June 2007 - Fractint - mailman.xmission.com

FOTD 24-06-07 (Rainy Day [Not Rated])
by Jim Muth 24 Jun '07

24 Jun '07

FOTD -- June 24, 2007 (No Rating) Fractal visionaries and enthusiasts: Today's FOTD is shamefully late. But I have an excuse. On Saturday morning the weather was so good that Fractal Lady got an uncontrollable urge to visit her old alma mater in State College, which is about 85 miles from Fractal Central. Our day was very pleasant though a bit too sentimental for my taste. When we got back to F.C. well after dark, we were exhausted. With no chance to create a new fractal last evening, I dredged an old one from the fractal bone yard this morning, and declared it FOTD for June 24. The image is a scene along the negative X-axis of the parent fractal that results when the formula Z^(2.003)+C is iterated 10 levels up the log ladder. I could hardly give rating to a fractal that has been lying in the virtual dust for a year or two. But I did give it a name. I named it "Rainy Day" because I have been saving it for just such a day as yesterday. The included parameter file ran in 8-1/2 minutes on the old P200 machine. I estimate it would take around 1-1/2 minutes on the P2000. Those who do not consider calculating fractals from parameter files to be their cup of tea may view the image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> but because of the FOTD's lateness, Paul might not have a chance to post it for a few hours yet. Absolutely perfect weather prevailed throughout Central Pennsyl- vania on Saturday, making it a great day for nostalgia. The fractal cats greeted us eagerly when we returned, then promptly rushed to their food dishes. The FOTD for June 25 will appear on schedule in about 9 hours. Until then, take care, and keep the iterative faith. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Rainy_Day { ; time=0:01:30.00-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=-1.33533148191821700/+0.001624130111275\ 15/604124/1/95/-3.61649927851925845e-008 params=2.003/0/10/0 float=y maxiter=1750 inside=0 logmap=149 periodicity=10 colors=000CZeB_dA_d9`c8Rm7Um6Wm5Ym4`m3bm2fn1io0npE\ sqRxrQupQrnPolPmjOjhOggOdeNbcN_aMX_zcKvZKrUKmPKhKK\ cHKZEKUBKP9KK6II3GI1FJ2HK2IL2JL2KM2LN2MO3OO3PP3QQ3\ RR3SR3TS3UT4WT4XU4YV4ZW4_W4`X5bY5cZ5dZ5e_5f`5g`5hZ\ 7gY9fXBeWDdVFdUHcTIbSKaRMaQO`PQ_OSZOQcNThNVmNXrNZv\ N`zNbzNdzNfzNizNkzNmzNozNqzNszNuzNwzNyzMxzMwzmvSmu\ RmtQmsPmrOmqNmpMmpLmoKmnJmmImlHmkGmjFmiEmhDmiCmhDm\ hDmhDmhDmhDmhDmhDmhDmhDmhDmhDmhDmhDmhDmhDahDwhDvzD\ fhDghDihDjhDlhDml7mhDeeIYaON`QRZTUYVXXX_VZbU`eTbhR\ dkQfnPhmOilOikOikNijNiiNjiMjhMjgMjgMjlWepe`toWxyRv\ zTtzUrzVpzWnzXmzYkzZiz_gyaexbdwcbvd`ueZsfXqgWohWmg\ WjfWgeWedWccWabW_aWY`WW_WUZWUZWUYWUXWVWWWVWXUWYTWZ\ SW_RW`QWaQWbPWcOWeNWgMWiLWkKWmJXrI_rHbuFevHhwJkxLn\ yNqzPtzQwzSzzUzzWzzYzz_zz`zzbzzdzzfzzhzzizzjzzkzzl\ zzlzzmzznzznzzozzpzzpzznzzlzzjzzhzzfzzdzzczzazz_zz\ YzzWzzUzzizzhzzgzzgzzfzzf } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100, p=real(p2)+PI q=2*PI*floor(p/(2*PI)), r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

1 0

FOTD 23-06-07 (Almost a Minibrot [Not Rated])
by Jim Muth 23 Jun '07

23 Jun '07

FOTD -- June 23, 2007 (Not Rated) Fractal visionaries and enthusiasts: I was away at Old Fractal Central all day Friday, which explains the insignificant and hurried fractal for today. The image, if that's what it might be called, lies in the parent fractal that results when the formula Z^(sqrt(2))+C is calculated 123 levels down the logarithmic ladder. I named the image "Almost a Minibrot" because the little midget in the center looks surprisingly like a quadratic midget, even though its formula uses the square root of 2 rather than the number 2 itself. I gave the result no rating. The calculation time of 1-1/4 minutes is about all the time the image deserves. The best way to view the finished image is to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it is posted. The weather was perfect all the way from New Fractal Central to Old Fractal Central and back on Friday. The old fractal cats were pleased to see me. They must have thought I had abandoned them forever. The new fractal cats, having missed their regular treat, were a bit sulky when I returned. But a later-than-usual treat eased their moods. The next FOTD will appear in 24 hours. Until then, take care, and make that big decision with confidence. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Almost_a_Minibrot { ; time=0:01:15.85-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 center-mag=-1.32580711928304300/-0.167967700359305\ 60/824.0658/1/62.5/-1.23373533611470521e-014 params=1.4142/0/-123/0 float=y maxiter=5000 inside=0 outside=summ periodicity=10 colors=000SBPTBOVCMWCKXCJYCH_DF`DEaDCbDBdCCfBCgACi\ 9Dj8Dl7Dn6Do6Eq5Er4Et3Ev2Fw1Fy0Fz0Fx1Iw1Lv1Nt1Qs1S\ r1Vq1Xo1_n1am1dl1fj1ii1kh1ng1pd8obEn`KmZRlXXkVbjYp\ lVlkThjQdjO`iMYiOWfPVcRU`SSYURVVQSXPPYNM_MJ`LGbJDc\ IAeH7iD4fG5dI5aK5_N6XP6VR6SU7QW7NY7DMUDFSB5ID9QEDY\ GHeHLlGKeGJ_FJUFIOEIIEHC6C2AF4EH6IJ8LMAPOCTQERY4WS\ G_MSdGchBn`LqTVsLcuObpRalU`gX_c_Z_bYVeXRq_3hWN`SfR\ CyTOzV_zXkzZwz`shbpSdmB_jCVhCRfCMcDIaDD_DAY89YB9YD\ 1U65WB9YFC_KGaOKcTBhgHfaNdXSbSY`NcZIiR4hV9hYDh`Ihc\ MhfQkbYsgvmZegQQXM6aHAfDDk8Hp4Km6Ok7Ri9VgAYdCabDd`\ FheImZGkTFjMDhGCgLHfQMeVQe_VddZdiccriYoh`mgckfeieh\ gdkjYpg`necmcflaij_liYohRplWrg_tbcvYgxTypBruIkyPjq\ RjjSicUiXVhQXhJYfIWeHUdHTcGRbFPaFOXGRTHUOHXKI_FJbB\ JdTbMov2ju4et6`t8XsASsCNrEJrFNmLRhRVdXZ_bbWhfRnoLy\ lMviNsgOpdPmaQj_RgXSdVTbXTaYT`ZS__SZdW_`SZYOZVLZRH\ ZODZJ9`LAZMAXNAWOAUQBSRBR } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100, p=real(p2)+PI q=2*PI*floor(p/(2*PI)), r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

1 0

FOTD 22-06-07 (Out of Balance [8])
by Jim Muth 22 Jun '07

22 Jun '07

FOTD -- June 22, 2007 (Rating 8) Fractal visionaries and enthusiasts: With its inadequate coloring, yesterday's FOTD showed what can go wrong with an evaporated fractal. Today's image is another evaporated one, but this time I put far more effort into the coloring, and the extra work has paid off. The image lies in the parent fractal that results when 2.72 parts of Z^(-2.7) are subtracted from 8.5 parts of Z^(-1.6). This parent is an oversized Mandeloid with X-axis symmetry, which has been rotated 180 degrees. It has a surprisingly large ring at the end of its main stem and an extra circular bay where its East Valley should be. Today's image lies on the northern shoreline of this extra bay. As the bailout radius of one-googol shows, the image has been totally evaporated, and the residue made visible by the 'bof61' inside fill, the fill that almost always works best with evap- orated images. And yes, there is a quadratic midget at the center of the image, but, being inside stuff surrounded by more inside stuff, it has almost vanished. I rated the image at an 8 because it actually seems to picture a real (meaning a 3-D onjective) object. I named the image "Out of Balance", though in this case it is not life that is out of balance, it is the elements of the image. The calculation time of under 3 minutes is not too bad, but an even better choice is to view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A mostly sunny, breezy and rather warm day here at Fractal Central on Thursday, with a high temperature of 84F 29C went un- noticed by the cats, who were more interested in watching for the baby rabbits that have been hopping around the yard, eating Fractal Lady's flowers. When the rabbits never showed up, the cats eventually lost patience and fell asleep. It thundered in the evening, but the rain never arrived. My day was about average. But tomorrow I plan on a trip back to Old Fractal Central to say hello to the old fractal cats, Thomas and Tippy, and pick up some more things I left there. I'll try to post the FOTD for June 23 on schedule, but there is no guar- antee. Until next time, take care, and how does one recognize the real reality when he meets it? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Out_of_Balance { ; time=0:02:36.38-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+0.49734046783936980/+0.607634194530533\ 00/197902.1/1/-60/-4.51899531683785938e-009 params=8.5/-1.6/-2.72/-2.7/0/1e+100/0/0 float=y maxiter=1400 inside=bof61 logmap=yes periodicity=10 colors=00084N64L45K25I05H3AJ5EL7IM9MOCQPEURGYTIaUL\ eWNiXPmZRq_QtaPwcPzdOyeNxeNwfMwfMvgLugLthKthJsiJri\ IqjIqjHpkHokGnlFnlFmmElmEknDknDjoCioCioAbc8XT6QH4K\ 68O8CSAFWCJZEMbGQfIUiKXmM`qOctQaqR`oS_mTZjUXhUWfVV\ cWUaXS_XRXYQVZPT_OQ`MO`LMaKJbJHcHFcGCdFAeE8fD6fH5e\ K5eN5eR5dU5dX5d`5cc5cf5cj5bm5bp5bs5bV8e7BgEHjLNmST\ pZZreduljxspzrmwrktrhrrfordlrajr_gqXdqVbqT_qQXqOVq\ LSqJPqHNnIOlIPiIQgIRdISbITaIUiJVVJWTJXRJYOJZMJ_JG`\ HGaEKbCKc9Kd7Ke4Kf2Kq0Kq9OiHSiQWiY_jfcjnjmvoztijrh\ jqhjogjegjoeqkmwiejgdjfdjdcjcdjlbj`ijZajYajY`kY`lZ\ aniWlY`kY`jY`iY_hY_gY_fYVeY_dXZbXZaXZ`XZ_XYZXTYXYX\ XYWDEADBAD8ADAADBADCADDAADAJDKMEJVEIWFIZHH_IHbJGdM\ FfOFhQEkTDlVDnXCp_BraBvcAyfAmaGbbLXcQRdVLe`Ffe9gj3\ ho6Yl8OiADfC3cE4dF5dG6eI7eJ8fK9fMAgNBgOBhQChRDiSEi\ UFjVGjWHkYIkZJl_Jl`LhaNebPbcQ_dSXdUUeWRfXOgZLh`Iia\ EhaFgaGfaHeaIdaJcaKcaLbaM } 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=========================================

1 0

FOTD 21-06-07 (The Inside Supreme [7])
by Jim Muth 21 Jun '07

21 Jun '07

FOTD -- June 21, 2007 (Rating 7) Fractal visionaries and enthusiasts: It's either the longest day of the year, the shortest day of the year, or just another day exactly 12 hours long, depending on where on earth one lives. Here at Fractal Central, it's the longest day. The sun rises at 5:36am and sets at 8:42pm EDT, though the twilight begins shortly after 4am and lingers until 10pm. On the longest day of the year, it's only proper that the FOTD should be above average. And I think I have posted an above- average one. It's an evaporated scene in the parent fractal that results when 5.5 negative parts of Z^(-1.5) are combined with 0.5 negative part of Z^(-5.5) and (1/C) is added. An evaporated fractal is one in which all the exponents of Z are negative and which has such a large bailout radius that all the points are trapped. These fractals must be calculated with an active inside fill such as 'bof61' to avoid a totally flat blank screen. The drawback to evaporated fractals is their slowness. They are slow because they consist totally of 'inside' stuff. In today's case, the parameter file takes 24 minutes to calculate on the fast 2000 mhz machine. On the old 200 mhz work horse, it would take 2-1/2 hours or more. But I have sent the calculated image on ahead to Paul at the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it will soon be posted for instant enjoyment. I named today's image "The Inside Supreme" because it's all inside. I rated it at a 7 because that's what I think it's worth. If I had put more effort into the colors, I might have been able to rate it at an 8. Wednesday was absolutely perfect here at Fractal Central. Every aspect of the weather was in the middle of the comfort range. The fractal cats celebrated the perfection by finding a strong shaft of sunlight and resting in it until it moved out of reach. In my department, the commercial work was about average, but I had an exceptionally efficient day, and finished in notably less time than usual. The next FOTD will appear in 24 hours. Until then, take care, and don't be haunted by fractal entities. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Inside_Supreme { ; time=0:24:28.59-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=+0.42867296563386100/-1.702442513543234\ 00/3.132496e+008/1/-143.5/-0.000168553882913445585 params=-5.5/-1.5/-0.5/-5.5/0/1e+100/0/0 float=y maxiter=5500 inside=bof61 periodicity=10 colors=000qcppamo_jnYhnWemUblS`kQYjOViMThKQhINgGLf\ EIeCFdADc8Ac78d97dA7dC7eD6eF6eG6eI6fJ5fL5fM5gO4gP4\ gR4gS4hU3hV3hX3iY2i_2i`2ia2gg9flGerNdwTdlMdaGdRAdG\ 4dF4eF4eE4fD4fD4gC4gB4hB4hA4i94i94jA6jA7jA9kAAkABk\ ADkAElAGlBHlBImBKmBLmBNmBOnBPnBRnCSoCUoCVoCWoCYpCZ\ pC`pCapCbkB_gBXcAU_ARW9OS9LN8IJ8FF7CB797663644DA4K\ F5RK5XQ6cV6j_6pdBpUGpJKp8On9SlAVjAZiBbgBeeCicCmbDp\ `DtZEwYEvXGvWHvWIvVKvULvUMvTNvSPvSQvRRvRSuQUuPVuPW\ uOYuNZuN_uM`uLbuLcuKduKesJfqJfpJgnJgmIhkIhjIhhIifI\ ieHjcHjbHj`Hk_GkYGlXGlVGlTGmSFmQFnPFnNFnMEoKEoIEpH\ EpFEpEDqCDqBDr9Dr8DrAFsBHsCJsDLtENtFOtGQtHSuIUuJWu\ KXuM_sOaqQcoSemUgkWiiYkhZlfZleZldZlcZlbZlaZl`Zl_Zm\ ZZmYZmXZmWZmVZmUZmTZmSZnRZnQZnPZnOZnNZnMZnLZnKIrd2\ uy4sv6qs8oqAnnCllEjiGhfIgdKeaMc_OaXP`VRZSTXPVVNXUK\ ZSI`QFbOCdNAfL7hJ5jH2kG0ZL7MPDATJ5QJ1OJ7LOCISHFWNC\ _S9cX6ga4kNM`8bRtixsgurer } 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=========================================

1 0

FOTD 20-06-07 (Emergency Back-up [None])
by Jim Muth 20 Jun '07

20 Jun '07

FOTD -- June 20, 2007 (No Rating) Fractal visionaries and enthusiasts: The power was out most all afternoon here at Fractal Central, and there was also a sizable job to finish. As a result I had no time to find a worthy fractal for today. But this situation has been prepared for. I had a marginal fractal stored away for a rainy day, and today was that rainy day. I named the image "Emergency Back-up", though I gave it no rating. If I had had more time to work on it, I might have brought it up to a level worth a rating. The image lies in the parent fractal that results when 1/10th negative part of Z^(-6.2) is combined with 1 negative part of Z^(-1.2) and (1/C) is added. The included parameter file finishes in 2-1/4 minutes, about the same time it will take to go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the finished image there. A very hot and muggy day, with a temperature of 93F 34F here at Fractal Central on Tuesday was interrupted by a short but violent thunder-storm in the afternoon. The only bad effect on F.C. however was a power outage. The cats watched the excite- ment from their theater-seat window. The next FOTD will appear in 24 hours. Until then, take care, and be an eagle, not a slug. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Emergency_Back-up { ; time=0:02:17.45-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-1.68272471511077300/-5.720484837930027\ 00/1877591/1/85/1.81416267908823814e-006 params=-1/-1.2/-0.1/-6.2/0/0/0/0 float=y maxiter=1500 inside=0 outside=tdis periodicity=10 colors=000TP7TQ7UR7UR7US7VS7VT7WU7WU7WV7XV7XW7VV6X\ W7YW8ZW9_WAaXBbXBcXCdXDfYEgYFhYGiYGkZHlZImZJnZKp_L\ q_Lr_Ms_Nu`Ov`P`YQ`ZQ``R`aS`bT`cU`dU`YX`U_ZRdYQaYP\ _XOYXOWXNUWMSWMPVLNVKLVKJUJHUIFTHDTHATG8SF6SF4RE2R\ D0QC0RD0RE0SE0SF1SF2TG3TG4UH5UH6UI7VI8VJ9WJAWKBWKC\ XLCXLDYMEYMFYNGZNHZOI_OJ_PK_PL`QM`QNaROaRPaSQbSQbT\ RbTScUTcUUdVVdVWdWXeWYeXZfX_fY`fYagZbgZch_ch_dh`ei\ `fiagjahjbijbjkckkclldmldnleomepmfqmfqlcnl`lkYjkVh\ jSfjPdiNaiK_hHYhEWgBUg8Sh5Rg6Qg6Qf6Qf7Qe7Qe7Qd8Qd8\ Qd8Qc9Pc9Pb9Pb9PaAPaAPaAP`BP`BP_BP_COZCOZCOYDOYDOY\ DOXDOXEOWEOWEOVFNVFNVFNUGNUGNTGNTHNSHNSHNSHNRJLRLK\ RMIROHRQGRREQTDQVCQWAQY9QZ7Q`6Pb5Pc3Pe2Pg1Ph0Pj0Nl\ 0Pk0Qk0Rk0Sk0Tk0Uk0Vk0Wk0Xk0Yj0Zj0_j0aj0bj0cj0dj0e\ j0fj0gi0hi0ii0ji0ki0li0ni0oi0pi0qh0rh0sh0th0uh0vh0\ wh0xh0zi0yh0yg1yf2ye2xd3xc4xb4xb5xa6w`6w_7wZ8wY9wX\ 9vWAvWBvVBvUCuTDSO6SO7SP7 } 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=========================================

1 0

FOTD 19-06-07 (Siegel-Disk Sunrise [7])
by Jim Muth 19 Jun '07

19 Jun '07

FOTD -- June 19, 2007 (Rating 7) Fractal visionaries and enthusiasts: Yesterday's image showed Siegel Disks. Today's image wreaks havoc with those disks. Siegel disks are spirals that circle forever but never draw any closer to the center. Today's image not only changes the disks into star-like objects, it totally obliterates the lower halves of them. This craziness came about when I duplicated yesterday's image but rotated the orientation of the slice about 2 degrees from the Julia direction of the Julibrot. To do this it was necessary to use a special Julibrot formula which rotates the slices. I think this is the first time I have used this particular formula in an FOTD image. BTW, the Julibrot is the 4-dimensional assemblage of all the Julia sets and all the perturbed Mandelbrot sets. In four-dimensional space, all kinds of crazy and unimaginable things can happen, and today's image is one of them. In today's image, the lower half of the remnants of the Siegel disks is obscured by a grossly enlarged and distorted view of the part of the Mandelbrot set that corresponds to the Siegel disks. I named the image "Siegel-Disk Sunrise" because that's what it reminds me of. Then I rated it at a 7 to reward myself for the extra 10 minutes or so I spent working on the colors. The calculation time of 1-3/4 minutes can be sidestepped by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. Monday proved to be a lovely sunny day here at Fractal Central. True, the temperature of 88F 31C could have been a bit cooler, but the humidity was not all that bad, and a gentle breeze kept the air stirred. All in all, the fractal cats approved. My day was busier than I would have liked, but the work was finished in plenty of time for the day's FOTD to be completed. The next FOTD will appear in 24 hours. Until then, take care, and choose wisely. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= SiegelDisk_Sunrise { ; time=0:01:49.35-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2a passes=1 center-mag=0.0337456/0/0.9146906/1/-37.5 params=88.512/1.442/92.381/-1.198/-0.390541/-0.586\ 788/0/0/-5/0 float=y maxiter=3600 inside=bof60 logmap=yes symmetry=none periodicity=0 colors=00000006C0AE0CG5EIAGKFIMKKOPMPUPQZSMcVIhYLm\ _OraQwcTweWwfYwg`whbwicwjdwkewlfwmgwnhwoiwpjwqkwrl\ wsmwtowuqwvsxwvyzzzzzKqgIpeGnbEm_CkYAjV8hS6gQ4eN2d\ K0cILWOeOTYIOQCKIMAMIIQEQXCWbAah8fn6lt4qvEpwNpyWoz\ dotXgoP`iHTdAMLPb2csrkhqfmqbqqYvqUzkVseVl_VeUVZOVS\ IVLCVE7V8IPBTJDbEGm8Iw3Kp2Gj2Dd2A_8BVEBQJBLPBGVBB_\ B6eB1jBHd9W_7kV5zQ4mZC`fKOnSBvZGtYKrYOpYSnYWlY_jYc\ hYggYbb_ZYaVTbROdMJfIEgE9iA5j99e9Da9HX8LT8PO8TK8WG\ KXDVXBeX9pX7`0lmT5lR3TYqYWcEB6HMIJXTLgdNroSlpXfqa`\ qeVrjProJssDswJhzOZoNSeNMWNGVH_UCsXIl_NfaT_dYUgcNi\ hHgjGflGemGdoFcpFbrFasFaaMaLSa4Y_7cYAiWCnUFtTHySNr\ RTkQYdPcYOhRNnKNsEUoI`kMfgQ9wBJh9SU7`F5i04zaDvXKrT\ QnPWjLafHgbDmZ9sV5yYAu`EqbIneMjhRfjVcmZ_obXnXTnRPn\ MMmGImBFm5Bm08hF7dT6`f6Xh5Tj5Ql4Mm4Io4Fq3Bs38t3GnA\ OhHWbOcXVbUWbSWaPWaNWMXU7eSMaP`ZMoWJj_RecY`geWklSn\ sOlmKkhHibDhYAfSimelqfoug } frm:SliceJulibrot2a {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=real(p5+9) } END PARAMETER FILE=========================================

1 0

Re: Siegel Disk Fractal
by jackoftradez＠comcast.net 19 Jun '07

19 Jun '07

. Loox like my "amoeba" animation <g> http://www.fractal-animation.net/vid/amoeba.zip .

1 0

FOTD 18-06-07 (Siegel-Disk Fractal [7])
by Jim Muth 17 Jun '07

17 Jun '07

FOTD -- June 18, 2007 (Rating 7) Fractal visionaries and enthusiasts: Today's image of a Julia set shows a Siegel disk fractal. My math encyclopedia implies it is the only Siegel disk fractal, though it is obvious that a mirror image fractal exists at C=-0.390541+0.586788i. The Siegel disks are the flat but irregular concentric rings filling the 'inside' part of the Julia set. They were made visible by the 'bof60' inside fill. These rings are actually the limiting case of spiral arms that have tightened to infinity, where they will take an infinity of revolutions to converge an infinitesimal bit closer to the central point. The spiral arms have become true closed curves, just as the circumference of a circle of infinite radius on a flat plane becomes a true straight line. I know of no special significance in fractals that contain Siegel disks, though I feel that there must be something of value in them. Why else would they have earned an entry in the math encyclopedia? One thing certain is that today's fractal contains some interesting sub-images. If I find anything of unusual worth, I'll post it as tomorrow's FOTD. I rated today's image at a 7 for its mathematical interest. The name I gave it -- "Siegel Disk Fractal" -- is its description. The calculation time of 37 seconds is true on the P2000 machine. On the P200 it would take about 2 minutes. On the FOTD web site, however, the image has already been rendered, and is posted for instant viewing. To see today's image as well as many past images, direct your browser to: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and enjoy the enigmatic Siegel disks. With a high temperature of 88F 31C here at Fractal Central, and with the sunshine dimmed by haze, Sunday was too summery to be considered perfect. But it was good enough to satisfy those who had planned Father's Day outings. At the same time, the indoor climate was good enough to please the fractal cats. And the work was slow enough to give me a restful day, which is all I can ask for on a Sunday. The next FOTD will appear in 24 hours on the same mailing lists and on the FOTD web site. Until then, take care, and be alert for flying Siegel-disc saucers. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= SiegelDisk_Fractal { ; time=0:00:37.41-SF5 on P4-2000 reset=2004 type=julia passes=1 center-mag=0/0/0.9363296 params=-0.390541/-0.586788 float=y maxiter=1500 bailout=4 inside=bof60 logmap=yes symmetry=origin periodicity=no colors=000K75Y35k05yiJiaNUUQV`YWgdXnkXtrZhe_YTaNGb\ C4cT8dhCexFbiR_WbXInU4y`DjgLXnUIta4_lDGvMN4J_EDlO7\ Sfublwmrxo_cpIKtVBwg2dMAN1IO7IPCIQHIQ9VQ2fGHU6WIWS\ StP`lNfeLlZJrSIwbGhmFUxEFszZEiZ7Yb1NegdA_YGTSMMMSF\ GXGO_2kLGWbHceJYEIdT6d89fHChQFjZ4Qn9YkDdiKlsoJmYYj\ IJuHTpHbkeDaXPcP`eNl1LkCKkNIkYzpOjnVWlagxH`tOUqVNn\ a5mvBlnb`5XcFSfPMiZTd5QfFNhPKjZq07gCHZOQQ_ZkIz`SsR\ am62fCKiERhFYhGdgY0mrahanrVmnOljMtiJohh61ZKGQYUEkX\ GkbSm05I4MMkKViIch9KOCUVFbaTXaNdd_Y6TbJNgWL42KFDJQ\ NI`YJjXIk_IkbHkemYCXdShKQVYZIKtajORkYogIYiV8GlBOjD\ WiFchY8D5fTBi`ya7bfQ0Iv6SqCals1`_PdmvEXpTgyaUrdx5V\ _JGVRNQYULd`aGyD2FFIPGXZsMsfVoUck5PsB`mADfVqsOnmrJ\ 7eTKTbW5NY9WaDcdkUr7jiAkhCkhFkg4wjBqhG7UHIYHS`Had7\ F_BQbE`e5`78cHBfQEiZ_VgQcg9t5DoPOa6jKQbRVWYZOdcHk9\ HkR9ciCfhFiguuxgqrUnleDviVQEH`GXdDBkFUiXFkTOjPWiLc\ h4mp9lmDkjvCckQ1cWCW`Nb8L } END PARAMETER FILE=========================================

1 0

FOTD 17-06-07 (Pressing Minibrot [6])
by Jim Muth 17 Jun '07

17 Jun '07

FOTD -- June 17, 2007 (Rating 6) Fractal visionaries and enthusiasts: Today's image came about when I subtracted 5 parts of Z^2 from 3.35 parts of Z^3 and added (1/C). Curiously, the 1/C did not turn the fractal inside out, but it did create a somewhat distorted Mandelbrot set rotated 180 degrees, with an extra stem fragment lying some distance beyond the main stem. Ignoring this extra fragment, I checked instead a spot off to the north side of the actual main stem. Not very deep inside this spot I found today's scene, which I have named "Pressing Minibrot". I gave it this name because the whole image looks as though it has been pressed against a pane of glass. The rating of a 6 might be seen as a bit liberal by some, but I did put a bit of extra effort into the image, which helps justify the rating. One good point that cannot be denied is the calculation speed of the image, which is 9 seconds on the P2000 and only 44 seconds on the P200. This is a bit faster than it would take to go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the finished image there. But viewing the image on the web site does away with the hassle of calculating parameter files. Partly cloudy skies and a high temperature of 81F 27C made con- ditions pretty much ideal here at Fractal central on Saturday. At least the fractal cats must have thought so, for they spent several hours looking out the window. My day was not too busy, but I suffered an attack of severe laziness. The next FOTD will appear in 24 hours. Until then, take care, and get in there with the big-time thinkers, whoever they are. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Pressing_Minibrot { ; time=0:00:09.66-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=+0.46563561954888720/+0.015792627220296\ 66/226192.6/1/63.75/7.78858089134359943e-011 params=-5/2/3.35/3/0/0/0/0 float=y maxiter=255 inside=0 outside=tdis periodicity=10 colors=0003MsARkHVcOZWVbPafHhj9on2NaThkAahHVeO68G9\ DJCILEMNHRPJVRM_TCKIFPMIUPLZSQcBPcLmnmfkh`hcUeZzgX\ meW`dVQHHPLKPPMPTOOXRO`TCAmGKfKU`2KN7OPBSRGWSK_UfD\ CcHFaKHZOKXRMVUOSYRQ`TnEAeNHXWONJeONcOQaOU_OXYO`W1\ oq9kiHgaajAZhFWgJTeNQdRSnYQxyXp8VmDTjIRhMPeRsKGlOJ\ fSM_WPU_Su9SnGTgMU`SUUYVd_Ya`X_`XYaWWaWUbWSbVQcVzp\ JsmLmkNfiP`gRUeTbu__qZXmYUjXRfWdkr`imYghUfcRdZbn7_\ lBYjFVhJTfNQdRy43sA7nFBhKFcPJYUNTZRNEuOKoOPjOUdOZ_\ LO2MR7MTBNVFNYJO_NOaRTdpQVzP_jTe6SdBRdGQcLPcQLroMo\ kMmhNjdNhaOeYG8aID`JI_KMZLRYMVXN_W5a6CbFIcNM6QNISO\ TUw57kHF_TNTEORLQQRSPYUzK24qs8nnBljEjfIgbLeZslDhiJ\ YfPGleJiaMfYdtZaqY_oXXlXVjWSgWQeVZWlbO9`QCZSFXUIVW\ KTYNR_QPaTuKlnOhgSd`WaU_YXlrUijRfbylqqjlihgbfcVdZh\ 09c8E_GIWONSWRAzHEtLHnOLhSQPzPStPUoPXjOZdOa_DRoGVi\ JYdM`_GFuIKoKPjLUdNZ_`POnBAiGEeLH`QLXVOS_SA6gDDdGK\ aJR_MYXF22HA8JIELPKNXQySE } 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=========================================

1 0

FOTD 16-06-07 (Golden Emptiness [8])
by Jim Muth 16 Jun '07

16 Jun '07

FOTD -- June 16, 2007 (Rating 8) Fractal visionaries and enthusiasts: In today's formula I took the same math expression that created the Fractal Ringers image of June 8, changed the real(p1) value to -2.5, the real(p2) value to 2.5, and the function to 'recip'. The result was a totally different parent fractal, which is better seen than described. Today's image is located on the eastern extremity of the parent, very near the point where the main stem of a midget joins a large irregular hole. I named the image "Golden Emptiness" because of the gold effect of the open areas, which have been brought to life by the 'fmod' inside fill. I rated the whole works at an 8. I think the effect of gold on blue is good enough to earn it. The brief calculation time of 2-1/2 minutes only adds to the excitement. (If a fractal can be emotional, that is.) Of course, the simplest and fastest way to see the image is to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the completed image is posted for instant pleasure. A day with perfectly average weather at Fractal Central on Friday went un-noticed. The cats were too busy chasing each other around the house and the human was too busy working. Luckily, the human still managed to find time for a fractal. The cats always find time for their treat. The next FOTD is scheduled to appear at this same time tomorrow at this same place. Until then, take care, and be cheerful. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Golden_Emptiness { ; time=0:02:24.60-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+3.46135766659610900/-0.563138691824576\ 20/2.119956e+009/1/80/7.22562509127694e-006 float=y params=-2.5/1.5/2.5/2.5/0/0/0/0 maxiter=1500 inside=fmod proximity=0.00032 periodicity=10 colors=00000KG`_GZbFXeFVgMUiSTkZTmdSojSpgLndFma9k_\ 3jZBgYJeYJaYJYYJUYJQYMMYPJYRNYUQYXUYZXYa`YdcXfgXij\ WlnWnqYlnZjl_hj`ghaeecccdbae`_fZXgYViWTjURkTOlRMmP\ KnOImMJmLJlJJlIJkGJkFJjDJjCJiAJi9JgEMeIOcMRaQT_UVh\ _ZjYYlWXnUWpSVrQUtOTxMUvKTtITrGSpFSnESlFRjGRhIQfJQ\ dKQbLP`MPZNOXOOWOOVNOXLP_HQaDSd9Tf5Uh1Vb3RY5OT6LO8\ IJAFEBC9D94E6BF9HGCNGETHHZHJdIMkJMjIOjIPjIQiHRiHSi\ HUiGVhGWhGXhFYhF_gF`MaUQdZVfcZhhcjmekpglrdhracsZ_s\ WVsURtRMtOItLDuI9uG5uI9uKCuMFuOIuPMuRPuTSuVVuWZuYa\ u_duaguaiubjucfsdcpe_nfXkgTigQgeRhdRibRjaRk_SlZSmX\ SnWSoUSpTSqRSrQSsOSsPTtQVtQXuRZuR`vSbvTdwTfwUhxUix\ UhxWgyYbyV_qSYiPVaNTUKQMHOEGNBFM7GOCGNHGMLHLQHKVHJ\ ZGIXFHVEGTDFRDEPCCNBELAGJBHLAHO9IRAJSBKVBLYCM`ENcH\ OeKPgPQiTRkTSmTToTUrSUtSUwSUySUzSUzRXzR_zRbzRezOcv\ RcrUcmYZh`accdZhgVkjSomPspMwsJzvGvrFsnEpkDlgCicBe`\ AaY9_V8YS5WP7UM9SJBPGDMDE } 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=========================================

1 0