July 2007 - Fractint - mailman.xmission.com

FOTD 14-07-07 (Belated Pinwheels [8])
by Jim Muth 16 Jul '07

16 Jul '07

FOTD -- July 16, 2007 (Rating 6) Fractal visionaries and enthusiasts: The parent fractal of today's image was created by combining 10 negative parts of (1/Z) with 2 negative parts of Z^(-5) and then adding (1/C). This parent is little more than a spidery network of radiating shafts, with today's image being located on a spiralling filament extending from a bud near the point where the radiating shafts converge. I named the image "Belated Pinwheels". I have forgotten what inspired such an unlikely name, but it sounds rather enigmatic, so it will remain. The rating of a slightly-above-average 6 shows that I am satisfied with the day's production, but feel that it leaves a lot of room for improvement. The calculation time of 2-1/2 minutes is conveniently brief. Even more convenient is viewing the already-calculated image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The temperature was a bit too warm, the humidity was a bit too high, the sky was a bit too hazy and the threat of rain was a bit too high for perfection here at Fractal Central on Sunday. But it was perfect enough for the fractal cats, who gave up on the chipmunks in the yard, and spent the day chasing each other around the house. My day was lazy. I doubt that tomorrow will be a repeat however. In any case, the next FOTD will appear in 24 hours. Until then, take care, and can a fractal image bring a mystic revelation? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Belated_Pinwheels { ; time=0:02:31.04-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-2.21453853770298400/+1.091584484885334\ 00/1.29646e+007/1/97.5/-2.83378731532474282e-006 params=-10/-1/-2/-5/0/0/0/0 float=y maxiter=2800 inside=0 logmap=220 periodicity=10 colors=0007PU8QN9QGAQ9BR3CQ9DREEQJFRMGQOHRQIQTJQVK\ QXLO_MMaJLbGIdEFeBCf99gBAdDAdFAdHAdJAdLAdNBcPBcRBc\ TBcVBcXBcZBe_Aa`9``8Xa8Zb7Vb6Wc5Sd5Ud4Qe3Mf2If2Fg1\ Bh07h04e53cA3aF2_K2YP1WU1UY1LZ9CZHDXIDWIDUIDTIDRID\ QIHRKKRMNRORRQUSSXSU_SVcUXfUZiZ`mZbpcdscfvcgmegmme\ mmcmmbmm`mmZhjYcmWZrVUvTPwRLwQLwOLwMLvLLrJLmINfNP`\ SQUXSOaTHfVBkW5oYBg_H``MTbSMdYEeb72ly6ksAkmDjgHjaL\ jWOiQSiKViFTeKRbOP_SOWWMT_KQZINYHJaFGeDDiCAmFCjIDg\ KEdNFfPGcSIeVJbXK`_LYaMVwOSwPPwQMwRJwSHwYIwbIlgIll\ IjjKiiLhgNffOeePdcRcbSaaT`_V_ZWZYXLOQ8FJ7JY7MlFOjM\ PiTQh_RgfSfaXgXagSfgNjgIogDtg9xgAwfAvfBufBtfBsfCre\ CqeCpeDoeDneDmeCjgBgiAek9bm8_o8YqH`oQbnZdlgfkohjli\ dij_gkUdlPblKRoSGqZMrVRsRWtN`uKevGjwCwx5oy9hzDazHU\ zKNzOGzS9zVLz_XzcmzngzgjzdbzaVzZNzWFzT8zRAzMCzIEzE\ GzAPzCYzDfzFozGxzJwzHvzFuzDuzCtzAsz8sz7hz9YzAczyNz\ BRzGUzKYzP`zTdzYgza1zg2z` } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 15-07-07 (The Lost FOTD [?])
by Jim Muth 15 Jul '07

15 Jul '07

FOTD -- July 15, 2007 (Rating ?) Fractal visionaries and enthusiasts: Today's image is several months old. It is a curiously interes- ting image, but it has not been posted until now because I lost the parameter information when I saved it in the wrong format. But it can still be viewed on the FOTD web site, where I have already sent it. The fractal object in the image is obviously a distorted version of the Mandelbrot set. The irregular stretching indicates it was created by one of the four-dimensional Julibrot formulas, but I have no idea which formula created it, much less what the parameters might be. I twisted and turned the M-set in four-dimensional space in every way possible. I even used the Fractint explorer/evolver, but I can't even come close to re-creating the particular distortions in today's image. I rated the image as a question, and named it "The Lost FOTD". I have no idea of the calculation time. The image is or soon will be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> It's probably best to give Paul a chance to post the image on the web site before rushing there to see it. Saturday was near perfect here at Fractal Central, so perfect in fact that fractal lady and I decided to spend the day exploring the state park. The fractal cats were a bit cranky when we got back in the evening after we had been gone most all day, but an extra generous treat of tuna and cheddar soon lifted their spirits. The next FOTD, complete with parameter file this time, will appear in around 6 hours. Until then, take care, and be at ease with the mysteries of fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com SORRY, NO PARAMETER FILE===================================

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FOTD 14-07-07 (Straight-Edged Julia [8])
by Jim Muth 14 Jul '07

14 Jul '07

FOTD -- July 14, 2007 (Rating 8) Fractal visionaries and enthusiasts: Today's image is almost a Julia set of East Valley of the Mandelbrot set. But in this case, the word 'almost' means a huge difference. True, the scene is sliced within 1/10th of 1 degree of the true Julia orientation, and the outer shape of the fractal is what would be expected of an 'East Valley' Julia set. But the inside is unlike any Julia set that I have seen. The corresponding Mandelbrot point is located inland very near the edge of a tiny bud on the northern shore of East Valley. The diagonal straight edge is the remains of that shoreline. This edge inspired the name "Straight-Edged Julia". But how can a near circular shoreline become straight? The answer involves a four-dimensional abstraction. But a pretty good analog can be given in three dimensions. Imagine a long cylinder. When this cylinder is intersected by a plane at a right angle, the section is a circle. As the intersecting plane rotates, the section becomes an increasingly stretched oval, until finally, when the plane is parallel to the cylinder, the section consists of parallel straight lines. When a dimension is added, this is what causes the straight edge inside today's fractal, as well as the 'bridges' that appear so often in the four odd orientations of the Julibrot. The irregular disks in the upper left portion of today's image are created by rendering the image with the inside set to 'fmod'. Since I think the image is pretty good and I also enjoy the math part of today's image, I rated it at an 8. The parameter file takes just over 6-1/2 minutes to calculate on my fast fractal computer. On the slow machine it would take around 1/2 hour. But why not avoid calculation and view the image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A near perfect day prevailed here at Fractal Central on Friday, with lots of sun, blue skies, puffy white clouds and a tempera- ture of 81F 27C. A few drops of rain and a couple grumbles of thunder in the evening did not spoil the day. The fractal cats were rather restless most of the day, though I noticed nothing out of the ordinary in the vicinity. My day was about average. With a slow day expected tomorrow, fractal lady and I will likely take a short trip. It probably will not affect the FOTD, but if the FOTD is late, you will know we were late returning to F.C. Until next time, take care, and see the world with 4-D eyes. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= StraightEdgedJulia { ; time=0:06:40.74-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2a passes=1 center-mag=0/0/1.103753/1/-90/0 params=89.9425/\ 90.0832/90.1493/90.0832/0.266/0.0042/0/0/0/0 float=y maxiter=100000 inside=fmod periodicity=10 colors=000cIKeLKgOKiRKkUKmXKo_KqbKseKuhKwkKynIyqHv\ oGsmGpkFmiFjgEgeEdcDaaDZ_CWYCTWBQUBNSAKQAIPAMOCQNE\ TMFXLH_KIcJKgIMjHNnGPqFQoEOnFMlMKkSJhULeWMbYN__PYa\ QVcRSeSPfUMhVKjWHlXEnZBp_8r`6saFl`Oe`XZ`eT`dVacXbb\ Yba_c``c_bdZdeZeeYgfXhfWjgVlhUmhToiTpiXlg`hfceegad\ kYcnVbrRavN`yK_wL`vM`uNatOasOaoXgkdlglqctvbusaupau\ m`uj_vg_veZvbZv_YwXXwUXwSWwPVxMVxJUxGUxEWuFYsGZqH`\ oIamJckKdiLfgMheNicOkaPl_QnYRoWSqUTrSUpSVnSWlTXKdI\ QbMWaPa`TgZXmY`sXcpY`nYZlYWjYUhZSfZPdZNbYL`YIZXGXX\ DVWBTW9RV6PV4NU2QT4TS6WR8ZQA`PCcOEfNFiMzlLznKzqKzt\ KzwKzyKzvKzsKzqKznKzkKziKzfKzcKzaKzZAzW8zU6zPKzLKz\ HKzDKzBKzAKz9Kz8Kz7Kz5Kz4Kz3Kz2Kz1Dz5Ez8FzCGzFHzIH\ zMIzPJzTKzWLzZLzbMzeNziOzlPzoPzcAzTAzPAzMAzJAzGAzD\ KzASzERzIRzLRzPQzSQzWQz_PzbPzf0zi0zm0zp0zs0zw0zu0z\ t0zs0zr0zq0zp9zo9zn8zm7zl7zk0zj0zi0zh0zg0zf0zd0zb0\ z`0zZ0zX0zW0zU0zS0zQ0zO0z } frm:SliceJulibrot2a {; 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|<=real(p5+9) } END PARAMETER FILE=========================================

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FOTD 13-07-07 (Slip-Sliding Along [7])
by Jim Muth 13 Jul '07

13 Jul '07

FOTD -- July 13, 2007 (Rating 7) Fractal visionaries and enthusiasts: For today's fractal excitement I combined 4 negative parts of Z^(-1.3) with 0.25 negative part of Z^(-5.2) and added (1/C). The resulting parent fractal is a north-south string of large bays, with a prominent 'fan' opening east along the positive X-axis. Today's image is located in some fractal debris on the northern outskirts of the fan. Just to be different, I rendered the scene with the outside set to 'tdis' and the inside a brilliant bluish white. I named the resulting image "Slip-Sliding Along", though I have long since forgotten why I chose such an apparently inappropriate name. Despite the awkward name, I rather liked the image, so I decided to rate it at a respectable 7. The calculation time of a little over 2-1/2 minutes on the not-quite-supersonic P4-2000 machine is brief enough for all but the most impatient fractalists. But the impatient and patient alike will be pleased to totally forget such a mundane task as calculating a parameter file. The finished image has already been calculated and has been posted to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it may instantly and thoroughly be enjoyed. A near perfect day prevailed here at Fractal Central on Thurs- day, with blue skies, puffy cumulus clouds, low humidity, and a temperature of 81F 27C. This satisfied all but the hardest to satisfy. The fractal cats, ever easy to satisfy, spent most of the day waiting for the local chipmunks to appear. When the critters failed to show up, the cats satisfied themselves with their faces in their tuna dishes. My day was rather busy, which is why this FOTD is later than normal. Tomorrow will be slower, which can bode only well for the next FOTD, due to appear in 24 hours. Until then, take care, and pleasant dreams of fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Slip-Sliding_Along { ; time=0:02:38.51-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+1.10648424717369200/+1.669336853849603\ 00/267025.4/1/130/1.10968281001599944e-007 params=-4/-1.3/-0.25/-5.2/0/0/0/0 float=y maxiter=2000 inside=255 outside=tdis periodicity=10 colors=000MKOjUIiQHjscjtdiufivgiwhctfZrdUpcPnaU`w`\ ZjgWXnTJvQ5jP5ZN5ZO7ZPAZQDYRGYSJYTMXVPbdUioZbg`V_b\ NSdGKf8Ch04k26h48e6Ab9CZBEWDGTFIQIKMMIMRGNWEN`COdA\ Pi8Pn6Qs3Rlfwl`wlUwkNwkGwj9wdBzYEzSGvLJrEMmBNk8Om4\ Po_CgVFiQIkKLmIVnFepDoqAusFzzKuzQssVpt_ntektjitpfu\ meqicmfbib`d_Z`WYXTWTPUOL_MgRKfUHWyvWstVmrVfoU`mTU\ jSePRq3Sk4Ud5WY6YR7ZL8`E9b7Ad0BsK9nPDiVHd`L_fPVlTQ\ rXLxaLpcMheN`hNSjOKmPCoQ3rQ5pQ7nP9kPCiPEgOGdOIbNL_\ lQXkXZjc`hkbgrdezf`qeWgdRYcMObGE`EVPBkCB`HBQNBETAE\ V9EX7EZ6E`5Eb3Ed2Ef0EiKCSdAAdAAcAAcAAbAAbAAaAAaAA`\ 9APHGCQMJQOQPRXOTcNWjMYqL`yKctLYoMRjOK`OSQP`XPPcOD\ f_Blp8my5ms6ll8keAkZBjSDiLFhEHdJF`ODXTBTZ8VYAXXC_W\ EaVGcUIjRKiQJkOInLHoJGrEFtBEv8Dw4Bu4Bq4Cl4Ch4Dd4E_\ 4EV4FQ4G5ug9mhDeiHYjLQkPIlTAmX1ogQQso0v_7zKFyIDxGA\ vE8uC5s92sC4tG7tK9uOCuSEvWHv_JwcMmiMcoNTvOUsPVpQWm\ RXjSYfUGSNy7hrMXk`LkYKuuz } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 12-07-07 (Zexpe All The Way [5])
by Jim Muth 12 Jul '07

12 Jul '07

FOTD -- July 12, 2007 (Rating 5) Fractal visionaries and enthusiasts: For today's fractal we return to the Zexpe fractal so named by Lee Skinner. We explore it as it appears at a height of epsilon (2.718...) levels up the log ladder. At this slight height the parent fractal resembles a twisted cubic Mandelbrot set with an unusually intricate large bud where the western valley should be. Today's image is located in the east valley of a larger midget on a filament extending from the intricate large bud. I named the image "Zexpe All The Way", which is a reasonably accurate description of it. I rated it at an average 5 because the image is the second Zexpe fractal to appear in the past few days, and repeats never bring fractal satisfaction. The parameter file is lightning fast. It finishes in only 23 seconds on the recently retired but still quite functional P2000 which I am reconfiguring to run Fractint as efficiently as possible. An equally convenient way of viewing the image is to go to the FOTD web site and view it there. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With a temperature of 86F 30C and cloudy skies, the heat was not too bad here at Fractal Central on Wednesday, but the humidity was sky high, which made it as oppressive as the past couple days. The fractal cats ignored the heat but kept watch for the chipmunk or maybe two that have been scampering around the yard for several days now. My day was decidedly busy. Thursday will be the same. The next FOTD will appear in 24 hours. Until then, take care, and don't get lost in fractal complexity. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Zexpe_All_The_Way { ; time=0:00:23.23-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 periodicity=10 center-mag=-1.22969648826291200/+0.345960913903965\ 50/13434.19/1/-70/-4.92854923539454148e-011 params=2.71828182845905/0/2.71828182845905/0 float=y maxiter=1600 inside=0 logmap=32 colors=000eFUfGVgHWhIXiJYjKZkL_lM`mNanOcoPepQgqRir\ SksTmtUpuVsvWvwXxxYzy_z0HCCMKNRRZWZi`eVQWGGMA6DKBE\ UFFcKGhOHmTIrXJvaKzeLzhJscIrYHcNGAIOUDWKHaJLgRPlZT\ rfXwf5lMJMPHQRFTUDWWBZZ9a`7dc5ge4je3ke2me1nVShKrbJ\ naJkaIhaId`Ia`HZ`HW`GS_GP_GM_FJ_FFZECZE9ZE6ZJ5VO4S\ T4PY3Mb2Jg2Gd6LaAQZEUWIZTMcQQgNUlKYqIau9Sj1I_n24k9\ 5hG6eM6bT7__8Xe8UaBSZEQWGOTJMPLKMOIJQGGTEDVOEYYE_g\ EaqEczEeuJdqNdmRciWce_bLr``cbXhaTlaPp`k73bOFUdQqZN\ kbQffS`iUWmXQqZNBeMIdMPcMVbLabLgaLn`5V08_7BcDDgJGl\ PJpVNMZMP_MS_MV_MX_M__Mb_Ld`Lg`Lj`Ll`Lo`Lr`UnPToQS\ oUSpZRpcRphQqmQqrPqvOrzOrzNszNszMszMtzLuzevzawzZxz\ VyzSzzOzzkzzhzzfzzczzazzZzzXzzUzzzzczzbzzazzIzzMzz\ PzzSzzVzzYzzYzzZzzZzz_zz_zz`zz`zzyzzrzzlzzfzzvzzqz\ zmzzhzzdzzczzbzzbzzbzzazzazzazzazz`zz`zz`zzyzzlzzn\ zzmzz8zzBzzEzzHzzKzzNzzQzzRzzRzzRzzRzzSzzSzzSzzSzz\ Xzz`zzczzczzczzczzczzczzc } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100, p=real(p2)+PI q=2*PI*floor(p/(2*PI)), r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 11-07-07 (A Jolly Scene [5])
by Jim Muth 11 Jul '07

11 Jul '07

FOTD -- July 11, 2007 (Rating 5) Fractal visionaries and enthusiasts: I must once again apologize for the lateness of the FOTD. My excuse is that the weather was very hot on Tuesday and I felt lazy. It's really no excuse, but it is the truth. The image that I found when I finally mustered the energy to search is a scene in a valley of the Z^sqrt(2)+C Mandeloid as it appears a meager 1/2 level up the complex logarithmic hyper- spiral. This formula is one of my favorites. It is not as rich as its square, the classic Mandelbrot set, but there is only one fractal that can be generated by the formula Z^2+C, while the formula Z^sqrt(2)+C creates nearly an infinity of fractals, all different yet all strangely the same. I'll not try to describe the parent fractal, since it is so easily generated, but the image I found within it rather reminds me of a gala event, which inspired the name "A Jolly Scene". The rating of an average 5 says very little about the image. I did not put enough work into it to rate it any higher, and this type of image has been posted as the FOTD so many times that it has become hackneyed. The parameter file takes 9-1/2 minutes to run on the fast computer. On the slow machine it would take 45 minutes to finish. For convenience the parameter file has been calculated and posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With a temperature of 97F 36C and oppressive humidity here at Fractal Central, Tuesday was a day to be ignored. And indeed the fractal cats did ignore it. They concerned themselves with the chipmunks (I think there are two of them) that have been running around in the back yard grass. I concerned myself with work first and fractals second. The result speaks for itself in the parameter file. As always, the next in the series of FOTD fractals will appear in 24 hours. Until then, take care, and wait with bated but not abated breath. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Jolly_Scene { ; time=0:09:29.97-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=-0.11710695179565920/+1.315337975141092\ 00/6925.211/1/45/9.0035527644527491e-011 params=1.4142/0/0.5/0 float=y maxiter=8000 inside=0 logmap=549 periodicity=10 colors=000S8CQ9DOAELBFJCGGCHEDICEJ9FK7GL5GM7JO8MP9\ PRASSBVUDYVE`XFbYGe_Hh`TkbYnccrecufewhbxi_ujXqjXnj\ WjjVfjXcjY_j_Wk`TkaPkcLkdIkfEkgAkj8oh7kf6gd6cb5_`4\ W_4SY3OW2KU2GS1CR19Q1AP1AP1AO1AN1BN1BM1BL1BL1BK1CJ\ 1CJ1CI1CI1CH1DG1DG1DF1DE1EE1ED1EC1EC1EB1FA1FA1F91F\ 91FB3GD5HE6IG8JH9KJBLKCMMENNFOPHPQIQSKRTLSVNTWOUYQ\ VZRW`TX_EIaUXcijexxgtthqqjnmkkjliilghlfgldglcflael\ `dlZdlYclWblValTalS`mQ_mPZmNZmMYmKXmJWmHWmGVmEUmDT\ mBTmASm8Rq2Pm7RiBTeGVaKXYOZUT`RXbNadJefFihBnj7rl4v\ n6to8soAroCpoEopGnpIlpKkpMjqOhqQgqSfqUdrWcrYbr_`ra\ _scZteXwggzi`zkTwmStnRtlQskQsjQsiQshQsgQsfQseQsdQs\ cPsbPsaPs`PsZPsYPsXPsWPsVPsUOsTOsSOsROtQOuPOvOOwNO\ xOPyMQzLRzJRzISzHTzFUzEVzDWzBXzAYz9ZzA_zC`zEazGbzI\ czKdzMezOfzQgzShzUizWjzYkz_lzamzcmzemzgmzimzkmzmmz\ mmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmm\ zmmzmmzmmzmmzmmzmmzmmzmmz } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100, p=real(p2)+PI q=2*PI*floor(p/(2*PI)), r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 10-07-07 (Gateway Aside [4])
by Jim Muth 10 Jul '07

10 Jul '07

FOTD -- July 10, 2007 (Rating 4) Fractal visionaries and enthusiasts: Today's image is another unfamiliar side view of the prominent north valley of the Mandelbrot set. It is sliced in a different direction and the slice is centered at a different point, but the valley still appears as a narrow slit. It may seem surprising that the valley still appears as a slit when such a different slice is made of it, but we must remember that the whole valley is a four-dimensional thing, and the sharp edges of it are actually two-dimensional surfaces, making the ways in which it can be sliced nearly infinite. Yes, I realize that it makes no sense to think of a flat surface as being sharp, but in 4-D space this is true. The cutting edge of a 4-D knife would be a flat surface of 2 dimensions. I could rate today's image no higher than a 4. It actually might be a little better than yesterday's everyday slice of the north valley, but it is the second consecutive view of the same thing, which knocks a point or two off its rating. I named the image "Gateway Aside" since it is a side view of the gateway to the north bud. The calculation time of 1-3/4 minutes is well within reason. In fact, it is almost as reasonable as taking a trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the completed GIF image there. A high temperature of 97F 36C made Monday unpleasant here at Fractal Central. The cats noted how hot it was on the other side of the window, then turned their attention to a chipmunk scampering through the grass in the yard. My day turned busier than expected when two small but unexpected jobs came in, but the rush vanished when fractal lady pitched in to help. The day ended with me finding the fractal that passes for today's FOTD. The next FOTD fractal will likely appear in 24 hours. Until then, take care, and live every minute. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Gateway_Aside { ; time=0:01:42.05-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new periodicity=10 center-mag=-1.55118/0/3.057878/0.4822/0/-23.863381\ 4029281019 params=0/152/2/0/-1.141/0.273/-0.12499/\ 0.649525 float=y maxiter=25000 inside=255 logmap=4 colors=000iOKhPLgQMfRNeSOdTPcUQbVRaWSaWT`XU_XVZYXY\ ZYYaZXd_Wg`VjaUmcUjdTgeSdfRcgTclRchPaeO_bMY_KWXJUU\ HSQFQNEOKCMHAKEAJ99IB9ID9IE9IG9IH9HJ9HL9HM9HO9HP9G\ R9GT9GU9GW9GX9GZ9F`9Fa9Fc9Fd9Ff9Eh9Ei9Ek9El9En9EoI\ QrQatYmvexxduxdsxdpxdnxdlxcixcgxcexcbxc`xbZxbWxbUx\ bSxbPxaNxaLxaIxaGxaEx`Bx`9x`7x`4x`2x`0xZ5wX9wWEvUI\ vTNvRRuQVuO_uMctLctJctIcsGasF_sUYhUYZUYMUYPUYRUYTU\ YVUYXUYZUY`UYbUVdUSfUOhULjTHlREnOBpM7rJ4tG0wH1vI1v\ J1vJ1uK2uL2uL2uM2tN2tN3tO3sP3sP3sQ4sR4rR4rS4rT4qU5\ qU5qV5qW5pW6pa6pb6ob6oc6oi7oi7nj7nk7nq8op7no7mn7lm\ 7kl7jk7jj7ii6hh6gg6ff6ee6ed6dc6cb6ba5a`5`_5`Z5_Y5Z\ X5YW5XW5XV6YV6YU6YU6ZT6ZT6ZS6_S6_R7_Q7`P7`O7`N7aM7\ aL7aK7bJ8bI8bH8cG8cF8cE8dD8dC8dDBbDEaDG_DJZDMXDOWD\ RUEUTEWREZQEaOEcNEfLEhKFiLGiLKiMUiMciMejNgjNijNkjO\ mjOokOqkPskPukPvkQwlQxlQylRzlRzlRzlQzlPzlOzlOzlNzl\ MzlLzlLzlKzlJzlIzlIzmJzpK } 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 PARAMETER FILE=========================================

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FOTD 09-07-07 (Gateway to the North [5])
by Jim Muth 09 Jul '07

09 Jul '07

FOTD -- July 09, 2007 (Rating 5) Fractal visionaries and enthusiasts: Yes, the FOTD is a little late again today. I decided to take it easy on my day off. But a fractal was found, and here it is, better late than never in all its semi glory. I named the image "Gateway to the North". Actually, that's what it is. In today's image we have a side view (from above) of the valley of the large north period-3 bud of the Mandelbrot set. I found little in the image that I could consider above average, so I rated it at an average 5. The image is not a perturbed Mandelbrot set, nor is it a Julia set. It is an oblique slice of the 4-dimensional Julibrot figure. The actual orientation, as shown by the imag(p1) para- meter, is about 1/3 of the way from the Parabolic orientation toward the Elliptic. A good bit of stretching in the vertical direction was necessary to give the image reasonable proportions. Almost all of the 3-minute calculation time is spent calculating the few lines in the center that consist of 'inside' stuff, where the calculation almost comes to a halt. This slowness is due to the extreme maxiter of 350,000. As always, the image is or soon will be posted on the FOTD web site for instant viewing. The FOTD web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather was a bit too warm to be absolutely perfect here at Fractal Central on Sunday. But it came pretty close to perfec- tion. Much sun and a temperature of 93F 34C made water sports the activity of choice. For the fractal cats, the activity of choice was sleeping and eating. My day was notably lazy, which I hope does not show too much in the fractal. The next FOTD will appear in 24 hours. Until then, take care, and ease that stress with a fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= GatewayToTheNorth { ; time=0:03:09.88-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=1 center-mag=0/0/4.65/0.3987 params=0/32/2/0/0/0/\ -0.12499/0.649525 float=y maxiter=350000 inside=0 logmap=4 symmetry=yaxis periodicity=10 colors=000iOKhPLgQMfRNeSOdTPcUQbVRaWSaWT`XU_XVZYXY\ ZYYZZX__W_`V`aUacUadTbeSbfRcgTdlRchPaeO_bMY_KWXJUU\ HSQFQNEOKCMHAKEAJ99IB9ID9IE9IG9IH9HJ9HL9HM9HO9HP9G\ R9GT9GU9GW9GX9GZ9F`9Fa9Fc9Fd9Ff9Eh9Ei9Ek9El9En9EoI\ QrQatYmvexxduxdsxdpxdnxdlxcixcgxcexcbxc`xbZxbWxbUx\ bSxbPxaNxaLxaIxaGxaEx`Bx`9x`7x`4x`2x`0xZ5wX9wWEvUI\ vTNvRRuQVuO_uMctLctJctIcsGasF_sUYhUYZUYMUYPUYRUYTU\ YVUYXUYZUY`UYbUVdUSfUOhULjTHlREnOBpM7rJ4tG0wH1vI1v\ J1vJ1uK2uL2uL2uM2tN2tN3tO3sP3sP3sQ4sR4rR4rS4rT4qU5\ qU5qV5qW5pW6pa6pb6ob6oc6oi7oi7nj7nk7nq8op7no7mn7lm\ 7kl7jk7jj7ii6hh6gg6ff6ee6ed6dc6cb6ba5a`5`_5`Z5_Y5Z\ X5YW5XW5XV6YV6YU6YU6ZT6ZT6ZS6_S6_R7_Q7`P7`O7`N7aM7\ aL7aK7bJ8bI8bH8cG8cF8cE8dD8dC8dDBbDEaDG_DJZDMXDOWD\ RUEUTEWREZQEaOEcNEfLEhKFiLGiLIiMKiMMiMOjNQjNSjNUjO\ WjOYkO_kPakPckPhkQmlQrlQvlRzlRzlRzlQzlPzlOzlOzlNzl\ MzlLzlLzlKzlJzlIzlIzlHzlG } 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 PARAMETER FILE=========================================

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Re: Queshun
by jackoftradez＠comcast.net 08 Jul '07

08 Jul '07

. I just purchased ubuntu linux; I am going to buy a new system soon (there will be 6 PC's in my house now) and as soon as I get it, format the HD to lose vista f'n shmista, and install dual boot with Win XP and Linux. I am doing this cause I wanna learn Linux and hopefully dump MS altogether eventually. Queshun is: Is XFractint (fractint for linux) as good as DOS fractint? Anyone here have experience with it? How does it compare? Assuming I develop confidence with linux (of course), is it worth it to use xfractint then or should I continue with DOS? Any comments welcome. Thanx. JoTz .

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FOTD 08-07-07 (Zexpe Minus Zexpe [6])
by Jim Muth 08 Jul '07

08 Jul '07

FOTD -- July 08, 2007 (Rating 6) Fractal visionaries and enthusiasts: The Mandeloid that is created by the formula Z^(epsilon)+C is known as the 'Zexpe' fractal. It was given this name by Lee Skinner about 15 years ago. In today's fractal I have added to the 'epsilon' aspect by calculating the formula as it appears epsilon levels down the logarithmic ladder. I'll not describe the overall shape of the parent fractal, since it is quite easily created, but I will tell that today's scene is located very near the negative X-axis, in the area where the fractal splits apart. I named the image "Zexpe Minus Zexpe" and rated it at a 6. The calculation time of a very brief 34 seconds is true on the P2000 machine. It would be difficult to go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the image there any faster than this. A perfect summer day prevailed here at Fractal Central on Saturday. The blue skies, cooling winds, low humidity and a temperature of 84F 29C were perfect for any outdoor activity. Unlimited fractals made conditions pretty good indoors also. The fractal cats enjoyed the fractals, then asked for their treats. The next FOTD, whatever it may be, will appear in 24 hours. Until then, take care, and if an absolute vacuum is nothing, can it then be said that 'nothing' has an existence? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Zexpe_Minus_Zexpe { ; time=0:02:10.72-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=-0.67800738206661360/-0.001884972090448\ 18/2.453478e+012/1/112.364403452269812/0.145951271\ 887285572 params=2.71828182845905/0/-2.71828182845\ 905/0 float=y maxiter=650 inside=0 logmap=46 periodicity=10 mathtolerance=0.05/1 colors=000cplamn_jpYgrWdtUavSZxRWzPTxOSvMRtLQrJPpI\ OnGNlFMjDLhCKfAJd9Ib8H`BHXDITGIPIJLKJHNKDPK9RU6OcC\ LmIhwLzzPhzUZtYdobjvfimiieliYoiQriItfJndJhaJc_KYXK\ SVKNZOOaSPeWPh_QzbRzfRzjSznTzqTzhXz__zRbVIeN9hG1kD\ 2eB3_84V65P36J16E1AH1EJ1IL1LN1PP1TR1XT1_V1cX1gZ1j`\ MiTfhM`cTWZ_QUfLPmGTtKVuPWvUXwZZxc_yh`zmbzrczvdzzL\ zzPzzSzzVzzYzz`zzczzfzzizzlzzozzkzzhzzezzazzZzzWzz\ SzzPzzMzzJzzRzzPzzNzzLzzJzzHzzFzzDzzCzzFzzIzzKzzNz\ zQzzSzzVzzXvz_rzbmzdhzgcziZzhUzfPzeKzdFzcEzcFzcFyc\ FxcKwcPwcTvcYucbucfsccqcapcZncXmcUkcSjcPhcNfcKecIc\ cFbcD`cA_c8TcAMcBGcC9cD3cE8cIDcLIcPNcSRcVTcXUcYVcZ\ Xc`YcaZcb`cdacebcfUccLcaCcZ3cX2cZ2c_1da1eb1fd0ge0h\ g0ih4ji7kjBlkEmkInlLomPpnSqnWroZspbtqeuqavnZwkVxhS\ yfOzcLz`IzYEzWBzT7zQ4zN1zL9zIGzFNzDUzAaz7hz5oz2vz0\ wz2wz4wz6wz8wzAxzCxzExzGxzIxzKvzOuzRtzVszYrzaqzdpz\ hozknzomzrmzpQzVhzefzgdzi } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100, p=real(p2)+PI q=2*PI*floor(p/(2*PI)), r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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