August 2014 - Fractint - mailman.xmission.com

Multifractal Images
by Albrechtx 22 Aug '14

22 Aug '14

HI, A friend asked for published MFR images and I had to reply that all links are deleted because my Dropbox account has ended. When he replied that it´s pity as they are lost now, I renewed the account and decided to publish the complete collection. So here it is. The link displays a site with all images and some of my music as well. This time it will remain. Hope you like it. Feedback is welcome of course and tell me if you have difficulties to open it- ; https://www.dropbox.com/sh/zx1sjqtln4vtovk/AABAhwj_Ovy2WCAnFejh_9bOa?dl=0 ; Cheers, Abrecht

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FOTD 19-08-14 (1.4142 Minibrot [A-8,M-5])
by Jim Muth 20 Aug '14

20 Aug '14

FOTD -- August 19, 2014 (Rating A-8,M-5) Fractal visionaries and enthusiasts: The name of today's FOTD, "1.4142_Minibrot", says it all. The image is a view of a minibrot in the Z^(sqrt(2))+C Mandeloid as it appears at a level of 1.373 turns up the hyperspiral. At this not very lofty height the parent fractal resembles nothing as much as a lima bean with a short filament extending southwest and a long but disconnected filament extending north. Today's scene is located in the East Valley of a larger minibrot on the northern filament. Actually the hyperspiral does not produce an infinite variety of fractals, but is a loop of 4.4428828..., at which point the fractal returns to the one that exists at the zero level and starts the cycle over. The art rates an honest 8. I spent near a half hour on the colors. With a rating of 5, the math falls short however. The math is now old stuff. The calculation time of 1-1/2 minutes is fast enough to avoid impatience, and slow enough to enjoy the unfolding of the scene. And as always, instant relief is available on the web sites. Check the finished image at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> The weather was perfectly average here at FC today, with hazy sun and a temperature of 81F 27C. The fractal cats agreed. The humans also agreed. Until the next FOTD appears in a day or two or three, take care, and wonder what it's all about. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= 1.4142_Minibrot { ; time=0:01:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=BranchCutSqrt center-mag=-0.8578916604\ 056522/+2.65631676384417/1.102536e+010/1/117.5/0 params=1.373/0 float=y maxiter=1500 inside=0 logmap=248 periodicity=6 mathtolerance=0.05/1 colors=00000000000001002003004548A7CFAGKDJPGNUKRZN\ UcQYhTamWdr_hvclzhozmszrwzwzzrrzmjvhcreWmcOhaHc_9Z\ Y2MV5PT7OR9NPBMPDLPFKUHJUJIULHUNGZPFZREcLIcGMcAQf5\ Uc0Ye5UcAQcFPcKUcPZcUccZhZcmVgrPejKbbF_WAXO5UG0R9W\ 7t`GueOvjWwodxtlyxtypnehhMac2_bGYbUWbfZ_gaXhdUifRi\ iOjlLknJkgImaInWIoPHpJHqDHrBHn9Hj7Hf5Hc3H_1HW0HTFZ\ WTpYVVQXAJ_EHbHFeLDhPBjS9pQJuPTzOae`LfYPfVTfSXfP`f\ NddMYbLR`LLZVEYa8PmWZUy`ZobfedhXfjNzzzmmFflGfmGelH\ elHdlIdlIcmMcnPcoSbpWbqZbrabrdgibl`aqT`vK_zCZwDdtD\ iqEonEtkEyeKs_QmUWgOabIgXCmR6sL1xG7vQCuZIthNsqCiBP\ Y9aN7nC5_TMMibPfYRcUT`QVYMYVH_SDaP9cN5arsZVqX7oRGn\ MPnGYnBfn5on0wn7qiEkdKe`R_WXUSZQT`MTbIUdEUfAVh6Vi2\ VYHWMWXBjXIlSOnNVpI`qEgs9mu4sv0bkLN`d7Rx6Vr5Zm4ah3\ ec2iZ1lU6iTBfSGcRL`QQYPO_UNaZLccKegJglHiqGkvFmzHmu\ ImqJmlKmhLmdMm_NmWOmSbSfp6tD3Ofm0`n4Wo8RpCMqFGrJBs\ N6tR1uU3uR4uO6uL7uJ9uGOll } frm:BranchCutSqrt { ; Jim Muth Z=C=Pixel: Z=log(Z), Z=exp(1.414213562373*(Z+flip(real(p1))))+C, |Z|<36 } END PARAMETER FILE=========================================

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FOTD 18-08-14 (Blattaria Specimen [A-6,M-7])
by Jim Muth 19 Aug '14

19 Aug '14

FOTD -- August 18, 2014 (Rating A-6,M-7) Fractal visionaries and enthusiasts: Today's image is named "Blattaria_Specimen", and the image certainly does resemble a specimen of the order. Actually, the image is a Julia set of the valley at the western extremity of the main bay of the Z^(1.05)+C Mandeloid as calculated at a tiny 0.024 turns up the complex logarithmic hyperspiral and a little into the imag(y) direction. The art rates a 6; we have been here several times before. The math rates a 7; we have been here before but not at this level of the hyperspiral. The calculation time of 1-1/2 minutes will pass in a semi-flash. The web sites will eliminate the flash. The finished image is available online at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> Perfect weather prevailed here at Fractal Central today. Perfection is described as blue skies decorated with puffy white clouds, low humidity, and a temperature of 79F 26C. The fractal cats had a mostly pleasant day, but did get into a tussle when Jasmine leaped from the couch onto Nicholas and caused his tail to puff up. The humans spent the day working. The next FOTD will be posted in a day or two or maybe three or four. Until whenever, take care and I have nothing to say about current events in Saint Louis except that I am disappointed that the same old problem still exists even 50 years after the Civil Rights Act was passed, and after 50 years of the best-intended efforts to eliminate discrimination and poverty, and finally achieve true equality. It is actually starting to appear, at least to me, that achieving equality might be a wishful myth. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Blattaria_Specimen { ; time=0:01:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=BranchCutGenJul passes=1 center-mag=0.27373/0.0304405/1.025/1/-24.25/0 params=1.5/0.024/-0.18873/0.0144 float=y maxiter=1500 inside=0 logmap=4 periodicity=6 colors=0004YD4VC3RA3O92L72I62F52C72A927B25C38H3BM3\ DR3GV3I_3Ld3NhCOeKPcTQ``RZhSXcQVZOTVNRQLPLJOHIMCGK\ 7EI3DH9FPFGWLHbQEWUCQY9Ja7De46i20lPBnkLlgUjcai_igW\ qfSydVrcXlaZf`a_ZcUYeOWhHVjBUl5Sk8RkBPkEOkHNkKLkNK\ kQJkTIhVHfWGdYFbZE__DYaCWbBUcASe9Pf8Ng7Li6Jj5Hk9Ii\ DIhHIgLIePIdTJcXJa`J`dJ_hJZiI`iHbiGdiFfiEhiDjiCliB\ niApiArl8po7oq6nmAmiEmfImbLm_PmWTlSXlP_lLclIglEkkA\ nk7rk3vk0ykKcOcI0`G8YEGWCOTBVQ9bO7jL5rJ4yJ5tJ6pJ6l\ J7hJ7dJ8`J8WJ9SJ9OJAKJAGJBCJB8AQiKWdTa_bgVkmQtsMso\ NslOrhPreQqaQqZRpWSpSToPUoLUnIVnEWmBXm8XlCUlFSlJPl\ MNkQLkTIkXGk_EjZHjZKjZMiYPiYSiYUiYXhX_hXahXdhXggWi\ gWlgWogWqeYjc_da`Z_bTYdMWeGUgASh4Um5Tj7Sh8Re9QcAP`\ BOZCNWDMUELRFKPGJMHJKIp8yn9wm9ukAsjAqiBpgBnfCleCjc\ DibDgaEe_EcZFbXF`WGZVGXTHWSHURISPIQOJPNJNLKLKKJeUT\ dTScTScTSbTRbSRaSRaSR`SQ`RQ_RQZRQZRPYQPYQPXQPXQOWP\ OWPO7sN6pL6mK6jJ5fH5cG4`E } frm:BranchCutGenJul { ; Jim Muth Z=Pixel, C=p2: Z=log(Z), Z=exp(real(p1)*(Z+flip(imag(p1))))+C, |Z|<100 } END PARAMETER FILE=========================================

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FOTD 14-08-14 (Rectangular Break-Up [A-6,M-7])
by Jim Muth 16 Aug '14

16 Aug '14

FOTD -- August 14, 2014 (Rating A-6,M-7) Fractal visionaries and enthusiasts: Today's image is titled "Rectangle Break-Up" because that's exactly what it is. Like the previous image, it shows one of the strange rectangles in the Julia aspect of the Z^(2.003)+C Julibrot in a state of partial disintegration. The art rates a 6, the math, a 7. The calculation time of one measly minute will cause no impatience. And as always, the web sites can eliminate calculation completely. I'll continue exploring different aspects of the rectangle in the next few FOTD's. Then we'll move on to new and hopefully greater fractal things. Check the image on the FOTD web sites at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> Near perfect weather prevailed here at Fractal Central today, with a mix of sun and clouds, low humidity, refreshing breezes and a temperature of 77F 25C. Both the cats and the humans enjoyed the fine day. The next FOTD will be posted in a day or two. Until then, take care, and people will never learn to get along together until they are willing to hear and understand the views and problems of the other side. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Rectangle_Break-Up { ; time=0:01:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=branchcutgenjul passes=1 float=y center-mag=+0.00005839296655972/+0.073886902604897\ 41/267/1/4.25/0 params=2.003/6e-005/-1.7435/0.00024 maxiter=4200 inside=255 logmap=80 periodicity=6 colors=000potqlx<2>ncrmapm`n<7>hO`gMZfKY<3>dER<3>`\ BY_A_ZAaY9cY9d<3>k5Pn4Lq3Ht2D<3>h56f54c63<2>V70T80\ Q70<3>F40G30H20<3>J00J00K00L00L00M01M02<3>P66P77Q8\ 8<2>RBBRCCQDD<3>PHHPJIo`z<3>sWztVztUz<3>razrczqez<\ 2>pkzpzz<2>ozzzzz<21>zzz<4>zzz000<126>000 } frm:BranchCutGenJul { ; Jim Muth Z=Pixel, C=p2: Z=log(Z), Z=exp(real(p1)*(Z+flip(imag(p1))))+C, |Z|<100 } END PARAMETER FILE=========================================

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FOTD 13-08-14 (Rectangular Regress [A-5,M-8])
by Jim Muth 13 Aug '14

13 Aug '14

FOTD -- August 13, 2014 (Rating A-5,M-8) Fractal visionaries and enthusiasts: Today's formula is another new one: ------------------------------------------------ BranchCutGenJul { ; Jim Muth Z=Pixel, C=p2: Z=log(Z), Z=exp(real(p1)*(Z+flip(imag(p1))))+C, |Z|<100 } ------------------------------------------------ The formula is a Julia version of the 'BranchCutGen' formula. The image shows a variation of our old friend, the strange open rectangle in the Julia sets of the Z^(2.003)+C Mandeloid. The rectangle itself, distorted and partly filled in, fills the entire screen. The name "Rectangle Regress" refers to the infinite regress in the image. Such regress is quite common in fractals, and in today's image appears as the smaller rectangle just northeast of the center of the large rectangle. This smaller rectangle is an exact copy of the larger rectangle, and has an identical but even smaller rectangle near its center. The process continues to the limit of resolution. The art rates an average everyday 5. The math rates a slightly liberal 8 because of the regress and also because of the new formula, The calculation time of one minute should cause no problems, but the web sites are always there to eliminate the calculation hassle. The image has been calculated and posted to the FOTD web sites at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> After 3 inches, 7-1/2cm, of rain yesterday, today was a great improvement. The partly cloudy skies and temperature of 79F 26C were just what the doctor ordered. The conditions must have been just what the fractal cats' doctor ordered also. They spent most of the day at the windows watching the birds and the occasional passing squirrel, while the humans watched the work. The next FOTD will be posted within a reasonable time. Until reason prevails, take care, and the less the entropy the better the situation. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Rectangle_Regress { ; time=0:01:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=BranchCutGenJul center-mag=+0.00122607\ /+0.07382828/260/1/-23.75/0 params=2.003/0.0001/\ -1.7435/0.0001 float=y maxiter=1500 inside=0 logmap=79 periodicity=6 colors=000d_WbaY`c_ZeaXgcVieTkgRmiPokIrkOplUnlZlld\ jmihmofmtdmthjtlhtpftsdnm_igVdaQ_WLUQGPKBKE6F81A92\ A93A94A95A96A97A98AA9AAAAABAABAACAADAAEABFABGABHAB\ IABJABKJ7NXBKiEHvHEnGMgGUbE_`G`ZIaXKbWMcUOdSPdQReP\ TfNVgLXhKZiI_iGajEckDelBgm9in6no8jn9gmAclB`lCXkDUj\ EQjFNiGJhGFiHGhIHhJIgKIgKJgLKfMKfNLfOMeONePNdQOdRP\ dSPcSQcTRcUSbVSbWTaWUaXUaYV`ZW``XbZW`YVZWUXVUVUTTS\ SRRSPQRNOQLNPJMPHKOFJNDFMBINBKOBMPBOPBQQBSRBURBWSB\ ZTB`UBbUBdVBfWBhWBjXBlYBnYBmYDmYEmYGmYHmYIlYKlYLlY\ MlYOlYPlYQkYSkYTkYUkYWkYXj__kYYkWWlUUlSSlQRmOPmMNn\ KLnIJnGIoEGoCEpACp8Ap69o9AnBAmDBmFBlHBkJCkLCjNDiPD\ iRDhTEgVEfXFfZFe`FdbGddGcfHbhHbjHalI`nIasF`pI`mK`j\ M`gO`dQ_aS_ZU_XW_UZ_R`ZObZLdZIfZFhZCj`BkZAlXAlWAlU\ AlSAlRAlP9lO9lM9lK9lJ9lH9lG8lE8lC8lB8l98l83o88l8Ci\ 8Hf8Lc8Q`4WX8UZCS`FQaJOcMMeQLfTJhXHi`FkcDmgCnjApn8\ rOlZZwIVjQRYYOLdUQa_VZfYU } frm:BranchCutGenJul { ; Jim Muth Z=Pixel, C=p2: Z=log(Z), Z=exp(real(p1)*(Z+flip(imag(p1))))+C, |Z|<100 } END PARAMETER FILE=========================================

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FOTD 11-08-14 (Golden Perfection [A-7,M-8])
by Jim Muth 12 Aug '14

12 Aug '14

FOTD -- August 11, 2014 (Rating A-7,M-8) Fractal visionaries and enthusiasts: Start with the number 5, extract the square root, add 1 and divide the sum by 2. The result is 1.618034... the Golden Ratio. This number is also the exponent of Z in today's image, which is why I named it "Golden Perfection". To add to the interest, I calculated Z^(1.618034)+C one level up the complex logarithmic hyperspiral. At this not-so-lofty level, the parent fractal resembles a twisted Mandelbrot set rotated so that East Valley faces southwest and the large main-stem bud faces northwest. Today's scene lies on what should be the northern shore line of East Valley. The art rates a 7, since I really could have done a little more with the colors. The math rates an 8. This minibrot is one of the most symmetrical I have yet found in the fractal exponent range between one and two. The calculation time is 3-1/3 minutes, a time that could breed impatience. But this time may be saved by checking the FOTD web sites. Be sure to visit the FOTD web sites at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> Morning and early afternoon were perfect today here at Fractal Central, with sunny skies, puffy clouds and a temperature of 82F 28C. But later in the afternoon, heavier clouds moved in, with rain expected tomorrow. The fractal cats, who expect nothing more than play and food, were unconcerned with the coming rain. The humans, who will be working inside tomorrow, had equally little concern. The next FOTD will be posted in the appropriate time, whenever this might be. Until then, take care, and if religion is doing its job, why is the number one question of life, 'what happens to us after we die?' Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Golden_Perfection { ; time=0:03:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=BranchCutGen passes=1 periodicity=6 center-mag=-0.1804690692893928/-0.1268348854197519\ /7.09888e+011/1/-152.5/0 params=1.618034/1 inside=0 maxiter=3600 float=y logmap=428 mathtolerance=.05/1 colors=0008ZI9_G9`ECZFEXGGVHITIKRJMQJMUNMXRM_UMbYM\ eaMhdOfcPecQdbRbbTaaU`aVZ`WY`YX_ZV__UZ`TZbRYcQYdPX\ eOX_QWUSVPUVJWUEXULQPSJLZDHe6Dl09p4Fs7LvARh8KV7EH6\ 8452861C71G81J81N91RA1VB1YB1aC1eD1hD1gF6fGBfHFeIKe\ JOfHPhEPjCQkAQOMK0YE2WC4VB6UA8S8AR7CQ6EP5GN3IM2KL1\ MK0LKRKKpsCVnCCgAFa8IV6LP5OI3RC1U60W93UB5SD7RGAPIC\ NKEMNHKPJJRLHUOFWQEYSC`VAbX9dZ7f`6db8bcA`eBZfDXhEV\ iGTkHRlJPmLNoMLpOJrPHsRFuSDvUBwVEnWGeXJXYLOZNFZRGY\ VGXZGWbGVfGUjGTnGSrGRsJStMStOSuRTuUTvWTvZUwaUwcUxf\ VxiVykVynWzqWzsWjlgVfsUhdS_ePRfNIgL9hJAcIB_GCWFDRD\ ENCFJBGFJCDR9BZ69e37h8GkCPnGYqLftPovTxkWv`ZtQarmmW\ zzDvu0qt4ms8irBeqF`pJXoMTnQPnTekrcgzfhzikzlnzbkz`x\ z_zzZzzYzzYwzYtzYpzYmzYizYfzYczcnzcrzcrzcmzcmzchzc\ hzchzMmzKmzJmzcmzcmzcmzcmzcmzcuzcuzcuzmuzmzzmzzmzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:BranchCutGen { ; Jim Muth Z=C=Pixel: Z=log(Z), Z=exp(real(p1)*(Z+flip(imag(p1))))+C, |Z|<100 } END PARAMETER FILE=========================================

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FOTD 10-08-14 (Miracle Fractal [A-8,M-8])
by Jim Muth 11 Aug '14

11 Aug '14

FOTD -- August 10, 2014 (Rating A-8,M-8) Fractal visionaries and enthusiasts: Today's image is named "Miracle Fractal". The miracle is that, with an exponent of Z of 1.05, it exists at all, and also that I was able to find it. The parent fractal resembles an indian arrowhead, with small areas of chaos scattered along the edges. Today's image is located deep in one of these apparently barren areas of chaos on the northern edge of the large main open area. Both the art and math rate an 8. The extra coloring effort earns the art rating. The unlikeliness of finding a minibrot at all in the parent fractal makes the math also worth an 8. The calculation time of 7-1/4 minutes is a drag, but help is available at the web sites. For convenience, the image has been calculated and posted to: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> Near perfect weather prevailed here at Fractal Central today. The sunny skies, temperature of 84F 29C, low humidity and gentle breezes made both the fractal cats and people happy. Fractal cat Jasmine, who has her one-year birthday in ten days, was especially frisky. When she jupmed from the couch onto Nico, he gave her a resounding hiss. The next FOTD will be posted when it is ready. The FOTD's have been coming slower lately, but at least IMO, they are better. Until everything is ready, take care, and make progress. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Miracle_Fractal { ; time=0:07:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=BranchCutGen passes=1 center-mag=+0.01983111086924904/+1.915834481164043\ /5.107806e+011/1/125/0 params=1.05/1.5 float=y maxiter=3600 inside=0 logmap=-1032 periodicity=6 mathtolerance=0.05/1 colors=00000G50W60S60S50X40S70P90MB0JE0GH0EF0BD08C\ 05O02I00F0NL0IU0RE6_H0`U0fU0dL0bT0aM0_F0Y80W20VIKa\ XVhkeortzluzKpzEcmE`jEYgEVfDReDOdDLcDIbCFbCC_CAWC8\ SJAPPRTV`ZaedgjjprszzzKosFkpAfn5bk0Yh0Uf3Xh6Zj9`kC\ cmFeoIgpLkrPntUquYuwaxybzzawwatuaqr`op`jn`fk_ci__f\ _Wd_XbRafIdj9gn0ir3gp6en9clCajF_hIYfKWeNUcQSaTQ_WO\ YZMW`KV8_cBXdDUeFReHOfJLfLIgNFhPChR9iT6iV3jX1jY4fY\ 7cZA_ZCXZFU_IQ_KN`NJ`QG`SDaV9aY6a_3`Z6`Y8`XA`WC`VF\ `UH_TJ_SL_RO_QQ_PS_OU_NWZMXYMXYLXXLYWKYWKYVJYUJZUI\ ZTIZSH_SH_RG_RU_TUaUUcWUeXYgZYh_Yj`Ylbcnccpecqfcsh\ cuicwjcxfcvbmuZmsVmrRmqUmmXmi_mebmaeeYhfVkhRnjNqkJ\ tmFwnCpmBimAbm9Xm9Qm8Jm7Dm7GmAJmDMmGPmJSmMVmPYmS`m\ UcmXfm_imblmeomhrmkumnwmpummtmjrmgqmdomanm_mmXkmUj\ mRhmOgzLfzJgzJgzJhzJizJjzJjzJkzJlzJmzJmzJlzOkzSjzW\ iz_hzcgzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:BranchCutGen { ; Jim Muth Z=C=Pixel: Z=log(Z), Z=exp(real(p1)*(Z+flip(imag(p1))))+C, |Z|<100 } END PARAMETER FILE=========================================

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FOTD 07-08-14 (The FMOD Cycle [A-7,M-8])
by Jim Muth 08 Aug '14

08 Aug '14

FOTD -- August 07, 2014 (Rating A-7,M-8) Fractal visionaries and enthusiasts: NEW FORMULA!! Today's formula is another new one. Forget about the ersatz 'new' formula posted on August 4th, which has already been discarded. ------------------------------------------------------------- BranchCutGen { ; Jim Muth Z=C=Pixel: Z=log(Z), Z=exp(real(p1)*(Z+flip(imag(p1))))+C, |Z|<36 } ------------------------------------------------------------- Given impetus by Hal Lane, I decided to see how much I could simplify the BC formulas and still get the same fractals. Today's formula is about as far as I could take the process. When I analyzed the old formulas, I was surprised at how many terms simply canceled out or had no effect. Today's new formula is the result. The by-product is a 33-percent increase in speed. I named today's image "The FMOD Cycle" mostly because the image was rendered with the inside set to 'FMOD'. The cycle part of the name refers to the complex logarithmic hyperspiral of the Z^sqrt(2)+C fractal, which, starting at zero, repeats every 4.442... levels. Today's image is located 2.221... levels up the hyperspiral, which is exactly halfway back to the starting point and produces a parent fractal with X-axis symmetry. The art worth of the image impresses me as a 7; the math rates an 8, which is perhaps overblown. After all, the basic math is old stuff. Only the streamlined formula is new. Today's image is the actual parent fractal, made somewhat unrecognizable by the 'FMOD' inside fill. This is why it calculates in a matter of 22 seconds. If this is still too slow, the web sites can make things a bit speedier. Check the finished images at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> A mix of puffy clouds and blue sky, a temperature of 79F 26C, a passing afternoon shower, refreshing low humidity, and a gentle north wind made today a day worth waiting for here at Fractal Central. The fractal cats missed much of the day when they slept all afternoon. The fractal humans had an uneventful though busy day. The next FOTD will be posted in the appropriate time. Until whenever this might be, take care, and the governments tell the people what they can and cannot do, the big corporations tell the governments what to order the people to do, but who tells the big corporations what to tell the governments to order? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_FMOD_Cycle { ; time=0:00:22.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=BranchCutGen center-mag=-0.0840312/0/\ 0.778816/1/0 params=1.414213562373/2.22144146907933 inside=fmod float=y maxiter=1500 symmetry=xaxis proximity=0.049 periodicity=6 colors=000MCcLCbKBaKB`KB`JB_JBZJAZIAYIAYIAXHAWH9WH\ 9VG9UG9UG9TF8TF8SF8RE8RE8QE8QD7PD7OD7OC7NC7MC6MB6L\ B6LB6KA6JA5JA5I95H95H95G84G84F84E74E74D74D63C63B63\ B53A5395294284284273263163152142142131031021010010\ 00cGFbFEaFE`ED_EDZEDYDCXDCWDCVCBUCBTBBSBARBAQAAQA9\ PA9O99N98M88L88K87J77I76H76G66F65E55D55D54C44B44A4\ 3933833722622522411311211100000ol5mj4li4jg4if4ge4f\ c4db4f`ngangbngcngdngengfnggnghnhinhjnhknhlnhmnhnn\ honhpniqnirnisnitniunivniwnixngvlftkericqhcpgbofam\ e_kcZjbYh`Wf_VdYUcXSaWR_UQYTOXRNVQMTOLRNJQLIOKHMIF\ KHEJGDHEBFDADB9CA7A8687565354232111shJqfIoeHndHlcG\ kaGi`Fh_FfZEeXEcWDaVD`UCZSCYRBWQBVPATNASM9QL8OK8NI\ 7LH7KG6IF6HD5FC5EB4CA4A83973762652431321110kyYiwXh\ vWgtVfsUerUdpTcoSbmRalR`kQ_iPZhOYgOXeNWdMUbLTaLS`K\ RZJQYIPXIOVHNUGMSFLRFKQEJODINCHMCGKBEJADH9CG9BF8AD\ 79C68B6795684563453342221 } frm:BranchCutGen { ; Jim Muth Z=C=Pixel: Z=log(Z), Z=exp(real(p1)*(Z+flip(imag(p1))))+C, |Z|<36 } END PARAMETER FILE=========================================

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FOTD 04-08-14 (Squarely Rooted [A-8,M-5])
by Jim Muth 05 Aug '14

05 Aug '14

FOTD -- August 04, 2014 (Rating A-8,M-5) Fractal visionaries and enthusiasts: NEW FORMULA ALERT! ----------------------------------------------------- MandelbrotSqrt2BC { ; by several Fractint users p=p1, q=2*PI*(p/(2*PI)), r=p1-q, Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(1.414213562373*(Z+flip(q)))+C |Z|<36 } ----------------------------------------------------- Today's formula is a new one, an addition to the 'BC'or 'branch-cut' group of formulas, which are supposed to draw the other fractals resulting from the multi-valued nature of the complex logarithm. Since Z^(sqrt(2)) is the exponent I use most frequently, I have simplified the formula, and in doing so, I have also speeded up the calculation a little. But even from the beginning, the math of the 'BC' formulas has been questionable. The formula for the complex logarithm as listed in the second edition of "Fractal Creations" is . . . (1/2)In(x^2+y^2)+i(arctan(y/x)+2kPI where k can be any real positive or negative integer. The value I have entered for 'k' in today's image, -9.42477, shows the math flaw, since it is not an integer, but despite the flawed math, this fractional value still creates a fractal. (I'll not even try to guess what errors might be created by the spurious trig functions that I sometimes use.) The parent fractal of today's image is a chaotic indescribable thing with a long zig-zagging filament extending from its northeast side. Today's scene lies in the 'East Valley' area of a tiny minibrot on this filament. I named the image "Squarely Rooted" because the exponent of Z is the square root of 2. The artistic aspect is a little better than most recent images and rates an honest 8. Except for the new formula, I could find nothing new in the math, which rates a boringly average 5. The calculation wait of 3-5/6 minutes may be avoided by checking the web sites. Check the finished image on the FOTD web sites at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> Today brought a mix of clouds and sun, and a temperature of 81F 27C to Fractal Central, the historic center of fractal activity. After a relaxing week-end, the fractal humans got back to work; after a relaxing week-end, the fractal cats continued relaxing. The next FOTD will be posted in a day or two, or maybe three. Until whenever, take care, and when watching the media news, try to separate the propaganda from the facts. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Squarely_Rooted { ; time=0:03:50.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotSqrt2BC passes=1 center-mag=+1.381338385604301/+0.8059894596556334/\ 6.963546e+011/1/-50/0 params=-9.42477/0 float=y maxiter=1800 inside=0 logmap=441 periodicity=6 mathtolerance=0.05/1 colors=00000B01D02F03H04J05L06N17P28R39T4AV5AX6AZ7\ A`8Ab8Ad8Ae7Af7Ag7Ah7AiAAjCBkFDlHGmKInMKoOMpRPqTRr\ WTsYVs_Yrb_rdbrgerihrkkrnmvpozsqzutzwwzvzzuzztzztz\ zszzrzzrvvqsrppmpmhomcnlbnlamk_lkZljYkjXjiVjiUihTh\ hRhgQggPVkfYlg`mibnjakiahhaehabga_faYfaVeaSdaPdaMc\ aIbaFbYDWVBQRAKO4EK08H02GALFMcEXvUbuhguwluxmnymgwk\ euictharf_pdYocWmaUk_SjZQhXOfVMeUKcSIaQG`PEbODcNCd\ MBeLBfKAgK9hJ9iI8jH7kG7lG6mF5nE5oD4pC3qC3YU4eT3mS1\ tR0uK7uEEv8Lv2SlAVcHYVO`MVcDaf4hi6kb8nX9pRBsLDvFEx\ 9CuJBsS9p`8niCheGbbKX_NRXRLUVFRZ9Oa4Li9AqE0sAGu7Wv\ 4kuGktSksckrokqzkoxdmwZkuTitNhsHloFplEtiCxfBtdCqbD\ m`EjZEfUFcPG_KHXFH_AMaEQc7UJ8ZK8WF8JB86hbulUqpKltc\ hw2dmcKtKjsSmq`pphsoqvnyykuqizjgUcdnWboP`pIUqGNrFG\ sE9hD3uC9vHEwMKxRPyWUz_TzcTzfzzjzzmzzpzztzzwzzzzzr\ zzkzzczzXzzQzzIzzBzz4zz3zz2zz2zz1zz0zz0zzBzzHzzNzz\ TzzYzzczzizznzzjzzgzzdzza } frm:MandelbrotSqrt2BC { ; by several Fractint users p=p1, q=2*PI*(p/(2*PI)), r=p1-q, Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(1.414213562373*(Z+flip(q)))+C |Z|<36 } END PARAMETER FILE=========================================

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Fwd: Fractint, and Satan Fractal
by Rick Ostidich 04 Aug '14

04 Aug '14

Friends! I forward here the mail I sent yesterday to mr. Tim Wegner, as he suggested me to do. It's about the fractal program Satan.exe, that I just published as free-ware. Have fun you all! -------- Good morning, mister Tim! This is Rick Ostidich, a computer programmer (machine language only!) from Italy. (I'm the author of the image viewer Ombra.exe for Dos, you probably remember about it!) I'm happily using Fractint since 1995 (I still have release 19.2), and today for the first time I searched the Web for FractInt - it's great to see you're still on business! The story is: one day, in 2003, I was playing with your "formula editor", and discovered a very interesting combination (sqrt+cosx), from which I created hundreds of beautiful and funny images. I named that formula "Satan", because there are a lot of evil monsters in it! (Mathematically speaking.) ;] Then, on 2006, I wrote the simple program Satan.exe that lets you use your mouse to zoom and move (in 4-dimensions) in real-time within the fractal landscape, and render any image to disk bitmaps, in whatever resolution. I also added some other features, and wrote a long documentation. Soon after that, I moved to other projects, and I left the program unpublished. (Though, in all of these years, I use it a lot every month, and always discover new stuff.) Few days ago I finally decided to publish it, as I should do with a lot of other programs of mine. Of course it's all released as free-ware, with no limitation. I don't want to make any money out of it. I got money. And also got admiration. (quote) ;] What I want is that other people enjoy the work that I've done for myself, and for the Science. So, last Friday, I created the facebook page "Satan fractal" (http://www.facebook.com/SatanFractal) where I posted 200 example pictures, and I've put a link to directly download the program from my personal site. (I'm building my site right now, but the Satan052.zip is already available in there.) The .zip file includes the program, the documentation, and 1'183 (!) images ready to render. All in a single Zip of 355 kilobytes ;] In that documentation I wrote a lot about FractInt, giving all the credits and thanks that you deserve. Currently, I'm not trying in any way to advertise my program - I didn't even ask my facebook friends to click 'like' on its page. But probably, it could deserve some attention from other fractal enthusiasts. At the times of my Ombra.exe (1995, too) it was easy: I just uploaded the program to x2ftp.oulu.fi, and that was all. This meant thousands of downloads every week, and even a letter from NASA that asked me permission to use Ombra for their activities. 8] Nowadays I don't even know where and how one should publish his/her works. I spend too much time in programming or going out for fun, and too little time is left for navigating the web. ;] Whom should I speak with, about this work that I've done? The first thing that came to my mind was "Fractint people"! So, here is this long email. (Sorry!) ;] In short: take a look at it, if you have the time and the will to do so. And, possibly, tell your friends you've found something new, and free! Thanks again, to you and to everyone at Stone Soup Group, and have a nice day! *Rick Ostidich*

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