February 2008 - Fractint - mailman.xmission.com

FOTD 20-02-08 (Fractal Sponge [No Rating])
by Jim Muth 20 Feb '08

20 Feb '08

FOTD -- February 20, 2008 (No Rating) Fractal visionaries and enthusiasts: Since I am not yet feeling up to par, today's discussion will again be brief. The image is a scene in the fractal that results when 7 negative parts of Z^(-1.5) are combined with 1 negative part of Z^(-6.6) and (1/C) is added. I gave the image no rating, though for some reason now forgotten, I named it "Fractal Sponge". The calculation time of 2 minutes is brief enough to give no one trouble. And for even more convenience, the finished image will soon be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A typical midwinter day prevailed here at Fractal Central on Tuesday, with partly cloudy skies, a few stray flakes of snow, and a temperature of 34F 1C. The fractal cats enjoyed the sunny periods, rolled over, then went to sleep. After taking it easy all day Tuesday, I hope to be back to near full prodctivity by Wednesday. (I write the FOTD discussions on the previous day.) The next FOTD will likely be posted in 24 hours. Until then, take care, and search for something. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fractal_Sponge { ; time=0:02:02.68-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+1.325464621083165/+0.049273549792319/\ 1.948911e+007/1/7.5/1.23877376398406902e-007 params=-7/-1.5/-1/-6.6/0/0/0/0 float=y maxiter=1200 inside=0 logmap=157 periodicity=10 colors=000LJLzyuzsuzquzvuzkozokzhgziduaZwdVrXRrZNm\ VHmTEhPAhL6hJ0cG0cE0ZA0X60T40R00P00ER04qRAk`GggJdk\ LbmNZoRXqTTsVRuZNv`LzbHzeGzgCziAzm6zo4zq2zkAzgGzdL\ z`RzXZzTdvPiuLosGivCex8`z4Xz0Rz0Nz0Hz0Ez0Az0HgAPCN\ V0LZ0Lb0Je0Ji0Hm0Hq0Hu0Gx0Gz0Ez0Ez0Ez0Gz4GvHHoVHgg\ J`uJTzJLzPNzTPzXPxbRqeTiiTbdVXZXRVXLPZGJ`AG`4Ab04d\ 00d04Z06T0AN0CH0EC0H80J20L00P00R00T00R00P00N00L00L\ 00J20H60GA0GE0EH0CL0AN08R08V06Z04b02e02g06g0Ag0Eg0\ Gg0Jg2Ng2Rg4Tg6Xg8`gAbgCegCigEmgGogHsgJvgLxgLPbX0Z\ gHmgezgzzgzzdzzbzz`zzZzzXzzTzzRzzPzzNzxLzxJzvGzuEz\ sCzqAzo8zm4zk2zi0zg0ze0ze0zi2vkAsmGooNksVgu`dvg`xm\ XuqVqsTmvRixNezLbzJZzHVzGTz00A00E00H00L00N00R20V40\ X80`A0dE0eG0iJ2mL4oN6sRAvTCxXEzZGz`HzLZx8oo0ze0zZ0\ zb0zd0ze0zg4zk8zmCzoHzqLzsRzvVzx`zzdzzgzzmzzqzzvzz\ zzzzzzvzzozsgzg`zXTzNLzCEz06z00z00z0zzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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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No FOTD for Feb 19
by Jim Muth 19 Feb '08

19 Feb '08

There will be no FOTD for Feb 19 because I came down with a case of the Hong Kong, or something else, flu. I almost never get the flu, but this time I did. I seem to have reached the recovery stage however, and unless there is a serious relapse, The FOTD for Feb 20 will appear on schedule. JIM

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FOTD 18-02-08 (Two Sides of a Coin [7])
by Jim Muth 18 Feb '08

18 Feb '08

FOTD -- February 18, 2008 (Rating 7) Fractal visionaries and enthusiasts: Unfortunately, with a viral attack, I am not feeling up to par, (me, not the computer), so today's discussion will be brief. The left half of today's image is half evaporated; the other half is normal. And the dividing line runs right through the center. I'll not describe the parameter tricks that created the unusual effect. They are clear from the parameter readings. The rating of a 7 seems appropriate for such an unusual image. The name "Two Sides of a Coin" describes the two dis-similar halves of the picture. The calculation time of 10-1/4 seconds is so fast as to be completed almost before it starts. And if running parameter files is inconvenient, the finished image is posted for instant enjoyment on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The temperature reached 41F 5C here at Fractal Central on Sunday, but heavy clouds kept the mood depressed. At least, the forecasted rain held off until after dark. The fractal cats held off asking for their daily treats until after dark also. Ignoring the coughs and sneezes, my day was fair enough. The next FOTD will be posted in 24 hours. Until then, take care, and search through the darkness for the light. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= 2_Sides_of_a_Coin { ; time=0:00:10.16-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip center-mag=+9.91007278492382100/+5.580966722131834\ 00/287477.6/1/-20/0 params=-4/-1.6/-0.8/-7.7/0/\ 11666860000000000.0 float=y maxiter=1000 inside=atan periodicity=10 colors=000btTgvOmxJrzEpwQnt`lqkjovklrlinmgjndfobcn\ camd_keZjfXigVhhTfiSejQdkOclNeiWggcidljbth_rfYqdWo\ bTn`RmYPkXNjUKhUIgPGdQEdJBZM9a00KJ5_C8VSAaSDa`FbeH\ ciKczZdrOezcezTfzZfzcazhYzUUiTPdTLZTHUSCOS8JS4ES0e\ vPzzZpoUpeZpWbqMgqClq2pDdGCgLCiQBkVBm_BpdAriAtnAvr\ 8tm6rh4pd2n_0mW6pYBrZGt`LvaRuSXtJbsAhr1cc5ZP9VBCbT\ BijBldDn_EqVFsQHvLIxGJzBKtDcoFvtGqxHltMopQqlUshYuv\ hFsmPpqYmufjyoglZd_JaO3cRBeUIfXQh_XjbdkdkjYejS_iMU\ iGOiAIxWoecnOkn6sn6jm6al6Tk6Kj6CjKRdXeZitTgoWekYdf\ _bbbaYd_UfZQhVPfROeNNcJMbFLaBK_7JZ3IYDQUMYQVeMcmIl\ uFfrD`pCVmAQk9TdBWYCZSEaLFcFG_AUW6fS2sO9nLGiINdFU`\ B`W8gR5nM2uIRTQo0Yl6_jBahHbfMddRenQowQxnYVee1h_1jV\ 1lQ1nL1pG1rB1qAEpARo9co9pjCofEnaGmYJmTLlPNkLPkMTdN\ WZO_SObMPfFQi9Ql3ZpDftNnwXko`hgde_hbSl_KpXDtbKmgQf\ mW_raTfh_WofLvmOjnQZoSNpUBqW0r`sRakWbc_cXccPhdIleA\ pe3tVIsKXsAjsGlmMnhRpcXrZ } frm:MandelbrotMix4 {; 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, 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 17-02-08 (Going to Pieces [7])
by Jim Muth 17 Feb '08

17 Feb '08

FOTD -- February 17, 2008 (Rating 7) Fractal visionaries and enthusiasts: Visionaries see things, sometimes supernatural things, that ordinary people miss, but skeptics know that these things seen by visionaries exist only in the visionaries' minds, and therefore are not real. So far, so good, but then we get to fractals, which exist only as ideas in the mind until they are made real by a computer. So, depending on the definition of the word 'real', fractals can be real, unreal, or somewhere in between. Of course, it does not necessarily follow that the supernatural visions of visionaries are real . . . or could they be real . . . ? Regardless, today's image is worth the 7 points I gave it. It's a scene quite deep in the western east-style valley of the Z^(2.99)+C Mandeloid. In the case of the Z^2.99 fractal, the east and west valleys are quite different. Instead of broadening into a wedge, the valley on the west side of the main bay of today's parent fractal is starting to pinch off. The pinching has little effect on the presence of cubic minibrots, which are quite numerous and quick to find. I named the image "Going to Pieces", though I have forgotten why I gave it this name. The calculation time of 6-1/3 minutes is about what would be expected for an above-average image. (Can so many images actually be above average?) Why not escape the chore of calculation by viewing the already-calculated image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A really pleasant midwinter day prevailed here at Fractal Central on Saturday, with full sunshine and a temperature of 34F 1C. The fractal cats must have agreed, for they passed much of the afternoon at the back window, watching for squirrels. My day was spent taking it easy, an occupation that takes some getting used to. The next FOTD will appear in 24 hours. At least, it is scheduled to. Until next time, take care, and when skeptics tell you that fractals are all in the mind, remind them that the mind is quite real. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Going_to_Pieces { ; time=0:06:21.85-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotN float=y center-mag=-0.4160061105507027/-0.0015889616893713\ /9.619985e+011/1/-23.5/0 params=2.99/0/0/0/0/0 maxiter=10000 inside=0 logmap=1054 periodicity=10 mathtolerance=0.05/1 colors=000b_MbZNbYObXPbXQbXREFBGKCIOCKSCMUCOUCQUDS\ UDUUDWUDYUDZUDYUCXUCWUCVUCUUCUUBTUBSUBRUBQUBQUAPUA\ OUANUAMUAMUALUDKWFKYHJ_JIaLIcNHePGgRGfTFeVEdXEc_Db\ aCacC`eBZgAYiAXk9Wm8Vo8Uq7Ts5Qz7Su8UpAWkBXfDZaE`XG\ bSFbMHcOJcQKcSMcUNcWPcYQcZSc`TcbVcdWdfYdhZdj`dkadm\ cdoddqfdsgduidwjdxgfpehicjaalV_nNYoGTlMPiRLgWHd`Da\ e9_j5Xo1Vt7XnCYiI_cN`ZTbTYcOcgGbdJbaLbZNbWQaTSaQUa\ NXaKZaH`TTcLceCUh4Uj6Uh7Ug8Ue9UdAUbBUaCU_DUZEUXFUW\ HUUIUTJURKUQLUOMUNNULOUKPUIQUHNUPKUWHQcF7jH9hJAfKB\ dMCcNDaPF_QGZSHXTIVVJUWKSYMQ_NPaONcQLeSKgUIiWGkYFm\ _DoaBqcAseFJBJ40NJ6HYCBkI6lJ7lK9lLAmLCmMDnNFnOHnPI\ oPKoQLoRNpSOpTQqTSqUTqVVrWWrXYrXZqY_qY`pZ`pZapZao_\ ao_bo_cn`cn`dmadmaelbelbflbgkcgkchjdhjdijdjiejiekh\ fkhflgglggmggnfhnfhoeioeipUj2VkJWlMXmPXnSYoVZpY_q`\ _rc`sfatibulbvocwqdxteywMzzOzzPzzQzzRzzSzzUzzVzzWz\ zXzzYzzZzzbzzbzzbzzbzzbzz } frm:MandelbrotN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 16-02-08 (Iteration Feathers [8])
by Jim Muth 15 Feb '08

15 Feb '08

FOTD -- February 16, 2008 (Rating 8) Fractal visionaries and enthusiasts: Today's image is a further excursion into the debris at the edges of East Valley wedges. The scene of today's fractal is actually in the valley on the west side of the main bay of the Z^(3.01)+C Mandeloid, but this valley is a mirror image of the valley on the east side of the bay, and therefore has the same characteristics. In my opinion, the image is one point better than yesterday's, and honestly earns its rating of an 8. If I had a bit more time to work on the coloring, I might have been able to raise the rating to an 8-1/2. The fractal picture reminds me of nothing as much as fancy feathers, which is why I named it "Iteration feathers". The calculation time of 3-1/4 minutes is suitably brief. The finished GIF image is available as always on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy clouds and a chilly temperature of 36F 2C made Friday a rather unpleasant day here at Fractal Central. The only plus was that it stayed dry. The fractal cats were too busy chasing each other around the place to be concerned with the weather. My day was perfectly average, as I suppose tomorrow will be. The next FOTD is due in 24 hours. Until then, take care, and branch out into those curled-up higher dimensions. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Iteration_Feathers { ; time=0:03:15.26-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotN passes=1 center-mag=-0.3862006268294/+0.0060172237532/\ 2.616311e+009/1/35/0 params=3.01/0/0/0/0/0 float=y maxiter=2400 inside=255 logmap=418 periodicity=10 colors=000iVJiVJiUIhUIhTIgTIgTHfSHfSHeRHeRGdRGdQGc\ QGcPFbPFbPFaOFaOE`NE`NE_NE_MDZMDZLDYLDYLCXKCXKCWKC\ WJCVJBUIBUIBTIBTHASHARGARGAQG9PF9PF9OE9NE8NE8MD8LD\ 8LC7KC7KC7JB7IB6IA6HA6GA6G96F95E95E85D85C74C74B74A\ 64AEW9EV9DU8DS8CR8BQ7BP7AO7AM69L69K58J58I57G47F000\ 46E45D35C34A2492382371261241130120018ym7wk7vj7ti7s\ h7qg6pf6oe6mc6lb6ja6i`5h_5fZ5eY5cW5bV4aU4_T4ZS4XR4\ WQ4VP3TN3SM3QL3PK3NJ2MI2LH2JF2IE2GD2FC1EB1CA1B9197\ 186075054043022ZKKilObcKXVGPOCBK8474q2gk1be1Y_1TU1\ OO0JI0EC09604mtWlsVkrVjqUjpUioThnTgnSgmSflRekRdjQd\ iQciPbhPagOafO`eO_dN_dNZcMYbMXaLX`LW_KV_KUZJUYJTXI\ SWIRVHRVHQUGPTGPSGORFNQFUUZUPUUOUKNDJMCJLCIKBHKBGJ\ AGIAFH9EG9DF8DPcCE8BD7BC7AB69A68A58957846745635534\ 52342231221110000ozAmz9lz9jz9gz8gz8fz8ey8cx7bw7`u7\ _s7cq6ho6mm6rk5vi5zg5ze5zc4zc4zc4zc4zc3zc3zc3zc2zc\ 2zc2zc2zc1zc1zc1zc1zc0zzz } frm:MandelbrotN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 15-02-08 (A Whole New World [7])
by Jim Muth 15 Feb '08

15 Feb '08

FOTD -- February 15, 2008 (Rating 7) Fractal visionaries and enthusiasts: While searching for fractals Thursday, I found a whole new world -- not that this was much of a discovery, since I find a new world every time I visit fractal land. But this discovery was a bit more interesting than usual, and in my opinion, it was worth the name I gave to today's image. The new world is in East Valley of the (-Z)^(2.1)+C Mandeloid, which has started to broaden into a wedge. At first glance, the inside edge of this wedge appears perfectly featureless, but with fractals, things are seldom as they appear. When I checked this edge more closely than ever before, I found tiny irregulari- ties, which enlarge into curious gill-like features filled with minibrots like the one in today's image. If there had been more time to work on the coloring, the image might have rated an 8. As it is, the rating of a 7 will have to do. The calculation time of 5 minutes is slightly slow, though still well within reason. Also within reason is the trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the finished image there. A mostly sunny day with light winds and a temperature of 37F 3C graced the Fractal Central area on Thursday, while the fractal cats graced their shelf by the window, watching for excitement. I graced the work desk most of the day, but finished in time to find the day's FOTD. The next in the near-endless series of moderately impressive fractal images will be posted in 24 hours. Until then, take care, and when we run out of ideas, a miracle sometimes happens. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Whole_New_World { ; time=0:05:04.78-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMiN passes=1 center-mag=+0.256859403185/-0.075292790494/\ 8.72292e+007/1/-155/0 params=2.1/0/0/0/0/0 float=y maxiter=2600 inside=0 periodicity=10 colors=000f9gg8fh7ei5cj4bk3al2`j5Zh7Yf9XdBWbDU`FTZ\ HSYJRXPUWUWV_YUd_UiaXebZbca_dcXefTfhQgkNhmKizwizpc\ zm6yh9xcCwZFuUIsPLqKOoFRmATk5Vi8WgAYeAWcAUbASaAQ`A\ OZAMWAKUAIUA7UAJIhmJgmKfmLemMdmNcmNamO_mPYjQWgRUdR\ SaPRZNPWMPTKPQJPNHPKFPIEPJCPKBPL9PM8PMO4_WIebVjjhp\ quukffeTT_FEV10X44Z78`ACbDFdFJfINhLQjOUlRYmT`kUZiV\ YhVXfWWeXVcXUbYT`ZR_ZQY_PX`OV`NUaMSbLRbKTWJUQIWJIX\ DHY7H`0Lb0Pd1Tg2Xi4`k5dn6hp7lr8on9lkAihAgeBdbCb_C_\ WBWTATQAPMAMIAIECGGEIIGJMIMPKOTLRWMTZNW`OXcNZeN_hN\ ajNbmMdoMerMgtMhDy_Gu`IqaKmbNicPfdRceU`fWYgYWhVWeS\ WcPW`MWZKWWHWUEXRBYP9ZNA_PB`RCaTDbVEcXFeZGg`HhbIjd\ JkfKmhLojMplNqnNppMolLniKlfJicIg`HeYGbVG`SFZPEWMDU\ JCSGBQDAPAAO7BP8CR8CT9DW9EZAEaAFdBGfBGiCHlCHnCOYLU\ IUTJVSJWRKXRKXQLYPLZOMZOM_NN`MN`LOaLObKPbJPcIQdIQd\ `EbdHghJllMqoOvpPupPupQupQtpRtqRtqStqSsqTsqTsrUsrU\ rrVrrVr`HoaGmbFlcDkdCjeBh } frm:MandelbrotMiN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=(-z)^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 14-02-08 (Split in Infinity [7])
by Jim Muth 14 Feb '08

14 Feb '08

FOTD -- February 14, 2008 (Rating 7) Fractal visionaries and enthusiasts: Though today's image looks nothing at all like a typical scene in East Valley, it actually is an East Valley scene. Well, to be honest, it's not East Valley of the Mandelbrot set that the scene lies in, it's East Valley of the Z^2.01+C Mandeloid. And to further confuse matters, the parent fractal has been rotated about 180 degrees by the MandelbrotBC3 formula, so that East Valley lies on the west side of the complex plane. As a result of the rotation, the negative X-axis split now intersects East Valley, and works no end of mischief with it. Instead of terminating in a point, the valley has broadened into a wedge, with totally new elements along the north and south corners of the wedge. Today's scene lies in some of this new stuff on the south side of the valley-wedge. I rated the image at a 7, even though I was a bit cursory with the coloring. Then I named it "Split in Infinity". The name implies that fractals are infinite, and the East Valley in today's parent fractal is all split up. The calculation time of 7-1/2 minutes is slightly slow. So why not get relief by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> By the way, sometimes Paul cannot calculate and post the images immediately. If they are not there when you visit, try again a little later. Freezing rain fell all morning here at Fractal Central on Wednes- day, while the temperature hovered just below freezing. Strange- ly enough, when the temperature rose 3 degreess above freezing in the afternoon, the rain changed to snow. The fractal cats amused themselves watching the passers by slipping and sliding on the icy sidewalks. My day was spent working. The next FOTD is due in 24 hours. If all goes well, it will appear on schedule. Until then, take care, and seek the right light. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Split_in_Infinity { ; time=0:07:33.03-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-0.252278582924513/-0.008434427532035/\ 7.078046e+012/1/165/0 params=2.01/0/20.3/0 float=y maxiter=5000 inside=0 mathtolerance=0.05/1 colors=000c8Mc9McAMdBMdCLdDLdELeFLeGLeHLeIKfJKfKKf\ LKfMKfNKdMJcMJbLJaLJ`KJ_KIZJIYJIXIIWIIUHHTHHSGHRGH\ QFHPFGOEGNEGMDGLDGKDGMHKOLOQOSRSVTWZVZbXbfYfi_imam\ qbptcqqcqocrldrjdrhdsedscesaetZetXeuUfuSfuQfvNfvLg\ vJgwGgwEgwCMvE0vGCnDOfA_Z7jR5fO9cMC_KFXIIUGLQEONCR\ JAUG8XD6_F4`G3aI1bJ0brV1pZHobXnekoelofmofnneomeome\ oldokdokdpjdpjcpicphcphbqgbqfbqfbqeaqeardarc`rc`rb\ `rb`raYo`Vl_Si_PgZMdYJaYH_XGYXGWXGUXGSWFQWFOWFMWFK\ WFIVEGVEEVECVEAVE9UJAUOAUTAUYAUbAUgAUkAViCWgEWfFXd\ HXbIYaKY_LZYNZXO_VQ_UR`ST`QUaPWaNXbLZbK_cIacHbcIbd\ KbdLbeMbeNbfPbfQbfRbgSbgUbhVbhWbhXbfZdd`ebaf`cgZeh\ XfiVhjTjkSkl4ca5rWIkaVdfgYksSppTmmTkjUigUgdVebVcYW\ aTX`PX_KYYGYXBZW7ZV8XU8VU8UT9ST9QS9PS9NSALRAKRAIQB\ GQBFPBDPBBPCAOC8OC6ND5ND3MD1MD0MDI6HL7KO7OR8RT8UW8\ YZ9``9cc9gfAjiAmkAqnBtqBwsBuoLtkUsgcrdlp`ioYgmVdlR\ bjO`iLYgIWfEUdBRc8Pb5Nc7M } 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 13-02-08 (Golden Pilgrimage [6])
by Jim Muth 13 Feb '08

13 Feb '08

FOTD -- February 13, 2008 (Rating 6) Fractal visionaries and enthusiasts: New but minor formula alert! Today's image is based on a formula I wrote some time back as a speed test. I'm not sure if it's the fastest way to draw the (-Z)^(1.618)+C fractals or not, but I know that some of my formulas that draw the same figures are notably slower. The image shows a minibrot lying rather deep in the northern branch of Seahorse Valley of the parent Mandeloid. Since I can find nothing extraordinary about it, I rated it at a measly 6. The name "Golden Pilgrimage" is simply a rather poetic phrase referring to the golden ratio, which is the exponent of Z in today's image. The calculation time of 11 minutes borders on slowness, so I recommend viewing the image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Light snow Tuesday morning here at Fractal Central turned to heavier snow in the afternoon, while the temperature hovered around 16C -9C. By evening about 5 inches, 12cm, had piled up. The fractal cats observed the action with disinterest. My day was occupied with more serious work. The next FOTD will appear in 24 hours. Until that wonderful moment, take care, and get the smickey-algebroe curve. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Golden_Pilgrimage { ; time=0:11:05.21-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotGold passes=1 center-mag=-0.74240875714785280/+0.032914523503643\ 36/434085.6 params=0/0/0/0 float=y maxiter=10000 inside=0 outside=tdis periodicity=10 colors=000ceG_`JVXMRSPNNTIJWEEZAAaCL_DWZEfYFpXHnSI\ lOKjKLhFNfBOd7Qb5R`5SZ5FgO7pp7mo7jn9gmBemDblF_kHXj\ JVjLSiNPhPNhRMdRM_QMTPJOQIMRILUIPZJVdL_hLcgKbgJbfJ\ bfIaeIaeHadHadG`cG`cF`bF`bE_aE_aD_aD__E`YF`WGaVGaT\ HbRIbQIcOJcMKdLKdMSaMZ_MeXMmVMtSMzQMzOPzSRtWTm_Vfb\ X_fZTj`Mm_LlZKkYJjXIiWHhVGhUFgTEfSDeRCdRBdJAOCA7FF\ DHKIKNNMNSPOXROaUOfWOkYOpYNpVLjTJeRH_PGVNEPLCKJAEH\ 998OI7aR7q57r57r59r5Dr5Hr5Kr5Or5Rr5`h7j_CsRGrVDqYA\ qa7pd5oh5ok5no5nr5ct5TuIIwV8xgCwhGwiKwjOwkSwkWwl_w\ mcwngwnkwoowpswqvwqssppopnkokhohdnf`ncYmaUmZQlWNlU\ JkRFkPCkKMTFWBGTCGRDHPEHNFHLGLJHPIHTHHXGI_FIcDIgCJ\ kBJoAJr9JqAIpBIpCIoDInEInFHmGHlHHlIHkJHkJHjINjISiI\ XiHbhHghHl7sC7pD7nE8lFCiFFgGIeHMbHP`ISZJWWJZUKaSLd\ QLZNPTLTNJXHH`BFd7Dh7Bl8CfHCaPCXYDReDMnDHvDCtHEsLF\ rOGpSIoWJnZKmbLkfNjiOimPgqRftSexTdzUczScyQbxObwMav\ KauI`tG`tFcqKdoIfmGgkEhjC } frm:MandelbrotGold {; Jim Muth z=p1, c=p2+pixel, a=((sqrt(5)+1)*0.5): z=(-z)^(a)+c, |z| < 16 } END PARAMETER FILE=========================================

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FOTD 12-02-08 (Eastern Enterprise [7.5])
by Jim Muth 12 Feb '08

12 Feb '08

FOTD -- February 12, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: With a load of work to clear away on Monday, I had only limited time for a fractal search. But I still managed to find a respectable one for today's FOTD. The search left little time for the FOTD discussion however. Today's image is a near-Julia set of one of the East Valleys of the (-Z)^(1.467)+C Mandeloid. I say one of the East Valleys because the Mandeloid has several of them. The valley in question is little more than a string of scattered, only loosely connected bits of fractal stuff, making a near-Julia set that consists of mostly inside area brought to life by the 'bof60' inside fill. I named the image "Eastern Enterprise" when I could think of nothing better. Then I rated it at a 7.5, which includes the usual 1/2 point for my coloring. The calculation time of 4 minutes is reasonable, but not quite as reasonable as a trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to instantly view the completed image there. After a morning low of 5F -15C the temperature rose to 18F -8C here at Fractal Central on Monday. The sky remained clear, but with such frigid temperatures and a biting wind, the sun gave little comfort. The fractal cats kept close to the heat most of the day. As for me, I kept myself busy wrapping up the big job. The task was almost finished when I called it quits at 4pm. The next FOTD will be posted in 24 hours. Until then, take care, and see you in fractal land. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Eastern_Enterprise { ; time=0:00:00.00-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=EvenMoreSlices passes=1 float=yes center-mag=0.223837/0.0792099/0.8378746/1/75/0 params=1.467/0/0.075/0/0.603771266/0.249173157/0/0 maxiter=1750 inside=bof60 logmap=yes periodicity=10 colors=0000EK0FONGSQHWTI_VJcXKgZLk`MobNsdNufQugTti\ VsjYqk`pmbnnekogiqjgrmdtobur`vuYxweyzfzzzwzztxzqvW\ ntYkrZhp_enablb_jcXheUffRdgObiL`jIZkFYlHZiI_gJ`eKa\ cMbaNcZOdXPeVRfTSgRThOUiMWjKXkIYlGZmEUpMPsUKv`RwdX\ xgbxjiymoypuzszzvvyuryumyuiyudxu`xuWxuSxuNwuJwuEwu\ Awu6wu7rr7np8jm8ek9ah9Yf9TdAPaAL_BGXBCVB8Tdz7az9_z\ AYwCVuDTrERoGPlHMjJKgKIdLGaND_OBXQ9UR7SSAURCVQFWPH\ XOKYNMZMO_LR`KTaJWbIYcH`dGbeFdfFagI_hLYiOVjRTkURlX\ Pm_MnbKoeIphGpjJohLofOndQnbTm`VmZYlX_lVbkTdkRgjPij\ NkjMzlc_yVWpXShZO``KTbHLcKNdNOdPQdSRdVTdXUd_VebXed\ Yeg_ej`elaeuUmxVqzVuzVywPsqKnnNmkQlhTkeVkbYj_`iXch\ Uehuaekf_bjVdfZebafZdgVgiRjjNmkJplFskJpjMmjPkiShiV\ fhYch`a`jYTtULzRHtMEkIBbD8U9EVAKWBQWCWXDaXEgYFmYFk\ cJiiNhoQfuUezXWxUMwSOxQQyPRyOzzNzzLzzKzzJzzIzBzzRu\ zfpzulzwgzybzzYzzTzzOzzJzzEuxGspIqhKckURnbEqkJmdNj\ YRgRWcK_`DvXsyUqzQozNmgMe } frm:EvenMoreSlices {; Jim Muth ; P1--exponent, P2--angle, ; P3--M center, P4--J center, z=pixel+(p4), c=p3+(pixel*p2): z=(-z)^(p1)+c, |z| < 16 } END PARAMETER FILE=========================================

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FOTD 11-02-08 (East Revisited [6])
by Jim Muth 11 Feb '08

11 Feb '08

FOTD -- February 11, 2008 (6) Fractal visionaries and enthusiasts: Today's image is a new view of the East Valley minibrot that made its debut in the FOTD of February 8. Today's view happens to be sliced in the Parabolic direction, which is defined by the real(c) and real(z) axes. Actually, the oddly shaped hole at the center is not exactly the same one that was the minibrot of Feb 8. Minibrots in the Mandelbrot set come in families, the members of which are located by examining the position of the holes in the minibrot's Julia set. I named the image "East Revisited" for obvious reasons. I rated it at a 6 because I feel that's what it's worth. The calcula- tion time of 6-1/2 minutes is quite reasonable, as also is viewing the finshed image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunday here at Fractal Central could have been better. The temperature started at freezing, but fell steadily during the day to 10F -12C by 8pm. In addition, a series of heavy snow squalls with near white-out conditions left the ground covered with 3 inches, 7cm, of blowing snow. The fractal cats observed all this with dis-interest, rolled over, and returned to sleep. My day was busier than anticipated. I'm not sure about tomorrow, but the next FOTD is due to be posted in 24 hours. Until then, take care, and where does it all go? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= East_Revisited { ; time=0:06:25.47-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=1 inside=0 center-mag=+0.00000000025482716/+0.000000000000000\ 00/3.105068e+008/1.447e-005/90/2.4233320905509e-010 params=0/90/0/0/0.275976577981/-0.006756061446/0.4\ 04325508607/0.658046718998 float=y maxiter=6000 logmap=460 periodicity=10 colors=000RcTOe`8gZCeYGdYKbYOaXS_XWZX_XXcWWgUWkTWo\ SWfZXZeXQkXIrXAxXFsUJoRNkORgLVcIZ_FbWCfSAaU8XW7SY6\ N_5Ia4Db3Fd8GfCHhHJiLKkQLmUMnYLkWKhVJeUIbSH_RGXQFU\ OFRNEOMDLKCIJBFIACG99F86E84DB6FE8GG9HJBILCJOELRGMT\ INWKOYOPVVJSdDPn7Mx2Pt4Rp5Tl6Wi7Ye9_aAbZBdVCfREiOF\ kKGmGHpDJr9Kt5Lv2Mr4Pn6Sk7Ug9XdAZbD`aFb`HdZJfYLhXN\ jVPkURmTToRVqQXsPZuO`vYWtgSrqOqdImTDjH8gKAeMBdPCcR\ DbUEaWF_ZGZ`IYcJXeKWhLUjMTmNSoORqPQRcZ1rf6sdBtbGu`\ LuZQvXVuV_qTai_c_feRl8EVBJTENSHRQKVPNZOQbMTfLWjJZn\ IvrHjjNUbTRWZNOcKHdG9eD2eF7cHCaIH_KMYMR`NWmPjzQozQ\ lzQjzQhzQ`zQczQXzeLYwFLwGRwGXwGawQgFSdJUaNWZQXWUZT\ Y`QzaNzcKzeHzmEoZ1pX7qVCrTHsRNtQSuOXvMbwKgxJluKmsL\ mpLmnMnlNniNngOoePobPo`QoZRpWRpUSpSTqPTqNUqLUqOVpR\ WpUXoXYo_Znb_nd_mg`mjalmblpcksdkuhksmirrgqyepzcoza\ nz_mzYlzWkzUizShzQgzOfzMezKdzIczGbzEazDZzJXzPUzVSz\ `PzfNzlOzhOzdOz`PzXPzTPzP } frm:SliceJulibrot2 {; 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|<=9 } END PARAMETER FILE=========================================

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