May 2003 - Fractint - mailman.xmission.com

FOTD 04-05-03 (Sargasso Seaweed [7])
by Jim M. 04 May '03

04 May '03

FOTD -- May 04, 2003 (Rating 7) Fractal visionaries and enthusiasts: As I said in yesterday's FOTD, during the month of May I will restrict my fractal explorations to a single fractal -- the fractal that appeared as the FOTD for May 3, which was yesterday. I am doing this because in my continuing haste to find ever more fractals, I rarely stay with a single fractal long enough to become familiar with its various parts. And this parent fractal that I have chosen for May is one of the most varied I have yet found. Today we take our first venture into the parent fractal for May, which will serve as the parent of the FOTD images that will appear during the rest of the month. Today's image is located in the area where the edge of the large fan-like element merges into the 'East Valley' area of the obvious Mandel-shape on the right. I have named the image "Sargasso Seaweed". I gave it this name because something about it reminds me of rafts of seaweed lazily floating on a nearly calm ocean. But I could easily have given the image a name such as "Holey Iterations", since it has more holes than one can shake a golf course at. These holes are not Mandelbrot midgets, nor are they Julia sets. In fact, I don't know what they are, except just plain 'holes'. Such holes often appear in images created with the MandelbrotMix series of formulae. They also appear in certain parts of some fractals created with the MandelbrotBC1 formula, which draws the more remote levels of the fractals that contain a fractional power of Z. Today's image undergoes some curious changes when the bailout radius, which is the imag(p3) parameter, is raised to a sufficiently high value. These changes are the beginning of fractal 'evaporation'. They appear suddenly and unexpectedly. Finding the exact point of the beginning of fractal breakup is a challenging task, though in some cases, worth the effort. I used the MandelbrotMix2 formula to create the parent fractal for May, as well as all images that will appear during this month. This formula works exactly like the MandelbrotMix4 formula except that it has two additional changeable parameters, which can be used to change the starting point of Z. After studying today's image for all of 5 minutes, I decided that it was worth a rating of an above-average 7. The render time of 20 minutes, at least on my machine, is a bit slow, but relief can be found on the internet in the form of the completed image, which is or soon will be posted to the FOTD web sites. Paul's site is at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's is at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> On Saturday, good luck once again prevailed here at Fractal Central. There was little sun, but the rain held off and the temperature reached 63F 17C, producing conditions that any fractal cat would find enjoyable. Being fractal in nature, the dynamic cat duo thoroughly enjoyed their afternoon in the yard. At one time, the cat from two doors down made a brief appearance in the brush at the bottom of the yard. I think he was just trying to be friendly, but Tippy once again chased the other cat back down where Tippy feels he belongs. Today is once again threatening rain. Hopefully, the good luck will continue, and the rain will hold off. But there is no guarantee. Somehow, I got myself dragged into spending today looking at old junk at one of the local antique emporiums, so the duo will have to remain indoors until we return late this afternoon. Until next time, take care, and be ever more alert to signs of fractals in the world around you. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Sargasso_Sea-Weed { ; time=0:20:33.41--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+1.26815170075631500/-3.043295039151435\ 00/127119.9/1/70/1.31606140499340718e-008 params=-10/-1.1/-1/-11/0/525/0/0 float=y maxiter=1500 inside=0 logmap=196 periodicity=10 colors=000h09g06f03e00d70cG0bI0aJ0`F0XA0V60T11Q03P\ 09L1S44JO6YA9TQAaICdQFiOGoHJpTLyQMuOLpFJn6IQLAOY4M\ j0Jx0Ip1Yj9mmDfoI`rMTsQOuVIx_Ayc4zg0zl0zp0zr0zs0yu\ 0xu0vv0ux0sx0py0oz0mz0lz0jz0iz0gz0cz0_z4VyAQvIMuPI\ sVDpa9oi4moFpjPrf_sa`uYavTbxPcvQdvSevSbvTSvTOxSLyS\ IzSFzSCzS9zSdzS1zSbzS0zS0xS0zS0tS0zQ0qP1rO6lMXgLFf\ JT`IO`GSVFPYFOXFL`FJcFIfFFjFDmF`pF9uFgxF6zFFY6MXFT\ XM`VTgV`oTgvTozTvzIxzOfzSPzX7z`0y_0uY0pX4mV9iTDdSI\ `QMYQP_JX`Daa6ic0od0uX0pO0lF1g73cD1aJ0aO0aT0aY0ac0\ ag0`m0`r0`x0`z0`z0`z0`z0cz0dz0fz1iz4jz7lzAmzDpzGrz\ JszMuzPxzSyzVzzYzz_uz`mzafzc_zcSzdLzfDzg6zi0zi0yf0\ yc0xa1x_4xX7vVAvSDuPGuOJuLMsIPsGTrDXrA_r9ap6dp3go1\ jo0mo0pm0sm0vr0zm0yj0xg0vd0ua0s_0rX0rOaFVaMacTia`g\ c_gcYgcYgcXgcVgdVgdTgdSfdSfdQfdPffPfgOfjMfmMfpLfsL\ auO_vQXxTSyXPz_MzaIzdFzgCzj7zm4zp1zs0zv0zy0zz0zz0z\ z0zz1zz4zz9zzDzzGzzLzzLzz } frm:MandelbrotMix2 {; 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 20.0 PAR-FORMULA FILE==================================

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Multifractal
by Albrecht.Niekamp＠t-online.de 03 May '03

03 May '03

Hi, is this post-fractint? Kinda pick up the pieces and make something new of it? I hope not. It was supposed to be an update to Mandelmania but it turned out to become something different, more a tool then a formula. A tool to be used without leaving fractint, which lets you compose your image,- or the first approach to it. It mixes 4 fractals with seperate inside/ outside options.Two basic formulas which are ismand compatible and two hybrid mandel and julia variations. Of course a huge number of inputs is needed, but I have tried to make them as easy and comfortable as even possible. The p1 values are used as Julia seed and shared to define the default mandel, I call it shape. If you need both, start with the Julia values, see what basic image you get and define it further with the P6 input,(real P2) after the dot. The first 2 digits are used, they even can be negative, a "minus" will be applied to this value only. The other two digits are used to define the 2nd shape. This one has many variations of mirrored mandels that can be combined to one special shape. Use the evolver, max mutation for example 0.003. Both are written by Puskás István. The default one is modified to enforce Julia compatability and to use the "warp"effect for further modification. The inputs are sorted as shape/ in/out1 and in/out2 factor,border, maxiter. Border1 can be fractional, a border value of 1.4567 would appear as (factor1).000014567. The primary input Real P5 consists of five digits, shape, out1, out2, in1, in2. You type the number of the fractal to be used and add five to reset it, not the shape of course. A "minus" will shut off in/out1. Number 3 is Many_mods (mandel) by Linda Allison with a modification by Sylvie Gallet. I like this because it creates beautiful structures and its very complex. The circular form can be changed if you take a mandel as basic shape. It mixes very well with the hybrid Julia, (Nr.4),own write, which also gains complexity with the warpeffect, as it shares iteration. This one can be replaced by a different frm, if it dosnt need an additional input. The other ones are "built in" so some rewriting would be necessary in order to replace them. If you want the shape only, no in/out options, just type one number. Do not forget to set ismand according to your selection. The secondary input consists of 2 digits.You type the number out1/out2 and in1/in2 (or zero) to use the second basic formula, 3 if you want to use it for both, add five to use it as shape. This input is optional. Resetting generally adjusts the concerned part to the screen instead of the surroundings, it also helps avoid chaotic spots due to overcomplexity. Many-mods gains complexity, the number of "sides", (real P3,2nd input) is doubled if called as in/out option and again if twice f.e "(bailout).00008". This also creates the multiplication in "cockpit", I think. Imag P5 is optional, one or two digts, 1 for resetting the internal counter after shape (1) or after in/out1 (2), 3 if both. Add five or only 5 to use the warpeffect on the shape. This sometimes helps if you dont get an inside image and lets you see the difference. Counter resetting starts the calculation of the warp effect from zero. If you dont reset it and use the same factor for all options, the effect will increase with iteration. If you want to shut off the many_mods multiplication add 10 for in/out1, add 20 for in/out2 or 30 to shut it off completely. The Lake input ,2nd input, is radically simplified (sorry, Sylvie), you just type one six digits number, 2 digits for each value. 324151 means a frequency of 320, a level of 41% and an amplitude of 0.51. Any valid input activates the lake effect. The functions are used for the calculation of the warp effect, possibly a new factor must be found if changed. Fn1 is shared with many_mods, so if you dont warp the shape it is free to use. I did not use fn4 or fn5 for the 2nd function as at least 2 lines are needed to scroll the text. If you dont want the outside options set the values higher then bailout, or vv maxiter higher then maxiter on the x-screen. It was not possible to include twoway border values and separate bailout values, P6 is needed. Its a good idea to have a hardcopy available when doing the inputs, also some basic pars ready to modify. There is one problem: Many_mods is n o t compatible with the lake effect, as they both define "c", applying the effect to "z" does not do the job and the image is partly distorted. P l e a s e tell me, if you see a solution, maybe only Sylvie can help. If you have questions or bugs to report, please dont hesitate and -- please post your images. Writing this was like a trip into a new country, and when you finally detect, that it´s much more complex then it´s parts, well- that´s it. Fractal Greetings, Al. ---------------------------------------start-par-------------------------- - The_flying_mandel { Albrecht Niekamp Apr, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=exp/exp/exp passes=t center-mag=-0.426332/0.037594/0.8912656/1/-90/3.88578058618804789e-016 params=-0.2724234748374889/0.09260841700491348/384.00001/256.1113/2048.0\ 0008/768.00004/1025.01536/2560.01536/18115.11/0 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200022000<4>A85CA6EC7GE8IF9KHA<13>keOmgPoiQqjRslSunT<2>zsX<25>CB7\ A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<23>eeegggiiijjjlll\ nnn<2>sss<25>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<29>034 } The_gate { ; Albrecht Niekamp Apr, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=exp/exp/exp passes=t center-mag=0.512575/-0.480315/2.675131/1/-90/3.88578058618804789e-016 params=0.5125888851588488/-0.4719992675557726/384.00001/256.3601/2048.00\ 008/768.0256000000001/768.01536/2560.01025/11113.11/1.324051 float=y maxiter=3072 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=200000<23>eeegggiiijjjlllnnn<2>sss<25>BBB999777<2>222000012<24>0b\ o0cq0es<3>0kz<25>09C08A068<2>022000211<22>keOmgPoiQqjRslSunT<2>zsX<25>CB\ 7A96875<3>000400<23>o00q00s00<3>z00<30>200 } Hades { ; Albrecht Niekamp Apr, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=exp/exp/exp passes=t center-mag=-1.09933852316632100/+1.00410963532720300/204.7945/1/-169.999\ 999999999545/4.83828255237739313e-013 params=-0.1738944669942329/-0.3000579851680044/384.00001/256.1113/3072.0\ 0016/768.0001600000001/768.01536/32.01025/34231/5 float=y maxiter=3072 inside=maxiter outside=tdis logmap=yes periodicity=0 rseed=-2436 colors=20009C<19>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<22>keOmgPoiQqj\ RslSunT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>00\ 0<23>eeegggiiijjjlllnnn<2>sss<25>BBB999777<2>222000012<3>07A } Cockpit { ; Albrecht Niekamp Apr, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=exp/exp/exp passes=t center-mag=-1.16761/0.932037/6.553424/1/-47.5/-3.77822773067748585e-014 params=-0.1738944669942329/-0.3000579851680044/384.00001/256.1113/3072.0\ 0016/768.0001600000001/768.01536/32.01025/34231/5 float=y maxiter=3072 inside=maxiter outside=tdis logmap=yes periodicity=0 rseed=-2436 colors=000XXX<10>oooqqqsss<2>xxxzzzyyy<25>CCCAAA888<2>222000000<56>00000\ 0000<2>000111332<23>ldTnfUpgV<3>xn_<27>A86875654443222000<52>000000000<2\ >000111333<15>VVV } No_admission { ; Albrecht Niekamp Apr, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=exp/exp/sin passes=t center-mag=0.222172/-0.0164743/3.404629/1/-90/-1.23373533611470521e-014 params=0.3009095217749565/-0.00961206396679584/384.00001/256.3601/2048.0\ 0008/768.0256000000001/768.01536/64.01025/11193/0 float=y maxiter=3072 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=200000<25>iiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0cq0es<3\ >0kz<25>09C08A068<2>022000211<24>oiQqjRslS<3>zsX<25>CB7A96875<3>000400<2\ 3>o00q00s00<3>z00<30>200 } Mandala { ; Albrecht Niekamp Apr, 03 ; ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=postpar.par formulaname=multifractal ismand=y function=exp/exp/exp passes=t center-mag=0.128196/0.0103203/1.14051/1/-90/3.88578058618804789e-016 params=0.1044648579363384/-0.01168858912930693/384.00004/256.00768/2048.\ 00005/768.00008/384.01536/384.01025/18939/5 float=y maxiter=2048 inside=maxiter outside=tdis logmap=5 periodicity=0 rseed=-2436 colors=200000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<22>keOmgPoiQqj\ RslSunT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>00\ 0<23>eeegggiiijjjlllnnn<2>sss<25>BBB999777555444222 } Speedtest { ; Time 1min10sec p4 2giga 1600/1200 ; Albrecht Niekamp May, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifrac_239 ismand=n function=exp/exp/exp passes=t center-mag=0.117455/3.33067e-016/2.552858/1/90/3.88578058618804789e-016 params=-0.173894466994232/-0.3000579851680044/384.00001/256.1133/2048.00\ 008/768.0256000000001/768.01536/2560.01025/4/35.324051 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=0000200000101221532653863A84DA5EB5HB<2>7NG8PI8RJ9TKAVNAXM<3>DdTDf\ VEhWFjYFlYGn_Gp`Prd<3>zzz<2>_ulRsgHqaHo`GmZFkXFiX<5>BYOAWMAUL9SK<4>6IC5G\ B5DA<3>254243121000001023025047049<5>0BL0DN0DP<3>0JX0KZ0L`0Mb0Nd<3>0Sl0T\ n0Up4Yr8atCgvGkxKqz<3>4_s0Vq0Uo<6>0Ma0L_0KY<3>0FQ0DO0DM<3>08E06C06A04804\ 6024012000100<12>R0LT0NV0PX0P<3>d0Wf0Yh0Z<3>p0e<3>xOtzUxyOuwIquCns6iq0g<\ 2>k0bi0`g0_e0Z<3>Y0SW0RU0O<8>C0AA09807506304102010<9>0L20N20P30R30T40V40\ X3<3>0d40f50h5<3>0p6<3>WxZczeUyY<2>0s8<4>0i60g60e60c4<2>0Y40W30U4<5>0I20\ G20E20C20A1081061040 } Thousand_Julias { ; Time 22m35s p4_2giga_1600/1200 ; Albrecht Niekamp Apr, 03 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=exp/exp/exp passes=t center-mag=-1.16373570930467300/+1.00897822713355100/131.0685/1/132.5000\ 00000000682/-1.31000071901254955e-012 params=-0.1738944669942329/-0.3000579851680044/384.00001/256.1113/3072.0\ 0016/768.0001600000001/768.01536/32.01025/34231/5 float=y maxiter=3072 inside=maxiter outside=tdis logmap=5 periodicity=0 rseed=-2436 colors=2000Ub<13>09B089067<2>021000210<22>keNmgOoiPqjQslRunS<2>zsW<25>CB\ 6A95874653442220000400<23>o00q00s00<3>z00<25>C00A00800<3>000<2>554776998\ BBACCB<16>eedggfiihjjillknnm<2>ssr<25>BBA998776<2>221000011<24>0bn0cp0er\ <3>0ky<10>0Wd } Thousand_mandels { ; Albrecht Niekamp Apr, 03 ; ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=exp/exp/sin passes=t center-mag=-0.175549/-0.304679/1.39428/1/-90/-1.23373533611470521e-014 params=-0.173894466994232/-0.3000579851600044/384.00004/2500.2333/2048.0\ 0012/768.00008/2500.01536/32.01536/18435/5 float=y maxiter=2048 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=200211<24>oiQqjRslS<3>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z0\ 0<25>C00A00800<3>000<25>iiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0\ cq0es<2>0jy0kz0jy<30>000 } Thousand_mandels2 { ; a bit chaotic, but... ; Albrecht Niekamp Apr, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifractal ismand=y function=exp/exp/sin passes=t center-mag=-0.57996076807419270/-1.17390745582887600/27.8856/1/-152.5000\ 00000000142/1.65777114258247593e-013 params=-0.173894466994232/-0.3000579851600044/384.00004/2500.2333/2048.0\ 0012/768.00008/2500.01536/32.01536/18435/5 float=y maxiter=2048 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=20007A<20>0bo0cq0es<2>0jy0kz0jy<24>09C08A068<2>022000211<24>oiQqj\ RslS<3>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<2\ 5>iiijjjlll<3>sss<25>BBB999777<2>222000012<2>068 } Mandala2 { ; 5*many_mods ; Albrecht Niekamp May,03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult239.frm formulaname=multifrac_239 ismand=y function=exp/exp/exp passes=t center-mag=4.44089e-016/-2.22045e-016/0.5706667 params=-0.1738944669942329/-0.3000579851680044/384.00001/256.0076/256038\ 4.00008/1536.0256/768.01536/5120.01024/38888/2 float=y maxiter=3072 inside=maxiter outside=tdis logmap=yes periodicity=0 rseed=-2436 colors=200U00<9>A00<4>000<25>iiijjjlll<3>sss<25>BBB999777<2>222000012<24\ >0bo0cq0es<3>0kz<25>09C08A068<2>022000211<24>oiQqjRslS<3>zsX<25>CB7A9687\ 5<3>000400<23>o00q00s00<3>z00<15>W00 } ---------------------------start-frm--------------------------------------- FRM:Multifractal { ; Albrecht Niekamp Apr, 03 ;only integers as first input, second input 5 digits to the right ;real(p2) factor1,border1 ;imag(p2) (-)maxiter1,input bas.frm1_2digits input bas.frm2_2digits ;real(p3) bailout,hyb.mandel: number of sides (Many_mods L.Allison) ;imag(p3) factor2,border2 ;real(p4) maxiter2,factor3 ;imag(p4) border3,maxiter3 ;real(p5) 1digit_shape only 5digits: shape,out1,out2,in1,in2 ; 1_mand 2_jul 3_hyb.mand 4_hyb.jul +5_reset (not shape) <0_no in/out1 ; optional basic frm2: out-nbr 1digit in-nbr 1digit 3_both +5_shape ;imag(p5) 1digit : 1_iter1reset 2_iter2reset 3_both +5_shape effect ; 2digits : many_mods multipl. shutoff +10_in/out1 +20_inout2 +30_both ; optional input2: frequency_2digits level_2digits amplitude_2digits ; d=real(p2) fac1=trunc(d) b1=(d-fac1)*100000 ; d=imag(p2) da=(d<0) if (da) d=-d endif mi1=trunc(d) d=round((d-mi1)*10000) p6=trunc(d/100)/10 d=d-1000*p6 if (da) p6=-p6 endif p7=d/10 ; d=real(p3) ba=trunc(d) mm=round((d-ba)*100000) ; d=imag(p3) fac2=trunc(d) b2=(d-fac2)*100000 ; d=real(p4) mi2=trunc(d) fac3=round((d-mi2)*100000) ; d=imag(p4) b3=trunc(d) mi3=round((d-b3)*100000) ; da=real(p5) t=(da<0) if (t) da=-da endif start=2-t dd=trunc(da) if (dd<5) start=0 endif vb=(dd==3)+(dd==4) da=round((da-dd)*100) d=trunc(dd/10000) vb=(d==3)+(d==4)+vb dd=dd-d*10000 d=trunc(dd/1000) or1=(d>5) d=d-5*or1 vv1=(d==3) vv2=(d==4) dd1=(d==2)+(d==4) dd=dd-d*1000 d=trunc(dd/100) or2=(d>5) d=d-5*or2 vv3=(d==3) vv4=(d==4) dd2=(d==2)+(d==4) dd=dd-d*100 d=trunc(dd/10) inr1=(d>5) d=d-5*inr1 v1=(d==3) v2=(d==4) d1=(d==2)+(d==4) dd=dd-d*10 d=trunc(dd) inr2=(d>5) d=d-5*inr2 v3=(d==3) v4=(d==4) d2=(d==2)+(d==4) d=trunc(da/10) ab=(d>=5) d=d-5*ab da=da-10*d bb1=(d==1) bb2=(d==2) d=da ab=(d>=5) d=d-5*ab ab1=(d==1) ab2=(d==2) ; d=imag(p5) dd=trunc(d) d=round((d-dd)*1000000) le=(d>10000) da=trunc(dd/10) so1=((da==1)+(da==3)==0) so2=((da==2)+(da==3)==0) dd=dd-10*da wo=(dd>=5) dd=dd-5*wo ir1=(dd==1)+(dd==3) ir2=(dd==2)+(dd==3) if (le) freq=round((trunc(d/10000))*10) ;frequency_lake effect by S.Gallet d=d-freq*1000 level=(trunc(d/100))/100 ;water level d=d-level*10000 ampl=d/100 ;amplitude of the wave angle=real(rotskew*pi/180) t=exp(-flip(angle)) h=1/real(magxmag) q=h/0.75*imag(magxmag) tanskew=tan(imag(rotskew*pi/180)) w=2*q*t v=2*h*(tanskew+flip(1))*t z3rd=center+(-q-h*tanskew-flip(h))*t z=pixel-z3rd s=imag(conj(w)*z)/imag(conj(w)*v) if (s<=level) da=level-s z=z+2*da*(1+ampl*sin(freq*da^0.2))*v endif z=z+z3rd endif if (ismand) if (vb) c=0.4*log(sqr(pixel^mm)) z=z*le else c=z*le+pixel*(le==0) z=0 endif else c=p1 z=z*le+pixel*(le==0) endif t=0 d3=(ismand==0) u=d3 : if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) ;frm: Albrecht Niekamp else z2=fn1(z)+c ;frm: Many_mods Linda Allison sqz2=cos(z2) z=c*(1-sqz2)/(1+sqz2) endif else if (ab) z=z*z+c+c*c-p7 ;frm: Pusk s Istv n else z2=z*z ;frm: Pusk s Istv n modified z=z2*z2+(p6+u)*z2+c-p1*(d3==0) endif bo=|z| If (wo) t=t+1 if ((t<mi1)+(bo>b1)) u=2*(fn1(t/fac1)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) else c=z*le+pixel*(le==0) endif else z=z*le+pixel*(le==0) c=p1*u endif wo=0 if (ir1) t=0 endif endif elseif (start) t=t+1 if (start==2) if (bo>b2) u=2*(fn2(t/fac2)) rs=or1 ab=bb1 if (dd1) if (rs) z=pixel endif c=p1*u vb=vv2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=1 endif elseif (t>mi2) u=2*(fn2(t/fac2)) rs=inr1 ab=ab1 if (d1) if (rs) z=pixel endif c=p1*u vb=v2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=1 if (ir2) t=0 endif endif elseif (start==1) if (bo>b3) u=2*(fn3(t/fac3)) ab=bb2 rs=or2 if (dd2) if (rs) z=pixel endif c=p1*u vb=vv4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=0 endif elseif (t>mi3) u=2*(fn3(t/fac3)) ab=ab2 rs=inr2 if (d2) if (rs) z=pixel endif c=p1*u vb=v4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=0 endif endif endif bo<=ba }

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FOTD 03-05-03 (The May Parent [NA])
by Jim M. 03 May '03

03 May '03

FOTD -- May 03, 2003 (Rating NA) Fractal visionaries and enthusiasts: The Mandelbrot set is sometimes called the most complex object in the world of mathematics. And it truly is a complex object. But there are other fractal objects created by other fractal formulae, which are more complex than even the M-set. Of course, since the M-set is infinitely complex, these other objects would appear to demand a higher order of infinity. Today's image could be one of these 'higher' fractals. It is titled "The May Parent". I give it this name because, for the rest of the month of May, I shall use it as the source of my FOTD images. This limitation in no way implies a shortage of images or a reduction in their quality, though on occasion I will go beyond my normal style of image with a midget at the center. The formula mixes one negative part of Z^(-11) with ten negative parts of Z^(-1.1), then adds 1/C before being calculated with a bailout radius of 625. In some places, the oversized resulting fractal is filled with holes like a swiss cheese. In other places, it appears to hold the usual Mandel-stuff. In yet other places, it is filled with rings, while a prominent fan-shaped element fills the center. The variety is endless, and the fractal has midgets hiding almost everywhere. I gave today's image no rating, since it is not really a finished product, but rather the source of the next 28 FOTD images. The render time of a little over one-minute should give little difficulty, but for extra convenience, the completed GIF image is posted to the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The rain that was expected here at Fractal Central on Friday never arrived. Instead of the rain, we had a mostly sunny day with a temperature of 81F 27C. The fractal cats thoroughly enjoyed the unexpectedly pleasant day, and spent several hours romping in the yard. Today is starting cloudy and quite a bit cooler -- once again threatening rain. Will good fortune prevail, giving the fractal duo another good day? Only time will tell. My day will turn good when the work is finished, so until next time, take care, and see you in 24 hours with the next image. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_May_Parent { ; time=0:01:11.96--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=3.56788/-0.692098/0.1341384/1/135/-3.77\ 822773067748585e-014 params=-10/-1.1/-1/-11/0/525/\ 0/0 float=y maxiter=400 inside=0 logmap=yes periodicity=10 colors=000CHgEIfGJgIJgKKcLLhNMePMiR\ NhTOjVPkXPkYQl_RlaSmcSmeTmgUmiVmjVmkTmlRmmPmmOmnQl\ oSjpUipWgqYfr_dsacscate`ugZwiYzkUwmRroOrqLmsImuFhw\ CFw9Au69t69t69s69s68r68r68q68q67p67p67o67o66n66n66\ m66m65l65l65k65k64j64j64i64i64i65g75f85e96cA6bB6aC\ 7`D7ZE7YF8XG8WH8UI9UJ9UK9ULAUMAUNAUOBUPBUQBURCUSCU\ TCUUDUVDUWDUXEUYEUZEUZCUYAUX9UY9UY9UY9UY8UZ8UZ8UZ8\ UZ7U_7U_7U_7U_7T_FScMSfURi`RleYeidZmkTqrMuyGowMjvS\ etY`scVqiQpoLnuGmzHmxImwJmvJmuKmtLmrMmqMmpNmoOmnOm\ mVm8Wx9Xw9YwAYwAZwB_wB`wC`wCawDbwDcwDcwEdwEewFfwFf\ wGgwGhwHiwHiwHgwJewKcwMawN_wOYwQWwRUwSSwUQwVOwXNwY\ LwZJw`HwaFwbDwdBwe9wg7wh5wi3wk1wl0wm6whBwcGwZLwURw\ PWwK`wFewAjw5mw6ow7qw8sw8uw9wwAywAvwFtwJqwOowSmwXj\ w`hweewicwnawrIw8NwBRwEVwGZwJcwLgwOkwQowTswVtwUuwU\ vwUvwUrwWnwYkw_gw`dwb`wdYwfUwgQwiNwkJwmGwnCwp9wr5w\ t2wu8whEwWKwJPw7Ow9OwAOwBOwCOwDOwFOwGNwH } frm:MandelbrotMix2 {; 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 20.0 PAR-FORMULA FILE==================================

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FOTD 01-05-03 (Fractal Epicycles [8])
by Jim M. 03 May '03

03 May '03

FOTD -- May 01, 2003 (Rating 8) Fractal visionaries and enthusiasts: This is the day, the day fractal fans have been waiting for with bated, but not abated, breath -- the day the FOTD resumes its one-a-day schedule. And we start with a fractal that earns a lofty rating of 8. I named the image "Fractal Epicycles" for no good reason. I simply liked the sound of the title. An epicycle is not an epihertz. It is not an electronic wave at all. It is a revolution around a moving point. Before men under- stood the true nature of the solar system, the retrograde loops the planets trace in the sky when they are near opposition were assumed to be a result of the planets circling a point that in turn circled the earth. As we discovered later, this is not so, and epicycles fell from favor, eventually going the way of the luminiferous aether. Today's image is a zoom into the curiously symmetrical image posted by Lee Skinner about 5 days ago. I lowered the bailout radius to 30, but left the other parameters unchanged. In fractals generated from formulae that contain negative powers of Z, the value given the bailout makes a huge difference in the final appearance of the image. Increasing the bailout causes the elements to shrivel and break into separate pieces which eventually shrink to nothing, leaving an image that consists entirely of 'inside stuff'. But even when the elements have 'evaporated' the ghost of the original image can still be raised by setting the inside fill to something like bof61. This ghost is sometimes the best version of the scene, though in today's image it is too chaotic and far too slow. Decreasing the bailout has the opposite effect. The elements increase in size until one expands to fill the entire screen, resulting in an image of a single featureless color. Using an outside coloring method other than the standard equal-iteration- bands occasionally results in an interesting variation, though this is the exception rather than the rule. Today's image renders in a relatively modest 7-1/2 minutes on my aging and overworked P200 machine, the one with the noisy exhaust fan that needs a pep talk to make it start turning. The finished GIF image is available on the two FOTD web sites, which have been slow lately, but will become more active now that the daily FOTD is back. The URL of Paul's site is: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's site is found at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather here at Fractal Central on Wednesday was fractal in nature, as it always is. The warm sun and temperature of 75F 24C brought out the best in the fractal duo, who passed most of the afternoon in the yard and on the porch, watching for intruding cats. At one time, the cat that lives three doors down the hill thought of walking through the duo's yard. His thoughts were quickly laid to rest when Tippy leaped to the attack position. Thomas observed the goings on with interest, presumably ready to run to help, (or more likely, for help), if things got too far out of control. Today is starting far less pleasantly, with lots of clouds, and rain threatening. On such days, the duo usually stays indoors, while I try to finish the work that needs to be done. And right now, I have enough to be done to keep me busy most of the day, so until next time, which will arrive in 24 hours, take care, and if an infinity of other me's exist somewhere out there, what practical difference does it make? After all, I will never meet them (or me). Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Epicycles { ; time=0:07:39.13--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.60678114611431010/+0.052890451621420\ 53/1894179/1/137.5/1.24117062995365846e-007 params=-3.7/-1/-1.6/-2/-0.4/-70 float=y maxiter=4500 inside=0 logmap=120 periodicity=10 colors=000PKsfRshTsKKrKKpIAoKKsFKnFGmDHkCIjAJi9Kh8\ Lg6Mf5Ne3Od2Pc1Pb7OaCN`IM_NLZTKYYJXcIWhHVnGUsFTxES\ yJPyOMyTKyYHzbEzgCKz9zzzzz4mpztUAqhDncGk_JhWMeSPbN\ S000000000000000000000000000000000000000000000000d\ A`zmUlC`lGZlKXzzVmTSmXQnaOneMniKkdMh`NeWObSQ_NRXJS\ YGbZEldPmjZnohnpijqjgqkdrk`slYsmVtnRunOuoLvpHwqEwq\ BrpDnoFjnHfmJamKYlMUkOQjQLjRHiTDhV9gX5gYCfbIfgOelU\ eqXfl_fhbgceg_hhWkhRniNqiItjEujAwiByhCzgDzfEzeFzdG\ wcHrcImbJhaKf`Le_McZNbYO`XP_XQ_VO_TN_RM_PK_NJ_LIXN\ HVOGSPFQRENSDLUDIZCGcBDhABm99m9CrBEcDGSFIPPKNUMLZO\ IcQGhSEmUBrW9wY7z_4za2zc0z`2ZY4XV5VS7TP9RMAPJCNGEL\ DFJAHH7IFBJGFKGJLGNMHRMHVNHZOHbPIfQIjSInUJrWJvYJz_\ JzaSzc_zegzgozimzkkzmizogzqfzsdzubzw`zx_zy`zzZzzXz\ zVzzTzzRzzPzzNzzLzzJzzHzzFzzDzzBzzGzzKzzPzzTzzYzza\ zzYzzVzzRzzOzzLzzTzzVzzXzz_zzazzczzfzzhzzjzzlzznzz\ ozzqzzrzzszzszzszzszzszzs } 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 20.0 PAR-FORMULA FILE==================================

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FOTD 02-05-03 (A Networking Fractal [6])
by Jim M. 02 May '03

02 May '03

FOTD -- May 02, 2003 (Rating 6) Fractal visionaries and enthusiasts: Today's image is a picture of just another midget, though a rather unusual one. The filaments surrounding the small central midget are some of the most intricately interconnected I have yet seen. They form a network almost as convoluted as the internet, and have inspired the name "A Networking Midget". The rather dull coloring held the rating to a 6. The parent fractal is an oversized thing created by combining negative portions of Z^(-0.9) and Z^(-9.5), then adding 1/C. Basically, it consists of a few irregular holes surrounded by an immense network of filaments. The filaments are filled with nodes, almost like a fractal internet. Today's scene is located on a filament deep in one of these star-like nodes. The ability to find fractals seems to work like skill at sports or music. One must constantly practice to keep in shape. During the past 2 months or so, while the FOTD has been on a once-per-week basis, my ability to find fractals seems to have suffered. Oh, I still know where to look, but the intuition that a good scene lies deep in a certain area of the parent seems to have vanished. I am sure that, as I continue to search for fractals every day, the intuition part of fractaling will soon return, but until it does, it is curious to be searching blindly, with my 'sixth sense' shut down. And I also noticed a letter from a disappointed FOTD fan yesterday. This fan saw the opening of the discussion, which read something like, "this is the moment fractal fans have been waiting for", and assumed I was announcing the release of the FOTD CD. Actually, the CD is basically finished. All the images and all the discussions are found and gathered. The only thing yet to be done is to change the names of the images so that the names correspond to the dates on which they appeared. If I could be satisfied with cryptic image names that can be matched with their discussions only with some effort, then the disk would be totally finished. I am working on the task of determining the dates and changing the names whenever I find the time. That truly glorious moment of CD completion is indeed within sight. Keep tuned. The big moment will soon arrive. Today's image requires 4 minutes to render from the attached parameter file. Time can be saved by downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The threatening rain never arrived on Thursday, and as a result, the Fractal Central watchcats had another splendid day on the porch and in the yard. The warm sun and temperature of 79F 26C was just what they needed to put them in a good mood. They got a bit skittish early in the afternoon when someone started hammering in the yard two doors up the hill, but soon realized there was no danger, and resumed their naps. Today is once again threatening rain. Hopefully, it will hold off until the duo finish their outdoor recreation. As for me, I've got a bit of work to accomplish, so until tomorrow, take care, and keep a stiff upper fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_NetworkingMidget { ; time=0:04:09.75--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-7.915378033606101/-31.14709243995971/7\ 911.543/1/40/1.15404776568350798e-008 params=-2.2/-0.9/-6.6/-9.5/0/0 float=y maxiter=750 inside=0 logmap=75 periodicity=10 colors=000KCJLCJLCKLBKMBKMBKMBKMBLMBLLALLALLAMLAMK\ AMLAMK9MK9NL9NL9NL9NL9NMAPNBROBTPCVQDXRDZXKcYPhZUm\ _Zr`cwacxbczcazd_zeYzeWzfUxgQwgMuhIshGqiFoiEmjDkjC\ ikCgkBflAel9dm8cm8an7`n6_o5Zo5Ym8YlAYkDXiFXhIXgKXe\ NWdPWcSWaUW`XWZZVYaVXcVVfVUhUTkURmUQpUPrUQpYQn`Rmc\ RkfSjiShlSgoWfiZfdbf_efVifQleLpeGseBwe6ze1P9AQCBQE\ BQGBQICQKCRNCRPCRRDRTDRVDSYES_ESaEScESeFThFTjFTlGT\ nGTpGTrG_jqWlpSmoPnnLomIplEqkBrkAoiAmhAkf9he9fc9db\ 9a`8__8YY8VX8TV7RU7OS7MR6KP6HO6FM6DL5AJ58I56G54F88\ GABHCEIEHJGKKJNLLQMNTNPWORZPUaQWdRYgS_jTamUZhXWcZU\ ZaRVcOQeMLhJGjHClGFiGIfGKcGNaGPZGSWGUUGXRGZOGaMGcJ\ GfGGhELgDPgCTgBYfBafAef9if9jeAjdBjcBkbCkaDk`Dk_ElZ\ ElYFlXGlWGmWHmVHmUImTJnSJnTKnUKnWLoYMo_MoaNocNmeOk\ gOiiOhkOfmPdoPbqPasP_uPYwQXyQVzQTzQRzRQzROzRMzRLzR\ MzSNzSNzSOzTOzTPzTPzUQzUQzURzVRzVSzVTzWTzWUzWUzXVz\ XVzXWzYWzYXzYXzZYzZYzZKzJ } 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 20.0 PAR-FORMULA FILE==================================

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