February 2008 - Fractint - mailman.xmission.com

FOTD 04-02-08 (Ogive to Infinity [7.25])
by Jim Muth 04 Feb '08

04 Feb '08

FOTD -- February 04, 2008 (Rating 7.25) Fractal visionaries and enthusiasts: Today's image, with all its Moire patterns, lies in the eastern part of the large period-2 bud of the Mandelbrot set. I named it "Ogive to Infinity". An ogive is a pointed gothic arch, and the ghostly arch in the background of today's image certainly is pointed. The buds on the arch are of various shapes. Yesterday's image was a close up of a similar bud on a similar ghostly arch in the vicinity of East Valley. The rating of a 7.25 includes a 1/4 point bonus for the effort I put into the coloring. If I had not been so hasty, I might have earned a 1/2 point bonus. The image is rather striking; the calculation time of 25-4/5 minutes is also striking. But it should be no surprise that the completed image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Today's image is actually many images in one. Every change of size or resolution totally changes the pattern inside the arch. Sunday began with dense fog here at Fractal Central, but by midday a breeze arose from the west and swept away the fog almost by magic. The rest of the day brought lots of sun and a temperature of 45F 7C. The fractal cats were unusually quiet for some reason. My day was lazy. The next FOTD will appear in 24 hours. Until then, take care, and is it real or isn't it? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Ogive_to_Infinity { ; time=0:25:49.45-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot2 passes=1 center-mag=-0.861346/0/35.65062/1/90/0 params=0/0/0/0/1/0/1e-100/0 float=y maxiter=15000 inside=0 logmap=-1068 periodicity=0 colors=00091OA2OA2NA3NA3NB4MB4MB4MB5MA5MA6M96M86M8\ 7M87LA8MA8LA9LB9LC9LCAKDALDBKDBLFBKFCKFCJFDKFDJGEJ\ GEIGEIGFHGFHHGGHGGHGFHHEIHDIIDIICIICIJCJJCJKCJKCJL\ CJLDKMEKMEKMEKNELNHLNGLOGLOHLPHMPIMPIMQKMQJMRINRLN\ SLNSLOSLOTLOTMPTMPUMPUMQVNQVNQWNRWNRWNRXOSXOSYOTYO\ TZOUZPUZPV_PV_PW`QW`QXaQXaQYaQYbRZbRZcR_cR_cR`dS`c\ SadSadSbdVbeUceTceScfRdfQdfPegOegNegMfhLfhKfhKghKg\ hKghKhiKhiLhiLiiLijLijLjjMjjMjkMkkMkkMkkMlkNlkNllN\ llNmlNmlOmmOmmOnmOnmOnnPnnPonPonPooQooQpoQpoRppRpp\ RqpRqpSqqSqqSrqSrqTrrTrrTsrUsrUssUssUtsVtsVttVttWu\ tWutWuuXuuXvuXvuYvvYvvYwvZwvZww_ww_xw`xw`xx`xxayxa\ yxayybyybzybzyczyczzczzdzzdzzezzezzfzzfzzgzzgzzhzz\ hzzizzizzjzzjzzkzzkzzlzzlzzmzzmzznzznzzozzozzpzzpz\ zpzzqzzqzzqzzrzzrzzrzzszzszzszztzztzzuzzuzzvzzvzzv\ zzwzzwzzwzzwzzxzzxzzxzzxzzyzzyzzyzzyzzyzzxzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

1 0

FOTD 03-02-08 (Astral Adventure [7.5])
by Jim Muth 03 Feb '08

03 Feb '08

FOTD -- February 03, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: Skeptics know that ghosts are not real, though I doubt that the ghosts know it. Ghosts or no ghosts, today's image is a picture of a bonafide ghost, or what I call a ghost bud. The perturbed Mandelbrot sets are filled with ghost buds that can be returned to their unperturbed glory by resetting initial Z to 0,0. But the ghost in today's image cannot be returned to its full glory because I don't know where to find it. All 4 parts of initial Z, (p1) and (p2), are already set to zero. Like all ghosts, the one in today's image seems to exist in another world, and only fleeting glimpses of it can be seen in this world. The location of today's scene is in the vicinity of East Valley, though some distance offshore, where nothing but trapped inside points should exist. I named it "Astral Adventure" because the astral plane is where ghosts are supposed to exist. The actual nature of the astral plane is another topic for another day, but at this time I will say that, though I am a skeptic, I am not a born-again skeptic. And I hear a lot of talk among theoretical physicists about many, though not necessarily astral, worlds, as well as much rebuttal from the born-again skeptics. I would like to have been able to rate the image at an 8 or 9, but I just couldn't find anything in it worth such a rating, so the scene ended up rated at a 7.5. The parallel comb-like fore- ground arms plus my coloting add the extra point. The calculation time of 9 minutes is not too much for such an unexpected image. But if this time is a little inconvenient, convenience may be regained on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image will soon be posted. I'm slightly sorry for the lateness of today's image, but I had to make an unscheduled trip to Old Fractal Central on Saturday, and didn't get back to New Fractal Central until near midnight. I can report that the old fractal cats, Thomas and Tippy, are still as lazy as ever. They actually raised their heads when I walked in. The new fractal cats, Nicholas and Cassie, stayed here with fractal lady all day, and she says they hardly noticed that I was gone. The next FOTD will appear in around 12 hours. Until then, take care, and rational thinkers know that ghosts are mere fantasies in the minds of the superstitious, but the ghosts, who have not heard that they are mere fantasies, continue their haunting. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Astral_Adventure { ; time=0:09:49.37-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot2 passes=1 center-mag=+0.09608900268348/+0.0117053191216819/\ 1114.51/1/15/0 params=0/0/0/0/10/0/1e-100/0 float=y maxiter=7500 inside=0 logmap=820 periodicity=0 colors=000YOEYOEZOEZODZODZOCZOCZOC_OB_OB_OB_OA_OA`\ O9`O9`O9`O8`O8aO7aO7aO7aO6aO6bO5aO6aO6aO6aO6`O6`O6\ `O6`O6_O6_O6_O6_O6_O7_O7ZO7ZO7ZO7ZO7ZO7ZO7ZO7ZO7ZO\ 7ZO7YO8XO8XO8XO8WO8WO8WO8WO8WO8VO8VO8VO8VO9UO9UO9U\ O9UO9UO9UO9TO9TO9TO9TO9TO9SPASPASPASPARPARPARPARPA\ RPAQPAQPAQPAQQBQQBPQBPQBPQBPQBPQBOQBOQBOQBOQBOQBNR\ CNRCNRCNRCMRCMRCMRCMRCMRCLRCLRCLRCLSALSAKSAKSmKSmK\ SmKSmJSmJSmJSmJSmIRmJSmJSmKSmKSmLSmLSmMTmMTmNTmNTm\ NTmOTmOUmPUmPUmQUmQUmRUmRUmSUmSUmSTmTTmTSmUSmUSmVS\ mVRmWRmWQmXQmXPmXQmYPmYPmZPmZPm_Om_Pm`Om`OmaOmaOma\ OmbPmbPmcPmcPmdPmdPoePqeQsfQufQwfQygQzgQzhRzhRziRz\ iRzjRzjRzjRziSziTzhTzhUzhVzgWzgXzgYzfZzf_zg`zfazfb\ zfczedzeezefzdgzdhzdizcjzckzclzcmzbmzbmzbmzamzamza\ mz`mz`mz`mz_mz_mz_mz_mzZmzZmzZmzYmzYmzYmzXmzXmzXmz\ WmzWmzWmzWmzVmzVmzVmzUmzUmzUmzTmzTmzTmzSmzSmzSmzSm\ zRmzRmzRmzQmzQmzQmzPmzPmz } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

1 0

FOTD 02-02-08 (Deep HyperRadical [9])
by Jim Muth 02 Feb '08

02 Feb '08

FOTD -- February 02, 2008 (Rating 9) Fractal visionaries and enthusiasts: Unless I have an operational time machine hidden in the garage, the year it was 24 hours ago is, always was, and always will be 2008. But old habits are like old fractals. They die hard. Today's image takes us to a bud on the north shore of HyperEast Valley. I named the image Deep HyperRadical because it sits deep in the interior of the bud, and buds, along with their associated elements, are sometimes called radicals. This parti- cular bud is a very tiny one with a very high periodicity, which lies comfortably between much larger buds of much lesser periodi- city. I have no idea why today's image, which lies inside this tiny bud, should appear to have a cycle of 6. Yes, there are more unusual scenes of varying cycles lying as deep as it is possible to go into the center of today's image, and likely extending to infinitesimal infinity. These scenes are not mere boring fractalish repeats of the top scene. Each level has a character of its own. The maxiter of today's image is an arbitrary choice. As the maxiter is increased, the open areas with the twisting greenish arms gradually fill in, until ultimately they are filled solid with fractal debris. In my opinion, the image rates an honest 9. It is worthwhile artistically and interesting mathematically. And its calcula- tion time of 3 minutes is not bad either. Of course, for extra convenience, the finished image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Absolutely miserable weather prevailed here at Fractal Central on Friday. The day began with one inch, or 2.5cm, of sleet on the ground. The sleet changed to freezing rain by 9am, and it rained steadily for the rest of the day, while the temperature slowly rose to above freezing by afternoon, leaving an inch of heavy wet slush everywhere. The fractal cats watched from the front window shelf as I squeegeed away the sloppy mess by hand. The rest of my day was easy enough, though a small but hurried design job is expected tomorrow. The next FOTD will appear in about 24 hours. Until then, take care, and is the Mandelbrot set infinite or half infinite? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Deep_HyperRadical { ; time=0:03:13.47-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot2 passes=1 center-mag=+0.2689640429736179/+0.005486652797290\ 472/5.9811e+007/1/105/0 params=0/0/0/0/1/0/1e-100/0 float=y maxiter=1900 inside=0 periodicity=0 colors=000hzRizQizPizPjzOjzOjzNkzNkzMkzMlzLlzKmzKm\ zJmzJnzInzInzHozHozGozFpzFpzEpzEqzDqzDqzCrzCrzBszA\ rzBrzCrzCqzDqzDqzEqzEpzFpzFpzGpzGozHozHozIozInzJnz\ JnzKnzKmzLmzLmzMmzMlzNlzNlzOlzOkzPkzPkzQkzRjzRjzSj\ zSjzTizTizUizUizVhzVhzWhzWhzXgzXgzYgzYgzZfzZfz_fz_\ UzKWzRXzXZzc_ziazpbvvVruNntGjtFfsGMeHNhIOkJPnKQqLR\ tMSwNTzAAA3F8CH9KH9NH9QHATHCWHDZHEaHFdHGhHHlNFpTDt\ `AwfKtiUqlcynmzpzzrzztzzvzzxzzzzezSdzXcz`cRdMqKMqK\ MqJMqJMqIMqIMqIMqHMqHMqGMqGLrFMqGMqGNqHNqHNqIOqIOp\ JPpJPpKPpKQpLQpLRoMRoMRoNSoNSoOSoOTnPTnPUnQUnQUnRV\ nRVmSWmSWmTWmTXmUXmUYlVYlVYlWZlWZlXZlX_kY_kY`kZ`kZ\ `k_ak_ak`bj`bjabjacjbcjbcjcdicdideideieeiefiffhfgh\ gghgghhhhhhhiigiigjigjjgkjgkjglkflkfmlfmlfnlfnmfom\ eonepnepneqoeqoerpfsoernernermdrmdrldqkcqkcqjcqjbq\ ibphbphapgapQEzZQugapnpgooipnkpmlqlnrkprjqsisthuuh\ ythwthvthtshsshqshprgoqgo } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

1 0

Date
by David M Fisher 01 Feb '08

01 Feb '08

Jim, You are a year late with the FOTD. David M Fisher

1 0

FOTD 01-02-08 (One in a Googol [9.9])
by Jim Muth 01 Feb '08

01 Feb '08

FOTD -- February 01, 2007 (Rating 9.9) Fractal visionaries and enthusiasts: Today's image must be seen to be believed. If it's a result of imprecision, which is still a possibility, then imprecision must be considered as a formula for good fractals. BTW, doubling or halving the real(p3) parameter makes a noticeable difference in the purplish pattern filling the minibrot. I did not want to rate today's image at an absolutely perfect 10, so I gave it the next best rating, a penultimate 9.9. As promised, it's a scene in Hyper-East Valley of the HyperMandel- brot set. I named it "One in a Googol" because a perturbation of only one-googolth part of 1 makes all the difference. To see how much difference 1/10^-100 can make, reset the real(p3) parameter to zero. I will not try to analyze today's image, it is far too complex and I'm already mentally congested as it is. I'll wait until the end of the month, when, after a month's exploration, I'll have a better idea of what's going on in Hyper-East Valley. But most likely, even then I'll have little idea of what's going on there. The calculation time of 2-1/2 minutes is quite reasonable for an image that comes so close to perfection. But a simpler way to achieve the near-perfection is to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is posted, and view it there at leisure. Thursday turned out as good as could be expected in this part of the country in midwinter. Lots of sun and light winds made the temperature of freezing quite comfortable. The fractal cats chased each other up and down the hallway until they ran out of energy and settled for a rest in the sunniest spot they could find. Except for the day's fractal discovery, which IMO is one of the most serendipitous of all time, my day was totally average. The next FOTD will appear in 24 hours. Until then, take care, and be as skeptical of rogue fractals as a true-believing skeptic. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= One_in_a_Googol { ; time=0:02:30.03-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot2 center-mag=+0.25874105460425120/-0.001343883319138\ 25/5.553303e+007/1/-162.5/-1.93254204222670367e-007 params=0/0/0/0/1/0/1e-100/0 float=y maxiter=3200 inside=0 periodicity=0 colors=000ZLgjGguCgtDftEftFftGftGftHftIfsJfsKfsKfs\ LfsMfsNfsOfuMssOfqPUoRHmO0nS4nW7p_AreDtjGvpczumrnc\ fdOYUPSLQQFQIBMLBRJESHGSIITKJTMLWOLYQMYSM`UNcVNfWO\ iXPlYRoZUr_Wu`Zxa`yc`zd_zfYtgWqeRocMiaId_F`YCXW9TX\ 6SX3SY7SYASZESZIS_MS_PS`TS`XSa`SacSbgSbkSfoQbnSZpT\ VsVSqWOqXKoZGm_Dk`9ib5gc2edNdbRd`UeZXeX_eVbeTebRh_\ PkXNnUMlSNjRNiQNgONeNNdMObLO`JO_IOYHORDPXGObJNhMMn\ PLtPKrPIqOHoNGnMFlLDkKCiJBhIAfG8eF7cE6bD5`C3_B2YA1\ X90YH2ZO3WW1ZV4`V7bVAdVCfVFhVIkUKmUNoUQqUSsUVuUYwU\ _qSXkQVeOS_MQVKOPILJGJDEG7CE2BC4AF69I88KA7NC6QD5SF\ 4VH3YJ2_L1bL0fM0dM3cN6aNA`ND_OGYOKXPNVPQUORVPTTPVR\ QWPQYNRZMR`KSaIScGTeETfDUhBUi9Vk7Yp2Vl6Sh9PdCQaDRZ\ DSXETUETRFUPFVMGWJGXHHXEHYBIZ9I_6J`3Ja0K`1J_5I_9IZ\ DHYGHYKGXOGWSFWWEVZEUbDUfDTjCQpBTmCVkCYiC_gCbeCdcC\ faDi_DkYDnWDpUDqQ8rSDrUHrWLsYPs_Ts`Ysbatdetfithmti\ qljhdj_YkSQkJIlABl2Ci4Dg6 } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

1 0