hours in the yard. When evening came the duo was ready to settle for the night. Today is starting foggy. We'll see what develops. It's now time to wrap up the little work yet to be done and enjoy a day with not much else to do but relax. Between bouts of relaxation, I'll find the fractal that will appear as tomorrow's FOTD. Until next time, take care, and take time out to ponder a fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Iterative_Wreaths { ; time=0:02:05.34--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-1.12781826180191500/+3.156480392217424\ 00/288207.2/1/152.5/-1.82667648160328433e-008 params=1.7/-7.1/7.1/-1.7/0/1e+100 float=y maxiter=1200 inside=bof61 outside=tdis periodicity=10 colors=000ARHDUIFWIIYJK`JMbKPdKRgLUiLWkMZnM`pNbrN`\ bHZOCX97WFDWKIWQOWVTW_ZVecVjiVpnVuwhzz00ASP9RU9PX9\ Oc9Ng91KG4TF7`hAiDCqDFzEIkELhENeFQbFT_FVXGYUG`RGbO\ HeLHhIHjFImCIp9Ir7Ir8Ks9MtAOuBQvCSvDUwEWxFYyG_zHaz\ HbYJM6L55K25J07M39P5AS72Hp2Hqdqhfrfgsdhtciuaju`lvZ\ mwXnxWoyUpyTmvRjsPgpNdnMakK_hIXfGUcFR`DOZBMW9JT8GR\ 6DO4AL28J17M47O66R96TB6WE5YG5`J5bL4eN4gQ3jS3lV3oX2\ q_2ta2vc7uaCt`Gs_LrYPqXUpWZoUbnTgmSklQpkPtkOsjQrjR\ rjSqjTpjUpjVojWnjYnjZmj_lj`ljakjbkjchhaff_cdYacX_a\ VX_TVYSTXQpGXlFZiDafCcbBf_9hX8kT6mQ5pN4rPCYSGUUKRW\ NOYRL_UIbYEdaBfd8hh5jk2dj9ZiFTiLNhRHhXVkehmnYfhN`b\ CVX1PR6VSB_TFdTKjUPoVTtVVrTWqSXpQYoPZnO_mM`lLbjKci\ IdhHegGffEgeDhdCecGcbK`aNZ`RW_UUZYSYaPXdNWhKVkIUoG\ UrIVnKVjMVgOVcQV`SVXUVUWVQXVNUTOSSOPRPNQPKOQINQFMR\ DLRAJS8IS5HT3GT1FT6cCCaII_OOYTUWZZVcdTijRnpPtuOyrR\ upTrmVnQliKeaFZVASN5MG8PH } 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 } END 20.0 PAR-FORMULA FILE==================================

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Re: Quantization Error in ATAN
by SherLok Merfy 01 Jan '04

01 Jan '04

On Tue, 30 Dec 2003, Jonathan Osuch wrote: > On Monday 29 December 2003 08:53 pm, you wrote: > > > I'll send some of both for your entertainment, but I think this > > problem is as old as the code for the palette. The image looks fine > > in PSP, but the squares get very rectangular in fractint. Without the > > borders, fractint's own palette would be similar (but not mirrored at > > every other row). > > > > Oh, and BTW, maxiter is potentially irrelevant with ATAN. About > > twenty moons ago, I jenerated something that only did one > > [iteration] and still ended up with many colours. > > Ah, I see. The code for atan looks like this: > > coloriter = (long)fabs(atan2(new.y,new.x)*180.0/PI); > > I'll change it to: > > coloriter = (long)fabs(atan2(new.y,new.x)*colors/PI); > > I'll have to put in some code for backwards compatibility, so it won't quite > look like that. Thanks for pointing out the problem. Thanks for taking orders like you had children to avoid. I might look for an arbitrary number of colours from ATAN, but for the most part, I think darkening or lightening the imaj in PSP will do. The important problem, IMV, is the rounding from 24bits to eighteen. I don't really like using a graymap that isn't exactly gray, although it tells me that there's a hack for getting 768 levels of gray under hicolor and truecolor (assuming gamma=1) and that some users might appreciate GIFs that accomodate EGA. They're using computers that are more than ten years old, so I appreciate their dedication to alleviating the burden on our landfills. I think this might be the source of problems for stereograms, too. Or it might mask the problem. Maybe I should try 1bit stereograms. For printing, there is physically no other kind, and I'm kinda curious as to whether that means I must dither. > > BTW, if you like Linux, but you don't hav twelve days to > > download three CDs over POTS, then you might look at Linux Format > > magazine. It's a lot messier than their > > mandrakelinux.com/en/92errata.php3 paje would tell you, but it's still a > > lot easier to waste more than 64meg of RAM under Linux than under DOS. > > Already use a Mandrake distribution. Planning to switch to SUSE. Got any particular reason? Some inviting things are on my DVD, but I don't think I'll ever get around to using everything that I installed. (And one reason I'm in AIX over DOS now, is because the last time I made sndconfig work, I used DOS to disable my card, first). Debian seems to be the one for network-only distribution. And there's an Edmonton based distribution, MaxOS, that people I've met might run.

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FOTD 31-12-03 (Fiery Pastels [9])
by Jim Muth 31 Dec '03

31 Dec '03

FOTD -- December 31, 2003 (Rating 9) Fractal visionaries and enthusiasts: Today's discussion will once again be short, as there is still some work I must finish before the end of the day. I actually found today's image several weeks ago, but I have been saving it since then, to present it as a quality end to the FOTD year. It is perhaps the best image of the month, maybe even of the year, at least in my opinion. But I could still rate it no higher than an 9, which is excellent enough. The image shows a very well defined midget lying in the fractal that results when portions of Z^(-1.4) and Z^(-4.1) are combined and (1/C) is added. The parent appears as a bloated and indescribable Mandeloid with a smaller, far more conventional Mandelbrot set in its northern suburbs. Today's scene is located in a cut-off filament in the East Valley area of the smaller M-set. The cut-off nature of the filament is reflected in the eight cut-off 'elephants' surrounding the midget. I named the image "Fiery Pastels" because of the fiery red background and the pastel effect of the entire scene. The wait of 7 minutes while the image renders can be avoided by downloading the finished GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The 52F 11C temperature on Tuesday here at Fractal Central was pleasant enough, but the wind was far too high for cat comfort. The duo spent less than one hour in the outdoors, and the rest of the day wishing the wind would die down. They were not all that unhappy when evening came, but I gave them a treat of tuna just to be sure. Today promises to be another repeat. Now if I can only find a fractal repeat . . . Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fiery_Pastels { ; time=0:07:20.22--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=-0.43142567276170910/+3.130775435388886\ 00/3.507041e+009/1/20/5.71769986824899323e-006 params=0.41/-1.4/0.14/-4.1/0/-50/0/0 float=y maxiter=900 inside=0 logmap=141 periodicity=10 colors=000U3AX2AZ1A`0Ae0Af0Ak0Ak0An2Ao5Aq9AsDAuHAv\ KBvNDxSFyWIz_KzdNzhQzmTzpVxnWqnXknZenZakZZjZWhZSgZ\ OeZMdZNbZQbZTaZWbZZaZabZdaZgbZjaambdpagsbjuamvcpxa\ sybxzczzczzezzazzazy_xxXsvWpsVkpSgmQbjOZhNVdQQ_TMX\ WJTXIQ_HObFMdFKgEMjDMkBOnAOq9Ns9QpDSnHTmJVjNWhQXgV\ ZdX_baaadaVnaOxaJzdMzeQzhpzjpzkmzjkzhhzghzegzdezbd\ yabv_asZapXanWamVakTahSagQaeJadOadNabMaaznjzmhykhv\ kgsjgpjemhejhdggddedaebZdbWdaTbaQb_Na_0ID0JF0KH0MI\ 0NJ0OK1QM3SN5TQ8VS9WTBXVEZWH_XJaZ2z83yA4xB5vD7uE7s\ F8qH9pIAnJBmKBmNDkOEjQFhSHgTHeVIdWJbXKaZ1703924B45\ E77H99IDAKFBNIDQKFSOHVSIXVJ_XT3SS7TQ9VQDVOFWOIWNMX\ NOXMSZMWZKZ_8zFAyIBvKDqNEnQHkTIgWJdZbz7zzTzzVzzVyz\ VxzVuzWsyWpxWnvWkuXjsXgqXepXbpXasZZvZXyZVzZTz_Qz_O\ z_Mz_bzOWzTQzXAz9BzABzBDzDDzEDzFEzHEzIFzJFzKFzMHzN\ HzOIzQIzSIzTJzVJzWKzXKzZpz0_zHBzdDzbDzbEzbEzbFzbFz\ aHzaHzaIzaIzaJz_JzSMzNQzJ } 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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 30-12-03 (Something Fishier [6])
by Jim Muth 30 Dec '03

30 Dec '03

FOTD -- December 30, 2003 (Rating 6) Fractal visionaries and enthusiasts: Today is the next-to-last day of the year 2003 here at Fractal Central, (and everywhere else as well), and there is a bit of work I want to put behind me before the year changes. Today's discussion will therefore be short and to the point. The image is a scene in the fractal that results when 0.3 parts of Z^(-9.5) are combined with 3 parts of Z^(-1.5) and (1/C) is added. The parent fractal is one of those disorganized, rambling things that results when negative powers of Z are combined. Today's image is as much a demonstration of the program features as a discovery of a new fractal. I have rendered the image with the outside set to 'fmod' and the inside set to 'bof61'. I normally prefer to avoid program trickery, but in today's case, using the available features results in a more interesting image. The image as it is, rates a 6. When rendered in the normal manner, the image rates only a 4. The two extra rating points were IMO worth the departure from fractal purity. Something about the image reminds me of fish. I therefore named it "Something Fishier", though I can see really nothing in the picture that could be associated with fish. The render time of 27 minutes is slow, but can be avoided by downloading the finished GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Monday was quite pleasant here at Fractal Central. The sky was mostly sunny, the temperature reached 54F 12C, the wind was light, and the cats were happy. Today started wet, but the rain moved out quickly and the sun is now appearing. I expect the cats will be happy again. The next FOTD, the last for 2003, is already in the works, and will appear right here in about 24 hours. Until then, take care, and keep looking for fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Something_Fishier { ; time=0:27:08.65--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+1.72463778859888/+0.14466193464504/2.8\ 39504e+007/1/5/-5.201420565093e-008 params=3/-1.5/\ 0.3/-9.5/0/0/0/0 float=y maxiter=1200 inside=bof61 proximity=2 outside=fmod periodicity=10 colors=000BIGAIGAIGAIG9IG9IG9IG9IG8IG8IG8IG7IF8IG9\ IH9IIAIJBIKBILCIMDINDIOEIPFIQFIRGISHITHHURG_JEWJDX\ KCYLAXKBYKCZKC_KD`KDaKEbKEcKFdKFeKGfKGgKHhKHiJIiJK\ jJMkJOlJRmJTnJWoJYpJ`rJbtJevJgxJjyJlzKjyLhxMewNcvO\ `uPZtQWsRUrSRrTRrUQqVRqWRpXRpYRpYSoZSo_So`SnaTnbTm\ cTmdTmeTlfUlgUlhUkiUkjVjkVjlVjmVinWioWipWhqWhtVgqW\ hoWimWjkWjiXkfXldXlbXm`YnZYnWYoUYpSZpQZqOZrL_sMZrN\ YrOXrPWrQVrRUrSTrTSrURrVQrWPrXOrXNrYMrZLr_Kr`JraIr\ bHrcGrdFreErfDrgCrgBrhDsiFsiHsjIskKtkMtlNtlPtmRunT\ unUuoWupYvpZvq`vZbzrcvsewsgwtiwtjwulxvnxvoxwqxxsyx\ uyyvyyxyzzzzzzzzzzzzzzzzzxzzwzzuzztzzszzqzzpzyozxm\ zwlzvkzuizuhztfzsezrdzqbypayp`yoZynYymXylVykUyjSyj\ RxiQxhOxgNxfMxeKxeJxdIxcGxbFwaDw`Cw`Bw_9wZ8wY7wX5w\ W4wW3tY5rZ7p_8m`AkaCibDgcFddGbeI`fKYhLWiNUjPSkQPlS\ NmTLnVIoXGpYEq_BqaCr`Dr_ErZFsZGsYHsXIsXJtWKtVLtUMt\ UNuTOuSPuSQuRRvQSvPBXGBXG } 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 } END 20.0 PAR-FORMULA FILE==================================

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by mdoctorow＠comcast.net 30 Dec '03

30 Dec '03

>From Osher Doctorow Ph.D. Here's a slightly more general Lemma. LEMMA 3. In the equation: 1) dy/dt = A1(exp(t) - y) + exp(-t) y^2 if y = k exp(t), then A1(t) = k. PROOF. dy/dt = k d(exp(t))/dt = k exp(t) from calculus, and y^2 = k^2 (e^t)^2 = k^2 e^(2t), so we get: 2) ke^t = A1(e^t - ke^t) + e(-t)k^2 e^(2t) which simplifies to: 3) ke^t = A1e^t(1 - k) + k^2 e^t since e(2t)e^(-t) = e^(2t - t) = e^t. Divide through by e^t: 4) k = A1(1 - k) + k^2 and solve for A1(t): 5) A1(t) = (k - k^2)/(1 - k) = k(1 - k)/(1 - k) = k. Q.E.D. REMARK. It follows that if y = (1/e)exp(t) (which is exp(t - 1)), then A1(t) = 1/e. LEMMA 4. If (dy/dt)(1) = 1/e, then there is a real positive value of A1(1) which satisfies equation (1) and such that 0 < = A(1) < = 2. PROOF. From (1) for (dy/dt)(1) = 1/e, we get a quadratic equation in y(1)^2 with A(1) in two of the coefficients, and from the square root in the quadratic equation this is always real if and only if 0 < = A(1) < = 2. Q.E.D. REMARK. It is interesting that the values of A(1) and y(1) are linked, especially when constrained by (dy/dt)(1) = 1/e. The linkage is quadratic, that is to say an algebraic quadratic equation in y(1) with A1(1) in two of the coefficients. The equation is in fact: 6) y(1)^2 - A1(1)ey(1) + (A1(1)e^2 - 1) = 0 This is a parabola in the A1(1)-y(1) plane across different pairs of values of (A1(1), y(1)). It is also interesting that "exponential Information," or as I refer to it in Rare Event Theory "Knowledge", of the form y(t) = kexp(t), is an inverse of the Shannon Information-Entropy kernel (in fact, the Hartley Information) log(t) to base 2 up to a constant. Osher Doctorow

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[Fractint] A Lemma or "Subtheorem" on Exponential Explosion Cosmology
by mdoctorow＠comcast.net 30 Dec '03

30 Dec '03

>From Osher Doctorow Ph.D. mdoctorow(a)comcast.net A Lemma is a "sub-theorem" or intermediate stage Theorem on the way to (hopefully) more important results. Here's one based on the previous ideas with a proof. LEMMA 1. In the differential equation model: 1) dy/dt = A1(exp(t) - y) + y^2 exp(-t), y(1) = 1, the condition (dy/dt)(1) = 1, that is to say dy/dt is 1 at time t = 1, holds if and only if: 2) A1(1) = 1/e which is to say A1(t) at time t = 1 is given by 1/e, which is the boundary of Exponential Explosions. PROOF. Set dy/dt = 1 in (1), in which case exp(1) is e^1 = e and y is y(t) = y(1) = 1, and exp(-t) = exp(-1), so we get: 3) 1 = A1(e - 1) + 1/e and solving for A1: 4) A1 = (1 - 1/e)/(e - 1) = [(e - 1)/e]/[e - 1] = 1/e. Q.E.D. REMARK. We can thus regard A1(t) as a function or curve which takes on the Exponential Explosion boundary value 1/e when t = 1. It is a sort of Generalized Exponential Explosion Boundary. LEMMA 2. In equation (1) except that y(1) = 1 is not assumed, if the solution is y(t) = (1/3)exp(t) (so that y(1) = e/3), then A(t) = 1/3. In that case, the Universe is accelerating at least in reference to variable y with respect to time t. PROOF. Substituting y(t) = (1/3)exp(t) into (1), we get: 5) (1/3)exp(t) = A(t)[(2/3)exp(t)] + (1/9)exp(2t)exp(-t) = exp(t)[(2/3)A(t) + 1/9] and therefore (dividing through by exp(t)) A(t) = 1/3. Then dy/dt = (1/3)exp(t) so the acceleration is d(dy/dt)/dt = d[(1/3)exp(t)]/dt and since d(c f(t))/dt = cdf(t)/dt for a constant c, this is (1/3)exp(t) which is always positive for all real t. Q.E.D. REMARK. In Lemma 2, no discontinuity at t = 1 is assumed. We could still define A(t) separately in [0, .05) without changing the Lemma basically. The relationship of y(1) and (dy/dt)(1) to 1/e is now proportional to the inverse of 1/e which is e. Osher Doctorow

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Revision of the "Explosive Exponential" Theorem-Proof
by mdoctorow＠comcast.net 30 Dec '03

30 Dec '03

>From Osher Doctorow Ph.D. The Big Crunch "Exponentially Exploding Julia Set Boundary" theorem and proof from my last posting has a very subtle error. If y(1) = 1, then the solution y = exp(t) or e^t (in other notation) does not hold unless there is a discontinuity at t = 1, since e^1 = e which is approximately 2.72. This would not be surprising at a "singularity" at t = 1, but it would need to be incorporated into the definition and theorem and the proof. Another difficulty is that the whole proof of equation (6) requires that y = exp(t) be one solution, but y = exp(t) exceeds 1 except at t = 0, since in Rare Event Theory y is between 0 and 1. I'll try to revise the theorem and proof and eliminate the "backwards- forwards" parts that were intuitively motivated to obtain a clearer logical order, although it is interesting that intuition played a more "exploratory" role here than logic. Osher Doctorow

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FOTD 29-12-03 (Fractoid [7])
by Jim Muth 29 Dec '03

29 Dec '03

FOTD -- December 29, 2003 (Rating 7) Fractal visionaries and enthusiasts: Greetings once again from Fractal Central, the half-fantasy, half-real home of the world's most over-and-under rated fractals, and the totally-real home of the world's laziest, craziest cats. Today's fractal offering rates a very good 7, a rating that seems honest, at least at the moment. In a day or two it may seem far too high or low, but I will not know until the time comes and the rating has been fixed in stone. The name fractoid is a combination of the words fractal and android, though I can see nothing human-like in the image with its lilac swirls and beige background. The stripes in the background were created by rendering the scene with the outside set to 'tdis', an option that colors the points according to the distance they peregrinate (I like the word) before passing beyond the escape radius. The parent fractal is a distorted version of the Mandelbrot set, with the buds of the main bay rotated far around the shoreline in a CCW direction. Today's scene is located in a spiralling elephant trunk on the south shore of East Valley. The image takes 17 minutes to render from the included parameter file. That time can be cut drastically by downloading the completed image from Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The past several days were acceptable here at F.C., with no extremes of weather, no extremes of cat behavior and no further word from Ken. Today is starting as though it will turn into yet another perfect day. But such perfection cannot last long before something goes wrong, so until next time, take care, and don't bet your bippy. You might lose it, and bippies are hard to replace. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractoid { ; time=0:17:26.93--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.54306023277118430/+1.408216019104502\ 00/3.663052e+007/1/-94.9999918776349119/-3.9243277\ 7156226376e-007 params=1/1.1/-1/-1.3/0/0 float=y maxiter=3000 inside=0 outside=tdis periodicity=10 colors=000SZc`UWiOQrJJzEDyHGwJIuMLrONpQP3ep0hq0js0\ nu0pv0qs4rr8spCuoGumJvkOwiSxhVxfZyeazcezahz`izcjzg\ jyjefezLzWxzzzzrzrzjWhopfjkcfgkcc_ZZXVVVQQTMMQIHOD\ CM87J43PCDVIM`OUfUak_iqeqzozxjzvgzscyq`xpZvoWvmTuk\ QujOsiMshJrgHrfErgHmgJhgMchN_hPVhSQiTMiVHiXCiZ7mVE\ pSMsOTvL_yHfzDmzAszHpyMnwQjuVhr`epecni_knXisUgxSez\ OczMezvczuazs`zs_zrZzq3Gp7IpAJpDMpHOpLPpNSpQUoUVoX\ Xo__oc`ofcohcoffjehgcicck_`nW_oSZqOXrLXpMXoMXnMXkN\ XjNXiNXgOXfOXeOXcOWeSVfUUgXTg_ShcQiePigOjjNkmMmpLm\ rJnvIoxIozHhrHakGVeGOXEHQE9JE3CACH7JM3SQ0ZU8U`HPfP\ LkXGqeCwgHriLokOkmShoVeqZasaZueVwhSykOzoLuaPoPToVS\ oaQphOpnNquLqzJqzIszNvzQxzUzzZzzazzezzhzzkzxnxupvq\ rrnupjwngykcziazgcyeevcgq`hn_jiXkfVnaToZQqUPrQNoVL\ m_IicGghEcmCaq9Zv7Wz5Uz8TzATyDTwETsHTqJToLTmNSiPSg\ SSeTSaVS_XSXZSV`TXaT_cTacTceTffThhTiiTkjTnkTpmTrnT\ uoTvgWu`ZsU`rMcqEfp7hoIch } 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 } END 20.0 PAR-FORMULA FILE==================================

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[Fractint] Could the Big Crunch Be An Exponentially Exploding Julia Set Boundary?
by mdoctorow＠comcast.net 29 Dec '03

29 Dec '03

>From Osher Doctorow Ph.D. mdoctorow(a)comcast.net Indications accumulate that the Riccati Equation is the equation of Expansion-Contraction-Growth (ECG) across biology and physics and other fields, and that this is a type of motion distinct from the usual one-direction-at-a-time Curvilinear Motion. ECG involves motion simultaneously in 2 or more directions (often infinitely many). Since the Universe expands, it seems like an ideal testing case for the Riccati Equation. The general Riccati Equation is: 1) dy/dt = A(t) + B(t)y + C(t)y^2 where dy/dt is the speed of expansion or contraction of y at time t and y^2 is y-squared (y times y) and A(t), B(t), C(t) depend on time t and may or may not be constant real numbers. It turns out that we can prove the following, although the words "certain plausible conditions" are somewhat restrictive. THEOREM. Under certain plausible simple conditions, the Universe goes from a Big Bang in which Rare Event Theory applies and dy/dt attains its maximum ( = 1) to a Big Crunch in which dy/dt = 1/e where e is the exponential constant approximately equal to 2.72 and 1/e is the boundary of exploding Julia sets for the exponential functions c exp(x) (that is, c = 1/e). When c < 1/e, the Julia set is small, and when c > 1/e the Julia set is the whole complex plane (the latter statement can be seen from Robert L. Devaney (1990) Chaos, Fractals, and Dynamics, Addison-Wesley: Menlo Park, CA). PROOF. Since the Riccati Equation and its special cases the Logistic Equation and Simple Exponential Growth/Decay Equations often involve solutions equal to exp(kt) or rational expressions in exp(kt), put exp(t) (k = 1 for simplicity here) into the general Riccati Equation. Since d(exp(t))/dt = exp(t) from calculus, and exp(t) is extremely difficult to "cancel" from an equation usually unless all the terms involve exp(t), let us write A(t) = A1(t)exp(t), C(t) = C1(t)exp(-t). We don't have to change B(t) as will be seen below. Then we obtain: 2) dy/dt = exp(t) = A1(t)exp(t) + B(t)exp(t) + C1(t)exp(-t)exp(2t) since exp(t) squared is exp(2t) from elementary algebra. Since exp(t) divides out in (2) on both sides, we are left with: 3) dy/dt = A1(t)exp(t) + B(t)y + C1(t)exp(-t)y^2 But dividing through by exp(t) on both sides of (2) also leads to: 4) C1(t) = 1 - A1(t) - B(t) This in turn suggests the simplification: 5) B(t) = - A1(t) which also nicely simplifies C1(t) from (4) to C1(t) = 1 Now equation (3) becomes: 6) dy/dt = A1(t)(exp(t) - y) + exp(-t)y^2 When t = 0, dy/dt = A1(0)(1 - y(0)) + (y(0))^2. When t = 1, dy/dt = A1(1)(e - y(1)) + exp(-1)y(1)^2. Since the Big Bang was "explosive" in various senses, we can set dy/dt at t = 0 equal to 1, in which case 1 = A1(0)(1 - y(0)) + (y(0))^2. This is perfectly satisfied if y(0) = 1. Although this does not hold for y(t) as the radius of the Universe, it does hold if y in a neighborhood of 0 is the Rare Event Probable Influence since the latter is 1 at 0. Choose the neighborhood of 0 as [0, .05), that is to say t goes from 0 to less than .05, in accordance with the typical statistical .05 "level of significance". Choose A1(t) = 1 - t + t^2 in the Rare Event neighbor- hood of 0 and A1(t) = 1 - t in [.05, 1]. Then dy/dt at t = 1 equals exp(-1)y^2(1). This already implicates exp(-1) unless y^2(1) = 0 which needn't hold in general. If y(1) = 1, then dy/dt = exp(-1) = 1/e at t = 1. But y(1) = 1 and y(0) = 1 for continuous but non- constant y describes a cyclic universe, and 1/e is the explosive boundary. It should be noted that y(t) and t are between 0 and 1 in the Rare Event scale and that this scale should be restored in the neighborhood of 1 since 1 in the Rare Event scale corresponds to infinite time or to the supremum of finite times, which is a Rare Event (although A1(t) needn't change). Q.E.D. The words "Big Crunch" may not be precisely what we think of as a second "Big Bang", since for example at present the Universe is accelerating in size, but in Rare Events things may not quite be what they seem. Osher Doctorow

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All is well at F.C.
by JimMuth＠aol.com 27 Dec '03

27 Dec '03

Fractal Enthusiasts: The major part of the holidays have passed here at Fractal Central and all is still well. The cats have destroyed their catnip mice, the food is gone, there has been no further word from Ken with the blivot, but the fractals are still alive and well. The next FOTD will appear on schedule in 2 days. Until then, take care, and best wishes to all. Jim M.

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Important Message for Paul and Scott
by Jim Muth 23 Dec '03

23 Dec '03

At 08:28 PM 12/22/03 -0800, John W. wrote: >Whilst pondering this thread, I took a look at that original 1999 Blivot and >was astounded. This must be one of the all-time uglies of the fractal >world! I wonder how Jim would now rate it at, using his present, (ahem), >method? :-) Looking at the old fractal today, I also wonder how I could have chosen it. I must have been having a really bad day. P.S. Methinks that Ken should promote his commercial endeavors with words that are not in such common usage. Jim M.

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FOTD 23-12-03 (Concentric Circles [6])
by Jim Muth 23 Dec '03

23 Dec '03

FOTD -- December 23, 2003 (Rating 6) Fractal visionaries and enthusiasts: This will be the last FOTD until December 29, but have no fear, it is just the seasonal rush that is putting the damper on the fractals, and there is still today's image to discuss. The image is a scene in the fractal created by combining 8.6 negative parts of Z^(-6.6) with 9.6 negative parts of Z^(-1.1) and adding (1/C). It was calculated by the MandelbrotMix2 formula, which works the same as the MandelbrotMix4 formula, with the added option of manually adjusting initial Z. The parent fractal of today's image is an oversized thing consisting of a central Mandeloid with a large arm extending north and terminating in a large ring. Today's scene is located on a filament inside this ring. The location is reflected in the concentric rings surrounding the midget. It is these rings that inspired the name "Concentric Rings". When I found the scene, I rendered it first with the standard equal-iteration-band method. When this method produced a thoroughly ho-hum image, I tried the other outside options. I also tried evaporating the image and rendering it with the various inside fills. The best option I could find was to render the scene un-evaporated, with the outside=tdis, which is the 6-rated version that appears as today's FOTD. The render time of 9 minutes can be cut to a minute or two by downloading the finished image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A milder temperature of 54F 12C and as much sun as could be mustered on the shortest day of the year gave the fractal cats a good afternoon in the yard. Their greatest excitement came when a starling lighted on a nearby twig, causing Tippy to chatter in anticipation and Thomas to twitch his tail furiously. Luckily for the bird, the cats' bird catching days are pretty much behind them. Today looks to be a repeat. For me, it's work before fun, and the time to start working is now. Until next FOTD, which will be posted on December 29th, Take care, and see you in 6 days. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Concentric_Circles { ; time=0:09:34.85--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=-1.65813346453185800/+30.92368628273601\ 000/1.849903e+009/1/-5/0.0091790130718738816 params=-8.6/-6.6/-9.6/-1.1/0/0/0/0 float=y maxiter=1400 inside=0 outside=tdis periodicity=10 colors=000jszgiRfiSeiSeiTdiTdiUciUbiVbiVaiWaiW`iW_\ iX_iXZiYYiYYiZXiZXi_Wi_Vi`Vi`Ui`UiaTiaSibSibRicRic\ QidPidPieOieNjfOiePiePhdQhdRgdRgcSfcTfbTebUebUdaVd\ aWd`Wc`Xc`Yb_Yb_ZaZ_aZ_`Z``Y`_Ya_XbZXbZXcZWdYWdYVe\ XVfXVfWUgWUgVThVTiUTiUSjTSkTRkTRlSRmSQmRQnRPnQPoQP\ pPOpPOqONrONrNNsNMtNMtMLuMLuLLvLKuKKsKJrJJqJJrIItI\ IuIItHHsGHrFGrEGqDFoCFnBElAEjADh9Dg8Ce7Cc6Bb5B`4AZ\ 3AX19Y3AZ5AZ6A_8A`9A`BAaDAbEAbGAcHAdJAdLAeMAfOAfPA\ gRAhTBhUBiWBjXBjZBk`BlaBlcBmdBnfBnhBoiBpkBplBqnBrp\ CqoBpnBomBnmBnlBmkBlkBkjBjiBjiBihBhgAggAffAfeAeeAd\ dAccAbcAbbAaaA`aA_`AZ_9Z_9YZ9XY9WY9VX9VW9UV9TV9SU9\ RT9RT9QS8PR8OR8NQ8NP8MP8LO8KN8JN8JM8IL8HL8GK7FJ7FJ\ 7EI7DH7CH7BG7BF7AF79E78D78D77E87E97EA7EB7EC7ED7EE7\ EF7EF7EG7EH7EI7EJ7EK7EL7EM7EM7EN7EO6FP6FQ6FR6FS6FT\ 6FT6FU6FV6FW6FX6FY6FZ6F_6F`6F`6Fa6Fb6Fc6Fd5Ge5Gf5G\ g5Gg5Gh5Gi5Gj5Gk5Gl5Gm5Gn } 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 } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] Important Message for Paul and Scott
by Jim Muth 23 Dec '03

23 Dec '03

At 06:48 PM 12/21/03 -0600, Tim W. wrote: >In amusing myself with the "blivot" thread, I noticed that >if you do a google search for blivot, what pops up FIRST is: > >http://home.att.net/~Fractals_1/FotD_99-03-02.html . . . > >Funny that www.blivot.com doesn't show up until the 5th page. This is what has our friend Ken upset. He wants his business to come up first when a search is done. When I received the original letter, I thought it was a joke. I was ready to reply, requesting a small payment for advertising his company on the FOTD web sites. But as Tim says, Christmas is but 3 days away, and it's time to be nice to each other. Maybe we should introduce Ken to fractals. ;-) The FOTD will appear in 2 to 3 hours. Jim M.

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Re: [Fractint] Important Message for Paul and Scott
by Jim Muth 23 Dec '03

23 Dec '03

At 02:26 PM 12/21/03 -0800, John W. wrote: >Well, for a start off, this guy can tackle the publishers >of Webster's. I think that the first definition is very >applicable! >---------------------------------------------------- >Hypertext Webster Gateway <<blivot>> > >>From Jargon File (4.3.0, 30 APR 2001) (jargon) > >blivet /bliv'*t/ n. [allegedly from a World War II >military term meaning "ten pounds of manure in a >five-pound bag"] ..... <other definitions snipped> The spelling that appeared in the FOTD was 'blivot'. The definitions in the dictionary are for the spelling 'blivet'. Though both spellings are pronounced the same, I wonder whether they really can be considered the same word. The FOTD for Dec 22 will appear on schedule. Jim M.

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FOTD 22-12-03 (Fornever and Never [8])
by Jim Muth 22 Dec '03

22 Dec '03

FOTD -- December 22, 2003 (Rating 8) Fractal visionaries and enthusiasts: When I first came upon today's image, I rated it a 4, and almost decided to relegate it to the trash-bin of forgotten fractals that never made FOTD. But before deleting it, I tried a few thumbnail images of the same scene, using the various outside options. Most options produced little more than total chaos, but the 'tdis' and especially the 'fmod' options created interes- ting miniatures. I chose the 'fmod' option. The resulting image consists of the overlapping bubbles that appear so often with the 'fmod' option. Some bubbles are nearly circular, while others are peanut-shaped. All the bubbles put together create an image with an unusually vivid three-dimen- sional effect. And the traditional Mandelbrot midget is right where it belongs, at the center of the frame. The parent fractal of today's image, which was created by combining various negative portions of Z^3 and Z^5, appears to the visual sense as a Mandeloid rotated -90 degrees, with more extra bays and valley than one can shake an iteration at. The scene of the image lies in a supernumerary valley on the south- west shore of a smaller Mandeloid located on the main (negative- imaginary in this case) stem of the large Mandeloid. The rating of an exceptional 8 might be a bit overdone. I really did not give the image the attention to the coloring that a truly exceptional fractal should have. When I named the image "Fornever and Never", I had a reason. Unfortunately, I have now forgotten that reason. But it's an interesting name for an interesting fractal. And the waiting time of 10 minutes can be eliminated by downloading the comple- ted GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Saturday and Sunday were sunny but chilly days here at Fractal Central, with the temperature in the 30'sF, around 2C. The cats spent only a short time outdoors on both days. The rest of the time they spent stretched on their blanket by the large radiator in the living room. The tuna kept them happy when the rest of the world turned bleak. Today promises to be much milder. The fractal cats deserve the break. For me, it's work before fun. Until the next FOTD appears, most likely but not certainly 24 hours from now, take care, and watch your fractal language. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fornever_and_Never { ; time=0:10:03.30--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.03748528249124874/-1.214425735677524\ 00/2592058/1/65/1.0046787402018e-008 params=-0.8/3\ /-0.3/5/0/0 float=y maxiter=1500 periodicity=10 proximity=0.161 outside=fmod logmap=yes inside=0 colors=0004402401400400400400400400400400400400400\ 40060060060070170470671882A84D86G87I99L9AO9CR9EUAG\ XAH_AJbALfCNjCQmCRpCTnAUn9Wn8Wn7Xn6Xn4Zn4Zn4_n2_n1\ am0am0bm0bm0dm0dm0fm0fm0hm0hm0jm0jk0fk0dk0ak0_k0Zk\ 0Wk0Uj0Tj1Qj2Oj4Nj4Jj6Ij7Gh8Eh9DhAAhC9hD8hE6hG4hH4\ _N9UREOWJI_QDdW8ja4nh0tn0yv0zz0wv0pp0jj0bd2XZ4TU7N\ O9HJCCEE7AH47I2DJ1IJ0OL0UL0_N0XN0UN0RN0QN0NN0JN0IN\ 0GN0DO0CO09O07O06O04O01O00O00O00O00N00N20N60LA1LG2\ LJ4OI4QI4RI4TH6UH6XH6ZG7_G7aG7bG7fE8hE8jE8kD9mD9pD\ 9rCAtCAvCAwCArCCnCDjCDfCEbCEZCGWCGTCHOCHLCIICIECJC\ CJ9CL6CL4CN1CN4EQ8HRAJTENWHQYLT_OW`TZbXbfafjekmloq\ psuuwwwyztwzttyrpwolujgrdan_VhUPcQGYJAUG6RC1O78U4G\ _0Of0Wk0dr0ny0jzLdUzC1zECzGOzIazJntWkbfhOtdCzbEzdG\ zfHzfIzhLzjNzjOzkQzmRzmUzjWwfXpd_haaa_bUXfOWhHTjCR\ hEQfGQfHOdJObLNbNNaOL_RL_TJZUJXWIXZIW_HUaHUbHXbJ_b\ NdaQhaTkaUn_Xr__740640440 } 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 } END 20.0 PAR-FORMULA FILE==================================

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Jim Muth's FOTD
by Scott D. Boyd 22 Dec '03

22 Dec '03

I will be discontinuing my daily posting of Jim Muth's FOTD at the end of the year. The past three years worth of his FOTDs will stay on my Website however. Scott Boyd sdboyd56(a)swbell.net http://sdboyd.dyndns.org/~sdboyd/

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Re: Fractint Digest, Vol 10, Issue 7
by JackOTradez 22 Dec '03

22 Dec '03

Hey Osher - What you smokin' and where can I get some ? JoTz

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Important Message for Paul and Scott
by Jim Muth 22 Dec '03

22 Dec '03

I received this e-mail an hour or so ago: >Return-Path: <BLIVOT1(a)aol.com> >From: BLIVOT1(a)aol.com >Date: Sun, 21 Dec 2003 10:35:57 EST >Subject: FOTD Website >To: jamth(a)mindspring.com (Jim Muth) > >Hello Jim, >I am the owner of the federally registered trademark >Blivot which is listed in the Library of Congress. I >must ask you to eliminate the word blivot on your >website, unless you wish to be licensed by my >corporation to use my trademark. Usage of a >registered trademark and the trademark symbol without >expressed written permission is a federal offense. If >you wish to use my trademark e-mail me at > <blivot1(a)aol.com> for licensing agreement. Apparently the non-word 'blivot', which I might have used in a FOTD, is a registered trademark. Since I am not the owner of the offending web site/sites, I pass the letter on here so that Paul and/or Scott can be aware that someone might have his feathers ruffled. I have contacted the sender, telling him that the FOTD web sites are not mine. BTW, there will be no FOTD for today, December 21. Jim M.

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genetic art system
by Charles D McGee 21 Dec '03

21 Dec '03

i'm a longtime reader but a seldom poster, so seldom in-fact that i had to re-enroll in the list. this is the research project of my friend, kennon. he needs lots of people to use the site to get good aggregate data, and the viewers of this list could provide lots of helpful feedback. enjoy...dave please visit this website: http://studentweb.cs.bham.ac.uk/~msc92klb/ga/images.php To use this project, simply click on the images that look interesting. The first images you see are all random; click on the most interesting image and then it will load in the upper left corner and the rest will be mutations of it. To cross two images together, select two checkboxes; the page should reload automatically. Click on "random" to start with a new set of images, or click on "best" to see some of the best images generated so far. You can also change the colormap by choosing a new one from the drop down box. If an image looks interesting and you would like to look at it closer, click on the magnifying glass in the upper right corner. This is a research project designed by Kennon Ballou. Please have fun, and feedback would be greatly appreciated. Enjoy! http://studentweb.cs.bham.ac.uk/~msc92klb/ <--kennon's page

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The Edge of Connectedness
by mdoctorow＠comcast.net 21 Dec '03

21 Dec '03

>From Osher Doctorow Ph.D. I have been posting to the Math Forum (access it by those keywords) in the subforums Geometry-Research and Math-History-List and also to ResearchMathematics(a)yahoogroups.com and Theory-Edge(a)yahoogroups.com and somewhat to CHORA(a)liverpool.ac.uk (a philosophy forum in England) on what I will here call the Edge of Connectedness. Mathematical and Theoretical Physics (physics respectively done by Mathematicians and theorists with mathematical knowledge inside physics) appears to be presently extremely dominated by the one-step-at-a-time one-path-at-a-time people whom I call the Curvilinear School because their paths look like straight lines or bent/curved lines. Opposed to that school are a few theorists like me who adopt an Expansion- Contraction approach in which simultaneous motion in different directions is the key thing. In my postings at the above sites, I am finding that just as the Edge of Chaos plays a critical role in Fractals and Chaos theory, so the Edge of Connectedness plays a critical role in Expansion-Contraction theory. What is the Edge of Connectedness? The Expansion-Contraction school roughly maintains that the Universe itself is mostly connected, in opposition to the Curvilinear school which has concluded (to the extent that it concludes anything) that the Universe is in its foundations mostly DISCONNECTED. The Edge of Connectedness is where Connected things come close to getting Disconnected but not quite. It is exemplified by a Hole in a Connected object. Unless the Hole is so big that it tears the object in two, it ordinarily does not disconnect the object entirely. Some connected objects can be "shot through" with holes and still stay connected. We say that they are porous for example. For those members of FractInt who want to explore this, take a look at my postings above. They tie together things that have not been tied together before in the Mainstream research literature and put them in a new light. After mastering the rather simple language, you might want to take a look at the rather forbidding-sounding names Pseudodifferential Operators and Parametrix and Parametrices, and Singular Support. These keywords lead to very complicated mathematical and physics literature, but look at the abstracts and the summaries and even some of the rough English which occasionally emerges because at that difficult level even quantitative people find a certain need to gather their intuitions verbally (not so much in Curvilinear mathematics, however). Osher Doctorow

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FOTD 20-12-03 (Baubles and Things [3])
by Jim Muth 20 Dec '03

20 Dec '03

FOTD -- December 20, 2003 (Rating 3) Fractal visionaries and enthusiasts: Have no fear, fractal fans. Despite my announcement that I will likely miss a few FOTD's between now and the first of the year and Scott's announcement that he will no longer be posting the new FOTD images on his web site after the first of the year, the FOTD will continue basically uninterrupted into the indefinite (but most likely not eternal) future. People might be temporary but fractals are forever. Today's image is a loser. I named it "Baubles and Things" because it reminds me of what one might see if they were to pull open a small drawer that hasn't been opened in years. Also, the name reminds me of one of the 'trendy' names one might see on a near-useless store that has replaced a very-useful store in the downtown section of some 'rejuvenated' small town. The rating of a 3 is a gift. The image is a scene in the grossly-bloated parent fractal that results when 5.5 parts of Z^(-0.93) are subtracted from 5.7 parts of Z^(-0.77) and (1/C) is added. Despite the near totally- chaotic nature of the scene, it was rendered by the convention- al, old-fashioned equal-iteration-band method. When rendered with the outside=tdis, the image becomes even more chaotic, though some may prefer the 'tdis' version. Today's pathetic image renders in 14 minutes, about 14 times as long as it is worth. But you may get what you paid for by downloading the completed GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> I will no longer list the address of Scott's FOTD web site. After the first of the year, he will no longer be adding the new FOTD images to his site. Friday was quite cold here at Fractal Central, with a tempera- ture that hovered just above the freezing mark all day and a few flakes of snow thrown in for fun. The fractal cats had no fun however. They spent the day sleeping on their blanket by the radiator. Today looks to be a repeat. I have a small to moderate amount of work to finish before I start the search for the next FOTD. So until the next FOTD appears in either one or two days, take care and take care again. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Baubles_and_Things { ; time=0:14:21.72--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-351.30556131984170000/+388.73448651068\ 660000/7404.484/1/102.5/3.8578131286715056e-008 params=-5.5/-0.93/5.7/-0.77/0/8 float=y maxiter=3600 inside=0 logmap=280 periodicity=10 colors=000PFVMDYLC_LCaKBcKBeJBfJAhIAjI9lH9nH9oG8qG\ 8sF7uF7wF7xGKvGXtGirZYGYUBXQ7ZV6__6ad5bh5cbKUQYdTk\ `QcXOWUMOQJGzc8JF1iOekQfmSgoTgqVhsWhuYivZiqagldegg\ dbjbYm`Tp_OsYJvXQo`WhdaahgVlmOpsHtyAxxGtxMqxSmxYjw\ cgwicwo`wtYnufevoXvx_wqaxkbvgbudbtabrYbqVbpSboPVeW\ OXaHNhAEn_9fx5Zq6Zj7Zc8ZX8ZQ9ZJAZCBZ5BZEDaNFdVGfJP\ p8YzBZqD_hF__H`RJ`JIXGHUEMQPRN_WJj`GtaKqbNncRkcUhd\ Xee`bfc_ffXeVWdKVc9UfHWiPXlXYod_rl`tsaVYU5DMAEbFMd\ KTfO_gSKEVKFYKG`KGcKHfKIiKJlKKoKLrKMuKMsLOrMQpNSoO\ TmOVlPXjQYiR_gRafSbdTdcUfbUgfQjjMmnIprEsvAvtClrDbq\ EToFJnGAiUUeWcMZZ3VV6SX8PZBN`DKbGIdIFfLChNAjQUlSUn\ TUdUUVVULWUBWU2VU5UU7TUATUCSUERUHQUJQZLPZOOZQNZTNc\ VMcXLc_KcaKccKcZKcVKhQKmMJrJJvHJzEIzCIz9Iz7Iz5LzAO\ zERzITzMWzQZzU`zYczafzehzikzmnzqpzuqzqrzmrzjszfszb\ tz_tzWuzTvzPvzLwzIwzExzAxz7yz3yz0xz1wz1vz1uz2tz2sz\ 2rz2nz6jzAgzDczH_zKXzOTzR } 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 } END 20.0 PAR-FORMULA FILE==================================

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Thanks for providing the space for the FOTD.
by Hal Lane 20 Dec '03

20 Dec '03

On Fri, 19 Dec 2003 13:08:40 -0600, Scott D. Boyd wrote: > I will be discontinuing my daily posting of Jim Muth's FOTD at the >end of the year. The past three years worth of his FOTDs will stay >on my Website however. >Scott Thanks for providing the space for Jim Muth's Fractal Of The Day images. I often view them on your and Paul's sites. - Hal Lane ############################## # hallaneAT earthlinkDOT net # ############################## --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.553 / Virus Database: 345 - Release Date: 12/18/03

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FOTD 19-12-03 (Lacy Bubbles [6])
by Jim Muth 19 Dec '03

19 Dec '03

FOTD -- December 19, 2003 (Rating 6) Fractal visionaries and enthusiasts: Things will be quite busy for the next two weeks here at Fractal Central, so there may be a number of days on which the FOTD fails to appear. This is no cause for concern. I will post a notice on the days when there will be no FOTD. The good news is that after the first of 2004, the FOTD will be back on its regular schedule. Fractals are forever. Today's scene lies in the parent fractal created when 4.25 parts of Z^(-7.6) are added to 4 parts of Z^(-1.5) and (1/C) is added. The image is an evaporated one, meaning it doesn't exist, at least as an inside vs. outside fractal. The image consists of nothing but trapped 'inside' points, made visible by the 'bof60' inside fill. This fill creates images much like those created by the 'fmod' fill -- scenes of bubbles overlapping bubbles, such as those that appear in today's image. When trying to think of a name for today's image, I was undecided whether the image was lacy or bubbly. After a few minutes indecision, I decided on the name "Lacy Bubbles", a good compromise. The rating of a 6 was much easier to determine. It seems as though at least half of my current FOTD's rate a boringly common and alltogether average 6. The render time of 17 minutes is a bit slow. I recommend the relief from the wait that can be found on the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The freezing temperatures and brisk winds kept the dynamic fractal duo ensconced in the warm indoors all day Thursday. Realizing how cold it was outside, they didn't even ask to venture forth. In the evening, I rewarded their patience with a dish of prime tuna. And today is starting just as cold. Most likely, the duo will remain indoors for the entire day. The work is again starting to back up, so I had best get on it. Until next time, take care, and see you soon. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Lacy_Bubbles { ; time=0:17:43.86--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.32397176109759400/-0.135254552039921\ 60/31313.17/1/-175/-2.52921648277726341e-008 params=4/-1.5/4.25/-7.6/0/1e+100 float=y maxiter=1200 inside=bof60 periodicity=10 colors=000zzwvwqtvorumptknsilrgjqehpcfoadn_bmY`lW_\ lUYkSWkUUjXSi_QibOheNhgMfdLeaKd_JcXIbVHaSG`QF_NEZL\ DYICXGBWDAVB9U89T68R57Q56P55O54N54L43K42J41I40H40G\ 4AOCKWJUcRckYmseqvhMXLMXL4XL5_N5bPhPIiQJiRK_tXcu`g\ vcebbdJac0aKkDMcEOXE1hzmxzmxzSuYSqbSmgSjkTcgTXdTQa\ TJZSLTRNOKNGQPJGcU7J3DM7JOBVw7sl4sA1cI80BDS4FIbyLY\ iNUU``dWiqM1mOAjQIgSReUZbWf`VgSVgKUgBUg3Vd3Wa3XZ3Y\ W3ZT3_Q3`N3aL3bI3cF3dC3e93f63g33h13nJ7s`BxqFwlEvhE\ udEu`EtXEsTDsPDrLDqHDqDDrFKrHQrJWrLasNhsPnsRtsSzpZ\ qndhlj_PoSPhOPbLPWHu4edFS9K0u1LjAI_IGcPmZQaUQQleDd\ _EXVEZRluu4WUaTSURRMknv_a_VLMTNKSOIQPGQNRPPKlFMfIK\ `LIVOG_CBUJDgECYKDK_Lk5qeBg_GYULOMEHNIGOMFfuq7nNDe\ KJYHiSf6psBihGbZLWO5jGLO5MP8FQbBNW7LP3JJ7MKAOKEQLH\ SLLUMOWMSYNV_NYbNadOdfOhhPkjPolQrnQupQqnOnlNkjMhhL\ efKbdJ_bIX`HUZGRXFOVELTDIRCFPBiNohMnhLnhLnhKmhJmhJ\ mgIlgIlgHlgGkgGkgFkgFkmCl } 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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 18-12-03 (The Phantom Wave [5])
by Jim Muth 18 Dec '03

18 Dec '03

FOTD -- December 18, 2003 (Rating 5) Fractal visionaries and enthusiasts: Today's image has been named "The Phantom Wave". Don't ask me why I gave it such a name -- I have no idea. The name might refer to a wave of bubbles or a wave of midgets, or even a wave of FOTD images calculated by the MandelbrotMix4 formula. More likely, it's a wave in my imagination. But whatever the reason, there must be some kind of wave connected with the image, which lies in the parent fractal created by subtracting 0.9 parts of Z^(1.2) from 2 parts of Z^(-1.2) and adding (1/C). The bubbly effect in the image was achieved by rendering the scene with the outside=fmod and the proximity=3. At the moment I am not sure how the 'fmod' option works and how the proximity affects it, but the information is somewhere in the monumental stack of help included with the Fractint program. I could rate the image no higher than a 5, a rating that is ho-hum average. No, I do not expect a rush to see the image when I admit in the discussion that it is un-exceptional, but the fun lies in finding the FOTD images and writing about them. Profit is obviously no motive in the creation of the FOTD. The render time on my worn-out P200 machine, which just barely keeps slogging along, is almost exactly 6 minutes. On the state- of-the-art units out there the image will render notably faster. The fastest way of all to see the phantom wave is to download it from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> and examine the image very carefully for any signs of a wave. The Wednesday rain here at Fractal Central changed to snow at 2pm, but ended within an hour before accumulating on the ground. The cats, who spent the entire day indoors, were not concerned with the change-over. They needed only a small treat of tuna in the evening to maintain their good spirits. Today is starting partly cloudy, breezy, and cold -- the kind of day that keeps fractal cats indoors and the fractal human busy working on the next FOTD, which will appear in 24 hours. Until then, take care, and be at peace. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Phantom_Wave { ; time=0:06:00.08--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.38515755772367030/+0.157082089485032\ 80/89131.38/1/-30/2.018383862823e-010 params=2/-1.\ 2/-0.9/1.2/0/0 float=y maxiter=1200 inside=0 proximity=3 outside=fmod logmap=yes periodicity=10 colors=000pgopgmoglngknfkmfjlfilehkehjegjdfidfhdeg\ cdgccfccebbebadb`ca`ca_baZa`Za`Y``X__WZ_WZ_VYZUXZT\ XZTWZSVYRVYRUYQTXPTXOSXORWNQWMQWLPVLOVKOVJNUJMUIMU\ HLTGKTGKTFJSEISDHSDHRCGRBFRBFQAEQ9DQ8DP8CP7BP67O09\ O3BN6DN9FMCGLEIKHKKKMKNOKQOKRP9SP9SQ9SQ9TRATRATRAU\ SAUSAUTBVTBVUBVUBWUBWVCWVCXWCXWCXXDYXDYXDYYDZYDZZE\ ZZE__E__E__E_`F``F`aF`aFabGabGabGbcGbcGbdHcdHceHce\ HdeHdfIdfIegIegIehJfhJfhJfiJgiJgjKgjKhkKhkKhlJjkKh\ jKgiKehLdhLbgLafM`eMZdMYdMWcNVbNUaNS`OR`OP_OOZOMYP\ LXPKXPIWQHVQFUQEVRBUQCUQDTPETPFSPFSOGROHRNIRNJQNJQ\ MKPMLPMMOLNOLNNKONKPNKQMJRMJRLISLITKIUKHVJHVJHWJGX\ IGYIFZHFZHF_GE`GEaFCcGDbGDaGEaGE`GF`GF_GG_GGZGGZGH\ YHHYHIXHIXHJWHJWHJVHKUHKUHLTHLTHMSIMSINRINRINQIOQI\ OPIPPIPOIQOIQNGRPIQNJPMLPKMOJNNHPNGQMESLDTLBUKAWJ8\ XJ7ZI5_H4_I2`H3`H3`H3`H3`G3TnHUmJWmLXlNYlP_kR`kTbj\ VcjXeiZfi`ghbihdjgflghmfj } 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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 17-12-03 (Too Much to Endure [8])
by Jim Muth 17 Dec '03

17 Dec '03

FOTD -- December 17. 2003 (Rating 4) Fractal visionaries and enthusiasts: Today's low-rated image lies in the 2-part parent fractal that appears when one part of Z^(1.1) is subtracted from 0.3 part of Z^(-1.1) and (1/C) is added. This parent consists of two large but distorted Mandeloids with much chaos surrounding them. Today's scene lies in the East Valley area of the less-distorted Mandeloid. I named the image "Too Much to Endure" because of the vast amount of chaos in the scene. This chaos could have been reduced by using a broader color palette and turning on the logmap, but I wanted to emphasize the chaotic nature of the scene, and the way the chaos mingles with order. As so often happens, a midget lies at the center of the frame. It is a thoroughly average midget with little to brag about. As a result, and because the disorder is excessive, I can rate the image no higher than a 4. And the render time of almost 15 minutes is excessive. But this is the only chance you will ever have to see this particular midget, so take advantage of the opportunity while it still exists. The 15-minute wait for the image to render may be avoided by downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather was pleasant enough here at Fractal Central on Tuesday, with adequate sun and a temperature of 54F 12C. The fractal cats enjoyed the conditions to the fullest, which at their advanced age is not very much. When settle-down time came, they were ready to settle down without complaint. But it's raining this morning. What this means to the cats has yet to be determined. As for myself, I've got a bit of work to get out of the way before the day ends, and the best way of doing it is to start. Until next FOTD, take care, and see you soon. (In 24 hours, in fact.) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Too_Much_to_Endure { ; time=0:14:42.54--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.02407524282701938/-0.632799848504139\ 70/2.240317e+007/1/44.999999938593831/7.4002309662\ 0912035e-008 params=-1/1.1/0.3/-1.1/0/0 float=y maxiter=3000 bailout=9 inside=0 periodicity=10 colors=000jYckXdkWdlVelUemTenSfnRfoQfoPgpOgqNhqNhr\ MhrLisKitJitIjuHjuGkvFkwEkwDlxClxCluDirEfpFcmG`jHY\ hIVeJScJQ`IOZIMXHLVHJSHHQGGOGEMGDJNFGTHD_JAeLCfMDg\ MFgMGhMIhNJiNKiNMjNNjNPkOQlORlOTmOUmOWnPXnPZoP_oP`\ pPbqQcqQerQfrQgsQisRjtRltRmuRmvSnuRntRnsRosRorQoqQ\ opQppQpoPpnPpnPqmPqlOqkOqkOrjOriNriNrhNsgNsfMsfMse\ MtdMtdMtcLubLuaLuaLu`Kv_Kv_KvZKvYJwXJwXJwWJwVIxVIx\ UIxTIxSHySHyRHyQHzPIyQHyQHyRHyRGxSGxSGxTFxTFwUFwUE\ wVEwVEvVDvWDvWDvXCuXCuYCuYBuZBtZBt_At_At_At`9s`9sa\ 9sa8sb8rb8rc7rc7rd7qd6qd6qe6qe5pf5pf5pg4pg4oh4oh3o\ i3oi3sm2oi3lf4hc5e`5aY6ZV7VS8SP8OL9LIAHFBECBA9C76D\ 33EQ2i00E12G23H34I46J57K68L6AM7BN8CO9EPAFQBGSCITCJ\ UDKVEMWFNXGOYHPZIR_IS`JTaKVbLWdMXeNZfO_gO`hPbiQcjR\ dkSflTgmUhnVkqUioUhmUglUfjTdiTcgTbfTadT`cSZaSY`SXZ\ SWYRUWRTVRSTRRSRQQQOPQNNQMMQLKQKJTMOVNSYOX_P`aQddS\ ifTmiUrkVvmWzkVwjVtiVrhVo } 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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 07-12-03 (Scorpio the Scorpion [6])
by Jim Muth 16 Dec '03

16 Dec '03

FOTD -- December 07, 2003 (Rating 6) Fractal visionaries and enthusiasts: Today's image is a dynamic one -- an image of a midget in the Z^1.09+C Mandeloid, which has been sliced 96 turns up the hyperspatial logarithmic spiral. It is incredible that a midget could be found in a fractal with an exponent as close to unity as 1.09, but today's image does not lie. The midget is there for all the world to see. But it doesn't look like a midget. It looks more like a comet tearing through the solar ejecta, complete with coma and tail. This appearance reflects the shape of its oversized parent fractal. I could have named the picture something like 'N.E.O.' or 'Solar Wind', but before giving the image a name, I looked more closely and noticed in the comet's tail an object that vaguely resembles a scorpion. I named the image "Scorpio the Scorpion", which is the name assigned the constellation in the southern sky that resembles a scorpion. Scorpio is also a sign of the zodiac, and one of the 12 signs of Astrology. Do I believe in Astrology? Yes, the study known as Astrology most certainly does exist. Do I believe that the science, (or pseudoscience), of Astrology has any truth behind it? That is a much harder question to answer. Astrologers certainly do believe that Astrology is a valid study, or they would have discovered its uselessness long ago, and it would have died. (Of course, they could be charlatans, preying on the gullible.) Skeptical scientists certainly are convinced that Astrology is a waste of time and effort, for they know of no possible way the position of the heavenly bodies could affect the character and fate of a person on earth. IMO, the question is not quite decided. I assume the validity of Astrology is greatly overblown, but is it zero? A little more than wish fulfillment would appear to be necessary to keep Astrology alive and apparently well for these thousands of years. I look at the clock on the wall above my desk and see that there is a correspondence between the position of the hands and the position of the sun in the sky. Every evening, when the hour hand reaches six, night falls. The hour hand does not affect the sun, yet the correspondence does exist. Does some similar correspondence exist that could give Astrology a modicum of validity without the need for the heavenly bodies to exert an effect on a person on earth? Almost but not absolutely certain- ly, it does not. Well, I've been reading 'Skeptical Inquirer', a magazine that always makes me pause to ponder, and I find myself once again drifting from the fractal topic. Today's image rates a 6, the most common rating of the FOTD's. Its render time is just under 9 minutes on my machine. This time is a bit slow, and may be cut by more than half by downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The snow ended by noon on Saturday, followed in the afternoon by some sun, but the damage had already been done. Even though the temperature rose to just above freezing, the ground was covered by deep snow, which confined the fractal cats to the freshly- swept porch. Deprived of their outing, the cats fell into sullen moods, which were lightened only when the tuna appeared. Today looks to be just as cold, and the snow is still out there. I suppose the cats will need more tuna. I plan on doing as little as possible for the rest of the day. Check back in 24 hours to see if I succeed. Until then, take care, and be happy in your leisure. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ ScorpioTheScorpion { ; time=0:08:52.45--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-0.37960693446691730/-2.000764325613529\ 00/332.6669/1/-40/-1.32272665043231541e-012 params=1.096/0/96/1000 float=y maxiter=10000 inside=255 logmap=93 periodicity=10 colors=000DKNEJLFHJGGHHEFIDDJBCKAAL88M76N54O31P43Q\ 54R65S77T88U89V9AWACXBDYCEZCF_DH`EIaFJbGLcHMbHNaIO\ `JQ_KRZLSYLTXMVWNWVOXUPZTQ_SQ`SRaSScSTdSUeTTeSUfSU\ gRVhRViQWjQWkPWlPXmOXnOYoNYpNZqMZrKbqL`rMZrMYsNWsO\ UtOTtPRuQPuQOvRMvSKwSJwTHxTGxb`ymvzltylrxlqwlowlnv\ llulktlitlgslfrldqlcqlapl`olZnlXnlWmkUlkTkkRkkQjkO\ ikMhkLhkJgkIfkGekFekDdkBckAbk8bk7ak5`l3Zk4_k4`j4aj\ 4bi4ci5dh5eh5fg5gg5hf6if6jf6ke6le6md7nd7oc7pc7qb7r\ b8sa8ta8u`8v`8w`8wb8tc8qd8oe8lf8jg8gh8ei8bj8`k8Yl8\ Wn8To8Qp8Oq8Lr8Js8Gt8Eu8Bv89w86yA2xC3xE4xG4xI5xK5x\ M6xO6xQ7xS8xU8xV9xW9xXAxYAxZBx_Cx_Cx`Dx`DxaExaExbF\ xbFxcGxcHxdHxdIxeIxeJxfJxfKxgLxgLyhMyhMyiNyiNyjOyj\ PykPykQylQylRymRymSznRynSxoSwoSzpTzpTzqTzqUzrUzrUz\ sVzsVztVztWzuWzuWzvWzvXzwXzwXzxYzx_zyazyczzezzgzzi\ zzkzzmzzozzqzzszzuzzwzzyzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 16-12-03 (Ethereal Iteration [8])
by Jim Muth 16 Dec '03

16 Dec '03

FOTD -- December 16, 2003 (Rating 8) Fractal visionaries and enthusiasts: The celestial appearance of today's image inspired the name "Ethereal Iteration". It is one of my better recent images, the first to rate an 8 in several weeks. Most of the heaven-like appearance is due to the coloring, which I found totally by chance. While I sat watching the colors cycle, today's palette flashed by. I quickly stopped the cycling and backtracked a few steps. Only a minor bit of touching up was needed before today's image was finished and ready to be crowned FOTD for December 16. The parent fractal is a curiously distorted Mandeloid, most of which lies beyond the top border of the default screen. North of the Mandeloid lies a rounded area of chaotic broken filaments and bits of spirals, almost serving as a shadow to the Mandel- oid. Today's scene, which mirrors the nature of the filaments very well, lies in one of these filaments. The midget itself was one that I found by instinct. There is no two-way symmetry at the surface of the parent fractal to indi- cate that the midget is there. How I find midgets such as the one in today's image is as big a mystery to me as to anyone else. Often I come upon them without even trying, while idly noodling around in some newly-created fractal. But that's how it is in the mysterious land of fractals. The rating of an 8 might be a bit liberal, but after so many 6's and 7's recently, I deserve it. The render time of 3 minutes is within the realm of reason, and can be cut in half by download- ing the finished GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Monday was too cold and windy here at Fractal Central for the fractal cats to have a good day, but they took their disappoint- ment stoically. In the evening their reward was a dish of flaked tuna. Today is starting cold and calm, but due to turn warmer. It should be a better day for the duo. For me, it will be an acceptable day once the work is finished and the next fractal has revealed itself. But that time is yet several hours off, so it's time to get started. Until 24 hours have passed, take care, and what does it all mean? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Ethereal_Iteration { ; time=0:03:41.68--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.08297230542334892/+5.277060130765460\ 00/174630.3/1/80/2.21423986923596772e-008 params=0.95/1.1/-1.05/-1.1/0/0 float=y maxiter=800 inside=0 logmap=75 symmetry=none periodicity=10 colors=000JAWKAYLA_MAaNAcOAePBgQCiRFkSImTKoUNqVPsW\ SuXUwYXwYZwYawZcwZfw_hw_kw_mwWjvSgvOevKbvH_vDYv9Vv\ 5Sv2Qv6Qr9QoCQkFQhIQeMQaQQZUQVYQSaQPeQLiQImQFiODeM\ CaKBYIAUG9QE8MC7KA6K85K64K43K32K6DK8NDBX9Df4Gp0Iz6\ KwBLtGNrLOoRQlWRj`TgeUeeQeeNfdJgdGhdCid9jd6je9heCf\ edAbXBZPCWHDS9EP1EO3DN5CM7BL9AKB9JD8IF7HH6GJ5FL4FN\ 4KR5OU5TX5X_5ac6ef6ji6nl6mi7mg7me7lc7la7l_7kY7kW7k\ U7hV8fV8dW8bW8`X8YX8WY8UY8SY9QZ9NZ9L_9J_9H`9F`9D`9\ BILFMKJQKMUKQYKUaJXeJ`iJcmJalK`lLZkLYkMWkNVjNTjOSi\ PQiPPiQNhRMhRKgSJgTIgTHhVHiWHjXHkYHlZHm_Hn`HoaGpbG\ qcGrdGseGtfGugGvhGwiFufEtcDsaCqZBpXAoU9nR9lP8kM7jK\ 6iH5gE4fC3e93d7GZITTSeNbqHllLjgPhbSfYWdUZc68c7Ha7Q\ _8ZY8gW8pUAlXBlZDm`EnbGodIpfKqhMr_OsSQtRSuRUvRWwRY\ xQ_yQazQczQezPgzPizPkzPmzOozOqzOszOuzNwzMxzLyzKzzJ\ zzIzz2zz2zz2zz7zzCzzGzzLzzPzzUzzYzzbzzfzzkzzozztzz\ xzzrzzlzzgzzazzWzzRzzLzzG } 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 } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] FOTD 15-12-03 (Splotchy the Midget [4])
by Jim Muth 15 Dec '03

15 Dec '03

At 11:53 AM 12/15/03 -0600, you wrote: >Jim Muth wrote: >> >> The render time of 10 minutes has been made a >> bit more interesting by using the 'inside=b' >> option.... > >I am sure everyone knows you really meant the "passes=b" option. I assume so, but then one never can be sure . . . Jim M.

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FOTD 15-12-03 (Splotchy the Midget [4])
by Jim Muth 15 Dec '03

15 Dec '03

FOTD -- December 15, 2003 (Rating 4) Fractal visionaries and enthusiasts: Today's mediocre image consists entirely of 'bof61' inside fill. But it is not a scene in an 'evaporated' fractal; it is a glimpse of something that might have existed, but never did. It is a scene in the blank screen that results when 1.1 parts of 1/Z are subtracted from 1.1 parts of Z^(0.8) and C is added. When one is exploring the world of fractals, blank screens usually mean a dead end, but like so many other things in life, there are exceptions. Today's image is one of these. The image consists of a string of splotches, vaguely defining a midget at the center. This midget is not a real midget. It is a virtual midget that almost but not quite exists, and needs just a little extra energy in the form of the 'bof61' inside fill to make it fully manifest. The result is not all that might be desired, rating only a 4. The render time of 10 minutes has been made a bit more interest- ing by using the 'inside=b' option, which is quite a bit of fun to see in action. As always, those who feel more serious about their fractals can escape the fun by downloading the completed image from Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> That long-promised philosophy appears in the version of today's FOTD that has been posted on the philofractal list. Snow and cold rain on Sunday kept the fractal cats indoors. The conditions were so unpleasant however that they were happy to sleep by their radiators for most of the day. In the evening I gave them their small treat of tuna, and they ended the day peacefully. Today is starting cloudy and breezy, with some slushy snow on the ground. But it is not too cold. It remains to be seen how the duo will take such conditions. I usually take conditions as they come. The work is moderate, the weather is moderate, the next FOTD will appear in 24 hours. Until then, take care, and don't despair. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Splotchy_theMidget { ; time=0:10:35.92--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=b center-mag=+0.58105390826287010/-0.018056876277498\ 32/9829.255/1/-10/-2.82683806918093694e-011 params=1.1/0.8/-1.1/-1/0/0 float=y maxiter=1200 inside=bof61 logmap=yes periodicity=10 colors=000JKBtqjtqltqntqptqrtqttqvuquvjtvbtMqKOqIP\ qGQqFSqDTqBUqAWq8Xq6Yq5`q4co4em4hk3jj3mh3of2rd2tc2\ qd5oe8lfBjgzhhHeiKcjN`kQZlTXmWUnZSoaQpdOqcNqcLqcKq\ cIqbHqbFqbEqbDq`CoZClXBiVBfTAcSA`Q9YO9VM8SK8QJUqlV\ qkVqkWqkWnkXkjXhjYfjYcjZ`jZYi_Vi_Si`Pi`NibOddP`ePX\ gQTiRPjRKlSGnTCoT8qU4rU0sT5sSAsREsQJtPNtPStOXtN`uM\ euLiuKnuKrtPqsUpsZzrcsrgo`XZJNI1D24B969F87MA5SC4YF\ 7YI9YKCYNEYPHYSJYVMYXOY_RYaTYdWYgYYi`YlbYndYhc`bcb\ XcdScgMciGckBcmLboUaqc`sl_uuZvUkoTkpRlqPlqOlrMmsKm\ tJmtHnuFnvEnvFltFkrFjpFioIPBFhmFgkFfjFehFdfFceFbcF\ aaF``F_ZGZXGYWGXUGWSGVRURPUTNGSMGRKGQIGPHGOFGNDFPA\ GOBGOBGOBGOBGOBGOBGOBGNBGNBGNBGNBGNCGNCGNCGNCGMChK\ ChMXhMChMChcChMCtc0s71r81q82sU2oA3mA3lB4kB4jC5iD5v\ D6gE6fE6eF7dG7cG8cH8cI9cI9cJAcJAcKBcLBcLCcMCc50b61\ a71`72_82_82Z93Y93XA4XA4WB4VC5UC5TD6TD6SE6RE7QF7QF\ 7PG8OG8NH9MI9MI9LJAKJAJKB } 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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 14-12-03 (Forever Fractal [7])
by JimMuth＠aol.com 14 Dec '03

14 Dec '03

FOTD -- December 14, 2003 (Rating 7) Fractal visionaries and enthusiasts: Today's fractal scene lies in the not-quite-imaginary land that is created when 1.3 parts of Z^(0.92) are subtracted from 1.3 parts of Z^(-1.08) and (1/C) is added instead of straight C. This parent fractal appears to the sense of sight as a twisted, stretched, pinched-off Mandeloid with a large bud on the north- west shore of the main bay. This large bud might or might not be the period-2 bud. I did not check. The shoreline of this large bud is crowded by unusually plenti- ful and unusually small sub-buds, each bud with a band of chaos stretching out and terminating in a flat disk. Today's scene is located near the terminal point of one of these bands of chaos on the west shore of the large bud. When rendered using the normal equal-iteration method, today's image is pretty boring, but the 'tdis' option (I should use this option more often) really brings it to life, giving the whole thing a kind of art-nouveau appearance, reminiscent of the turn of the 20th century. And curiously enough, the scene maintains its attractiveness when zoomed both into and out of. This trend could continue forever, which is why I named the image "Forever Fractal". When rating time arrived, I decided on a 7. It's an above- average scene, at least by my standards. And the render time of just over 5 minutes on my tired old machine is bearably short, at least for a Sunday, when many have nothing to do but watch the TV. Those who would rather not miss 5 minutes of that game may down- load the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The promised philosophy is already written, and will appear in tomorrow's philofractal version of the FOTD. Friday and Saturday were chilly here at Fractal Central, with temperatures both days just above freezing. But there was just enough sun to make outdoor life bearable for the fractal duo, who spent just enough time outdoors to prevent cat boredom. However, today started with heavy snow, which is just now changing to rain. I fear the worst moods might be in store for Thomas and Tippy. For me, the worst has been avoided. By working all day Saturday, I avoided the work back-up that was threatening. But there is still a bit of work to be cleared away before Monday, so until next time, take care, and be skeptical of things that are not true, while being wise enough to know the difference and tolerant enough to know that you could be mistaken. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Forever_Fractals { ; time=0:05:11.35--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.17434825437380250/-0.158570929431714\ 50/1.873532e+009/1/-52.5/0.000439570302683295333 params=-1.3/0.92/1.3/-1.08/0/0 float=y maxiter=1200 inside=0 outside=tdis periodicity=10 colors=000zzUzOOzLQzJQzHTzETyCUyAUy9Uw5Ww4Wu2Yu0Ys\ 0Zs0Zs0Zq0`q0`o0bo0bm0dm0dm0dl0`l0Zj0Yj0Wj0Uh0Th0O\ h0Mf0Lf0Jd0Hd0Gd0Cb0Ab09b07`05`04f00`02W07T0CM0HJ0\ ME0TA0Y50`20f00l00q00w00z02z04z05z07z09z0Az0Cz0Ey0\ Gu0Hs4Jq7LoAMmCOlz`jzhfzcdOWbTY`WZZZ`Y``WpWAqXErYH\ sZJt_Mu`OvaTwbWxcYyd`zebzffzgjzhlziozjqzkuzlyzmzzo\ zzozzqzzrzzqzzqzzqzwqzsqzmozhozdozZozTszWozYlzZjz`\ fzbdwd`sfZohWllUhmQdoO`qMYsOTuQOwSLyUHzWEzYAz_7za4\ zc0ze0zg0zi0zk0zm0m00Z00L00700000000000200500702A0\ 7C0AG0GH0JL4OM5VQ9_TMcWPfYRj_SoaUscWudZwcaxady_gzY\ jzWmzUpzSrzQtzOuzMtzKszIqzGozEmzCkz0iz0gz0ez0cz0az\ 0_z0Yz0Wz0Uq0Sj0Q`0OT0MJ0KC0IA0GA0G90G90H70H70H50H\ 50J40J40J20J20L20L00L00L00M00M00M00M00O00O00Q00S00\ U00W00Y00_20a40c50e70g92iC4jE5lG7nH9pJArLCtMEvOGxb\ HzqJzzLzzj0zlQ4jT9jTCjTGjUJjUMjUTjWWjWZjWbjWfhYhfY\ hfZhdZhdZhb`h``h`bhZbjZbj } 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 } END 20.0 PAR-FORMULA FILE==================================

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No FOTD for Dec. 13
by Jim Muth 13 Dec '03

13 Dec '03

Fractal fans: Due to an unexpected heavy work load, there will be no FOTD for December 13. The FOTD for December 14 will appear on schedule. Jim M.

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FOTD 12-12-03 (Spoor of the Beast [7])
by Jim Muth 12 Dec '03

12 Dec '03

FOTD -- December 12, 2003 (Rating 7) Fractal visionaries and enthusiasts: When I started the FOTD on the Fractal-Art list in April of 1997, I intended to post a few fractals and discuss whether fractals really are art. I had no idea the FOTD would become such a major part of my life. But that's the way things go sometimes. Here we are, 6-1/2 years later, still as enthusias- tic about the FOTD as we were the first day. Today's image was created with the MandelbrotMix3a formula. It is a scene in an evaporated fractal that results when various portions of Z^(-1.3), Z^(-2.5), Z^(-4.6), and Z^(-6.4) are combined, then (1/C) is added. (Fractals with negative expo- nents 'evaporate' when the escape radius is raised to 10^100.) The M-Mix3a formula does not automatically calculate a critical point. This task must be done by hand, which is not easy, and makes the formula quite burdensome to use. But when a critical point is finally found, the results can be worth the effort. Whether today's image was worth the effort is up to the individ- ual viewer to decide. My decision was that the image earns a rating of a 7. Finding a name for the image was kind of fun. While studying the scene, I fancied myself looking down on a jungle from above. There below me was the scene of a kill, and leading to the scene were the tracks of various scavengers. I named the image "Spoor of the Beast", though no beast appears in the picture. The render time of under 4 minutes is fast enough, but a minute or two can still be saved by downloading the completed image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> I must now take a moment to apologize to those who are disappoin- ted that the promised philosophical pontificating did not appear today. I have been too busy to ponder. But the philosophy will appear as promised in a day or two. After all, anything worth having is worth waiting for. Thursday was pleasant enough temperature-wise here at Fractal Central, with a high of 50F 10C and much sun, but the wind gusted to 50mph 80kph all afternoon, and the noise it made in the trees and bushes spooked the fractal cats, who dared not venture beyond the porch steps. In the evening, we comforted them with the customary treat of tuna. and they settled to sleep satisfied. Today is starting rather agreeable. We'll see how the rest of the day goes. And I've got that load of work to finish before it starts to pile up. I have already rambled on longer than I had intended. Until the next FOTD in 24 hours, take care, and beware of the wild fractal beasts that are lurking in the vicinity. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Spoor_of_the_Beast { ; time=0:03:49.21--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix3a function=recip passes=1 center-mag=-9.081882577005382/-6.444497511562424/1\ 94430.2/1/-32.4999999962004082/1.5461261916594e-008 params=1/-1.3/0.8/-2.5/-0.5/-4.6/-0.3/-6.4/1.07557\ 97065275/1e+100 float=y maxiter=1200 inside=bof61 periodicity=10 colors=000P3sM8nJDiGHdDM_AQV7VQ5ZL_\ rr`traurbqpbnncjlcgjcdhd`fdYddVbeR`eOZeLYdMWcMVbNU\ aNS`OR_OQZPOZPNYPMA0KAAJAFIAKGANFAPEOTDIVJDYP8aVUg\ acmgzzzzztzzphlmfgidbfbXc`S_ZNXYIUWKTUMRSPPQRNUULM\ WKKYII_HGbFEdDCfCAhA8j9BbHEVPHOXKGdN8lP1tQ7rRCqSHp\ TNoUSnVXmValY`h_`da_`c_Xe_UfaWfcXfeZff_ghagjbgkdgm\ ehofhphhrihtkiuliwniyoizpRghOciL_jIWkFSlCOm9Kn6Go3\ Dp6Gq8JqBMqDPrFSrIUrKXrM_sPbsResTgsVhqWioXjmZkk_lj\ `mhbnfcoddpcfqagr_hsYisXgqYepZdo_bm`ala_kbZicXhdWg\ eZba`ZYbUUdQRfPShPSjOSlOTnNTpNTrMUtMUvLUwLUoQ`gVf_\ _mSdsRboRakR_hQZdQYaQWYPVUPTRPSNPRKMURJXYG_dEbkHdg\ KedNf`QgYTiVWjRZkOalLdiPfgSheWkbZm`boZerWitUlvSorQ\ poOqlMriLseJsbHt_GuXEvTCvQBwN9xK7yH6yI8wI9uJAtJBrK\ CqKDoKFmLGlLHjMIiMJgMKfLJgLIgKHgKHhKGhJFhJFiIEiIDi\ IDjHCjHBjHBjLFgPJdTNaXR_`VXdZUhbRkfPjhQijRikShmTgn\ UgpVfqWfsXetYdvZdw_cy`cz`XsbQlcKedDZe7Sf } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 11-12-03 (School Days Fractal [6])
by Jim Muth 11 Dec '03

11 Dec '03

FOTD -- December 11, 2003 (Rating 6) Fractal visionaries and enthusiasts: Today's fractal is named "School Days Fractal". I have not the slightest idea why I gave it this name, but for some strange reason, the name seems right, and therefore the image will remain so named for all eternity. The parent fractal is an irregular thing with X-axis symmetry, created when 5 parts of Z^(-1.3) are subtracted from one part of Z^(-8.6). At first glance, this parent appears to have few promising areas to investigate when the goal is to find hidden midgets. True, there are a few obvious small M-sets lying about, which give some hope, but these are little more than reflections of the M-set itself. However, notice the northernmost part of the parent fractal, where a bit of something interesting lies. Surely, no midgets will be found in this series of fragments and Julia-like spirals. That's what I thought when I first checked the area. But I was wrong. For some reason, I got the feeling that often comes over me when I am near a midget in an unlikely location. My persistence paid off, and at the end of my quest, I came upon today's scene, which BTW rates another 6. The scene is almost as interesting when an outzoom or two are done, and I did have a bit of difficulty deciding where to stop. I think I've found the best magnitude, but others might disagree. It's worth a check. As always, the render time, which today is 17 minutes, may be avoided by downloading the pre-rendered GIF image from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> In yesterday's FOTD I said that I would wax philosophical today on the philofractal list if I had the time. I did not have the time. I'll try again tomorrow. The rain moved in early Wednesday afternoon here at Fractal Central, cutting short the cats' time outside. The chilly temperature of 46F 8C only made things worse. As a result, the duo sulked admirably, and needed an extra dish of tuna to restore their spirits. This morning the rain has ended, but the wind has arisen. We'll see how the duo adjusts. I'll adjust very well as soon as the work is behind me. Until next time and next FOTD, take care, and see you in 24 hours. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ SchoolDays_Fractal { ; time=0:17:49.62--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+0.67507676878145810/+1.767666155180351\ 00/2.397265e+008/1/29.9999671749570034/1.754618232\ 14984e-005 params=-5/-1.3/1/-8.6/0/525/0/0 float=y maxiter=1800 inside=0 logmap=315 periodicity=10 colors=000anx_ozVozPnzLnzNozNqzNszNuzPvzPxzPxzPzzP\ zzRzzRzzRzzRzzRzzTzzTzzTzzTzzTzzNzjHzGCz0Az0Az0Az0\ Az08z08z08z08z08z06z06z16z16z36z63z83z83zA3zC3zC6z\ E6zE8zE8zEAzEAvECsECnEEhGEeGG_GGXGHRGHNGJHGJEGPGLV\ HP_JVeJY0Pz6TxCVsJXnP_hXacacYhgTnhNsjJocGnYEjRAhL8\ eE6c81_00Y00V00T00L0HE0eC3gC8hCCjCGlCJnCNnCRoCVqAY\ sAauAevAhvAlxAozAszAvz8zz8zz8zz8zz8zz8zz8zz8zz3zz0\ zz0oz0ez0Vz0Hz06z00z00z03z18z8EvGHqLLlTRhmccrdYzhV\ wnPvwJzxGzzAzz3zz0zu0zs0zq0zp0zo0zn0zm0zl0zk0zj1zi\ 3zh6zg8zfAzeCzdExcGvbHsaJo`Ll_NjaPgeRchTalVYoXVzYT\ x_PzaLzcJzcJzaLz_LzXNzVNzTPzRPzNPxLRvJRuHTuETsCVqA\ Vo8Vo3Xn1Xl0Yj0Yj0_h0_g0_g0Xc0V_0TY3RVAPRGNPJLLPJH\ VHGYGCcE8hC6lA1q80v60z30z10z00z00z00z00z00z00z00z0\ 0v03s08n0Ch0Gc0JY0NT0RP0VJ0YE0a80e10h00l0Co1NsCYvJ\ azNczRgzThzXlzYnzaqzcszgvzhxzlzznzzqzzsvzunzuezuXz\ uPzuGzuzzNzzVxz_zzgzzlzzs } 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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 10-12-03 (Your Highness [7])
by Jim Muth 10 Dec '03

10 Dec '03

FOTD -- December 10, 2003 (Rating 7) Fractal visionaries and enthusiasts: Today's venture into Fractal Land takes us to the fractal created when one-half part of Z^(-7.5) is added to 5 parts of Z^(-1.5) before (1/C) is added. The resulting fractal consists of two separate parts -- a main part with several large bays and a smaller area of non-critical stuff located some distance to the southwest of the main part. I have examined this cut-off area for over an hour without finding signs that midgets might lie there. It does have some striking tree-like elements however, which I might use in some future FOTD. Today's scene is located rather deep in the southern branch of the valley that cuts off the prominent bud at the eastern end of the string of bays comprising the main part of the parent fractal. The image is named "Your Highness", which is a term used when addressing a person of very high rank, such as a king. The name was inspired by the royal blue color of the midget at the center. This color extends to the arms radiating from the midget, giving them an unusually sharp, royal definition. Before deciding on the standard 'equal-iteration-band' version of today's scene, I tried the other outside options, and also the various 'evaporated' inside options. The other outside options create an image that is too busy. The inside options applied to the 'evaporated' version are either too busy or too simple, the lone exception being the bof61 option, which creates an exaggerated, rather hectic variation of the standard version. If I had been in a different mood, I might have chosen this variation. I rated today's picture an above-average 7, a rating that might be a bit more than it deserves. But I do like the deep-blue color of the midget and its arms, and I decided to reward myself. The render time of 11 minutes is getting to be a habit. Relief is at hand however on the FOTD web sites, where the GIF image may be found, already rendered. Those sites are at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> I am currently reading the NovDec issue of 'Skeptical Inquirer' magazine, a publication of CSICOP that I have been reading for many years. Ever since I came to realize that its main agenda is to promote the materialistic philosophies, and that it uses science chiefly to add validity to its claims, I no longer take it as seriously as I once did, but I still find it quite entertaining and informative, often containing much to ponder. If I have time, I'll do some public pondering in the philo- fractal version of tomorrow's FOTD, when, depending on one's point of view, I will spread either wisdom or superstition. Tuesday brought partly cloudy skies and a temperature of 43F 6C to Fractal Central. The fractal cats were neutral about the conditions, and did little of note while they were outside. When they came in, they asked for tuna, but when they got none, they settled for their regular food, Today, I fear the next rain area is moving in. Hopefully, the cats' indifferent mood will continue through the rain. As for me, I'm about 1/3 of the way through the day's work. If I'm lucky, I'll finish before the rain arrives. Until next time, take extra care and then a bit more care. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Your_Highness { ; time=0:11:24.43--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+2.12998426754146700/-0.194913908321507\ 00/4.144484e+008/1/59.999963718102002/3.7033972414\ 5712923e-005 params=5/-1.5/0.5/-7.5/0/525 float=y maxiter=1500 inside=0 logmap=238 periodicity=10 colors=000FDAHEAHFAKGAKHANIANJAQKAQLATMBTNCWQCWTCY\ WCYZCabCaeCegCehCiiCijCmkDmlCqmCqoCtqBtsBwuBwwAzyA\ zzAzy9zx9zw9zu8zs8zq8xoNwmQukTsjWqiVohUmgWkfYie_gd\ afecededcgcbibaka`m``o_aqZ`sYcuX`wWexV`zUgzT`zSXzJ\ ZzIUzGXzFUzDVzCUzBSzARrAQw9Ph8Ns8Mc7Li7KX6Ic5HT5GY\ 4FQ3DO3CM2BK2AJ2AJ2AI19H19H18G18F18F17E17D17D16C16\ B15A15A159100048048047036036025024024013012F12P01U\ 00UK9UK8UK8UK8UK8UK7UK7UK7UK7UK6TJ6SI6RH6PG5OF5NE5\ ME5LD4KC4JC4IB4HA3GA3F93E83C82B72A6296285174164153\ 1420m20m10m00hUzhUzhUzhUzhUzhUzhUzhUzLBgKAeJAcJ9aI\ 9_H8ZG8XF7VE7TD7RC6PB6NA5M95K94I84G73E63C52B429317\ 215103001PcnOamOalN`kN_kNWjM_iMZhMZhLYgLYfLXeKXeKW\ dJVcJTbJTbIRaIR`IQ_HQ_HOZHOYGNYGMXFLWFLVFKVEKUEJTE\ JSDISDIRDHQCHPCGPBKOBPNBUMAZMAcLKhKUmJcrJmwIuzHzzH\ zzGzzFzzEzzEzzDzzCzzBzzBzzAzzWzzUzzTzzSzzRzzPzzOzz\ NzzMzzKzzJzzIzzHzzMzzRzzW } 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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 09-12-03 (Minus-Minus Midget [6])
by Jim Muth 09 Dec '03

09 Dec '03

FOTD -- December 09, 2003 (Rating 6) Fractal visionaries and enthusiasts: The following paragraph is about a spam e-mail scam. Those who would rather not read about spam e-mail should skip to the third paragraph. ;-) Among the 150 or so pieces of junk mail that I found in my e-mail box this morning was an 'official' notice, claiming to be from my Earthlink ISP, informing me that they needed to confirm my billing information. The link led me to a web site where I was to enter my credit-card number, etc. (No personal informa- tion is in the fractal-dedicated machine that I used.) My opinion (actually I'm almost certain) is that the letter is a scam, intended to fraudulently acquire credit-card numbers, and even if it is serious, which I doubt, then Earthlink is so inept that I would rather not be connected with them. Who wants an ISP that can't even keep track of the billing information of its own customers. ;-) I guess I should not be too hard on them, after all, I sometimes lose track of my own fractals. But today's image is one I most definitely have not lost track of -- not yet, at least. It is a scene in the fractal that appears when 24 parts of Z^(-1.1) are combined with 26.4 parts of Z^(-11) and (1/C) is added. The 8 loop-like elements surrounding the midget are typical of fractals that have been created by combining negative powers of Z and adding 1/C. I have never seen these loops in fractals that contain a positive power of Z, though most likely, if I tried hard enough, I could find some. In the parent fractal of today's image, the filaments extending from the buds terminate in rings, kind of like the finger-ring on the end of a window-shade string. This ring-like nature is reflected in the midgets lying in the area, as today's midget, where the rings are stretched into eggs, demonstrates. I named today's image "Minus-Minus Midget" because of the two negative exponents of Z that were involved in its creation. My first impression was to rate it at a 7, but then I thought I saw a trace of muddiness, and reduced the rating to a 6, which is still a bit above average, though a boringly common rating. The render time of 11 minutes borders on slow, especially for those with other tasks for their machines. But the 11-minute wait can be cut to a minute or so by downloading the completed image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> A sunny but chilly late autumn day passed uneventfully here at Fractal Central on Monday. The cats thought that the tempera- ture of 37F 3C was a bit chilly and the snow was still a bit too deep, but they did venture onto the path in the yard, which had been cleared but was still wet. After an hour or so, they came indoors to pass the rest of the day sleeping. Today appears to be a slightly-warmer repeat. The work is about average; the cats' mood is average; all else is about average. Most likely, except for the fractal I will find when the work is finished, the day will be forgettable. And never forget that the next FOTD will appear in 24 hours. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Minus-Minus_Midget { ; time=0:11:36.73--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-4.19038823132904300/+9.692158006020868\ 00/6.749878e+007/1/62.5/0.000196657495929342119 params=24/-1.1/26.4/-11/0/525 float=y maxiter=1700 inside=0 logmap=243 periodicity=10 colors=000930600930B40C80E90HC0JE0KG0MJ0PK0QN0SP0T\ Q0`Y0hc8pkGxqPzyXzzczzkzzqs8xm0zp3ssHhvh_ylPzuEzz4\ yz8uz9pzBkzCfzEczG`yC_sBYm8Xf6T_4ST1QN0PH0M90K30J0\ 0H00G00K00N00Q01T04X09`0Ec1Jf4Mi6Qm9VpBYsJYvQYyXYz\ cYziYzzYzzY0QT0PT0PT8PTGN`NN`VNebNciMbqMbyM`zM`nQY\ XVVE_S0cQ0`V0YY0Vb0Se0Pi0Nm8XcJeVTnNexEpz4zz0zz0zz\ 0zz1zz3zz4zz4Kz6Ez88z91zB0zC0zC0zH0zM0zP0zT0xY0u`0\ qe0mi0im0fq0cv1_y1Xz3Tz3QzBVyJYmPb`XePbiCim0pp0nm0\ nk0ni1nh4me8mcCmbGm`JnYKnVKnTKnQKnNKnMKnJKnHKnEMnB\ Mn9Mn6Mn3Mn1Mn0Mn0Mk0Qi3Vf4_e8cb9h`CmYGqXHvTKzSMzP\ PzNTzQYzTbyXfsYkm`pecu_eyThzNkzGmz9pz3sz0uz0pz0mz3\ hz9ezG`zMYcQTYXQSbMNhJHnEBuB6y89u6Bp4Ek3Mf1Nb0PY0Q\ T0SP0TK0VG0XB0Y60_10`00b03c3KeB`fKqhSzi_zk_zm_vn_s\ p_nq_ms_puXuvTyxSzzPzzNzzKzzHzzGzzCzzBzz8zz4zz3zz0\ zz0zz6zzEzzMzzKzzJzzHzzGzzEzzCzzBzzBzz9zz8zz6zz4zz\ 3zz1zzBzz9zz6zz4zz1zz0zz0 } 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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 08-12-03 (The Second Scorpion [5])
by Jim Muth 08 Dec '03

08 Dec '03

FOTD -- December 08, 2003 (Rating 5) Fractal visionaries and enthusiasts: It's a busy Monday here at Fractal Central, so the discussion will be correspondingly short. In yesterday's discussion, I mentioned an element in the image that reminds me of a scorpion and inspired the name. Today's image is a close-up of that scorpion, which fills the center of the screen and faces the upper-right corner of the frame. (Perhaps I should have called it a lobster.) The curled-up tail of the scorpion is clearly visible, though a bit of imagination is needed to see the claws. The background has a theme of square rather than smoothly curving spirals, one of the more unusual types of spiral. Since I spent almost no time finding the image, and only a few minutes writing this discussion, I can rate the image no higher than an average 5. The 11-minute render time can be cut significantly by download- ing the completed GIF file from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> A cold, windy Sunday here at Fractal Central produced moody cats who sulked around the house most of the afternoon. Two treats of tuna were needed to restore their spirits. I'm beginning to wonder how much tuna is too much. If we need to continue giving them so many tuna treats, the duo might grow bored with tuna and demand something like lobster. Well, I've got that work to finish, so I'd best start moving. Until next FOTD, take care, and keep those iterations coming. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ TheSecondScorpion { ; time=0:10:58.28--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-0.38011718899537150/-2.001815087683078\ 00/1599.36/1/-52.5000000000051159/8.14260464609972\ 701e-012 params=1.096/0/96/1000 float=y maxiter=10000 inside=255 logmap=176 periodicity=10 colors=000dKUeKUfKUgKUhKUhKUhKUhKUhKUhKUhKUhKUhKUh\ KUhKUhKUhLUhMUhNVhOWhPXhQYhRZhS_hT`hUaiVbjWckXdlYe\ mZfoYfoWfoUfoTfoRfoPeoOeoMeoKeoJdoHdoFdoEdoCcoAco9\ co7co6cn7bn7am7am7`m7`l7_l7Zl7Zk7Yk7Yj7Xj7Wj7Wi7Vi\ 7Vi8Uh8Uh8Tg8Sg8Sg8Rf8Rf8Qf8Pe8Pe8Oe8Od8Nd8Mc8Mc9L\ c9Lb9Kb9Kb9Ja9Ia9I`9H`9H`9G_9F_9F_9EZ9EZ9DaA8_9BZ9\ DX8FW8HV8JT7MS7OR7QP6SO6UN6WL5ZK5aI4cH4fG4hE3zD3zC\ 3zA2z92z71z82z93zA4zB5zC6zD7zE8zF9zG9zHAzIBzJCzKDz\ LEzMFzNGzOHzPHzQIzRJzSKzSLzTMzUNzVOzWPzXPzYQzZRz_S\ z`TzaUzbVzcWzdXzeXzfYzgZzh_zi`zjazkbzlczrezodzlczj\ czgbzdazbaz_`zX_zVazSczQezNgzKizIkzFmzCozAqz7sz3uz\ 5wz6zz7zz8zzAzzBzzCzzDzzFzzGzzHzzIzzJzzLzzMzzNzzOz\ zQzzRzzSzzTzzVzzWzzXzzYzz`zz_zzZzzYzzXzzWzzVzzVzzU\ zzTzzSzzRzzQzzPzzPzzOzzNzzMzzLyzKyzKyzIxzGxzExzCxz\ Awz8wz6wz4xz5wz6wz7wz8wz9wzAwzBwzCwzDvzEvzFvzGvzHv\ zIvzJvzKvzLuzMuzNuzNuzOuz } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 06-12-03 (Fractal farworks [5])
by Jim Muth 06 Dec '03

06 Dec '03

FOTD -- December 06, 2003 (Rating 5) Fractal visionaries and enthusiasts: Today's image is a kind of freak. To begin, it is an 'evaporated' scene in a fractal created by a formula that I invented at random, using nothing but alternating 1's and 4's. In addition, the 'all-inside' picture has been rendered with the inside=fmod option, with the proximity set to 0.24177, a setting that is rather critical. The resulting image consists of dark zig-zagging arms highlighted by points of fiery brilliance. But strangely, the brilliant points exist only in the upper two-thirds of the image. The lower third is a dull black and blue. Near the center lies the ubiquitous midget, appearing much like an exploding skyrocket. This fireworks effect inspired the name "Fractal Farworks". The mis-spelling is intentional, representing both the infinitude of the universe of fractals and the way the word is pronounced here in the local area. After meditating on the image for several minutes, I could find no reason for rating it higher than the 5 which I assigned it. The render time of the parameter file is a moderate 6 minutes, which can be cut significantly by downloading the completed image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> With snow and sleet falling all day Friday and the temperature hovering around freezing, the fractal cats had as pleasant a day as possible, sitting on their shelves by the windows, watching the birds outside scrounging for food. Their day ended with a treat of tuna. Snow is still falling this morning, with around 1 foot 30cm on the ground. I guess the cats will have a repeat day. As for me, I'm simply going to relax and watch the snow. In between snowflakes I might find a fractal. And if I do, which is a near certainty, the fractal will appear as tomorrow's FOTD. Until then, take care, and then take more care. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Farworks { ; time=0:06:10:15--SF5 0n a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=mandelbrotmix4 function=recip passes=1 center-mag=+2.03354144153070000/-0.028206890074231\ 47/30377.39/1/-89/1.78200502964909191e-010 params=14/-1.414/1/-14.14/-1.4/1e+100 float=y maxiter=1800 bailout=9 inside=fmod proximity=0.24177 logmap=yes periodicity=10 colors=0000UzzS`zMgzFoz9vzGozMizSbzYXzcQziKzjLzjMz\ kNzkOzlPzlPzmQzmRzmSznTznTzoUzoVzpWzpXzpXznWzmVzlU\ zkTzjSziRzgQzfPzeOzdNzcMzbLzaLzcNzdOzeQzfRzhSziUzj\ VzkXzmYznZzo`zpazqbzr_zrYzrWzsTzsRzsPztMztKztIzuFz\ uDzuBzu9zvZzvwzwrzwnzxizxezyazyXzzTzzOzzKzzGzzJzzM\ zzPzzSzzVzzYzz`zzczzfzzizzlzzozzrzznzzkzzhzzezzbzz\ _zzWzzTzzQzzNzzKzzHzzHzzHzzHzzHzz`zzbzzczzezzgzzhz\ zizzjzzkzzlzzmzznzzozzozzpzzqzzrzzszztzzuzzuzznzzh\ zzazzWzzSzzPzzMzzJzzFzzCzz9zz6zz3zz2zz2zz2zz1zz1zz\ 1zz1zz2zz3zz4zz4zz5zz6zz7zz7zz8zz9zzAzwAyrFxnKwjPu\ fUsaZqYcoUhmQmkMriOpgPneQlcRkaSi_TgYUeWVdUWbPX`KYZ\ GZYE_WC`UBaTCU`DMgDFnBEj00K9Cc8B_7AX69T58Q89PB9OD9\ NGAMJALLAKOAJRBITBHWBGZCF`CEcCDeCCdGDcKEcOFbSGaVHa\ ZI`bJ_fK_iLaeJcbHe_FgXEiUCkQAmN8oK7qH5sE3tB2uEAuHI\ vKQvNXwQdwTlwWstVqqUonUmkTkhSieSgbRe`Rd_Qf_PgZOiZN\ jYMlYLmXKnXJpWIqWHsVGtaZT } 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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 05-12-03 (Austral Astrals [7])
by Jim Muth 05 Dec '03

05 Dec '03

FOTD -- December 05, 2003 (Rating 7) Fractal visionaries and enthusiasts: To create today's image I added a tiny bit of Z^i to the Mandel- brot set and examined the East Valley area of the resulting fractal, which on the large scale is indistinguishable from the M-set itself. But though that tiny imaginary part makes no difference on the large scale, it does make changes on the smaller scale, especially in the area near the real axis. Today's image is one of a midget in the East Valley area of the M-set. The midget has been shifted and changed somewhat by the addition of the tiny imaginary part to the formula. But by far the greatest part of the effect of the image is a result of rendering the outside with the 'fmod' option. The blue background appears to be blended unusually smoothly for a 256-color GIF image, but a close examination will still reveal traces of color bands. Because of the extra effort I put into smoothing the background, I have decided to again reward myself with a rating of 7. After a few moments study, I named the image "Austral Astrals", which might be roughly translated as 'southern stars'. I had no good reason for choosing such a name. The words simply sounded good to me. Those who plan to run the included parameter file will find them- selves facing an 11-minute wait to see the image. Those who decide to download the completed image will see it faster. The GIF file of the image may be downloaded from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Thursday was cloudy and chilly here at Fractal Central. The cats managed about 30 minutes in the yard before the temperature of 36F 2C chilled their ears and brought them indoors to their window shelves. The traditional evening treat of tuna eased their chagrin. But this morning we have around 6 inches, 15cm of snow on the ground, and it is still snowing heavily in big fat 'quarter-pounder' flakes. The local weather experts are forecasting up to 16 inches 40cm by the time it ends later Saturday. The cats will not be happy about this. I'll be happy however, for despite my advancing age, I still enjoy watching the snow fall. And for some reason, fractals appear to look better in snowy weather. Until next time, take care, and I guess I'll be shoveling off. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Austral_Astrals { ; time=0:11:41.73--SF5 on a p200 reset=2002 type=manzpower passes=1 center-mag=+0.26761112108950750/-0.003830805561863\ 68/1.094852e+010/1/-5/0.00133 params=0/0/2/4.4e-006 float=y maxiter=2500 bailout=9 inside=0 proximity=0.04 outside=fmod periodicity=10 colors=000AVzAUzAUzAUyAUxAUwATwATuASuASsARrARpAQoA\ QmAPlAPkAOjAOi9Nh9Ng8Mf8Le8Kd7Jc7Ib7Ha6G`6F_5EZ5DY\ 5CX4BW4AV29U4AT5BS6BR7CQ8CP9DOAENBEMCFLDFKEGKFHKGH\ KHILIIMJJNKKOLKPMLQNLQOMQPNQQNQROQSOQTPQUQQVQQWRQW\ SPXRQXRQXRQXQQXQQXQQXPQXPQXPQXOQYOQYOQYNQYNRYNRYMR\ YMRYMRYLRYLRZLRZKRZKRZKRZJRZJRZJSZISZISZIS_HS_HS_H\ S_GS_GS_GS_FS_FS_FS`DT_FS_GS_HR_IR_KQ_LQ_MP_NP_PO_\ QO_RN_SNZUMZVMZWLZXLZZKZ_KZ`JZaJZcIZdIZeH_fH`gHehJ\ khKoiLuiMzkMyiNxhNtgOvfOueOtdPscPrbQqaQp`QpZRoYRoX\ SnWSnVSmUTmTTlSTlRUkQUkOVjNVjMViLWiKWhJXhIXgHXgGYf\ FYfEYbJV_NTWSRTWOQ_MMdKJhHFmFCqD9uBHoHOjNVeTa`ZeZ`\ hWciPbfQadRabSa`TaZU`XU`VV`TW`QX_OY_MY_KZ_I_ZG`ZEa\ ZAdXCaZE__FY`HWaIUcKRdMPeNNfPLhQJiSHjUEkVCmXAnY8o_\ 6p`4qY4nW4lU4iR4gP4dN4bL4_I4YG4VE4TA2RC4RD5RF6RG8R\ H9RJARKCRLDRNEROGRPHRRIRSKRTLRVMRWORXPRZQR_SRaTRbU\ RcWReXRfYRg_REYdEYdEYcFYc } END PARAMETER FILE=========================================

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FOTD 04-12-03 (Silver Journey [7])
by Jim Muth 04 Dec '03

04 Dec '03

FOTD -- December 04, 2003 (Rating 7) Fractal visionaries and enthusiasts: Today's discussion will be short, as I must get things wrapped up before the fifth storm of the century to appear this century arrives. At least that's the way the local media is presenting the coming period of unpleasant winter weather. Today's silvery image lies in the fractal that results when 0.39 parts of Z^5 are subtracted from 1.3 parts of Z^3. The 'tdis' outside coloring option created most of the sinuous silvery effect. The name "Silver Journey" was the first thing that came into my mind while I was contemplating the image. I will not concern myself with the question of where the name was located before I thought of it. When rating the image I was undecided between a 6 or a 7, and to do myself a favor, finally decided on a 7. The waiting time of 5 minutes to run the parameter file can be eliminated by down- loading the completed image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Wednesday here at Fractal Central was mostly sunny but quite cold and blustery, with a temperature that barely reached freezing, and a wind that let no one forget the arrival of winter. The once-dynamic cats tested the outdoors only a few minutes before deciding that such conditions are best appreciated from their window shelves inside the house. In the evening we gave them a treat of tuna to ease their frustrations. Today is starting cloudy and just as cold, though the wind is gone. Snow and sleet are due later today. We'll see how the dynamic cats adjust. I'm going to adjust by finishing the small amount of work now on the shelf and getting any chores done before the predicted bad weather appears. If I finish early enough, I'll check the latest issue of "Skeptical Inquirer", which has sat unread on my shelf for several weeks. When tomorrow arrives, the next FOTD will appear regardless of the weather. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Silver_Journey { ; time=0:05:20.98--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=mandelbrotmix4 function=ident passes=1 center-mag=+0.36324468569947000/+0.001674684322820\ 00/2.470857e+008/1/115.00000007684983/1.2494980819\ 9409373e-006 params=1.3/3/-0.39/5/0/0 float=y maxiter=700 inside=0 outside=tdis periodicity=10 colors=000N3SL6VJ8XIAZGC`FEbDGdBJgALi8Nk7Pm5Ro4Tq7\ DW92AF6ILDPRLWXScb_jhfqmmxdbwWSwNHvE6v52v42m32e22X\ 14P06H5BL9GODKSHPVMUYSYaXbeagifknkprptvlothjscer_`\ qYXqXTqWPqVLrVHrUErUArU6sU2sU2sU2sW2tX7tYDuZJu_OuX\ ViV`YSgMQmAPpGOqMNsRMuXLwaKxgKzlLzkMOiNMgOKePIdQGb\ RE`RD_RJYROXRUVRZURcTRiRRnQRsPJiLC_I5RFBPJGONMNRRL\ VXKZaJbfIeeLgdOhcRibUjaXka_l`bn_eoZhpYkqXnrXpsVmqU\ jpTgnSemRblP_jOYiNVhbg8`h9YiBWjCUkDRlFPmGNnHKoJIpK\ GqLJoNLmONkQPiRSgTUeUWcWYbX_XU`SSaMQbHOcBMd6KbAJaE\ J`HJZLJYPJXSJVWJU_JTbJUaKU`LU`LU_MU_MVZNVYOVYOVXPV\ XPWWQWVRWVRWUSWUSXWYXYcX_hXanXcsZ`t_Yt`VtaStbPtcMt\ eJufGugDuhAui7uj5ukGokQjk`dkj_ktVjtTjtRitQitOitNht\ LhtKgtIgtHgtFftEftCetBet9et8cpAblCaiE`eF_bHZZJYWKX\ SMWOOVLQUHRTETSAVR7WQEYPKZPQ_OW`NaaNgbOceO`hOYkOVn\ OSqOPtPTrQWqRZpSboTenUhmVllWokXrjXuiSuhOufKXdGUbCS\ `8Q_ANZCKYEHXGEWIBVK8UM5T } 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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 03-12-03 (Basic Superstrings [6])
by Jim Muth 03 Dec '03

03 Dec '03

FOTD -- December 03, 2003 (Rating 6) Fractal visionaries and enthusiasts: One of the latest fads in physics is the theory of superstrings, or more recently, super multi-dimensional membranes, which twist and turn in an 11-dimensional spacetime, and somehow manifest in our everyday 4-dimensional spacetime as the various sub-atomic particles. This is supposed, or hoped, to be the beginning of the big breakthrough (yet another breakthrough) that will eventually lead to the holy grail -- a theory of everything that makes mathematical sense. Whether such a theory would make common sense is another story. It should be apparent that I hold little hope of this theory being the big one that would explain even physical, much less conscious, existence. I have seen too many breakthroughs come and go during the 40 or so odd years I have been following the latest trends in science. But breakthrough or not, superstrings are real. Today's image has captured a number of them encirc- ling a midget in a different part of the same fractal that held yesterday's image. I named the image "Basic Superstrings" because superstrings and supermembranes are currently looked upon as the most basic sub- atomic entities. The rating of a 6 is becoming boringly common, but it is the fairest rating I could give today's image. The render time of under 2 minutes is about equal to the time required to go on-line and download the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The temperature on Tuesday here at Fractal Central barely reached 40F 4C, while the winds continued unabated. Even the occasional burst of warm sun was not enough to lure the fractal cats outdoors. They spent another day indoors by their windows, watching the world go by. In the evening, I gave them a treat of tuna to ease their frustration. Now I must shift from fractal mode to work mode. But when the work is finished, I'll shift back into fractal mode. The results of that shift will appear as tomorrow's FOTD. Until then, take care, and stay fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Basic_Superstrings { ; time=0:01:50.45--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-1.78010197328101300/-0.143377273422810\ 70/2.749007e+011/1/14.9822749561698103/-0.145702029 params=7.5/-1.75/0.7/-7.5/0/525 float=y maxiter=300 bailout=9 inside=0 logmap=33 periodicity=10 colors=000J0YL3aN7cN9fPDhSFjSJlULqUPsWSuYWxYYz_az_\ czjjzsqzzxzzzzzzzzzzzzzchzFSz0Bz00u01s03q05n07l0Bj\ 0Dh0Ff0Hc0Ja0N_0PY0SW0UU0WS0YD0_00a05U0DN0NF0Y70fB\ 0qL0zW0zf0zm0zm0zm0zm1zm3zm5zm7zm9zmBzmDzmFzmHzmJw\ zLuzNszPqzSozNmzJmzFmzBmz7mzAmzKLzULzcLzmNzmNzmPzm\ PzmPzoLzqHzsDzuLzwUzxazyjzzszzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzqzzhzza\ zzfzzjzznzzjzzfzzazzYzzUzzPzzLzzHzzDzz9zz5zz1zz0zz\ 0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0z\ z0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0\ zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz\ 0zz0zz0zz0zz0zz0zz0zz1zz3zz5zz7zz9zzBzzDzzFzzHzz7z\ z0zz0zz0zz0zz0zz0zz0zz0zz1zz7zzDzzLzzSzzYzzfzzlzzs\ zzzzzazzFzz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz9zz\ JzzWzzfzzszzzzuzzszznzzlzzzzzzzzzzzzzzzzzzzzzzzzuz\ zszznzzjzzfzzazz_zzPzzLzz } 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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 02-12-03 (Harmonic Voltage [8])
by Jim Muth 02 Dec '03

02 Dec '03

FOTD -- December 02, 2003 (Rating 8) Fractal visionaries and enthusiasts: I have never learned to appreciate 'New Age' music. With a few exceptions, the genre seems to be 'over my head' (or maybe beneath me). And this is strange, because I most certainly do appreciate the traditional 'classical' music, which is approach- ing the verge of extinction, at least here in the USA. When hearing New Age music, I am inevitably struck by the way it appears to drone on and on in abject monotony. It sounds good for a minute or two but nothing interesting ever develops. Yet some people I speak to are enthralled by this music. They tell me it is the best thing to come along since music was invented. New Age music concerts are very well attended. Why then do I get nothing from it? Either the music is empty of meaning or it is filled with meaning which I cannot recognize. Most likely the truth, if an absolute truth exists, lies somewhere between these extremes. The experience of appreciating music is a co-operative effort shared by composer and listener. The composer places the seeds of enjoyment in his work, but it is up to the listener to supply the environment in which these might germinate into enjoyment. If a work lacks the seeds, it will quickly be forgotten. If a listener lacks the fertile soil in which a particular type of seeds might grow, the work will have no effect on him. I guess I'm in the latter class as far as 'New Age' music goes. Now what does this venture into music appreciation have to do with fractals? Well, the name of today's striking image from the M-Mix4 formula is "Harmonic Voltage", a title I borrowed from a computer-animation music video I saw recently on local TV. The visual part of the video was IMO spectacular, but the music that accompanied the animation was IMO bland to say the least. Surely, I thought, such spectacular images must inspire or be inspired by better music than this. Curiously enough, the fractal lady enjoyed the music but said 'ho-hum' to the visuals. I guess it's all in the mind of the beholder, much as some phil- osophers claim the entire real world is. Oh by the way, I really like today's image, which I have rated at an exceptional 8. The sinuous flames radiating from the central midget were produced by rendering the formula with the outside set to the 'tdis' option. One final note -- I wonder what today's scene would look like if it were 'evaporated'. To enjoy the image, run the included parameter file or download the image from one of the two FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Monday was partly cloudy and chilly, with a temperature of 50F 10C and the strong winds that the cats dislike. The duo spent most of the afternoon sitting by the window, watching the wind in the trees and the birds soaring by. They ventured outside for only a few minutes. Their moods were unusually bright for a day of confinement however, and no tuna was needed. Today promises to be similar, but even colder. It remains to be seen how the duo will react. My reaction will be satisfaction when the bit of work now on the shelf is finished. Until next FOTD, take care, and enjoy yourself. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Harmonic_Voltage { ; time=0:02:43.23--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.636639299894244/-0.4107349017976644/\ 8.656232e+010/1/-177.5/-0.000331809106303253276 params=7.5/-1.75/0.7/-7.5/0/525 float=y maxiter=1250 inside=0 outside=tdis periodicity=10 colors=000IDOFBNDBMBBMDAKDAJDAJD8ID8ID8HD7HD7FD7FD\ 7EE6DE6DE6BE4BE4AE4AE48E38E37E37F26F24F24F23F03F02\ F02F00F00F00D00F00I20K30M60O70RA2UB2VE2YF3_I3bJ3cM\ 4fN4iQ4kS6nU6qX6sY7v_7ya7zc8ze8zg8ziAzkAzoBzmAzkAz\ iAzgAzfAzc8zb8z_8zZ8zY8zV7zU7zR7zQ7yO7wM6wK6vI6vH6\ uF6uD4sB4r84r74q64q33o23o03n03m00n03n06o07o0Ao0Bq0\ Eq0Fr0Ir0Jr0Ms0Ns0Qs0Ru0Uu0Vv0Yv0Zv0aw0bw0ew0fy0iy\ 0jz0mz0nz0qz0rz0uz0vv2sq7rkDqfHoaMnXRmRVkM_jHeiBjg\ 6nf0se0yc0zb0wc0se0oe4jf7ffBbgEYgIUiMQjOKjSHkVDkZ7\ ma3me0ng0naFcXYVQoMKzDIz8Fz4Dz0Az07z06z04z04z04z03\ z03z03z02y02w02u00s00r00q00o00m00k00j00i00f00e00c0\ 0b00_00Z00Y00X00V00Y06Z0A_0Fa0Kb0Oe0Uf0Zg0bi0gj0mm\ 0qn0vo0zq0zu0zr0zq2zo3zn4ym7vk8ujAsiBqgDofFneHkcIH\ NcHOeHMYHSOcYQaXR_VUZTVXRXVQYUP_TOaRNbOMcMKeKJgJIi\ HHjFFkFDnEEmEEkDEjDEiDFiBFgBFfBFeAHcAHc8Hb8Ha8I_aI\ XZIVXHVVHUSFSQFRZEHZEHJDO } 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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 01-12-03 (Seasonal Wreath [8])
by Jim Muth 01 Dec '03

01 Dec '03

FOTD -- December 01, 2003 (Rating 8) Fractal visionaries and enthusiasts: Like so much of our current view of reality, fractals are non- intuitive. Before the theory of relativity, who could have thought that matter is a different form of energy, that electro- magnetic waves are transmitted by nothing, or that the present moment of time is not universal but unique to the individual observer? Before the quantum theory, who could have guessed that photons and electrons are incomprehensible things that can be seen as either waves or particles; or that, with a proper experimental set-up, it is apparently possible to change the past; or that the closest we can come to reality at the quantum level is the mathematical equations which describe it? Before fractals were discovered, who could have guessed that an expres- sion as simple as Z^2+C could lead to infinity? The world extends far beyond the part of it comprehended by an ant. It extends far beyond the part of it comprehended by the fractal cats. These lower forms of life (the cats would dis- agree here) lack the intelligence to grasp the vastness of exis- tence. But then there is man. Is our intelligence the highest form of intelligence possible? Is it sufficient to grasp the totality of existence? Apparently not. One-hundred years ago, we assumed that our local galaxy com- prised the entire universe. Then the telescope at the Mount Wilson observatory showed that we were hugely underestimating the vastness of the universe. In recent years we have been pon- dering an infinity of parallel universes combined into an infi- nitely more vast multiverse. Next, we might be thinking of an infinity of multiverses. And there are those 11 dimensions (up from 10) required for M-theory to make sense. How can we find a 'theory of everything' when our concept of 'everything' keeps growing? I sometimes feel that, due to the limitations of out intellectual apparatus, we are even today unaware of as much of existence as an ant going mechanically about its programmed chores. And artificial intelligence can be of little help, for we will design our computers to 'think' as much like ourselves as possible. If a computer actually were to start thinking in a truly new and original manner, we would likely fail to comprehend its unfamiliar logic, and assume it was malfunctioning. We would re-program it to 'think' more like ourselves. It is kind of discouraging. We are nearing the limits, and the limits are ourselves. 120 years ago, we thought we had discov- ered almost all there was to know; today it looks like we don't even know what we don't know, and even worse, because of our limited minds, we never will know. Oh, before I forget -- we have a fractal today. It is an 'evap- orated' scene in the fractal created by a whimsical formula of 1's and 4's based on the square root of 2. I named it "Seasonal Wreath" because it reminds me of the wreaths that decorate so many doors and windows at this time of year. I rated the image at an exceptional 8, which might be a bit liberal. But after almost three weeks of Mandelbrot images, it seems like a refreshing change. The render time of two minutes is well within reason, even though a download of the completed image might be a bit faster. That download may be found on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and on Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Sunday turned out to be another near-average day here at Fractal Central, a bland day, slightly chilly, with little to tell about. The partly cloudy skies and temperature of 48F 14C were barely acceptable to the cats, who were outdoors only an hour. Their spirits were lightened, however, by the last of the left- over turkey. This morning is starting mild with promises of a pleasant day. But a cold front with high winds is due around midday. The cats dislike wind and cold, so we'll have to hope for the best for them. Until tomorrow, take care, and take life one fractal at a time. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Seasonal_Wreath { ; time=0:02:17.81--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+2.32911156705464600/-0.065564664774447\ 56/15547.06/1/-67.5/1.6424422933e-010 params=14/-1\ .414/1/-14.14/-1.4/1e+100 float=y maxiter=1800 inside=bof61 periodicity=10 colors=000ZO`SUbL`dFffMd`TbV_aPf_JlZEmcDnhCnmBorAo\ w9r`VuEoqFlnFjkFghFedFbaF`ZFYWFWSFUPFRMFPJFMAAACFH\ 9FF6FD9JFBMGEQIGTJJWLL_MObOQfPTjRcnSmsUrwVzzWrxYhv\ Zbt_bsabrbbrcbqecpfcpgcoicnjcnkcmmclncloeinfgngenh\ cnianj_mkYmlWmnTmoRmpPlqNlrLlsJltHluFlrEfoEalEXiER\ fEMcEH`EBYE6VE1UI3TM4SQ5RT6QX8P`9OcANgBMkDLnEKrFJv\ GIyHJtNKpTLlYMhcNdhO`nPXs72lB3jF3iJ3hN3gQ4eU4dY4ca\ 4be4ah5_l5Zp5Yt5Xw5Wu6Vt6Ur6Uq7To7Tn7Sl8Sk8Rj8Qh9Q\ g9Pe9PdAObAOaAN`ANcEMeIMgLMiPLkSLnWLpZLrbKteKviKxl\ KZ4fa7dc9beB`gDZiFXkHWmKUoMSqOQsQOuSMwULrSKnRJjQIf\ PIkHaeFU_DMVBETCHSCKRCNQCQPCTOCWNCYMD`LDcKDfJDiIDl\ HDoGDqMLnRSkW_h`feenbju`etW`sSWrNSqJNpEIoAEn6Hl8Jj\ 9MhAOgBReCTcDWbEY`F`ZGbXHeWIgUJjSKlRLiPMgNNeLOcJP`\ HQZFRXDSVBTS9UQ7VO5WM3XK2XI3VH3TG4RF4QE5OD5MC6KB6J\ A7H97F88D78C87E87F87G96H96I96JA5KA5LA5MB4NB4OB4PA4\ QA4RA4SA4TA4TmCPs4UlBXeHZ } 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 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 30-11-03 (Mandelbrot-18 [6])
by Jim Muth 30 Nov '03

30 Nov '03

FOTD -- November 30, 2003 (Rating 6) Fractal visionaries and enthusiasts: This morning, as I sit by my fractal computer with an image that is not quite as good as I had hoped, I find myself once again pondering the meaning of it all. And I cannot be satisfied by shuffling the questions aside as meaningless or impossible to answer. Even if things such as the reason for human existence and individual existence as well are ignored, there remain things that might never be understood, such as the nature of the quantum world and of fractals. What is an electron, or a photon? Why are fractals filled with so many spirals? Why is pi equal to 3.14...? Why does 1+1=2? Why must there be truths which can never be proved? And why do we worry ourselves with such things? Due to our human nature we shall never fully succeed in purging ourselves of unanswered questions, but for now let's simply try to enjoy the world the way it is. There are fractals enough for everyone, and today's is but a single example. Today's image is a scene on an arm of the star connected to the period-16 bud on the north shoreline of East Valley. It is basically a refinement of the type of image that appeared as yesterday's FOTD, and is probably of equal worth. But because of the repetition, I could rate it at only a 6. It is another blazingly fast image, which will render in 1/2 minute or less on all but the slowest machines (of which mine is one). I have entered the mathtolerance=/1 into the parameter file so that the image, which is of quite a high magnitude, does not flip the program into arbitrary precision mode. If this were to happen, our 30-second image would suddenly become a two- hour image. The finished GIF image is available on the internet at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The Saturday weather remained mostly sunny but very cold and windy here at Fractal Central. The fractal cats remained indoors after testing the outside conditions for a few minutes. Howling winds and a temperature of 43F 6C are just not to their liking. They comforted themselves with left-over turkey. Today is starting with much less wind, but not as much sun. It remains to be seen how the dynamic duo will adjust. As for me, I have a bit of unavoidable seasonal shopping to do, but when that is finished, I'm going to take it as easy as possible. And I'll return to the forum in 24 hours with the first of the December images, an unusual one with a rating of 8, made with the MandelbrotMix4 formula and named "Seasonal Wreath". Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandelbrot-18 { ; time=0:00:41.25--SF5 on a P200 reset=2002 type=mandel passes=1 mathtolerance=/1 center-mag=+0.28603880275110390/+0.011533269280361\ 50/7.916774e+012/1.000/17.5/0 params=0/0 float=y maxiter=3200 bailout=9 inside=0 logmap=-879 colors=000eBoeCneDmeEleFkeGjeHieIheJgeKfeMdeNceOae\ Q`eR`dSccTfbUibVlaWoaXr`Zu`ax_ez_hzZdzZ_wYWtYSqXQn\ XNkWLhWKeVIbVF`TDYTAVS7SS4PQ1MQ0JS3GS4DS6AT77TAATC\ FTDJVFOVGSVJVXL_XMcXOgXPj_Qp`QucSydSzYVxSYrL`lFcf7\ f`1iV0jQ0gS4dT9aVC_XGXYLT_PQ`SO`XLa`IcdFdgCfl9gp6i\ s4iu0fv0dx0ay0`y0_r0Yl3XfCV_JTTQSO_QGfPAoO4vM0zM4z\ I9zFDzAIz7Oz3Sz0Xz0`z0dz0iz0lz4ozArzIuzOyyVzxazvgz\ uozsuixdJzPIzSIzVIzYIy`GycGyfGxiGxlFxoFvrFvuFvvVil\ jXazJSvIQrGPmGPjFOfFOaDMYDMVCLQCLMAJIAJF9IA9I67G37\ G0Y70x00y00y00y00y01z06z09z0Cz0Fz0Iz0Mz0Pz0Sz0Vz0Y\ z0`z0Xx0Ts0Qo0Oj0Om0Oo1Or7OsCOvIOxOOzSOzYOzcOzguC4\ oI6jO7fT9a_AXcCSiDOoFJuGFyIJyLMyMQxPVxS_xVcvYgv`lv\ covdpzlpzspzypzzpzzrzzszzuzzvzzxzzyzzyzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzxvzpszgoz`lzTgzMdzD`z6Yz0Vz0Tz0Tz1\ Tz6SzASzGSzLQzPQzTQzYQz_Qz_Pz`Pz`PzaPzaPzcPzcPzdPz\ dPzfPzfOzg0z9SzMQzOzzozzo periodicity=10 } END PARAMETER FILE=========================================

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FOTD 29-11-03 (Mandelbrot-17 [7])
by Jim Muth 29 Nov '03

29 Nov '03

FOTD -- November 29, 2003 (Rating 7) Fractal visionaries and enthusiasts: It's 8:30am and all is well here at Fractal Central. My 18-day tour of the Mandelbrot set is coming to a close. Starting December 1st we will move on to other formulas (MandelbrotMix4 perhaps) and other fractals. Was the tour of the M-set a success? Its purpose was to find new things in the well- explored areas of the Set. Did we find anything new? We certainly found some midgets that have never before been seen, but could these midgets actually be considered new? Like so many other things in the land of fractals, and in the world itself, it is up to the individual fractalist to decide. My own opinion is that I fell a little short of my original intent. I found nothing in the M-set that is truly new and has never been seen, but then I have an artistic temperament, and artists are never satisfied with the things they create. So I guess we'll call it a stand-off and look forward to better things to come during December. Today's image takes us to the star of the period-8 bud on the northeast shore of the main bay of the Mandelbrot set. Zooming in toward the center of the star, we suddenly stop and turn onto a side branch. We find a small spiral and stop to search for a midget. Since midgets are everywhere in the Set, our search soon uncovers a rather interesting little fellow -- the one that now appears at the center of today's image. It's not a bad image. In fact, it rates an above-average 7. True, this type of fractal has often been seen before, but I am rather pleased with the coloring, and because of that, decided to rate the image a 7 rather than a 6. Perhaps its best feature is its speed. With a render time on my machine of 11 seconds, it is the fastest FOTD image in many months. But despite the speed, the task of saving and renaming this letter is about equal to the task of downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The rain continued most all day Friday here at Fractal Central, and the temperature topped out at 59F 15C. The fractal cats, disliking wet ears and paws, decided to remain indoors and sulk, hoping the sulk would bring a treat of tuna. They were right. The tuna appeared. My day was reasonably pleasant. There was lots of left-over turkey, and as today's image shows, my luck in fractal-land was reasonably good. Now if we can only have three or four good days in a row . . . Until next FOTD, take care, and become one with your fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandelbrot-17 { ; time=0:00:11.48--SF5 on a P200 reset=2002 type=mandel mathtolerance=/1 center-mag=+0.37256619253914140/+0.090896004196444\ 92/2.650479e+010/1/-169.999987105916603/-7.4772394\ 485271565e-005 params=0/0 float=y maxiter=2400 bailout=9 inside=0 logmap=318 periodicity=10 colors=000ICHJDIKEJLFKMGLNHMOINPJOQKPRLQSMSTNUUNWV\ NYWM_XLaYKcZJe_Ig`HiaGkbFmcEodDqeCsfBugAwjDqlFknId\ pKZrNTtPMvSGxUAwRBvPCuMDtKEtHFsFGrCHqAIq8IFUtRYub`\ vncwzfwrgvjhvcivWjuPkuHluAluBmrBnoComCpjDqhDreEscE\ t`FuYFvWGwTGxRHyOHyMGxOFxPFwQEwREwSDvTDvUCvVCuWBuX\ BuYImSOeNUZI_RDeJ8kC3gD9dEEaFKZFPWGVTH_QIeNIjeWRxi\ 7vkDumItoNrqTqsYptbotgjscfq_anWYlSUjOPgKLeGHcCC`88\ Z44X0BV2IT3PS5WQ6bP7eR8gT9iV9kXAmZBo_Blb9jd8hg7ei5\ cl4an3_p2bn4dl5fj6hi7jg8meAocBqbCs`DuZEwYFeMLOBQND\ SMEULGWKHXJJZJK`IMbHNcGPeFQgESiETjJRcOQXTPQYOJbNCf\ M6XSJOYVFbfHcgIdgJehKfhLhiMjiNljOnjPokQqkSpiTnhVlg\ WjeYhdZfc`dbac`bb_baZc`Xc_WdZVdYUZ_SYaQXcOWeMUgKSi\ IOkGLmEIoCFqACs89t6Bo9DkCFgFHbIJZLLVONQRPMURIXTD_V\ 9bXCeZFh_Ij`Lk`OlaRmbUnbXoc_pdbqderehsfktfnugqvgtw\ awqWzkRzfLz`FzVAzQEzTHzWKzZNzaQzcTzfWziZzlaznazgaz\ `azVazOazIczJdzKTz2Qz1Nz1 } END PARAMETER FILE=========================================

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Re: [Fractint] Rotating an image?
by BillatNY＠aol.com 28 Nov '03

28 Nov '03

John, I don't know what level you're at with Fractint, but I wrote a tutorial for it a while back. You may find it useful. It's on the Links page of my main web site (the first one mentioned bleow). Bill Rossi http://members.aol.com/billatny/ http://www.arts4u.org/rossi/

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FOTD 28-11-03 (Mandelbrot-16 [6])
by Jim Muth 28 Nov '03

28 Nov '03

FOTD -- November 28, 2003 (Rating 6) Fractal visionaries and enthusiasts: After a very pleasant Thanksgiving day, on which I and the fractal lady (who is a great help but wishes to remain anonymous) had the dinner table entirely to ourselves, I ventured into the Mandelbrot set to see what I could find there. My travels took me far out the negative real axis, to a midget around -1.985, where I checked one of the many filaments extending from the little fellow. On the filament, just beyond the point where the broad chaos ends, I found a much smaller midget. The midget reasonably accurately reflects the nature of the broader area in which it lies, but when rendered with the normal equal-iteration-bands method, it lacks a certain something that would give it life. Whatever that missing something is, it was supplied when I tried the 'outside=fmod' option, with the proximity set to a very small 0.00001, and found an image that is different enough to be the FOTD for today. I could rate the resulting image at only a 6 however, because, IMO, the 'fmod' outside option introduces an element of artificiality into the image. Yes, I realize that the equal- iteration-band outside option is also artificial -- all methods of coloring fractals are artificial -- but when I first explored the Mandelbrot set, the flat iteration bands were the only coloring method available, and in my mind, this method repre- sents the 'true' fractal image. The included parameter file renders in 3-1/2 minutes on my machine, and faster on newer units. The wait for the rendering to finish can be replaced by a short pause while the completed image downloads from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The predicted rain failed to arrive here at Fractal Central on Thursday. Instead, the afternoon was partly cloudy with a temperature of 52F 11C, light winds, and scattered happy cats. The cats spent the afternoon in scattered places around the yard, doing nothing in particular other than just being cats. This morning however the rain is most definitely falling. I'll keep the bad news from the dynamic duo as long as possible. I'm not yet sure what kind of day I'll have. It's kind of a holiday made for shopping, but I kind of have some work to do. The only thing (almost) certain is that the next Mandelbrot image will appear in 24 hours. Until then, take care, and who knows what wonders lurk in the land of fractals? (Even the Shadow doesn't!) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandelbrot-16 { ; time=0:03:37.62--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=-1.98544215780481200/+0.000048925446947\ 36/9.506984e+012/1.0005/-167.369632363377747/-0.07\ 22266742894553948 params=0/0 float=y maxiter=1800 bailout=9 inside=0 proximity=1e-005 outside=fmod logmap=yes periodicity=10 colors=020zzXzzXzzXzzYzwbztdzqgzoiznlzknzhpzfszduz\ bxzbzz`zz_zzZzzYzzYzzYzzYzzZzz_zz_zz`zz_zz_zz_zzbz\ zbzxbzwbzudzsdzrdzpdznezlezkezigzghzehzdhzbjz_jzYj\ zXkxVmxTmwRmwMkzPmwTmsXmp_nndnkgngipelpbppYsrXwrTz\ rPzrOzpPzpPznRxnRxnTxmTwmVwmVwkXukXukYuiYuiYsi_sg_\ sgbrgbrfdrfdpfepdepdgndgnainainaip_ep_dr_br_Ys_XsZ\ VuZTuZPuZOwZMwXIxXGxXEzXCzX8zV6zV4zV0zV0zV0zT0zT0z\ T0zT0zR0zT0zT0zV0zV0wV0uX0rX4pZ6lZAkZEg_Ge_Kb_M_aP\ XaTVdVRdYPdbMfdKfgGgiEglAgp8ir4iu0Xu2iwCuxMzzVzzVz\ zVzuVzrVzlVzgVzdVwYVtTVpPXkOXfMX_KXXKXRIYMGYIGYCEY\ 6CY2CX6CTCARGAOM8MQ8KT6GZ6Ea4Ai68p6Ak4Cf4C_4EV4GQ4\ GM4IG2KA2K42M22O22K20M20O22O26P28P2AR2ER2GT2KV2MV2\ OX2RX2TY2VY2Y_4_b4db6ed8gd8keAlb2zeAnga_izKgz6kz4l\ z4nz2pz2sz0uz0wz0xz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0\ zz0zz0zz0zz0zu0zp0uk0nf0e_0YV2RQ2VO6XO8_MCbMEdKIgK\ KiIOlIPnGTpGVsEYuE_xCdzCe } END PARAMETER FILE=========================================

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Rotating an image?
by John Wilson 28 Nov '03

28 Nov '03

Here's one of those distorted midgets that have been discussed recently. I'd like to rotate something like this, to make the midget lie in the east/west direction. I'm sure I've seen a "rotate" command many times, but every time I want to use it, it seems to go into hiding. Am I dreaming, or is this readily achievable? John W. overpass { ; basic Mandy using fmod ; Version 2002 Patchlevel 4 reset=2002 type=mandel center-mag=+0.13493099800000000/+0.67232383950000000/15191.22/0.9996 params=0/0 outside=fmod colors=000InY<9>Hu_Hv_Hw`<2>Hy`GzaIzZ<3>UvLXuI_tE<10>ENNCKOAHP<3>24TEb1<\ 6>CZHBZKBYM<2>AWT9VW9VW<13>9Ub9Ub9Uc<11>ERdFRdFRc<16>NObNNbONb<2>PNbQMaP\ Ma<5>DHgBGh9Fi<3>1Bm<31>X7EY7DZ7C<3>b67<3>Pou<7>SZnSXmTUl<2>UOiVLhVLh<25\ >UgvUhwUiw<2>UlyTmzSly<21>6JK5HI4GG<2>1CA0A81A8<13>KLJ }

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Re: [Fractint] Rotating an image?
by BillatNY＠aol.com 28 Nov '03

28 Nov '03

John, Just open a zoom box. Then hitting <Control> + the key-pad plus <+> or minus<-> key will rotate the zoom box Bill Rossi http://members.aol.com/billatny/ http://www.arts4u.org/rossi/

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FOTD 27-11-03 (Mandelbrot-15 [7])
by Jim Muth 27 Nov '03

27 Nov '03

FOTD -- November 27, 2003 (Rating 7) Fractal visionaries and enthusiasts: Today's image shows a scene on the shore of the southern lobe of the main bay, rather deep in East Valley, in a chaotic area where the elements become pinched off. The pinched-off elements are obvious, but the area is actually quite a bit more chaotic than the image would suggest. Most of the detail beyond the foreground elements is due to the coloring, and will rapidly disappear if the colors are changed. In the picture, I have departed from my usual inside=solid-black routine, and given the inside of the midget an electric blue coloring, which suggests, at least to me, a window into an alternate reality beyond the one visible to the senses. To increase the impact of the brilliant interior, I have faded the colors to near black as they approach the midget. Despite the rather ordinary effect of the image, I have given it a rating of a 7, which equals above average. I put more effort into the coloring than meets the eye and decided to reward myself with a rating one point higher than what I would ordina- rily give. Due to its high iteration count, the image is a slow one, requiring over 1/2 hour to complete on my machine. But the time can be saved by downloading the completed GIF image from one of the FOTD web sites, which can be found at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The topic of identical Mandelbrot midgets has been raised on the list recently, and has been pretty well answered. I sometimes wonder about the philosophical aspects of this topic however. Except for their mirror image on the opposite side of the real axis, no two midgets are exactly identical. But with many midgets the difference is infinitesimal, and cannot be discerned by any means available to us. Can such midgets then be consi- dered identical? I guess it all depends on the meaning of the word 'identical'. In the Mandelbrot set, the shape of the midgets remains within the range where they are recognizable. The same is not true in fractals created by more exotic formulae, where midgets can be distorted totally beyond recognition. Finding extremely dis- torted midgets in exotic fractals might make an interesting fractal project for a future series of FOTD's. Now on to more important things. Another average day's weather here at Fractal Central brought the fractal cats an average afternoon in the yard. The partly cloudy skies, temperature of 55F 13C, and light southeast winds were so average that those with no great interest in the weather have little memory of the conditions. Today is supposed to bring rain, but it is starting sunny. We'll see how things go as the day progresses. Things will likely go pretty well for me. The work is caught up and somehow I managed to avoid having to go to any Thanksgiving dinners. If my good luck holds out later today, I'll find one of the infinity of great fractals that still lurk undiscovered in the Mandelbrot set. If not, I'll return in 24 hours with another acceptable scene. Until then, take care, and be aware. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandelbrot-15 { ; time=0:31:44.87--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=+0.25620301284127930/-0.000987866605141\ 90/3.070075e+011/1/-42.4940527126489584/-0.0001586\ 27323509942519 params=0/0 float=y maxiter=320000 bailout=9 inside=255 logmap=16000 periodicity=10 colors=000tbktbksajr`ir_iqZhqZhpYgoXgoWfnWfnVemUel\ TdlSdkSckRcjQbiPbiPahOahN`gM_fL_fLZeKZeJYdIYcIXcHX\ bGWbFWaEV`EV`DU_CU_BTZBTYASY9SX8RX8RW8SV8TU8UT8VS8\ WR8XQ8YP8ZO8_N8_M8`L8aK8bK8cJ8dI8eH8fG8gF8gE8hD8iC\ 8jB8kA8l98m88n78o78o99nBAnCBnECnGDmHEmJFmKGmMHlOIl\ PJlRKlSKlULkWMkXNkZOk`PjaQjcRjdSjfTihUiiVikWilWikV\ gkUejTcjTajS_iRYiRWiQVhPThPRhOPgNNgNLfMJfLIfLGeKEe\ JCeJAdI8dH6dH5eJ5eK5fM5fN5fO5gQ5gR5gS5hU5hV5iX5iY5\ iZ5j`5ja5jb5kd5ke5lg5lh5li5mk5ml5mm5no5np5or5os5ot\ 5pv5pw5px5nw6lv6ku6it6gs6fr7dq7cp7ao7_n7Zm8Xl8Wk8U\ j8Si8Rh9Pg9Nf9Me9Ke9JeFHeKFePEeUCdPBbK9`F7ZB6XB4VB\ 4WA3VB3VB3UB3UC3TC3TC3TD3SD3SD3RE3RE3RE2QF2QF2PF2P\ G2PG2OG2OH2NH2NH2NI2MI2MI1LJ1LJ1KJ1KK1KK1JK1JL1IL1\ IL1IM1HM1HM0GN0GN0GN0FO0FO0EO0EP0EP0DP0DQ0CQ0CQ0CQ\ 8BNFALJ8AKAJKAAKBAKCAKCAKDAKDAKEAKFAKFAKGAKGAKHAKI\ AKJAKKAKKAKKAKKAKKAKKAhzz } END PARAMETER FILE=========================================

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Doesn't look like a fractal!
by John Wilson 27 Nov '03

27 Nov '03

My recent attempts to resurrect some antique software to a reasonable purpose have come to naught. My "Fractal Programming in Turbo Pascal" produces fractals in a "PCX" format, which are readable using the same software. However I cannot read them in any other graphics program, to convert them to, say, GIF's, in spite of suggestions in this group, and the kind donation of an elderly graphics file converter which *should* have done the job. ( The "screen_restore" command renders the "PCX" files by writing pixel columns from left to right). Anyway I've abandoned this research for a while, as I have obtained a copy of "Fractal Creations" from e-Bay, and a copy of the CD from Tim, (thanks again). The great fractals obtained by FRACTINT pioneers inspired me to look again at the basic Mandelbrot and Julia sets, and I stumbled upon this one, which is a variant and a zoom into one of the pioneering efforts. To me it doesn't look at all like a fractal...until color cycling is turned "ON". Very odd, and I think a better color scheme could make it quite remarkable. John W. ---------------------------------------------------------------- fmod_zoom { ; Test of outside=fmod with 'mod' bailout ; Version 2002 Patchlevel 4 reset=2002 type=julia passes=1 corners=0.24028190305/0.24057818099/0.56447971722/0.56470192568 params=-0.7387588245570118/0.1409069307481326 float=y maxiter=120 inside=fmod proximity=0.009 outside=fmod colors=zzzG9NdR8A`D<3>q7sBD9ACY8Av<3>B34OF7`RB<3>u_L4j8xz`W_P29DLFQdMb<3\ >dnH<3>ABRXHIsN9pmJ<3>wBO<2>U89WP6Ye3_v0<3>rPq<2>d2ZMAm<2>s_8<3>c7VbXYav\ `akX`_TezuEPw<3>W0c<2>uk3<2>M1QQBdVLt<2>T4khJneXqbkt<2>enngolfnjelgdjd<3\ >YAv<3>3c_4bQ6aG<2>v`A<3>oiH<2>lcBj`9gWz<2>UD0T`TSyu<3>pBUlKKgU9SPLRWYPb\ kNeULiBFj4<3>VGP<2>NBFYOHIe`1wtWJ8UFWSBs<2>lKl<2>rDC<2>Aco<2>bCx<3>1oNON\ a<3>b0e<2>Z0FX16X7K<2>USy<3>ayO2zWznt<3>E3T<3>`YA<2>K7L<2>h9a<3>q39<2>3Y\ RMiEdv0<2>pFeTMb4TZ<3>zdG<2>CBnbyQ<2>M2u<2>Lmtbu8<3>17c<3>YQt<3>VIM<3>pa\ 3<2>OMIRHEUBA517KAZZJz<3>xTz<3>c62 }

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Re: midget Mandelbrot sets
by JackOTradez 27 Nov '03

27 Nov '03

Hal - No to your question; my understanding (if correct) is that no two minibrots (out of an infinite number of them!) are EXACTLY identical (aside from the symmetry about the real axis). The differences may be too small to see, even an infinitesimal difference that you wouldn't see until you zoomed in a zillion times, but different they are. And NONE EXACTLY resemble the parent brot! Also, every single one of the minibrots are connected! It is ONE set - there are no minibrot "isolated" lakes! The connecting "line" also may be infinitesimally thin, but it is there. However, if you zoom in and explore around, you can find some minibrots that are distorted enough to easily see - like one lobe of the main cardiod bigger than the other, or a warp/distortion in shape somewhere. There are lots of these - I have seen many in my fractal travels. Stay Amazed! JoTz

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FOTD 26-11-03 (Mandelbrot-14 [6])
by Jim Muth 26 Nov '03

26 Nov '03

FOTD -- November 26, 2003 (Rating 6) Fractal visionaries and enthusiasts: Since I have another pile of work starting to develop and it's the day before the 4-day Thanksgiving holiday here in the U.S., today's discussion will once again be short. I don't want another backlog to get started. The scene of today's image is deep in a filament extending outward from the northeast shore of the main bay of the large midget at -1.75 on the main stem of the Mandelbrot set. The magnitude is just slightly into the range where arbitrary precision math is needed to maintain resolution, but despite this, the image still renders in 16 minutes, which is faster than some of the conventional-math images of the past few days. For a rating, I could give the image nothing above a 6. Hope- fully, before the present tour of our old friend, the Mandelbrot set, comes to a close, I'll find a scene worthy of a 9 ....... then again, that might be wishful thinking. To see the scene of the action, run the attached parameter file and return in 16 minutes, or download it from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Tuesday here at Fractal Central was eminently average. The partly cloudy sky, temperature of 46F 8C and moderate northwest wind made the cats act like average 13-year-old cats while they were out in the yard in the afternoon. Considering the behavior of average 13-year-old cats, this leaves little room for action. Today looks like a repeat with even less sun. I expect the duo will have a similar day. As for me, I've got some work to wrap up before that 4-day holiday begins tomorrow. Until next FOTD, take care, and one of these years I'll decide to devote my full time to fractals. See you in 24 hours. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandelbrot-14 { ; time=0:16:24.26--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=-1.74654440989129756/0.0083322745890837\ 53/5.755045e+013/1/-155/3.88578058618804789e-016 params=0/0 float=y maxiter=2400 bailout=9 inside=0 logmap=220 periodicity=10 colors=000J6GH6EKADPDCSGCVKBXOA_RAaU9dX8g_8jb7me6p\ i6sl5tn5pm9kkDfiGbgKYeNUcRPaVL_YGYaCWd7Th3PkFPeRO_\ aKUmHOxUUwccvZmuWwtTmsWcr_UrcTqgVpkWooYnsZmw`mzanw\ _osYooWpkUpgSqcQr_OrWMsSKsOItKGuGEuCCv6Av39rDIocRl\ Y_ikghfcgb`fZXeVUdRQcNNbJJaFG`BC`79d8Ag8Ak9Bn9BrAC\ uACxACuGGsLJpQNnVQl_UieXgj`docbtg`yjdqkgjkjbkmWkpP\ ksHkvAky3khHiSUhRVfQVdPWcOWaNX_MXZLYXKYVJZUIZSH_QG\ _PFRLFIHFgvFbpFZjskglhfeeeZbeS_dLXcEUb7RbNJQbBDq41\ zE0RPGtD2nC4hC5bB7XA9RAAL9Ci10e22a34Y45U57Q69M7AI8\ CaHWXFSSDOOCKJAGZ2JV4HR5GN7FJ8ET8vO9fJ9SvRUgLOTFIj\ `EfXDbUDZQDVNDRJDNGDJCDcFIXDGRCFLAEBkoCeiDccDcZEcT\ EcOFcIycwrcpkcidcbZcXScQLcJ9cvBclCccDcVEcMTcbQcXNe\ SKgNHiInk4fm6_o8TqAMsCYuxOw`OzmMzfLz`JzVIzPGzJOzoM\ zhLzbJzWIzQGzJ`zIXzHUzGRzFOzFLzEIzDxz5rz6lz7fz8az9\ WzAQzBKzCDzQEzOEzMEzLEzJFzHFzGFzE4zb7zX9zSBzNDzIhz\ dczMXzJRzHLzFTzORzMOzKMzI } END PARAMETER FILE=========================================

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FOTD 25-11-03 (Mandelbrot-13 [6])
by Jim Muth 25 Nov '03

25 Nov '03

FOTD -- November 25, 2003 (Rating 6) Fractal visionaries and enthusiasts: Had I not named today's image "Mandelbrot-13", I might have named it something like "Galaxia". It resembles nothing as much as a midget Mandelbrot set acting as though it were a black hole at the center of a giant galaxy. The giant galaxy is surrounded by four satellite spiral galaxies, which appear at first glance to be disconnected, but actually are connected to the main body of the M-set by infinitesimally thin filaments that do not show up in the image. The whole area is filled with smaller irregu- lar galaxies and scattered individual stars. Instead of going straight out the center line of a chain of buds, as we have done in the recent FOTD images, we entered the north bud and kept turning into smaller buds on the right to find the valley that holds today's scene. In fact, the valley that holds today's scene is of the sixth order. (It's the valley enclosing a bud on the side of a bud on the side of a bud etc. . . .) Areas such as this consist of almost total chaos, and a broad color palette must be used to reveal the subtle hidden order. Yes, there can be order in chaos, but who knows what it means. The parameter file runs in a moderately slow 12 minutes on my machine, which, considering the high iteration count of the elements, is not too bad. But 12 minutes is 12 minutes, and time may be saved by downloading the finished GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Monday turned out quite pleasant here at Fractal Central. The clouds cleared away by noon, the temperature reached 68F 20C, and the fractal cats were happy all afternoon. When evening arrived, they came indoors without coaxing, and settled for the night without tuna. But such good things cannot continue. A cold front that arrived overnight has dropped the temperature to near freezing this morning. It remains to be seen how the cat duo will adjust to the chill. My task is to finish the modicum of work waiting to be done. When it is finished, I'll see what I can dredge up from the depths of the Mandelbrot set. Whatever I find will appear as tomorrow's FOTD, so until then, take care, and where did yesterday go? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandelbrot-13 { ; time=0:12:12.86--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=-0.02364046275250382/+0.783659823068409\ 40/4.519853e+010/1/17.4999176198803177/7.992807071\ 13048106e-005 params=0/0 float=y maxiter=120000 bailout=9 inside=0 logmap=-9680 periodicity=10 colors=000DHdEFeFCfGAgH8hI6iJ5jK5kL3lM2mN1nO0oP0pQ\ 0qR0rS0sT0uU0uU0uU0uU0uU0uU0uU0uU0uU0uU0uU0uU0uU0u\ U0uU0uU0uU0uU0uU0vU0vU0wV0wW0xX0xY0yZ0y_0z`0za0zb0\ zc0zc0zc0zc0zc0zc0zc0zc0zc0zc0zc0zc0zc0zc0zc0zc0zc\ 0zc0zc0zc0zc0zc0zc0vc0oc1fc2Ya3VV3NR5HL6CH6AL8CL8C\ NACNACNCFRCFRCFVFFVFHVHHYHHYHHaLHaLLaNLfNLfNLfRNjR\ LjVIoVGoVEoYCsaAsf9vj7zo6zs6zv6zz6zz6zz6zz6zz7zzAz\ zAzzDzzGzzJzzNzzRzzVzzZzzczzfzzjzzmzzqzzuzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } END PARAMETER FILE=========================================

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Re: John Wilson PCX file format
by JackOTradez 24 Nov '03

24 Nov '03

John - get IrfanView. Aside from being the best multimedia player/viewer around, it's free! And it reads PCX format, which is an old paintbrush format. JoTz

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[Fractint] This is a simple zoom out of Jim Muth's Fractal of the day from Nov 24, '03
by Hal Lane 24 Nov '03

24 Nov '03

-------------------------------------------------------------------------- This is a simple zoom out of Jim Muth's Fractal of the day from Nov 24, '03. It shows the four-fold symmetry surrounding the eight-fold symmetry in Jim's fractal. At 38 minutes on a P400 for 1024 x 768 its a candidate for a 'disk' (RAM) video mode... Does anyone know if the midget Mandelbrot sets contained in the Mandelbrot set are exact copies of the original? <---<< - Hal Lane ######################### # hallane(a)earthlink.net # ######################### ================START 20.0 PAR-FORMULA FILE================================ Mandelbrot-12hhl { ; time=38 min @ 1024 x 768 on a P400 ; Mod of Jim Muth's FotD Nov 24, '03 ; by Hal Lane ; Version 2002 Patchlevel 5 reset=2002 type=mandel passes=1 center-mag=-1.31205579278384000/+0.06815268633219243/4.933665e+010/1/127\ .500420311381404/-0.00123778779799370992 params=0/0 float=y maxiter=300000 bailout=9 inside=0 logmap=36600 periodicity=10 sound=off colors=000OAzYXzVXzPXz<2>EXz8Xz4Xz0Xz<4>0Xz0Xz0Xz2Xz4Xz7Xz7Xz<3>EXzGXzIX\ zKXzKXz<3>RXzTXzVXzXXz<20>XXzXXzXXz<3>XXz0Xz7XzRXzXXz<15>XXz<4>XXzVXzTXz\ RXzRXzPXzOXzMXzMVzKRzIOzGKzGGzECzC8zA4zA0z80z70z40z70z40z40z20z20z00z<16\ >00z00z00z<2>00z00y20w70vA0rE0pI0nO0mR0kV0iY0ed0d<2>n0Yn0Xr0Xv0Xy8XzIXzR\ XzbXzkXztXzzXzzVzzX<3>zzYzzYzzYwzYvz`rz`ny`mw`ivbevbdtb`rbXrbVpdRndOndMm\ dIkeEieCie8ge4eg2eg0dg0bg0ek0bg0Yd0V`2RX7OT8MPCIMEEIIAEM7AO27R02T00X00`0\ 0b00e00e00g00i00i00k00m00m00n20p70pA0rE0tI0tM0vP0wT0wX0yY0z`0<3>zg0zi0zk\ 2zm2zn4zn4zn7zn7zn8zn8znAznAznCznCznEznEznGznEznG<5>znGznGznI } ================END 20.0 PAR-FORMULA FILE================================== --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.537 / Virus Database: 332 - Release Date: 11/6/03

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FOTD 24-11-03 (Mandelbrot-12 [7])
by Jim Muth 24 Nov '03

24 Nov '03

FOTD -- November 24, 2003 (Rating 7) Fractal visionaries and enthusiasts: The discussion will be short because of an unexpected job that came in about an hour ago. It's not a large job, but if I let it sit on the shelf, we could be getting ourselves into another backlog. Today's image from the Mandelbrot set is a study in finding order in chaos. The scene is located on the north shoreline of the first bud beyond the large bud at -1 on the X-axis, in the fifth valley of the valley series of a sub-bud. Almost total chaos prevails in this area, with only a few remnants of anything resembling order. The midget in today's image is surrounded by one of these quasi-orderly areas. The rating of a 7 might be a bit liberal, but I kind of like the image, and this is almost certainly the first time this particular midget has been seen by human eyes. The scene is one of very high iteration, with even a maxiter of 300,000 not quite resolving the midget. At 36,600, the logmap is also set unusually high. The result is a render time of 44 minutes, which can be eliminated by downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The Sunday weather was rather bland here at Fractal Central. The temperature in the 50's (around 13C), the hazy skies, and the light winds, were notably forgettable. The cats were happy in the yard however, and this was very memorable. As the day ended, the satisfied cats had their heads in their tuna dishes. And now it's time for me to tackle that building pile of work. When I finish, I'll tackle the Mandelbrot set. Until next time, take care, and try to avoid those inevitable dead ends. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Mandelbrot-12 { ; time=0:44:37.50--SF5 on a p200 reset=2002 type=mandel passes=1 center-mag=-1.31205579278384000/+0.068152686332192\ 43/9.947005e+010/1/127.500415974917757/-0.00080291\ 4198005093283 params=0/0 float=y maxiter=300000 bailout=9 inside=0 logmap=36600 periodicity=10 colors=000OAzYXzVXzPXzMXzIXzEXz8Xz4Xz0Xz0Xz0Xz0Xz0\ Xz0Xz0Xz0Xz2Xz4Xz7Xz7Xz8XzAXzCXzEXzGXzIXzKXzKXzMXz\ OXzPXzRXzTXzVXzXXzXXzXXzXXzXXzXXzXXzXXzXXzXXzXXzXX\ zXXzXXzXXzXXzXXzXXzXXzXXzXXzXXzXXzXXzXXzXXzXXzXXz0\ Xz7XzRXzXXzXXzXXzXXzXXzXXzXXzXXzXXzXXzXXzXXzXXzXXz\ XXzXXzXXzXXzXXzXXzXXzXXzVXzTXzRXzRXzPXzOXzMXzMVzKR\ zIOzGKzGGzECzC8zA4zA0z80z70z40z70z40z40z20z20z00z0\ 0z00z00z00z00z00z00z00z00z00z00z00z00z00z00z00z00z\ 00z00z00z00z00z00y20w70vA0rE0pI0nO0mR0kV0iY0ed0dg0\ bk0`n0Yn0Xr0Xv0Xy8XzIXzRXzbXzkXztXzzXzzVzzXzzXzzXz\ zXzzYzzYzzYwzYvz`rz`ny`mw`ivbevbdtb`rbXrbVpdRndOnd\ MmdIkeEieCie8ge4eg2eg0dg0bg0ek0bg0Yd0V`2RX7OT8MPCI\ MEEIIAEM7AO27R02T00X00`00b00e00e00g00i00i00k00m00m\ 00n20p70pA0rE0tI0tM0vP0wT0wX0yY0z`0zb0zd0ze0zg0zi0\ zk2zm2zn4zn4zn7zn7zn8zn8znAznAznCznCznEznEznGznEzn\ GznGznGznGznGznGznGznGznI } END 20.0 PAR-FORMULA FILE==================================

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FOTD 23-11-03 (Mandelbrot-11 [6])
by Jim Muth 23 Nov '03

23 Nov '03

FOTD -- November 23, 2003 (Rating 6) Fractal visionaries and enthusiasts: Today's trip into the Mandelbrot set takes us into a previously unexplored (at least by me) valley on the north shore of the main bay. The exact valley in question is the east branch of the sixth valley of the series of valleys along the center line of the large north bud. In this valley, which is far too remote to have been given a name, broad areas of quasi-order are sprinkled with scepter-shaped areas of near-total chaos. The midget in the image is located in one of these scepter-like areas of chaos. The nature of the area is reflected in the nearly-straight arms radiating from the midget. I have tried to raise the impact of the scene by giving it a rather intense color palette, though even the colors cannot raise the rating beyond that of an everyday 6. But it's still a striking scene, and the render time of five minutes is reasonably fast. Best of all, the completed image is available for download in GIF format on Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or on Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Saturday was a near perfect day here at Fractal Central, as expected. The dynamic fractal cats were near angels, as expected. They spent most of the day lounging in the grass, wishing more warm sun could get through the evergreen holly trees at the bottom of the yard. Luckily, the temperature of 66F 19C was mild enough to keep them comfortable. As I watched them just lying there, I remembered the days not too many years ago, when they would have spent the day dashing about like kittens. Today is due to be a repeat, though now, at 9:00am, a light fog is drifting in, and the grass is still too wet with dew for their sensitive paws. My plans for the day are still uncertain. The work is caught up, but there is always the chance that I'll be drafted into a trip to one of the countless local antique malls. Regardless, the next trip into the Mandelbrot set will appear in 24 hours. Until then, take care, and will the truth prevail? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandelbrot-11 { ; time=0:05:01.32--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=-0.10933292648738020/+0.894819222668978\ 30/1.17225e+012/1/-82.4993452471808979/-6.69956006\ 414049177e-005 params=0/0 float=y maxiter=36000 bailout=9 inside=0 logmap=-6619 periodicity=10 colors=000H00I00J00K00L00N00P00S65XEHbMSjUbramyhx0\ GR0MOOSKKZGGdDCj98q59n7Ak9BhBDeDEbFFZHGWJITLJQNKNP\ MJRnYBVgLArVmDgmGemJbmN`mQYmTVmXTn_QnbNnfLniInlFnp\ DnsAow7mw7jw7gw7dw6av6Zv6Xv5Uv5Ru5Ou4Lu4Iu4Ft3Gr5K\ p7Po9UnBZmDclFhkHmjK000000000KKK000000000aHZaM_aQ`\ aVaaZaacbagcaldaqe_qeXpeUoeRnfOmfLlfJkfGjgDigAhg7g\ g4fh7fzAffEfeHfdLfcOfbRfaVf`Yf_afYadZab`a_a`Yc`Wd`\ TfnVDnTCnRCnPBnNBnKBnIAnGAnE9nC9nA9e7JX5TO2bF0kR7h\ aEelLbgNabOaYPaTRaPS`KT`FV`AW`6X`6ZZ6_X6`V6aT6cR6d\ PFgJOkDXo7es1dm1cf1a_1`T1ZM1YF1W82XA4YC7ZEA`HDaJFb\ LIcNLeQOfSQgUThWWjZZkcblhfmmjnsnkokhkgdgdac`YcYVcU\ RcROcNKcKHcGDcCDcECcGBcIBcLAcN9eP9hS8kU7nW6qZAt_Ew\ `IzaMzbRzdVzeZzfczsfzsjzsmzspzslzkhzddzY`zRXzKPzRH\ zYOzaVzeazihzmozqvzutzqszmrzjqzfpzboz_mzWlzSkzPjzL\ izHhzEizIizLjzPjzSkzWkzZlzblzemzimzlnzpjziezbazWXz\ PTzIOzBJz3Lz4Nz6Pz7Sz9UzA } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD 20-11-03 (Mandelbrot-08 [6])
by gnome＠hawaii.rr.com 22 Nov '03

22 Nov '03

>gnome(a)hawaii.rr.com wrote: >> >> Strange, went to Paul's site, I get the >> main FOTD page, but the links to the >> individual FOTD pages keep giving me the >> ATT message page not found message. >> > >Sorry for the inconvenience. Things should now be closer to 'normal'. > >The Worldnet servers are being upgraded this week (for various reasons), >and they seem to have had an especially difficult day today. Hopefully >this was the worst part of their immediate problems. Thanks, Paul. Will try again! David gnome(a)hawaii.rr.com

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FOTD 22-11-03 (Mandelbrot-10 [7])
by Jim Muth 22 Nov '03

22 Nov '03

FOTD -- November 22, 2003 (Rating 7) Fractal visionaries and enthusiasts: After surprising myself with the things I found yesterday in the deep chaos on the northwest shore of the main bay, I decided to continue my exploration today in another chaotic area. Today's image continues the same theme as yesterday's, though this time we examine the northeast shore of the main period-2 bud of the Mandelbrot set rather than the northwest shore of the main bay. The overall appearance of today's image is similar to yesterday's, the increased coverage of orderly areas being the main difference. If today's image rather than yesterday's had appeared first, I might have given it a rating of an 8. Since it is a repeat however, I can rate it at only a 7. But with its gold chaos filled with hints of Siegel disks and the blue aura around the chaos, it is still a worthy image, well worth the 14 minutes required to render it from the parameter file. The time to download the finished image is far less. That down- load may be found at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> With its sun and temperature of 72F 22C, Friday turned out even more perfect than Thursday here at F.C., giving the dynamic cats their best day outdoors of the entire autumn. When dusk came, they were still reluctant to come indoors, and needed to be coaxed with a dish of tuna. Today looks like a repeat, both with the weather and the cats' moods. I have a small bit of work to finish before I can devote my energies to the difficult task of doing nothing. Until next time, take care, and will we ever know the single ultimate truth? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandelbrot-10 { ; time=0:14:14.26--SF5 on a p200 reset=2002 type=mandel passes=1 center-mag=-0.83728722273650410/+0.189817152724375\ 90/1.721983e+010/1/4.9999985713227062/-1.705006307\ 89077734e-005 params=0/0 float=y maxiter=250000 bailout=9 inside=0 logmap=2730 periodicity=10 colors=000AN3AO3AP2AQ2AR1AS1AT0AU0AV0AW4AX7AYAAZEA\ _HA`K8`R7_M7YG9WFBUEDSEFQDHODJMCLKBNIBPGAREASC9TK9\ QOFQQLOSQMTWJUaHVfFWlDXrBZwD`xEbxFexGgxHjxImxJoxLp\ yMnyNmyOjyPiyQgyReySdyQauOZqMWmKUiIRfGObFMZDJVBGS9\ EO7BK58G46D89CBCCEFBIIBLLAOOARR9VU9YX8`_8db7ge7jh6\ mk6qn5tq5wt4zv4yr6yo7yl8xi9xeAxbBx_DwXEwUFwQGvNHvK\ IvHKvDLuAMu7Nu4Ou1Pt4Os6Or9NqBNqENpGMoJMnLMnOLmQLl\ SLkVKjXKj_JiaJhdJgfIgiIfkIenHdpHdrHcqIcqJcqKbqLbpL\ bpMapNapOaoP`oP`oQ`oRhnSqnTznTsnUnmVgmWYmXYmXYlYXl\ ZXl_Xl_ZfW`aSbWPdRLfLIhGEjABl57m04j24g34f44e54d74c\ 84c94cA4cC4cD4cE4cF4cG4cI5cJ5cK5cL5cM6cN6cO6cQ6cR6\ cS7cT7cU7cV7cW8dX8fZ8h_8j`8la9nb9pc9rd9se9qdApcAoc\ AmbBlaBkaBj`Bh`Cg_CfZCdZDcYDbYDaXD_WEZWEYVEXVE_XFb\ ZFe_FhaFkcGndGqfGthGwiGujFsjFqkFokEmlEklEilEgmDemD\ cnDanDaoCcoCfoChpCkpBmqBpqBpqBqrArrArs9rs9rs8rt8rt\ 7rt7ru6ru6rv5rv5rv5rw4rw4 } END PARAMETER FILE=========================================

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