October 2005 - Fractint - mailman.xmission.com

Re: [Fractint] quaternion product correction
by Russell Walsmith 03 Nov '05

03 Nov '05

Tim, Your mention of POVRay (below) inspires me to inquire if Fractint can be enabled to provide the kind of looks at 3D objects such as are seen in this 'T-set' video at http://ixitol.com/html/videos.html This object, rendered in POVRay, is generated by the formula T-set { x=real(pixel), y=imag(pixel), v=p1 x1=y1=v1=0: a = x1^2 + 2*y1*v1 b = v1^2 + 2*x1*y1 c = y1^2 + 2*x1*v1 x1 = a+x, y1 = b+y, v1 = c+v z = x1^2 + y1^2 + v1^2 z < 100 } Perhaps it is a function of my still limited familiarity with Fractint, but thus far only 2D slices of this object have rendered therein, and those views only in planes perpendicular to one of the three axes. Does Fractint offer functionalities in this respect of which I am yet unaware? If not, would it be possible perhaps to port over some of the pertinent POVRay code? It would be awesome if this kind of 3D imaging were possible "in house". Ciao, Russell ----- Original Message ----- From: "Tim Wegner" <twegner(a)swbell.net> To: "Fractint and General Fractals Discussion" <fractint(a)mailman.xmission.com> Subject: Re: [Fractint] quaternion product correction Date: Tue, 25 Oct 2005 21:13:27 -0600 > > More concerning my correspondence with Wes Loewer. > > One of the things that attracted me to Hypercomplex numbers was that > there is a general way to calculate a function on the hypercomplex > numbers from the analogous complex function. Wes showed me how to do > the same thing with quaternions. It isn't quite as elegant, but it's > not hard. This means I could add fractal types quaternion and > quaternionj that are exact analogues (with equal generality) of the > hypercomplex and hypercomplexj types. (These are general because they > use a function variable that can be set to a variety of analytic > functions.) There are some quaternion types already in fractint but > they are less general. > > I guess I should check out POVray also for the same generalization > possibility. > > I'm enjoying the possibility of this project since I haven't > contributed any code to fractint for a long time. Jonathan has been > holding down the fort by himself. > > Tim > > > _______________________________________________ > Fractint mailing list > Fractint(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint

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Fractint Mail List?
by Vortex Swirling 31 Oct '05

31 Oct '05

Distribution seems to be working, but if you try the link to the archives it still is page not found. I guess they are doing work on it as they say. -- No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.1.361 / Virus Database: 267.12.5/149 - Release Date: 10/25/2005 -- No virus found in this outgoing message. Checked by AVG Free Edition. Version: 7.1.361 / Virus Database: 267.12.5/149 - Release Date: 10/25/2005

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FOTD 31-10-05 (Julia Variation-8 [5)
by Jim Muth 31 Oct '05

31 Oct '05

FOTD -- October 31, 2005 (Rating 5) Fractal visionaries and enthusiasts: It's Halloween here at Fractal Central, the day when ghosts come alive. Of course ghosts can not come alive. They are firmly dead. Skeptics who have never seen a ghost do not believe in them. They know that ghosts are entertaining figments of the imagination. Those who have seen a ghost do not need to believe. They know that ghosts do exist. Those who watch all the TV reality shows about hauntings don't know what to believe. My own opinion is that where there is such a widespread belief in ghosts, there must be something other than the currently understood and accepted psychological phenomena involved. This might or might not be actual disembodied spirits. And after today's image we might have a few more believers, for a kind of toy vampire-like ghost lies spreading its cape near the center of the scene. It is the blackest part of the fractal, and decorated by a pair of greenish, demon-like eyes. The image shows a Julia set of the Z^(1.618)+C Mandeloid as it appears 16 levels down the hyperspiral. The image consists partly of normal outside stuff and partly of inside stuff made more interesting by the 'bof61' inside fill. Unable to decide whether I like the image, I have rated it at a 5. The render time of 1-3/4 minutes is fast enough for all but the most impatient. The impatient can find relief for their impatience on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Warm sun, gentle breezes and a temperature of 66F 19C made the cats' day quite enjoyable here at Fractal Central on Sunday. They spent the entire afternoon lurking in the holly bushes, watching for something that never came. My day was reasonably good. Today is starting sunny and chilly, but another quick warm-up is expected. Until the next FOTD appears in 24 hours, take care, and fractals are good for the spirit. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Julia_Variation-8 { ; time=0:01:43.88--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=JuliaBC center-mag=0.0839311/0.0751566\ /0.9861933 params=1.618034/0/-16/0/0.0151917/-0.17\ 77604/0/0 float=y maxiter=255 inside=bof61 periodicity=10 colors=000KDg000QDITDHWHGZLFaOEdSDhWCiZCkXFiVIhTLg\ SOfQReOUdNXcL_aJb`He_GhZEkYCnXBqW9tV7wU6yS5xR5wP4v\ O4uM4tL3sJ3rI2qG2pF2oD1nC1mA0l90k80jMDi_Qimain`jn_\ kn_loZmoZnoYopXppXppWqqWrqVsqUtrUurTvrTvqSwpSwpRwo\ RxnRxnQxmQymPylPykPzkOzjOzjOzgPyePxcQxaQw_RvYRvWRu\ UStSStQTsOTsMTrKUqIUqGVpEVoCVoAWn8Wm6Xm4Xl2XlLURNW\ SOXTQZUR_VS`WVZXXYXZXY`WYcUYeTZgSZiR_lP_nO_pN`rM`t\ L`pOZlQXhSVdVU`XSXZQT`PUYQUWRVUSVRSWPTWNUXKUXIVYGW\ YEXZBXZ9Y_7Z_4Z`2_`0``0`i8iqHroKmmNilPejS`iUXgXTfZ\ PgWQhUQiSQjQQkNRlLRmJRnHRoFRe_HXs8VpETnJRlOPiUNgZL\ ecJchH`nFZsDXxBVzDXzEYyGZxH_vJauKbsMcrNdpPfoQgmShl\ TijUjiVigVifVhdWhcWgaWg`WgZXfYXfWXeVYeTYdSYdQYdPQl\ bJspMrmPqkSphUpfXoc_naanZdmXglUilShkUhkVhjWhjYgjZg\ i_giagibfhcfhefhffggfgiefjefkefmeendeodeqddrddsddt\ YjvRoxLtyMquNnrOknOhkPehQbdQ_aRXYSUVSRSTOOULLUJISG\ JREJPCJOAJN7K2Cg0Dj0Dm0Dp } frm:JuliaBC { ; Formula by Andrew Coppin e=p1, p=real(p2)+PI, q=2*PI*floor(p/(2*PI)), r=real(p2)-q, C=p3, Z=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|< p4+100 } END PARAMETER FILE=========================================

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FOTD 30-10-05 (Julia Variation-7 [6)
by Jim Muth 30 Oct '05

30 Oct '05

FOTD -- October 30, 2005 (Rating 6) Fractal visionaries and enthusiasts: Today's fractal is a Julia set of the Z^(1.618034)+C Mandeloid as it appears 2 levels up the abstract spiral. The exponent of Z marks the first 7 digits of the irrational number phi, which continues as 1.61803398874989484820458683436563811772... This number is the value of the 'golden ratio'. It is also the square root of 5, plus 1, divided by 2. The golden ratio has a strange way of appearing in the proportions of geometric figures when least expected. Unfortunately, the number appears to lose much of its strangeness when used as an exponent of Z, but it still makes some interesting images. This is the seventh in the current series of branch-cut Julia variations. The eighth and final variation will appear as tomorrow's Halloween day FOTD. For the month of November I will start a new theme, though I have not yet decided what it will be. When rating today's image, I was prepared to give it a rating of 7. But then I noticed some clashing colors and dropped it to a 6, which is still an above-average rating. The render time of 1 minute is true on my old P200 warhorse with 16mb of memory, which probably gets more use than the P4-2300 machine with 1gb of memory that I use for the graphic design work. As has been the case for over 8 years, the completed GIF image is available for viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Ample sunshine graced Fractal Central on Saturday, but chilly temperatures and a cool breeze made things a bit too cold for the fractal cats. After spending 1/2 hour in the holly thicket, they decided it was better to sit on their window shelf watching the birds fly by than to go out and actually try to catch them. My day was slow enough to be enjoyable but not so slow that boredom became a factor. Today is starting sunny and chilly, with a fast warm-up forecast. The duo should approve. The next FOTD will appear in 24 hours. Until then, take care, and why are some very important questions impossible to answer? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Julia_Variation-7 { ; time=0:01:00.48--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=JuliaBC center-mag=0.0593088/-0.150193\ /1.173709/1/-127.5/-1.23373533611470521e-014 params=1.618034/0/2/0/0.02938/0.23769/0/0 float=y maxiter=1000 inside=bof60 periodicity=10 colors=000rZzqYzpXzoWzlVziUzfTzdSzaRzZQzWPzUNzRLzO\ JzLHxJFvGIrDLnAOh8RcCUZFWUIYPLaKOeFSiDVmCYqB`uAcy9\ sjgqecp`_nWWkSShNOeIKcEGa9C`48_04Y37Y59X7BW9DUCGTE\ IQGKNIMJKOGNRCPT9RV5TX2VZ3TX4RW5QU6OT6NR7LQ8JO9INA\ GLAFKDIQGLVJO`MRePUkRWpOXkLXfJYbGYYDZUBZP8_L5_G3_C\ CXDLUETRFaOGiLHV_AGn3IeIKYWMQiNIwQJtTKrWLpZMnaNkdO\ ifPgiQelRcoS`rTZuUXxVVzVTpLifBzTLlGVZ3dL3fL3hL3iL3\ kL3mL3nL2pN2rP2tQ5sT7sV9sXBsZDs`FsbJobNkbRgbVcbZ_b\ bWbfSbjObnKboPZpUWpZTqcPrhMrlJsmNsnQtoUtpXuq_urcvs\ fvtivsjvrjvqjvpjvojvnjvnjvmjvljvkjvjjvijvijrhenhaj\ hYfhUchQ_gMWgISgEOgALg6Nh9OiCPiFRjHSjKTkNUkQWlSXlV\ YmYZm_VjZSgZOdZLaZHZYEWYATY7RYoL1jS4eZ6`e8WlARsCNy\ EQrHSlKUfNW`QZUT`OWbIZdC`XBeQBiJAmCAqOFm_KikPevTau\ UcuUduUeuUguUhtUitUktVltVmtVosVpsVqsVssVtsVurYoq`i\ pbcoeYngTmjNlmHkoBjr5jt0AJvPcebxPatL`pH`mEdYhiWjmU\ lqSnuQpyPrwSnvUjuXftZbsaZ } frm:JuliaBC { ; Formula by Andrew Coppin e=p1, p=real(p2)+PI, q=2*PI*floor(p/(2*PI)), r=real(p2)-q, C=p3, Z=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|< p4+100 } END PARAMETER FILE=========================================

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quaternion product correction
by Tim Wegner 29 Oct '05

29 Oct '05

This correction is way too long in coming, I hope it didn't mess anyone up. I have been corresponding with Wes Loewer, Fractint's arbitrary precision author. He is teaching math and physics in Nairobi, Kenya at Rosslyn Academy (http://www.rosslynacademy.com) which is an American curriculum K-12 school. We passed along this correction, which I have verified. In any case, it turns out that the formula for the quaternion product in both the Fractint docs and Fractal Creations 2nd Edition is wrong. The current (wrong) formula for quaternion (x,y,z,w) is: q1q2 = 1(x1x2 - y1y2 - z1z2 - w1w2) + i(y1x2 + x1y2 + w1z2 - z1w2) + j(z1x2 - w1y2 + x1z2 + y1w2) + k(w1x2 + z1y2 - y1z2 + x1w2) The correct formula is: Then q1q2 = 1(x1x2 - y1y2 - z1z2 - w1w2) + i(y1x2 + x1y2 - w1z2 + z1w2) + j(z1x2 + w1y2 + x1z2 - y1w2) + k(w1x2 - z1y2 + y1z2 + x1w2) Fortunately, this multiplication function isn't coded up in fractint anywhere, and as far as I know, none of the quaternion fractals is wrong. (At this point if they WERE wrong I'd leave them as is for backwards compatibility.) Also fortunately, the hypercomplex formulas in the documentation and in the code appear to be right. Clyde Davenport's book on hypercomplex numbers is now online. This was my main source on hypercomplex numbers. The link is: http://home.usit.net/~cmdaven/cmdaven1.htm A useful link that includes formulations of some analytic functions of the quaternions that would probably be suitable for fractal implementations (maybe even in fractint) is: http://world.std.com/~sweetser/quaternions/intro/tools/tools.html Tim

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FOTD 29-10-05 (Julia Variation-6 [6)
by Jim Muth 29 Oct '05

29 Oct '05

FOTD -- October 29, 2005 (Rating 6) Fractal visionaries and enthusiasts: An unexpected job came in yesterday afternoon, so I have little time to write today's discussion. I grew bored with the (sqrt(2)) sets, so today's image is a view of a Julia set of the Z^(1.2)+C Mandeloid as it appears 2 levels up the spiral. It is worth a rating of 5, at least in my opinion. For some reason it reminds me of a Trilobite fossil, though I have not given it any special name. The image was rendered in the normal manner, with the exception of the small amount of inside, which was set to 'bof60'. Since the image is at a very low magnitude, it is a very fast one, rendering in less than one minute. And even better, the finished image will soon be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Despite ample sun it stayed quite chilly here at Fractal Central on Friday. The fractal cats, who do not like chill, were outside only 35 minutes. They spent the rest of the day on their shelf by the window, wishing it were warmer out there. My day was uneventful. This morning is starting with clouds and equally chilly. I expect the cats will once again have a short outing. If all goes well, the next FOTD will appear in 24 hours. Until then, take care, and could it be that something is wrong with the universe? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Julia_Variation-6 { ; time=0:00:55.26--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=JuliaBC center-mag=0.328134/0/1.046414 params=1.2/0/2/0/-0.103/0/0/0 float=y maxiter=1000 inside=bof60 logmap=yes periodicity=10 colors=000SSWNPXIMZDJ_8Ga4Db3Ea3Ea3E`3E`3F_3F_3FZ3\ FZ3GY3GY3GX3GX6KW9OWCSVEWVH_UKcUNgTPkTSoSVsSXvSYsW\ Yp_YnbYkfZiiZfmZdpZatZ_w``vb`udatfatgbsibrkcrmcqod\ ppdoreotenvfmwfmqcnlang_obXoYVpTTpOQqJOqEMq7ymBqgF\ jbJcXMXSQQMUJHXCCYEHZFM_GQ`HVaI_bJccKhdLmdMqcNrbOs\ bPtaQu`Rv`SwUYwObwIgwClwBgtAbrAYp9Tn9Ol8Jj8FhETfGS\ ZISSKSKMSDNS6KR5GR5CR48R44R31R38FWF3wPArZHmgNhiQij\ SjkVkmXkn_loampdnrfnsiotkpumpon_inJgkKehKdeKbcK``L\ _YLYWLXTLVQMTOMSLMQIMPGMN99Y5Ih2Run7rkBpiEnfHldKja\ Nh_QfYTdVXbT_`QbZOeXLhVJkTHnQCsN7wUDh_JUePFkV0hY4e\ _8cbC`dGZfKWiOTkSRnWOp_MrcQogUlkYinafrecvh`yj_rlZk\ mYeoXZpWSrVMsUFuT8vT2tOBsJJrERq9ZpDYpGXoJXoMWoPWnS\ VnVUmYUm`TmcTheUdgU`iUWjUSlUOnVKpVFqVBsV7uV3vV9wWE\ wWKwXPwXNtVMqTLoSKlQIjOHgNGeLFbJE`IFbFGdCHf9Ih6Jj3\ Jk1RiBYgLeeVldcjgYiiSgkMfmHdoBcq5bs0dr1fr1hr1jr1lr\ 1nr1or1qr1sr1RXXTWWVWVXWU } frm:JuliaBC { ; Formula by Andrew Coppin e=p1, p=real(p2)+PI, q=2*PI*floor(p/(2*PI)), r=real(p2)-q, C=p3, Z=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|< p4+100 } END PARAMETER FILE=========================================

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FOTD 28-10-05 (Julia Variation-5 [7)
by Jim Muth 28 Oct '05

28 Oct '05

FOTD -- October 28, 2005 (Rating 7) Fractal visionaries and enthusiasts: Today's image, the 5th in the Julia variation series, is more of a human production than a part of the world of math. I rated it at a 7, but only around 5 of those points are in the mathemati- cal part, which is merely a large open area with ragged edges. The other 2 or so points were earned by me when I rendered the image with the flat black 'inside' set to 'bof60', and did the coloring. The image is a Julia set of the Z^(sqrt(2))+C Mandeloid as it appears at zero level of the BC formula. Most of the features consist of 'bof60' inside fill, which works best with the inside part of this fractal. Only a small part of the 256 possible colors of the GIF palette actually appear in the image, but despite this the image seems quite fully colored. With a render time of under one minute, the image is a fast one. Equally fast is the download from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The partly cloudy skies and temperatre of 54F 12C were pleasant enough for the fractal cats to enjoy several hours in the holly patch on Thursday. The day was un-notable for me. Today is starting with some clouds and quite chilly. The cats will need their fur coats. The next FOTD will arrive in 24 hours. Until then, take care, and where is the ultimate source of fractals? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Julia_Variation-5 { ; time=0:00:57.29--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=JuliaBC center-mag=-0.056338/-0.062630\ 5/0.9692117 params=1.414213562373/0/0/0/-0.0948\ /-0.1863/0/0 float=y maxiter=1000 inside=bof60 logmap=yes symmetry=none periodicity=10 passes=1 colors=000075066057348739A2AF6AK9AOCATFAXIAaLAeOFi\ UKl_PpeUsgZwiczlhzomzrtzuwzxzzzzzzzzzzzzzzzzzzzzzz\ `0meQPhRXGiAWl5abGdgBgk6nhTllFH5vPHgWTUcdFvyjsvZpt\ OmqCyxdfuhD9DUV7ivRjsIjq9Fw_NuRVsIbq92sZFZsQd``jJT\ qH1wJHtDWq7exnNeEtH_oZI4tMDvyUrV_aBeh6XJl`S`c_PggD\ ei`afZZdWWbTS_RPYOLWLITJERGBPD8NBBP9ER8HS7KU5NV4QX\ 3TY2W_3Z`4aa4db5gd6je6mf7pg7nh9liAjjCikDglEemGdnHb\ oI`pKZqLYrMWsOUtPTuQqL6cWYdYZdZ_d`_ea`ec`edaffafgb\ fhcgjcgkdgmdhnehpehqfhrfjtakuYlwTmxPeO8cPAbPCaPE_P\ GZQIYQKWQLVQNURPSRRRRTQRVPRWRXRTaNVgIXlEZqAbiEeaIh\ ULkMPnETq7WkCVeHV_MVURVOWVJ`VIaUHbUHcUGdUFdTFeTEfT\ EgTDgSChSCiSBjSBjSHlVMnXRo_Wqa`rcftfkvhpwkuymzzowu\ ntqnrmmohmmdmj`lgWleSkbOk`KkbJjcIidHhfGhgFghEfiDfe\ KebRe_YeXdeUkeRreOxeRseToeVkeYfe_beaZedUefQehMekHe\ mDeo9eq5epBcpGapM_pRZoXXoaVogTolSkiShfSecSa`SZZSWW\ STTSPQSMNSJLSGISCFS9CS69S } frm:JuliaBC { ; Formula by Andrew Coppin e=p1, p=real(p2)+PI, q=2*PI*floor(p/(2*PI)), r=real(p2)-q, C=p3, Z=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|< p4+100 } END PARAMETER FILE=========================================

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FOTD 27-10-05 (Julia Variation-4 [5)
by Jim Muth 27 Oct '05

27 Oct '05

FOTD -- October 27, 2005 (Rating 5) Fractal visionaries and enthusiasts: Today's image looks somewhat like a nuclear explosion. It is actually a picture of the Julia set of the Z^(1.25)+C Mandeloid as it exists only one level up the spiral. Or perhaps I should say 2.14159... levels down the spiral. The number PI works better as a ground level. The interesting Julia sets that can be created with the JuliaBC formula are very easy to find and they are literally endless in number. And, as today's 24-second render time shows, they are lightning fast. I'll post a few more low-order Julia sets before returning to the hoard of old, forgotten, mostly useless formulas. I want to check the Julia sets of a few of the square-root-of-two Mandeloids. Since today's fractal basically found itself, I could rate it no higher than a 5. The name merely indicates that it is the fourth in the series of similar images. (The first in the series was not an FOTD.) For the convenience of those with over- qualified computers, the completed image is available on the FOTD web site, which may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A chilly blustery day Wednesday produced just enough sun to keep the cats in a neutral mood as they lurked in the yard. With the work still caught up, my mood was good. Today is starting sunny but chilly, leading me to expect another marginal day for the cats. The next FOTD will appear in 24 hours. Until then, take care, and be with it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Julia_Variation-4 { ; time=0:00:24.06--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=JuliaBC center-mag=-0.0612658/0.043239\ /0.3908483/1/-90/3.88578058618804789e-016 params=1.25/0/1/0/0.09428/-0.0025/0/0 float=y maxiter=1000 inside=0 outside=real periodicity=10 colors=000HL8FM8DN7BO79P67Q65R53S51T54U77V89WACXBF\ YCHZEKaFNcGPfIShJUjKWfNYcQ_`T`YWbUZdRahOcmLfrHivEl\ zBoz8rz5tz6qz7nz8kz9hzAevBbrC_mDYhEVcFSZGPUHMQIJOJ\ GMJEMNIMRMMVQMZUMbYMfaMjeMmhKjkJhmIfoHdzGbzFazEczG\ qzHwzJqzKmzLczNYzOYwPYrRYmSYiUYhVYgWYeYYdZYc_Yb`ad\ adfchidkkfongrphurbkoYamTSjOIhJ8fNAgQChTEiWGiZIjaK\ kdMlgOljQmmSnpUnlTkiThfSecSb_R_XRXUQURQROQOMPNKPNI\ PNHONFOMDOMCNMANM8NL7ML5ML3ML2ML4NO6NR8OUAOWCOZEPa\ GPdHPfGQbFQ_FRWERTERQDSMCSJCTFBTCBT9EU8GV8IW8LX8NY\ 8PZ8SZ8U_8W`8Za8`b8bc8dc8eaAe_BeYDeWEfUGfSHfRJfPKg\ NMgLNgJPgHQhFShEThCVhAWi8Yi6Zi4`i3ak8YlDUnIQoNMpSI\ rXEsaAte6pf7mg8ig9fhAciA_iBXjCUkDQkDNlEKmFGmGDnGAo\ H6oI3pJ0pJ1lK1iL1fM1cN1`N1YO1VP1SQ1PR1MRGU`V`jhgtg\ drfbpf_neYldWjdThcRfcOdbMcaKaaH_`FY`CW_AUZ8SZ5QY3O\ Y1NW2RV2UU3YT3`S4dR4gQ5kP5nO6rN6uM6xP7tR7pT7mV7iX7\ fZ7b`7Zb7Wd7Sf7PhANiDLjGJ } frm:JuliaBC { ; Formula by Andrew Coppin e=p1, p=real(p2)+PI, q=2*PI*floor(p/(2*PI)), r=real(p2)-q, C=p3, Z=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|< p4+100 } END PARAMETER FILE=========================================

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Re: Fractint Mail List?
by Paul N. Lee 26 Oct '05

26 Oct '05

Vortex Swirling wrote: > > Does anyone know what is going on > with the Fractint mail list? If I > try to go into the archives I get > "page not found". This seems to be > true for all the xmission lists. > Did you try going up the list of sub-directories in the URL until it started working again?? I did and got the following message: "This Lurker installation is currently disabled pending a security audit by XMission personnel. We apologize for any incoveninece this may cause." Later, P.N.L. ------------------------------------------------- http://home.att.net/~Paul.N.Lee/PNL_Fractals.html http://www.Nahee.com/Fractals/

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FOTD 26-10-05 (Julia Variation-3 [6)
by Jim Muth 26 Oct '05

26 Oct '05

FOTD -- October 26, 2005 (Rating 6) Fractal visionaries and enthusiasts: Today's image pictures a Julia set of the Z^(1.15)+C Mandeloid as it appears 10 levels up the complex-log superspiral. At this level the Mandeloid resembles a pin-headed punching bag surroun- ded by acres of chaos. I chose the Julia set of an inside point near the bud side of the most obvious valley. Much of the image consists of an inside area brought to life by the 'bof61' inside fill. I gave the entire scene a heavenly blue tint that in my opinion raises its rating from a 5 to a 6. Some areas of the image appear to hold some interesting scenes, but I have no time to check these at the present time. There are far too many other fractals waiting. The name "Julia Variation-3" indicates that today's image is the third in the series of JuliaBC images. I am sure quite a few more are to come. With a render time of just under 15 minutes, today's image borders on the slow side. But the rendering may be avoided by downloading the finished image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> I am thinking of writing four more versions of the branch cut formula, one for each of the four remaining odd planes of the Julibrot. Most likely I will find little there that is more impressive than the scenes in the Mandelbrot and Julia sets, but it will be interesting to see what I can find. A steady cold rain fell all day Tuesday here at Fractal Central, with a raw wind and temperature of 43F 6C making things even worse. The dynamic duo kept their dis-satisfaction no secret. Luckily, I had stocked up on chunk light tuna ahead of time, and was prepared for the sulkiness. Today is starting breezy and chilly, but the clouds have cleared, promising a better day. The next FOTD will be posted in 24 hours. Until then, take care, and be at peace with all that is. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Julia_Variation-3 { ; time=0:14:51.44--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=JuliaBC passes=1 center-mag=-0.295117/\ 0.224777/0.634058/1/-42.5/-3.77822773067748585e-014 params=1.15/0/10/0/-0.61125/0.69209/0/0 float=y maxiter=2600 inside=bof61 periodicity=10 colors=000D92D94D96D98D9AD9GD9ID9KD9MD9OD9QD9SD9UD\ 9WD9YD9_DAaDBcDCeDDgDEiDFkDGlDHmDInDJoDKpDLqFMrHNs\ KOtKPuKQvKRwKSxNTyNUzNVzNWzNXzNYzNZzN_zN`zNazNbzNd\ zNfzNhzNjzNlzNnzNpzNrzNtzNvzNxzNzzNzzNzzNzzNzzNzzN\ zzNzzNzzNzzXzzZzz`zzbzzdzzfzzjzzmzznzzqzztzzwxzzuz\ wsztrzqqzopzlozinzfmzcmz`mzYmzVmzSmzPmzMmzKmzKmzKn\ zKozKpxKqvKrtKsqHtoDulDviDwgDxdDyaDz_DzXDzXDzqFzzS\ zzdzzizznzztzzyuzzpzzjzzezz`zzZzzWzzWzzWzzTzzTzzRz\ zTzzWzzZzzZzz`zzczzcxzevzhqzhozjlzmizmgzpazr_zrVzu\ QzxCzx0zz0zz0zzCzzQzzazzozzzzzzzxzzuzzuzzrzzrzzpzz\ mzzmzzjzyjzthznhziezdez_czV`zP`zKZzFZzDWzDWzDTzDOz\ DTzDZzDczDhzFmzKrzPxzVzz_zzdzzizxnzvtzqvzoyzoHzzDz\ zDzzDzzDzzDzzDzzHuzKrzNpzv9it9lq9lq9ln9ln9ll9ll9li\ 9li9lg9og9od9od9ob9ob9o_9o_9oX9oX9oV9qV9qSBtSDtPJv\ POvPRxNWxN`zKczKhzHmzHpzHuzFzzFzzDzzDzzDzzDzzDzzDz\ zDzzDzzDzzDzzDeqD`lFZiHTd } frm:JuliaBC { ; Formula by Andrew Coppin e=p1, p=real(p2)+PI, q=2*PI*floor(p/(2*PI)), r=real(p2)-q, C=p3, Z=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|< p4+100 } END PARAMETER FILE=========================================

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