June 2010 - Fractint - mailman.xmission.com

FOTD 06-06-10 (Terraces of Fire [8])
by Jim Muth 06 Jun '10

06 Jun '10

FOTD -- June 06, 2010 (Rating 8) Fractal visionaries and enthusiasts: I named today's image "Terraces of Fire". One look at its fiery terraces will give the reason. The parent fractal is hardly more than a rudimentary blob with a single sizeable bay and the remnants of an East Valley. Slices of long-gone elephants abound in this valley, with today's scene located not too deep in one of the remaining left-over elephant-trunk spirals. The terraced effect is a result of rendering the image with the outside set to 'tdis'. Making terraces is one of the things this option does quite well. The rating of an 8 is mostly due to this terraced effect, which is really all the image has going for it. The calculation time of 13 minutes is admittedly slow, but it is not excessive when the resulting image rates an 8. The thirteen minutes may be saved by surfing to the FOTD web site at: <http://www.Nahee.com/FOTD/> where the already-calculated image is posted for instant relief of impatience. The warm and humid conditions continued here at Fractal Central on Saturday. The temperature of 88F 31C was made worse by the air that was almost moist enough to swim in. The fractal cats, who do not swim, kept cool on the kitchen floor. In my depart- ment, all was quiet. The next FOTD will be posted in 24 hours. Until then, take care, and how many liters of water will a Klein bottle 30cm in diameter hold? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Terraces_of_Fire { ; time=0:12:53.59-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=round inside=0 center-mag=+0.15403642991044/-0.00092662965803/5.3\ e+10/1/-30/0 params=1.5/0/11/0 float=y maxiter=5000 outside=tdis periodicity=6 mathtolerance=0.05/1 colors=000nx8iwAdwBZvCUvEPuFKuGJtJIsLHsNGrPFqREqTE\ pWDpYCo_BnaAnc9me9mgBfaC_WDTQEMKFFEG89LIDPRHT`KXiO\ `rRYsQWtPTuORvOOwNMxMKyMQqIWiEaaAgU6mM3lN4kN5uN6sN\ 7qN8oN9mNAkJ9iG9fD9cA8`78Y48V18S38P58M78J98FB8CD8A\ F88H86K85N85Q8ATBFVDKXFOYHR_KV_PZ`U``Zcacfahicmkdr\ ofvsgzwizzjzwkzulzsmzqnzoozmpzkqzirzgszetzcuzdrzeo\ zfmzgjzggzhezibzj`zjYOkVLlTJmQGmOElOFlOHkOJjOLjOMi\ OOiOQhOSgOTgOVNffKigHlhFoiHnjJnkKnlMnmNnnPmoQmpSmq\ UmrVmsXltYlu_lv`lwblxclyfmlim`blcXleQlgKliQjhVih`g\ hefhkdhpchmajk`ki_lfYndXobWp_UrYTsWStTQvRPwPOxNNyV\ SdbXKja0hMWg6zh9xhBwhEviGuiJtiLsiOrjQpjTojVnjYmk_l\ kbkkdjkfighgdje`kcYmaUn_RpYOrWKsUHuSDvQAxO7yMDuOJq\ POnQUjS_fTdcUeaTe_TfZTfXTgWTgUShTShRSiPSiOSjMRjLRk\ JRkIRlGRlFRYOKJXE4e8jDZeC`aBcXAfT9hP8kK7nG6pB5s74v\ 34x68w8BwAEvDHvFKuHNuJQuMTqPVnSXkUZgXad_caaeYdgVgj\ SilOlnLopIqsEtuBww8yy5sx7 } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-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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Two Arthopods Today
by Roger Alexander 06 Jun '10

06 Jun '10

Add some inversion and outside=atan to the SJSPIDER01JULIA formula and fractint's built in spider formula and what do you get?-metallic creepy crawlies. Cyber entomologists can examine two specimens already on display at http://maxitersfractalfollies.blogspot.com and avoid the fuss and bother of a fractal specimen safari. Regarding spiders algorithmic or physical good old Wikipedia says "Around 50% of women and 10% of men have mild arachnophobia or worse." fract339.gif { ; a fractal that looks like a spider ; blank ; calctime 0:13:32.01 ; created Jun 02, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=spider passes=1 center-mag=0.462163/0.514114/3.05024/1/47.5000000000345821/1.20212631515\ 848045e-010 params=0.206244087038789/-1.168004394665365 initorbit=0.4/0.2 float=y maxiter=1500 inside=0 outside=atan invert=1.29858239072596e-005/0.617123228964258/0.608617971080958 periodicity=4 colors=000000111222333333444555666777777888999AAAAAABBBCCCDDDDDDEEEFFFGG\ GHHHHHHIIIJJJJJJKKKLLLMMMMMMNNNOOOPPPPPPQQQRRRRRRSSSTTTUUUUUUVVVWWWWWWXX\ XYYYYYYZZZ______``````aaabbbbbbcccddddddeeeeeeffffffggghhhhhhiiiiiijjjjj\ jkkkkkkllllllmmmmmmnnnnnnoooooopppppppppqqqqqqrrrrrrrrrssssssssstttttttt\ tuuuuuuuuuvvvvvvvvvwwwwwwwwwwwwxxxxxxxxxxxxxxxyyyyyyyyyyyyyyyyyyyyyzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzyy\ yyyyyyyyyyyyyyyyyyyxxxxxxxxxxxxxxxwwwwwwwwwwwwvvvvvvvvvuuuuuuuuutttttttt\ tsssssssssrrrrrrrrrqqqqqqpppppppppoooooonnnnnnmmmmmmllllllkkkkkkjjjjjjii\ iiiihhhhhhgggffffffeeeeeeddddddcccbbbbbbaaa``````______ZZZYYYYYYXXXWWWWW\ WVVVUUUUUUTTTSSSRRRRRRQQQPPPPPPOOONNNMMMMMMLLLKKKJJJJJJIIIHHHHHHGGGFFFEE\ EDDDDDDCCCBBBAAAAAA999888777777666555444333333222111000 } fract240.gif { ; buggies! ; blank ; calctime 0:13:12.36 ; created Jun 05, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=reb007.frm formulaname=SJSPIDER01JULIA center-mag=-0.654899/0.175292/1.264773 params=0.9533677175206763/-0.05410931730094302/-0.7139805291909542/0.959\ 2272713400677/0.4292733542893765/-0.717795342875454 float=y maxiter=1500 inside=0 outside=atan invert=0.3068025757622/-0.381389812921537/0.167455061494797 periodicity=0 colors=000zzzzzzzzzzzzyyyyyyyyyyyyxxxxxxxxxxxxwwwwwwwwwwwwvvvvvvvvvvvvuu\ uuuuuuuuuuttttttttttttssssssssssssrrrrrrrrrrrrqqqqqqqqqqqqppppppppppppoo\ oooooooooonnnnnnnnnnnnmmmmmmmmmmmmllllllllllllkkkkkkkkkkkkjjjjjjjjjjjjii\ iiiiiiiiiihhhhhhhhhhhhggggggggggggffffffffffffeeeeeeeeeeeeeeeddddddddddd\ dccccccccccccbbbbbbbbbbbbaaaaaaaaaaaa````````````____________ZZZZZZZZZZZ\ ZYYYYYYYYYYYYXXXXXXXXXXXXWWWWWWWWWWWWVVVVVVVVVVVVUUUUUUUUUUUUTTTTTTTTTTT\ TSSSSSSSSSSSSRRRRRRRRRRRRQQQQQQQQQQQQPPPPPPPPPPPPOOOOOOOOOOOONNNNNNNNNNN\ NMMMMMMMMMMMMLLLLLLLLLLLLLLLKKKKKKKKKKKKJJJJJJJJJJJJIIIIIIIIIIIIHHHHHHHH\ HHHHGGGGGGGGGGGGFFFFFFFFFFFFEEEEEEEEEEEEDDDDDDDDDDDDCCCCCCCCCCCCBBBBBBBB\ BBBBAAAAAAAAAAAA99999999999988888888888877777777777766666666666655555555\ 5555444444444444333333333333222222222222111111111111000 } frm:SJSPIDER01JULIA {; Ron Barnett, 1995 ; floating point required z=real(pixel)+flip(imag(pixel)*p1) c=p2+p1*real(p3)+flip(imag(p3)): z=z*z+c c=c/2+z |z|<=100 ;SOURCE: reb007.frm } Roger Alexander _________________________________________________________________ MSN Dating: Find someone special. Start now. http://go.microsoft.com/?linkid=9734384

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Art and Numbers
by Roger Alexander 05 Jun '10

05 Jun '10

A busy day yesterday and I didn't get to post. This must not become a habit. Art and algorithm. Two images are posted at http://maxitersfractalfollies.blogspot.com. One is a fractal the other is the painting "The Great Wave" by the Japanese artist Hokusai. The similarity in designs is intriguing. fract226.gif { ; reminds me of Hokusai's "The Great Wave" ; blank ; calctime 0:09:17.17 ; created May 23, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2000 type=formula formulafile=fract196.frm formulaname=Moe function=abs/cosxx center-mag=-0.04194775500193852/+0.48794277466039360/47.65718/1/-49.9999\ 999999999432/-1.14117049143658278e-013 params=-0.6664326914273507/-0.7950987273781549 float=y maxiter=3600 logmap=21 cyclerange=0/255 colors=00T00U00W00X00Z00`00a00c00d00f00h00i00k00m01m03m04n06n07o09o0Ao0C\ p0Ep0Fq0Hq0Iq0Kr0Lr0Ns0Ps0Qs0St0Tt0Vu0Wu0Yu0Zv0`v1`v3av4av6bv7cv9cvBdvCe\ vEevFfwHgwIgwKhwMiwNiwPjwQkwSkwTlwVmxXmxYnx_nx`oxbpxcpxeqxgrxhrxjsyktymt\ ynuypvyrvyswyuxyvxyxyyzzzzzzyyzxyzxxzwxzvwzuvzuvztuzsuzstzrszqszprzprzoq\ znpznpzmozlozknzkmzjmzilzilzhkzgkzfjzfizeizdhzdhzcgzbfzafzaez`ez_dz_czZc\ zYbzXbzXazW`zV`zV_zU_zTZzSZzSYzRXzQXzQWzPWzOVzNUzNUzMTzLTzLSzKRzJRzIQzIQ\ zHPzGOzGOzFNzENzDMzDMzCLzBKzBKzAJz9Jz8Iz8Hz7Hz6Gz6Gz5Fz4Ez3Ez3Dz2Dz1Cz0B\ z0Az08z07z06z04z03z02z00z00y00x00w00v00u00t00s00r00q00p00o00n00m00l00k00\ j00i00h00g00f00e00d00c00b00a00`00_00Z00Y00X00W00V00U00T00S00R00Q00P00O00\ N00M00L00K00J00I00H00G00F00E00D00C00B00A00900800700600500400300200000000\ 000000100300400600800900B00C00E00G00H00J00K00M00O00P00R } frm:Moe {; Mutation of 'Zexpe'. ; Original formula by Lee Skinner [75450,3631] ; Modified for if..else logic 3/19/97 by Sylvie Gallet ; For 'Zexpe', set FN1 & FN2 = IDENT and P1 = default ; real(p1) = Bailout (default 100) s = exp(1.,0.), z = pixel, c = fn1(pixel) ; The next line sets test=100 if real(p1)<=0, else test=real(p1) IF (real(p1) <= 0) test = 100 ELSE test = real(p1) ENDIF : z = fn2(z)^s + c |z| <= test ;SOURCE: fract196.frm } Roger Alexander _________________________________________________________________ Learn more ways to connect with your buddies now http://go.microsoft.com/?linkid=9734388

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FOTD 05-06-10 (Pleasant Patterns [8])
by Jim Muth 05 Jun '10

05 Jun '10

FOTD -- June 05, 2010 (Rating 8) Fractal visionaries and enthusiasts: Today's image is little more than a pleasing pattern. It has no minibrot at the center, though smaller quintic minibrots are scattered all through it. The name "Pleasant Patterns" refers to the general area of the parent fractal. On the surface, this parent fractal appears to be a Mandelbrot set, but the deeper one goes into it, the more it takes on quintic characteristics. The location of today's scene is in a small filament extending from the northeast shore line of the main bay of the large minibrot on the main spike of the parent. The image consists of a combination of hills and valleys. The most prominent hill lies in the center and is colored bluish- red, while the deepest valley surrounds the quintic minibrot in the upper left part of the frame. The rating of an 8 might be a bit liberal for an image with no well-defined quadratic minibrot at the center, but the combina- tion of hills and valleys adds just enough interest to justify the rating. The calculation time of a very brief 34 seconds means that very little time will have been wasted if the image fails to please. Viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> makes the viewing process even more efficient. At lunch on Friday, as images of dead oil-covered birds flashed on the TV screen, FL scolded me for showing too little concern about the environmental damage being done in the Gulf as a result of the continuing oil leak. She said I should be very angry at the responsible oil company. To avoid a luncheon squabble, I voiced no opinion, but such naive, feel-good short- sightedness kind of annoys me. Of course I'm concerned, but let's face it. *WE* are the real problem. We are the ones addicted to petroleum. We heat our homes with oil; we buy almost everything in plastic bottles; we absolutely need our cars if we want to do anything but sit in our front yards. Until we end our addiction, I suggest we fill our tanks in silence and stop pretending to care about the environment. I'll now have nothing more to say on this admittedly political topic. Fractals and weather are far more fun and sometimes far less frustrating. Midsummer conditions prevailed again on Friday here at Fractal Central, with oppressive humidity, hazy partly cloudy skies, thunder-storms on the horizon, and a temperature of 90F 32C. The fractal cats spent most of the day on the cool floor in the kitchen, hoping for an unexpected spill of cream, which never happened. My day was fair enough, and if everything goes well, tomorrow will be a repeat. The next FOTD fractal will be posted in 24 hours. Until then, take care, and continue the endless search for the perfect fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Pleasant_Patterns { ; time=0:00:34.16-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivbrot-2 function=recip float=y center-mag=-1.748847663485/+0.000310333759/1e+008/\ 1/180 params=5/-100000000/0/0 maxiter=1500 inside=0 colors=000q_Xm_Wh_Vd_U``TW`SS`RN`QJaPFaOAaN6aM2aL5\ cO8dRBfUEgWHiZKjaMkcPmfSniVplYqn`sqctteuvctubst`rs\ _qrYpqXopVnoUmnSlmRklPjkOijMhiLghJfgIefHdeKegNgiQh\ kTimWkpZlrantdovgpxhluiirjepkbmlZkmWhnTfoPcpM`qIZr\ FWsBUt8Rt5Pr7Rp9SoBTmDUlFVjHWhJYgLZeN_dP`bRaaTbzmc\ zhcyccxZcwVcvQctMcrJcpIbpBcp2cqAcsHetPfrXftcgukhws\ ixxiwufvpcum`tiYseVrbSqZPqVMpSJoOGnKDmHAlD7k94k62h\ 54e56b58_59Y5BV5DS5EP5GN5IK5JH5LE5NC5OBANAEMAIL9MK\ 9QJ8UI8YH7aG7eF6iE6mEPhzRfxTdwVbvX`uZZt`XsbVrcTqeR\ ogPniNmkLlmJkoHjqFirDhiLcaSZU_ULfPDnK5uF9qHCmIGiKJ\ eLNaMQYOUUPXQQ`MScITgEUjAWn6Xq2Yn4`k5ci6ff7hd8ka9n\ _ApU9cO8SJ7GLBNNFTPJZRNeTRkUUqRRkPPfNN`LLWea`yrdzp\ bzn`zl_zjYzhWzfVzdTzbSz`QzZOzXNzVLzTKxVLvWMuYNsZNq\ `OpaPnbQldQkeRigSghTfiTheXib`j_ckWglTjmQnnMqoJupGx\ kIufJrbLpYMmTOjPPhKReFSbBU`6VY2WW5XV7YU9ZUBZTD_SF`\ SHaRJaRK_ULZXs_YtZYuZZvZZ } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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FOTD 04-06-10 (Marshmallow Design [9.5])
by Jim Muth 04 Jun '10

04 Jun '10

FOTD -- June 04, 2010 (Rating 9.5) Fractal visionaries and enthusiasts: Today's image could almost be a photograph of a 3-D scene. Actually, there is nothing 3-D at all about it. It is totally 2-D, a flat scene in a fragmented elephant in the rudimentary East Valley of the parent fractal that results when the expres- sion Z^(1.5)+C is iterated 12 levels up the logarithmic ladder with the 'round' function applied. The 3-D effect is a combination of the coloring and the basic underlying iteration bands. But it is an illusion. The wrong colors will totally destroy the 3-D effect. Actually, the visual 3-D view we have of the so-called outer 'real' world is also an illusion. The images on our retinas are totally 2-D. The third dimension appears in our awareness when our mind (or brain if you're a materialist) compares and com- bines the two slightly different images sent to it by our two eyes. Does this mean that the 3-D solidity of the outer world is also an illusion? I often wonder. True, the outer world obeys the mathematical laws of 3-D space, but we ourselves invented mathe- matics and tweaked its rules so that it works correctly when we apply it to the world we assume exists around us. We can prove that the universe is three-dimensional by observing the orbits of the planets. It can be demonstrated mathemati- cally that stable planetary orbits are possible only in spaces of two or three dimensions. Of course, if we lived in a world of four spatial dimensions, we would have developed a math that demonstrates that stable orbits are possible also in spaces of four dimensions. Now back to the image. I named today's image "Marshmallow Design". I must have had a fleeting impression of roasting marshmallows while trying to think of a name. The rating of a 9.5 is exceptionally high, and includes a generous self-reward for the coloring, but I think the image is worth it. The calculation time of 1-2/3 minutes will be no problem for those who cook their own fractals. Those who prefer their fractals pre-cooked and canned may view the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> Typical summer weather made Thursday a typical partly cloudy summer day here at Fractal Central. The fractal cats thought the temperature of 88F 31C was a bit warm, but with the cool tile floor to stretch out on, they did not complain too much. My day was about average. The next FOTD will be posted in 24 hours. Until then, take care, and the greedy big-oil guys are getting worried. So keep pumping and reassure them that we still depend on them. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Marshmallow_Design { ; time=0:01:40.86-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=round logmap=270 center-mag=+0.159907326462106/-0.00233287824442478\ /1.136758e+013/1/-27.9/0 params=1.5/0/12/0 float=y maxiter=1500 inside=0 mathtolerance=0.05/1 colors=0004Ab17c48e79gAAiDBkGCmICoMEmQGiUHdYJ`aLWe\ MSiONmPJnNIoMHoLGpKGpJFqIEqHDrGDsECsDBtCAtBAuA9u98\ v87v77vEBzwmyykxxiwwgvvettcrraoo_llYiiWffVccT__RWX\ PSTOOPMLMKIJIGHGEFECDCABA8986764542321200100000000\ 00000000000AAAKKKUU_ZZYS`VLaTEjRJhSOfSTdSXbSa`SfZS\ kXSoWSn_QzzczxczuzvszrqmmocdmUXdSPWWGSU8OS0MQ0KO0I\ M0GKm`5gd9ciEceEcaBhY9mU7rQ5sO7tL6sS5rZ4qe3pl2os1n\ y1mn5ac9VUDNJHG9KUHLgPMtWMneRhoVbyZRjBPhANf9Le9Jc8\ Hb8F`7E_7FZEGYKHXQIWWJVbKUhLTnMStV_lcgdloXuwQorSjm\ TehV`cWWZXRUZMP_HL`KzzzzzEzzmzzEzzmzzDfRDcPIgPNjPS\ mPXpPasPevPhqSjlUlgWnbYpY_rUalTXfSTaROWQKQPGLOBFN7\ AM3HK5NJ6TI7ZH8dG9fEDgDHhCLjBPkATl9XjIRhRMf_HdhCcp\ 7UiHKbRBW`FX_IY_LY_OZ_R__U__MdRFiz8nzArzAszAtzFuzH\ vzJwzzxwzyxzzxzzpzzhzz`zzTzzLWzESzJPzOQzSRzWSz_Tzb\ UzfzzjzzmzzjzzgzzdzzbzzezzhWza`zVezOjzHozAtz4rzFqz\ Ppz_oziazVPzHCz3Bz2Bz2Bz2 } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-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 03-06-10 (Square-Root-of-Three Minibrot [8.5])
by Jim Muth 03 Jun '10

03 Jun '10

FOTD -- June 03, 2010 (Rating 8.5) Fractal visionaries and enthusiasts: The parent fractal of today's image was created by iterating the expression Z^(sqrt(3))+C with the MandelbrotBC3 formula at a level of 12 turns up the complex logarithmic hyperspiral with the 'round' function applied. This parent consists of a large circular main bay, with strangely enough, two large period-2 buds, one on the northwest shore line, the other on the north- east shore, with the whole thing resembling the head of Mickey Mouse. Today's scene is located on the western edge of the northwest period-2 bud. The MandelbrotBC3 formula takes advantage of the multi-valued nature of the complex logarithm. Unlike the expression Z^2+C, which, regardless of the value given real(p2), always draws the Mandelbrot set, an expression such as Z^(sqrt(3))+C has no single fractal associated with it. It has instead an infinity of different fractals, every one of which is the result of itera- ting the expression Z^(sqrt(3))+C. Asking which fractal is the correct one is meaningless. Today's image is named "Square-Root-of-Three Minibrot". The reason for the name is obvious. The rating of an 8-1/2 might be a bit liberal, but I did do some extra work on the coloring, and I feel I deserve the reward. The calculation time of 1-3/4 minutes is well within the comfort range for fractal generation. The comfort may be increased yet further by surfing out to the FOTD web site at: <http://www.Nahee.com/FOTD/> and viewing the image there, already calculated. Lots of sun and lower humidity made Wednesday a rather pleasant day here at Fractal Central. The fractal cats were up and about most of the day, getting into various kinds of mischief -- a good sign that they approved of the drier conditions, if not the higher temperature of 88F 31C. My day was acceptable, if not great. The next FOTD will be posted in 24 hours. Until then, take care, and if you're a serf, be faithful to your lord and master. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= SqrtThree_Minibrot { ; time=0:01:45.08-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=round passes=1 center-mag=-0.9914563737440867/+0.4862853210787398\ /1.758179e+011/1/-67.5/0 params=1.732051/0/12/0 float=y maxiter=3000 inside=0 logmap=162 periodicity=6 mathtolerance=0.05/1 colors=0004Kp5Kn6Kl6Kj7Kh8Kf8Kd9Jb9I`9HZ9GX9FV9ET9\ DRzzzzzzzzzzzzzzzzzzzzzzhzzUfzGpzwVzs_mpcDh_JaWPVS\ wUOtLLjCKb7KW2KOFJ000KKIPRHUYGYdG`lLkrOsuQzzS9cU7G\ R5MZ3K`2Jb8NeDQgJTjOWlT_oZbqcethhvagoWgiQfcKfYEeS8\ eM2eG6dRAc`EbkHbuQWqZPngIjrBgz5doBYeHRXMKNSDEX7GZz\ HmzImzMWZPQYSKXVEWY8V_EY`K`aPbiSdpVfwYhlVnbStTQyUS\ uUUqUVmVXiVYeV_aV`ZYXW`UTbQReNOgJMjGJlDHkBzzczzczz\ czzazzUzmUknqgkjjicmgXpeRrgWqh_qicqjgqllpmppntpoxp\ senwOmz6lqJehWZ_hSStLSpKSlJSiISeHSaGSZFSVESSESJRSA\ cS2oMVsNPqNKpNEoN9nI7iE5d94`52W11S72XC2aH2eN2jS2nX\ 2sa2wb7zcBzdFzeJzgNziRukVmmZcrSUvLKzEBz77zC8zG9zLA\ zPAzTBzZCzcDzhDzmHzrLzvPzzTzzSzzRSzQQzPPzONzNLzMKz\ LIzKHzKKzJKzIzzIzzHzzGzzGzzFzzEzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzz8zd8ze8zf8zg9zh9zi9zj\ 9zk9zlAzmAznAzoAzpAzqGzqLzqRzqWzqazqfzqkzqgzrdzr`z\ rYzsVzsRzsOzsLztHztazYjzi } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-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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Fmod Leaves
by Roger Alexander 03 Jun '10

03 Jun '10

Today's fractal is Fractint's spider fractal with some fmod coloring. It produced an effect which reminded me of the scaly leaves found on some plants, cypress trees being an example. On an unrelated note try out this site's fractal content http://fractalfoundation.org/ I liked it. On another unrelated note if fractals could talk I'm sure they would say "Check me out at http://maxitersfractalfollies.blogspot.com where I'm ready made." Pause... This whole post seems to be a series of unsuccessful segues. fract071.gif { ; fmod spider,somewhat plantish ; blank ; calctime 0:07:11.16 ; blank ; Fractint Version 2004 Patchlevel 9 reset=2004 type=spider center-mag=+0.61712322896425750/+0.60861797108095750/13282.06/1/47.50000\ 00000237961/3.88578058618804789e-016 params=0.206244087038789/-1.168004394665365 initorbit=0.4/0.2 float=y maxiter=1500 inside=0 proximity=2 outside=fmod periodicity=4 colors=0100200300400500700800900A00B00D00E00F00G00H00J00K00L00M00N00P00Q\ 00R00S00T00V00W00X00Y00Z00`00a00b00c00d00f00g00h00i00k00k01k02k03l04l05l\ 05m06m07m08n09n0An0Bo0Bo0Co0Dp0Ep0Fp0Gp0Hq0Hq0Iq0Jr0Kr0Lr0Ms0Ns0Ns0Ot0Pt\ 0Qt0Ru0Su0Tu0Tu0Uv0Vv0Wv0Xw0Yw0Zw0Zx0_x0`x0ay0by0cy0dz1dz1ez1ez1fz2fz2gz\ 2gz2hz3hz3iz3iz3jz4jz4kz4kz4lz5mz5mz5nz5nz6oz6oz6pz6pz7qz7qz7rz7rz8sz8sz\ 8tz8uz9uz9uz9tz9tz9tz9sz9sz8sz8rz8rz8rz8qz8qz7qz7pz7pz7oz7oz7oz6nz6nz6nz\ 6mz6mz6mz5lz5lz5lz5kz5kz5kz4jz4jz4jz4iz4iz4hz4gz4gz4fy4fy4ey4dy4dy3cy3cx\ 3bx3ax3ax3`x3_x3_w3Zw3Zw2Yw2Xw2Xw2Wv2Wv2Vv2Uv2Uv2Tv2Su1Ru1Qu1Pt1Pt1Pt1Os\ 1Os1Or1Nr1Nr1Nq1Mq1Mp1Mp1Lo1Lo1Ko1Kn1Kn1Jm1Jm1Jm1Il1Il1Ik1Hk1Hj1Gj1Gj1Gi\ 1Fi1Fh1Fh1Eg1Eg1Eg1Df1Df1Ce1Ce1Ce1Bd1Bd1Bc1Ac1Ab1Ab19b19a18a18`18`17_17_\ 17_16Z16Z16Y15Y15Y14X14X14W13W13V13V12V12U12U11T11T10S0 } Roger Alexander _________________________________________________________________ Win $10,000 from Hotmail! Enter Here. http://go.microsoft.com/?linkid=9729708

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Threads-I Like the Colors
by Roger Alexander 02 Jun '10

02 Jun '10

A question of nomenclature. Should these structures be called threads (or filaments) to distinguish them from the linear structures such as found in the classic mandelbrot? And what could the mandelbrot linear structures be called? Go to http://maxitersfractalfollies.blogspot.com to see what prompts this question. fract234.gif { ; filaments ; blank ; calctime 0:31:17.03 ; created Jun 01, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=2circles.frm formulaname=cenx=ceny_jul center-mag=0.0904633/-0.271478/13.83126 params=-0.8416089358195745/-0.2229987487411115/-0.1370891445661794/0.368\ 1142612994781/0.5048982207708976/-0.5791192358165227 float=y maxiter=1500 decomp=256 periodicity=0 cyclerange=0/255 colors=DHVCGUBET9DS8BR7AQ69P57O36N24M13L02K02K13L25M36N47O69P7AQ8CR9DSAE\ TBGUCHVDIWFKXGLYHMZIO_JP`KRaLSbMTcOVePWfQXgRZhS_iTajUbkVclXemYfnZgo_ip`j\ qakrbmscntepufqvgrwhtxiuyjvzjvziuyhsxgrwfqvdoucntblsakr`jq_hpZgoYfnWdmVc\ lUbkT`jS_iRYhQXgPWfNUdMTcLSbKQaJP`IN_HMZGLYEJXDIWCHVBFUAET9DS8BR7AQ58P47\ O36N24M13L02K02K13L25M36N47O69P7AQ8CR9DSAETBGUCHVDIWFKXGLYHMZIO_JP`KRaLS\ bMTcOVePWfQXgRZhS_iTajUbkVclXemYfnZgo_ip`jqakrbmscntepufqvgrwhtxiuyjvzjv\ ziuyhsxgrwfqvdoucntblsakr`jq_hpZgoYfnWdmVclUbkT`jS_iRYhQXgPWfNUdMTcLSbKQ\ aJP`IN_HMZGLYEJXDIWCHVBFUAET9DS8BR7AQ58P47O36N24M13L02K02K13L25M36N47O69\ P7AQ8CR9DSAETBGUCHVDIWFKXGLYHNZIO_JP`KRaLSbMTcOVePWfQYgRZhS_iTajUbkVclXe\ mYfnZho_ip`jqalrbmscntepufqvgswhtxhtxiuyhtxgrwfqveoucntbmsakr`jq_ipZgoYf\ nXdmWclVbkT`iS_hRZgQXfPWeOUdNTcMSbLQaKP`IO_HMZGLYFJXEIW } frm:cenx=ceny_jul { ; Kerry Mitchell 26aug98 ; ; "2 concentric circles" coloring method for Julia sets ; p1 = c = Julia parameter ; p2 = (both) circle center ; real(p3) = x circle radius ; imag(p3) = y circle radius ; bailout hardcoded to 10^12 ; use "decomp=256" coloring ; zc=pixel, c=p1, bailout=1e12, iter=1, rmin=1e12 cenx=p2, radx=real(p3), rad2x=radx*radx ceny=cenx, rady=imag(p3), rad2y=rady*rady: iter=iter+1, zc=sqr(zc)+c tempx=|zc-cenx|-rad2x tempy=|zc-ceny|-rad2y temp=tempx+flip(tempy), r=|temp| if (r<rmin) rmin=r, z=temp endif if ((|zc|>bailout)||(iter==maxit)) iter=-1 endif iter>0 } Roger Alexander _________________________________________________________________ MSN Dating: Find someone special. Start now. http://go.microsoft.com/?linkid=9729707

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FOTD 02-06-10 (Mandelbrot Picnic [X])
by Jim Muth 02 Jun '10

02 Jun '10

FOTD -- June 02, 2010 (Rating X) Fractal visionaries and enthusiasts: Today's image is an expedition into the Mandelbrot set. The trip takes us to a depth of over 10^17, which is not all that deep as images go, but still deep enough to require the much slower arbitrary-precision math routine. The tiny minibrot in the image is located in the Seahorse Valley of a much larger but still tiny minibrot on a filament extending northwest from the second bud out the main stem of the largest minibrot on the main stem of the parent Mandelbrot set. And with all this said, it's time to enjoy the image. In my opinion, the most striking features of the image are the brill- iant green area inside the ring of chaos and the 'resetting' of the count of elements as we approach the minibrot. This reset- ting to a lesser power of 2 indicates that the minibrot at the center lies in the attraction basin of a larger minibrot, and is not directly attracted to the M-set itself. The rating of an X is not a rating of a roman-numeral ten. It means I had a hard time deciding how to rate just another not-so- deep, deep view into the M-set. The name "Mandelbrot Picnic" expresses the fun of looking into the Mandelbrot set even after more than 30 years beyond its dis- covery. With an infinity to explore, there is, and always will be, something new to be found. The calculation time of today's image is not very much fun however. Requiring the slower arbitrary math, the image takes over 19 minutes on the 2000mhz machine. Those who do not appreciate delayed gratification can enjoy the instant variety on the FOTD web site at: <http://www.Nahee.com/FOTD/> While we were watching the news at lunch on Tuesday, FL made a comment about the 'evil' big-oil companies. I said nothing at the time, but I did leave a little comment at the end of this discussion. Lots of clouds and humidity, with a temperature of 84F 29C and showers of rain, made Tuesday a rather unpleasant day here at Fractal Central. The fractal cats checked the outside condi- tions several times before deciding to settle on the kitchen floor, where they not only could keep cool, but were within an easy leap if they heard a can being opened. My day was average; tomorrow will be near the same. The next FOTD will be posted in 24 hours. Until then, take care, and if we are so ready to condemn the greedy big oil companies, why do we continue to feed their greed by consuming their products? In my opinion, our resentment of 'big oil' is a sham. What we really resent is the way we have let the pet- roleum conglomerates become our overlords, and in so doing, have become their dependent and obedient serfs. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandelbrot_Picnic { ; time=0:19:22.72-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.7830528137696\ 68868412/0.005956939879739020396/1.354584e+017/1/\ -109/0 params=0/0 float=y maxiter=18000 bailout=6 inside=0 logmap=1072 colors=000AIKAKOAMSAOWCQ_EScGThIVlJWpLZlM`iNcfPebQ\ h_RjXTiSUlOVoJcrFmuAzt6wmBmcFcUJUKNQCRP6VO0Zillhnf\ hp`hqWhsQhuKhvFfsKdqOcoSamX`k`ZidYghTagOWgJQfEKfCL\ eAMd8Mc6Nb5NbIYaUg`SeYQdWObUMaSK`PIZNGYLFXJKWLOWMT\ WNXWOaVQeVRjVSnVT_RcLNm6KwIx4Lt8NqCQmGSjJUgNXcRZ`V\ `YYeZai_em_hq`luapyasrZokWldUhYReRPaKMZEKWANd7QlFT\ hNVeVXaa_ZiaVqcSxePtcSqaVm_YjY`fWccVf_UeWUeSUeOUeK\ UdGUdCUd8UdPVdeVdbDcZHdWKdSNdPQdLTeIWeEZeBae9Yd8Vd\ 6Sd5Pd3Md2Jd1GdAFhIEkRDnZCqgBtoBwhHoaNhVT`OYUHZMAc\ K0m8nz7an6Qe5DW41N4WdLywazzczvdzrfzngrlhpkjoiknhls\ gmrfmqekpZioSgnLefBcU1Xk5_l9YnDWpGUsKSuOQwSPyVPnMI\ dDCV46_9BdDFhHJmMNqQRvUVzYZwMTtBOr0JeFPUUVIh_PmdVr\ havmgzqnzvtzzazzKzzJzpIzgIzYHzPHzGxz_yzZyzZyzZzzYz\ zYzzYyzWxzUwzSvzRuzPtzNszLrzKjzSczZXzfQzmJztOzqTzo\ YzlbzjXzdRz_nzAfzG_zLSzUOzTLzRHzPDzO9zM6zLEzILzGTz\ E_zBgz9nz7lz5kz4fz9bzDZzI } END PARAMETER FILE=========================================

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Spirals
by Roger Alexander 01 Jun '10

01 Jun '10

The ubiquitous spiral-in its simplest form radius=angle. The 2 dimensional form of the cross section of a seashell, the 3 dimensional form of the vortex of a tornado. It's universality has an almost mystical appeal. Today's post uses a built-in formula of Fractint. Save some cpu cycles and check out the plotted image at http://maxitersfractalfollies.blogspot.com fract238.gif { ; metallic spiral ; blank ; calctime 0:06:15.09 ; created May 31, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=mandellambda center-mag=+1.03910068426197500/+0.42203389830508450/133.3333 params=-0.673329874568926/0.04385509811700797 float=y maxiter=12000 outside=atan cyclerange=0/255 colors=000000111222333333444555666777777888999AAAAAABBBCCCDDDDDDEEEFFFGG\ GHHHHHHIIIJJJJJJKKKLLLMMMMMMNNNOOOPPPPPPQQQRRRRRRSSSTTTUUUUUUVVVWWWWWWXX\ XYYYYYYZZZ______``````aaabbbbbbcccddddddeeeeeeffffffggghhhhhhiiiiiijjjjj\ jkkkkkkllllllmmmmmmnnnnnnoooooopppppppppqqqqqqrrrrrrrrrssssssssstttttttt\ tuuuuuuuuuvvvvvvvvvwwwwwwwwwwwwxxxxxxxxxxxxxxxyyyyyyyyyyyyyyyyyyyyyzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzyy\ yyyyyyyyyyyyyyyyyyyxxxxxxxxxxxxxxxwwwwwwwwwwwwvvvvvvvvvuuuuuuuuutttttttt\ tsssssssssrrrrrrrrrqqqqqqpppppppppoooooonnnnnnmmmmmmllllllkkkkkkjjjjjjii\ iiiihhhhhhgggffffffeeeeeeddddddcccbbbbbbaaa``````______ZZZYYYYYYXXXWWWWW\ WVVVUUUUUUTTTSSSRRRRRRQQQPPPPPPOOONNNMMMMMMLLLKKKJJJJJJIIIHHHHHHGGGFFFEE\ EDDDDDDCCCBBBAAAAAA999888777777666555444333333222111000 } Roger Alexander _________________________________________________________________ 30 days of prizes to be won with Hotmail. Enter Here. http://go.microsoft.com/?linkid=9729709

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