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FOTD 17-07-10 (Seahorse Madness [7])
by Jim Muth 18 Jul '10

18 Jul '10

FOTD -- July 17, 2010 (Rating 7) Fractal visionaries and enthusiasts: NOTICE! Today's image will calculate correctly only with the new version of the SliceJulibrot4 formula, which is included in today's parameter file. If you have the old version on file, discard it and replace it with the new version. The new version of the SliceJulibrot4 formula includes the ability to control the escape radius with the imag(p5) parameter, which is an important part of today's image. All images created with the old version of the formula will run correctly with the new version, but some images created with the new version may not run correctly with the old version. If the image turns out looking like featureless chaos, it was run with the old version of the SliceJulibrot4 formula. The correct image consists of amber elements with blue highlights, and is not at all chaotic. The work rush continues here at FC, so today's image is another quick one. Believe it or not, it's a scene in the Seahorse Valley area of the Mandelbrot set. But instead of lying in the Mandelbrot orientation of the Julibrot, today's view lies in the Oblate orientation, which is determined by the imag(c) and real(z) axes. Actually, the escape radius of today's image is 0.5, which means everything should cut off at a radius of 0.7071 from the origin. But today's scene lies well beyond that distance, yet it is not cut off. This is just one more in the unending string of mysteries connected with fractals. The name "Seahorse Madness" refers to the crazy, very un- seahorse-like image. The rating of a 7 includes more math than artistry. The calculation time of just over one minute will pass in a flash. Perhaps the best way to see the image is to hop on out to the FOTD web site at: <http://www.Nahee.com/FOTD/> where it is posted in all its glory for instant admiration. Friday began sunny and hot here at Fractal Central. By 2pm the temperature reached 91F 33C. But a gusty thunder-shower moved in at 3pm, which dropped the temperature to around 77F 25C for the rest of the day. Occasional showers continued until night- fall. In the human department, the work was still at fever pitch. The fractal cats continued sulking because, with the humans so busy, they were not getting enough attention. The next FOTD will be posted in 24 hours. Until then, take care, and be there. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Madness { ; use new version of formula ; time=0:01:11.51-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=1 center-mag=0/-0.0611855/6.547727/1/-90/0 params=0/0/90/0/-0.752/0/0.5/0/2/-8.5 float=y maxiter=2500 inside=0 outside=atan periodicity=6 colors=000_uW_uX`uY`u_`u`ataatcbtdbtebtfWuePvdIwcB\ xb5ybDwcKvdRtdYseeqflpfsngzmgyldykaxjZxiWwhTwgQvfN\ veKudHudFpaHlZJgWKcTMZQNVNPQKRMHSHEUDBV88X45Yvvvut\ strqtposomsmkrkirjgqhepfbpe`ocZoaXn`VnZTmXRmWPhUNc\ SM_RKVPJROHMMGILEDJD9ICBJGDJJFJMHJPJJTLJWNJZPJaRJe\ TJhVJkWJnXLoXNpXPpXRqYTqYVrYXrYZsZ`sZbtZdtZfuZguTf\ sNeqHeoBdm5dl8ajA_hDYfFWeIUcKSaNQ_POZSMXUKVXITZGSa\ EQcCOfAMh8LiDOjIQkMSlRVmVXn_Zoc`phcqlerqgsuitthtth\ uthuthvsgvsgvsgwsgwsgxrfxrfyrfyrfyrfEHuDGsDFqDFoDE\ mDEkDDiDDhDCfDCdDBbDB`DAZDAYIDXMFWRHVVJVSRYQZ_NeaL\ mcJteMscOraRq_TpZVpXYoV_nTbmSdlQflOikMkjLniJphHrhG\ gcLX_QMVVBRZGPbLOeQNiUMlZKpcJshIwlHziKvgMreOnbQk`S\ gZUcXW`ZY__ZZ`_ZaaYbbXccXdeWefWfgVgiUhjUikTjmSknSl\ oRmpRglUbiWYfZTccNchIcmDcr8cv3cz5cz7cz8czAczBczDcz\ F_zGWvISsJQpLMjMJdNG_PCUQ9PR6JS3EU5DV7DW9DYBDZDD_F\ DaHDbIDcKCeMCfOCgQCiSCkUC } frm:SliceJulibrot4 {; draws all 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), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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Threads (or Filaments) one more time
by Roger Alexander 17 Jul '10

17 Jul '10

More threads (or filaments). A re-sampled gif is scheduled for tomorrow. If you want you can avoid the risk of generating the par then saying I want my 15 minutes back by visiting the usual http://maxitersfractalfollies.blogspot.com for the completed version. fract313.gif { ; threads ; blank ; calctime 0:15:18.14 ; created Jul 16, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=kerrym.frm formulaname=starnear_jul center-mag=-0.497582/0.874017/7.559265 params=0.375/0.375/0.5/2/2/35 float=y maxiter=1500 inside=0 decomp=256 periodicity=0 colors=05F05F05F16G16G16G16G16G27H27H27H27H27H38I38I38I38I38I49J49J49J49\ J49J5AK5AK5AK5AK5AK6BL6BL6BL6BL7CM7CM7CM7CM7CM8DN8DN8DN8DN8DN9EO9EO9EO9E\ O9EOAFPAFPAFPAFPAFPBGQBGQBGQBGQBGQCHRCHRCHRCHRCHRDISDISDISDISDISEISEJTFJ\ TFKTGKUGLUHLVHMVIMVINWJNWJOWKOXKPXLPYLQYMQYMRZNRZNSZOS_OT_PT_PT`QU`QUaRV\ aRVaSWbSWbTXbTXcUYcUYcVZdVZdW_eW_eX`eX`fYafYafZbgZbg_ch_ch`ch`diadiaeibe\ jbfjcfjcgkdgkdhlehleilfimfjmgjmgknhknhlniloimojmpjmpknpknqloqloqmprmprnq\ snqsorsortpstpstqtuqturuuruvsvvsvwtwwtwwuxxuxxuxxvyyvyywzzvyyvyyuxxtxxtw\ wsvwsvvruvquuqtupstostorsnqsnqrmprlpqloqknpjnpjmoimohlnhkngkmgjmfjleileh\ kdhkcgjcfjbfibeiaeh`dh`cg_cgZbfZbfYaeX`eX`dW_dW_cVZcUYbUYbTXaSWaSW`RV`RV\ _QU_PTZPTZOSYNSYNRXMQXLQWLPWKPVKOVJNUINUIMTHLTGLSGKSFKRFJREIQDIQDHPCHPBG\ OBFOAFN9EN9EM8DM8CL7CL6BK6AK5AJ49J49I38I37H27H16G16G05F } frm:starnear_jul { ; Kerry Mitchell 09oct98 ; ; Julia set, colors by nearest approach to 5 point star ; p1 = Julia parameter ; p2 = center of star ; cabs(real(p3)) = star size of star (try 1) ; sign(real(p3)) = pixel flag: ; + = don't consider pixel--start after first iteration ; - = consider pixel ; imag(p3) = star rotation angle, degrees ; only use angles from 0 to 36 degrees ; use decomp=256, bailout hardcoded to 10^12 ; ; initialize iteration parameters ; c=p1, zc=pixel, done=0, iter=1 bailout=1e12, fmin=bailout ; ; star parameters ; center=p2, xcen=real(center), ycen=imag(center) r=cabs(real(p3)), pixelflag=0 if(real(p3)<0) pixelflag=1 endif phi=imag(p3)/180*pi, twopi=2*pi, temp=twopi/10 t0=phi, t1=t0+temp t2=t1+temp, t3=t2+temp, t4=t3+temp, t5=t4+temp t6=t5+temp, t7=t6+temp, t8=t7+temp, t9=t8+temp ; ; set up control points ; x0=r*cos(t0)+xcen, y0=r*sin(t0)+ycen x1=r*cos(t2)+xcen, y1=r*sin(t2)+ycen x2=r*cos(t4)+xcen, y2=r*sin(t4)+ycen x3=r*cos(t6)+xcen, y3=r*sin(t6)+ycen x4=r*cos(t8)+xcen, y4=r*sin(t8)+ycen ; ; if pixel flag =/= 0, then check pixel for how close ; it is to star ; if(pixelflag!=0) x=real(zc), y=imag(zc), t=imag(log(zc-center)) if(t<0) t=t+twopi endif if((t>t0)&&(t<=t1)) f=x*(y0-y2)+y*(x2-x0)-x2*y0+x0*y2 elseif((t>t1)&&(t<=t2)) f=x*(y1-y4)+y*(x4-x1)-x4*y1+x1*y4 elseif((t>t2)&&(t<=t3)) f=x*(y1-y3)+y*(x3-x1)-x3*y1+x1*y3 elseif((t>t3)&&(t<=t4)) f=x*(y2-y0)+y*(x0-x2)-x0*y2+x2*y0 elseif((t>t4)&&(t<=t5)) f=x*(y2-y4)+y*(x4-x2)-x4*y2+x2*y4 elseif((t>t5)&&(t<=t6)) f=x*(y3-y1)+y*(x1-x3)-x1*y3+x3*y1 elseif((t>t6)&&(t<=t7)) f=x*(y3-y0)+y*(x0-x3)-x0*y3+x3*y0 elseif((t>t7)&&(t<=t8)) f=x*(y4-y2)+y*(x2-x4)-x2*y4+x4*y2 elseif((t>t8)&&(t<=t9)) f=x*(y4-y1)+y*(x1-x4)-x1*y4+x4*y1 else f=x*(y3-y0)+y*(x0-x3)-x0*y3+x3*y0 endif fmin=cabs(f) endif : ; standard iteration, find polar angle of iterate ; iter=iter+1, zc=sqr(zc)+c x=real(zc), y=imag(zc), t=imag(log(zc-center)) if(t<0) t=t+twopi endif ; ; compute how close iterate is to each side of star ; if((t>t0)&&(t<=t1)) f=x*(y0-y2)+y*(x2-x0)-x2*y0+x0*y2 elseif((t>t1)&&(t<=t2)) f=x*(y1-y4)+y*(x4-x1)-x4*y1+x1*y4 elseif((t>t2)&&(t<=t3)) f=x*(y1-y3)+y*(x3-x1)-x3*y1+x1*y3 elseif((t>t3)&&(t<=t4)) f=x*(y2-y0)+y*(x0-x2)-x0*y2+x2*y0 elseif((t>t4)&&(t<=t5)) f=x*(y2-y4)+y*(x4-x2)-x4*y2+x2*y4 elseif((t>t5)&&(t<=t6)) f=x*(y3-y1)+y*(x1-x3)-x1*y3+x3*y1 elseif((t>t6)&&(t<=t7)) f=x*(y3-y0)+y*(x0-x3)-x0*y3+x3*y0 elseif((t>t7)&&(t<=t8)) f=x*(y4-y2)+y*(x2-x4)-x2*y4+x4*y2 elseif((t>t8)&&(t<=t9)) f=x*(y4-y1)+y*(x1-x4)-x1*y4+x4*y1 else f=x*(y3-y0)+y*(x0-x3)-x0*y3+x3*y0 endif f=cabs(f) ; ; update minimum distance ; if(f<fmin) fmin=f zmin=zc endif ; ; upon escape or maximum iterations: ; set "done" flag ; use minimum distance from star as polar angle of z ; for use with decomp coloring ; if((|zc|>bailout)||(iter==maxit)) done=1 t=log(fmin) z=cos(t)+flip(sin(t)) endif done==0 } Roger Alexander _________________________________________________________________

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Re: [Fractint] A Fetching Little Spiral
by Roger Alexander 16 Jul '10

16 Jul '10

On 2010-07-16 20:52, Paul N. Lee wrote: > Roger Alexander wrote: > > > > ....go to http://maxitersfractalfollies.blogspot.com > > to see the finished version.... > > > > I see that the "Followers" of your web blog are slowly growing in > number. Are there other places outside of the FractInt List that you > advertise your postings?? > > > Sincerely, > P.N.L. > > The only place I post my blog url is on the mailing list although I suppose with Google search surfers might find obscure niches where my blog is mentioned. The blogs main purpose is to stash precalculated images like Jims Muth's pages at www.Nahee.com. I also occasionally post humorous or domestics bits. _________________________________________________________________ MSN Dating: Find someone special. Start now. http://go.microsoft.com/?linkid=9734384

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A Fetching Little Spiral
by Roger Alexander 16 Jul '10

16 Jul '10

Escape time fractal and spiral,like day follows night. Hope you like this five armed symphony of self-similarity. This graphic is something of a slowpoke go to http://maxitersfractalfollies.blogspot.com to see the finished version and save some clock cycles. fract313.gif { ; a spiral ; blank ; calctime 0:41:44.05 ; created Jul 15, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2000 type=formula formulafile=_r.frm formulaname=RSQ-TT-MJ center-mag=+0.99684261974584600/+0.73345501955671440/2666.667 params=-0.8287301248207037/-0.6443372905667287/0.1785637989440596/-0.235\ 2061525315104 float=y maxiter=3400 logmap=80 cyclerange=0/255 colors=000302403503504604705805806907A07B08B08C09D1AE1AF1BF1BG1CH1CI1DI1\ EJ1EK1FL1FL1GM1GN1HO2IN2KM2NK2QJ2TH2VG2YE2`D2cB1fA1i81l71n51q41t21w00z03\ z07z0Bz0Fz0Jz0Nz0Rz0Vz0Zz0bz0fz0jz0nz0rz0vz0zz0xz0vz0tz0rz0pz0nz0lz0jz0h\ z0fz0dz0bz0`z0Zz0Xz0Wz0Uz0Sz0Qz0Oz0Mz0Kz0Iz0Gz0Ez0Cz0Az08z06z04z02z00z00\ y10x20v20u30s40r50p50o61n71l81k91i91hA1gB1eC1dC1bD1aE1_F1ZF1YG1WH1VI1TJ2\ SJ2RK2PL2OM2MM2LN2JO2IM2GJ2EH2CE1AC18916614312000101302503605806A07C19D1\ 9E1AF1AF1BG1BH1CI1DI1DJ1EK1EL1FL1FM1GN1HO2IO2JQ2IS2HV2GX2F_2Da2Cd2Bf2Ah1\ 9k18m17p15r14u13w12z00z20z50z70zA0zC0zF0zH0zK0zM0zP0zR0zU0zX0zZ0za0zc0zf\ 0zh0zk0zm0zp0zr0zu0zw0zz0zw0zu0zr0zo0zl0zj0zg0zd0za0z_0zX0zU0zS0zP0zM0zJ\ 0zH0zE0zB0z80z60z30z00x01v02s03q04n06l07i08g19e1Ab1B`1CY1EW1FT1GR1HO2JN2\ IM2HK2GJ2FH2DG2CE2BD2AB19A18817715514413212000000101201 } frm:RSQ-TT-MJ {; P1 is the Mandelbrot/Julia coordinates (real & imaginary) ; P2(real [decimal]) is the % remaining in Mandelbrot Space (0.13 = 13%) J=P1 M=P2 ; (Only the REAL NEED BE USED... quite different if IMAGINARY GIVEN K=1-M ; % Julia given from Mandelbrot z = Pixel: z = (M*(sqr(z)+pixel))+(K*(sqr(z)+J)) |z| <= 4 ;Equation entries of 1st image: p1 real=-0.05; p1 imaginary=0.65 ; p2 real= 0.1 ; p2 imaginary=0 (always) } Roger Alexander _________________________________________________________________ Learn more ways to connect with your buddies now http://go.microsoft.com/?linkid=9734388

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FOTD 16-07-10 (Back to the Mandy [6])
by Jim Muth 16 Jul '10

16 Jul '10

FOTD -- July 16, 2010 (Rating 6) Fractal visionaries and enthusiasts: When a big unexpected and very urgent graphic design job arrived at FC on Thursday, I turned to the always dependable Mandelbrot set for a quick fractal. Once again the set did not fail me. Within 10 minutes I had tracked down today's deep scene on the northwest shore line of the main bay. I named the image "Back to the Mandy" for the obvious reason. Since I had so little time for the coloring, I could manage only a rating of a 6. The calculation time of 11-1/2 minutes is on the slow side, but the magnitude of the image is over 10^17, so this time is still quite a bargain. Those who do not calculate may view the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> BTW, the web site will soon have a new logo featuring my all- time favorite fractal. Typical midsummer weather prevailed here at Fractal Central on Thursday. In central Pennsylvania this means a temperature around 90F 32C, rather high humidity, partly cloudy skies and a constant chance of pop-up showers. The day remained dry however. My day was exceptionally busy; FL shared the rush. The fractal cats were more concerned with the lack of attention than the summer weather. The next FOTD will probably be posted within 24 hours. Until whenever, take care, and maybe I'll give up this unpredictable graphic design business and make my living selling prints of even less predictable fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Back_to_the_Mandy { ; time=0:11:31.03-SF5 on P4-2000 reset=2004 type=mandel center-mag=-0.5332033253863\ 6112106947/0.49837305590697647813509/1.415616e+017\ /1/52.5/0 params=0/0 float=y maxiter=4500 bailout=9 inside=0 logmap=585 mathtolerance=0.05/0 colors=000CEbDFcEGdFHeGIfHJgIKhJLiKMjLNkMOlNPmOQnP\ RoQSpRUoSWmTYmU_mVamWcmXemYgmZim_kmQL5VM7ZOAcPCgRF\ lSHpTJmXMj`PhdSehVblY`p_UfXNYUkWYlVamUenThoS_pRSqQ\ KqQCrVKrZRsbYsfdtjktnrrprqmrnikleeiaZgYThWViVXjUYk\ S_lR`mQbmPcnYdoedpndqvdeuhUukIunLrnOonQlnTjnWgnYdn\ `anb_ndcifgdgk`ioWksRlwNvpXiwziuzcszYqzSozNmzFkz8i\ w9guAfsBdqCcpCanD`lEZjFYiGWgGVeHTcISbJQ`KPZKOYLNWM\ NUMMTNMRNMQOLOPLMPKLQKJQKI2jd7d_CZVHUQMOLRIGVDBTCF\ RBKPAPO9UM8ZKAcIChHEmFGrDIvCKzBIvBGrAEmAAh97c94Z81\ U81U70T70SMAXWCVeDTpFRpERoDSoBSnATn8Tm7Ul5VL3DG7FB\ CI6GK0LN9YHIkAehGecFeYEdSDbXL`bTYg`m00zz0z0XGCCKBC\ OACS9DW8D_7Dc6Eg5El3Fn2Kp1Qr0Wk8VdGUYOTkEfkDhhEmeE\ rbFv_FzYFzYBzU4zU9zUEzUJzUOzUTzzXzz_zzbzzezzhzzkzz\ nzzpzzrzztzzvzzxzzzzzzzzzzzzzZzzXzzQzzJzzDzzEzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzPz`NzfLzlJzrGzxGzwGzvFz\ uFztEzsEzpEzmEzjDzgDzdDza } END PARAMETER FILE=========================================

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Big rush = late FOTD
by Jim Muth 15 Jul '10

15 Jul '10

Fractal visionaries and enthusiasts: Due to an unexpected rush job here at FC, the FOTD for July 16 will be late. Sorry for the delay. JIM

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FOTD 14-07-10 (Whole New World [8])
by Jim Muth 14 Jul '10

14 Jul '10

FOTD -- July 14, 2010 (Rating 8) Fractal visionaries and enthusiasts: There are minibrots and there are more minibrots, and then there are things like the minibrot in today's image. I'm not sure if it's a minibrot or not. If either or both real(p3) and real(p4) are changed to zero, the image becomes just another scene not too deep in Seahorse Valley of the Mandelbrot set, but when real(p3) is set to 0.77 and real(p4) is set to the reciprocal of one-googol, the minibrot fills with totally new stuff, which can be zoomed into and explored, and therefore is not an artifact. The formula draws the hypercomplex Mandelbrot set, and it does so quite well. But how is it possible that a value as infinites- imal as the 10^-100 of real(p4) can make such a difference in the image? Regardless of how the image came about however, a whole new world lies inside the minibrot, waiting to be explored. I'll do a little exploration in tomorrow's FOTD, but I really want to get that FOTD web-site logo finished. The rating of an 8 is based on the mathematical interest. The artistic value of the image is everyday average. The calcula- tion time of 1-1/4 minutes will cause no pain to any fractal fanatic. The image is also available on the FOTD web site at: <http://www.Nahee.com/FOTD/> where if all goes well, the FOTD logo will soon be seen in its full glory! Nondescript weather prevailed here at Fractal Central on Tuesday. This means partly cloudy skies and a temperature of a humid 84F 29C. The fractal cats ignored the outside conditions and clung to the cool air most of the day. In my department the work was busy, but thanks to FL, it was finished without a hitch. Unfortunately however, due to the rush, the FOTD web site logo remains in the rudimentary stage. The next FOTD will be posted in 24 hours. Until then, take care, and I hear that Australia recently recorded the lowest temperature in that nation's history. This could mean that all the fuss about global warming has been a false alarm, but more likely, we're confusing weather with climate. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Whole_New_World { ; time=0:01:16.34-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=HyperMandelbrot2 passes=1 center-mag=-0.7583459371/+0.0768359714/28534.27/1/\ 34/0 params=0/0/0/0/0.77/0/1e-100/0 float=y maxiter=875 inside=0 logmap=-109 periodicity=0 colors=000OJiOJkOJlOJnOJoOJmOJkPJjQJhRJfSJeTJcUJaV\ J`XJZZJX`JWbJUdJSfJRhJPjJNkJMjLOiNPhPRfRSeTUdVVbXW\ aZY``ZZb`YcaXecVgdUieTkgRmhQojPqkNsmMtnLuoJslIqiHo\ fGlcFj`EhYHeXKbWM_VPXURTTURSWPRZOQ`OQbOQdPQfQQgRQi\ SQkTQmVQnWQpXQrYQtZQu_Qt`Tt`WsaZsaasbcrbfrciqclqdo\ qdqpeppfpogpohpoipnjpnkpnkpmlpmmplnploplppkqpkrpkr\ pjspjtpiupivpiwphxphyphypeuncrlaoj_lhXifVfdTccR`aO\ Y_MVYKRWIOUFLS10HDIRBFP9CN69L46J23HCUNBRMAPL9NL8KK\ 7IK6GJ5DJ4BI39I26H14H02G2nE1kF1hF1eF1cF1`F1YF1WF1T\ F1QF0OG0LG0IG0GG0DG0AG08G05G02G3g92bA2ZB2UC1QC1MD1\ HE0DE08F04GP`ZNYXMWWKUVJSUHQTGNSELRDJQBHOAFN8DM7AL\ 58K46J24I12HLjJKhIJfIIdIHbIG`IFZIEXIEVIDTHCRHBPHAN\ H9LH8JH7HH7FH6DG5BG49G37G25G13G01GIBWGAUF9TD8SC7QA\ 6P95O74M63L42K31I10HzzBvzCrcCzmChPCcODZMDULDPJDKIE\ AGE0FENzHOzIOzJPzKznMzmNzlOzjczihzgmzfrzdvzjzzmzzm\ zzmzzrzzvzzzzzzzzzzzzzzzz } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 15-07-10 (Mysterious Depths [8])
by Jim Muth 14 Jul '10

14 Jul '10

FOTD -- July 15, 2010 (Rating 8) Fractal visionaries and enthusiasts: Today's image takes us deep into the large period-3 north bud of the strange minibrot in yesterday's FOTD image. The name "Mys- terious Depths" refers to the strange things found there. I am not sure if images such as today's are real fractals or artifacts of mathematical imprecision, but whatever they are, they make some very interesting fractals. The rating of an 8 is based on the mathematical interest. The artistic value is little more than average. The image calculates in 3 minutes, fast enough to keep boredom away and slow enough for a fractalist to work up a little anticipation. The image may also be seen on the FOTD web site at: <http://www.Nahee.com/FOTD/> where it is posted in finished, ready-to-view form. Over one inch, 3cm, of rain fell here at Fractal Central over- night Tuesday. The local farmers say this certainly did not end the drought, but it did bring immediate short term relief. The rain shortage for the year is still over 10 inches, 25cm. The clouds cleared away early Wednesday afternoon, letting the temperature reach 84F 29C. The fractal cats must have approved of things. They were unusually active most of the afternoon. My day was busy, but under control. The next FOTD will be posted in 24 hours. Until then, take care, and be lucky. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mysterious_Depths { ; time=0:03:07.30-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=HyperMandelbrot2 center-mag=-0.7583373\ 90127983/+0.07684186174621/7.2e+011/1/-56/0 float=y params=0/0/0/0/0.77/0/1e-100/0 maxiter=1238 inside=0 logmap=982 periodicity=none mathtolerance=0.05/1 colors=000KLLKOMKRNKUOKXPK_QKbSKeUKhWKmYKr_KvaKzcz\ _lzVlwQlwMlvNkvOjvPivPhvQgvRfvSevSdvTcvUbvVavV`wQ_\ wLZwGZwBYw6YUDFUEMTFTTG_SHfSImSKtQTrPapUgncmlmsmrw\ nzxozypzzqzznzzkzzhYke`hcce`fcYi`VlYSnWQpXQrYQtZQu\ _Qt`Tt`WsaZsaasbcrbfrciqclqdoqdqpeppfpogpohpoipnjp\ nkpnkpmmpmnplpplqplspktpmuprupwvpwwpwxpwypwzpzzpzz\ pzzpzuncrlaoj_lhXifVfdTccR`aOY_MVYKRWIOUFLS10HDIRB\ FP9CN69L46J23HCczB_zAWv9Rr8Lm7Ih6Gc5DZ4BU39I26H14H\ 02G2nE1kF1hF1eF1cF1`F1YF1WF1TF1QF0OG0LG0IG0GG0DG0A\ G08G05G02G3g92bA2ZB2UC1QC1MD1HE0DE08F04GP`ZNYXMWWK\ UVJSUHQTGNSELRDJQBHOAFN8DM7AL58K46J24I12HLjJKhIJfI\ IdIHbIG`IFZIEXIEVIDTHCRHBPHANH9LH8JH7HH7FH6DG5BG49\ G37G25G13G01GIBWGAUF9TD8SC7QA6P95O74M63L42K31I10Hz\ zBvzCrcCzmChPCcODZMDULDPJDKIEAGE0FENzHOzIOzJPzKznM\ zmNzlOzjczihzgmzfrzdvzjzzmzzmzzmzzrzzvzzzzzzzzzzzz\ zzzzOPiKNkHRQFUQEWQCZRB`R } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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Cobalt Capilleries
by Roger Alexander 13 Jul '10

13 Jul '10

Another busy day at Action Central so today's posting will be brief- but not so brief I won't mention the completed fractal is on display at http://maxitersfractalfollies.blogspot.com. fract307.gif { ;Cobalt Capillaries-I just like the sound of it ; blank ; calctime 0:02:42.14 ; created Jul 13, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_k.frm formulaname=km_10 passes=1 center-mag=-0.189282/-0.728366/7.747816/1/127.500000000000014/-7.5946193\ 7782646146e-014 params=0.875/0.875/1.75/1.75/0.2483901486251411/-0.5270851771599475/-0.7\ 5/-0.75 float=y maxiter=1500 inside=0 decomp=256 periodicity=0 colors=05F05F05F16G16G16G16G16G27H27H27H27H27H38I38I38I38I38I49J49J49J49\ J49J5AK5AK5AK5AK5AK6BL6BL6BL6BL7CM7CM7CM7CM7CM8DN8DN8DN8DN8DN9EO9EO9EO9E\ O9EOAFPAFPAFPAFPAFPBGQBGQBGQBGQBGQCHRCHRCHRCHRCHRDISDISDISDISDISEISEJTFJ\ TFKTGKUGLUHLVHMVIMVINWJNWJOWKOXKPXLPYLQYMQYMRZNRZNSZOS_OT_PT_PT`QU`QUaRV\ aRVaSWbSWbTXbTXcUYcUYcVZdVZdW_eW_eX`eX`fYafYafZbgZbg_ch_ch`ch`diadiaeibe\ jbfjcfjcgkdgkdhlehleilfimfjmgjmgknhknhlniloimojmpjmpknpknqloqloqmprmprnq\ snqsorsortpstpstqtuqturuuruvsvvsvwtwwtwwuxxuxxuxxvyyvyywzzvyyvyyuxxtxxtw\ wsvwsvvruvquuqtupstostorsnqsnqrmprlpqloqknpjnpjmoimohlnhkngkmgjmfjleileh\ kdhkcgjcfjbfibeiaeh`dh`cg_cgZbfZbfYaeX`eX`dW_dW_cVZcUYbUYbTXaSWaSW`RV`RV\ _QU_PTZPTZOSYNSYNRXMQXLQWLPWKPVKOVJNUINUIMTHLTGLSGKSFKRFJREIQDIQDHPCHPBG\ OBFOAFN9EN9EM8DM8CL7CL6BK6AK5AJ49J49I38I37H27H16G16G05F } frm: km_10 { ; Kerry Mitchell ; originally conic-near_juli ; tweaked so user can directly input ; julia parameters (p4) originally hardcoded ; to 0,1 cc=p4, zc=pixel, maxr=1e12, minr=maxr, iter=1 a=real(p1), b=imag(p1), c=real(p2), d=imag(p2) e=real(p3), f=imag(p3): iter=iter+1, zc=sqr(zc)+cc, x=real(zc), y=imag(zc) conic=|x*(a*x+b)+y*(c*y+d)+e*x*y+f| if (conic<minr) minr=conic end if if ((|zc|>maxr)||(iter==maxit)) iter=-1 t=log(minr) z=cos(t)+flip(sin(t)) end if iter>0 ;SOURCE: kerrym.frm } Roger Alexander _________________________________________________________________ Game on: Challenge friends to great games on Messenger http://go.microsoft.com/?linkid=9734387

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FOTD 13-07-10 (Galaxial Attraction [6])
by Jim Muth 12 Jul '10

12 Jul '10

FOTD -- July 13, 2010 (Rating 6) Fractal visionaries and enthusiasts: Due to the unusual colors of today's image, I wanted to rate it higher, but I just couldn't shake the feeling that I had seen something similar so many times before. It takes more than just colors to make a great fractal image, so I finally settled for a rating of a 6, which is slightly above average. The generating expression combines 1.5 negative portions of Z^(0.6) with 0.25 negative portion of Z^(6.4) and then adds (1/C). The parent fractal is an area of scattered Mandelbrot sets with different degrees of distortion, all of them surroun- ded by clouds of smaller satellite M-sets, all the way to infinity. Today's scene lies in a satellite of a satellite very deep in what appears to be an East Valley of one of the largest M-sets. The name "Galaxial Attraction" means next to nothing. It's probably a carry-over from my wonder years, when I wanted to be an astronomer. Due to the extreme magnitude of the image, the mathtolerance entry in the parameter file is absolutely necessary. Without it, all kinds of weird things happen. The image actually lies beyond the range of perfect resolution, but the resulting break- down is hardly noticeable. The calculation time of 1-1/2 minutes is a fair price to pay for today's image. The real bargain price may be found on the FOTD web site, where the already-calculated image may be viewed instantly. The web site may be accessed at: <http://www.Nahee.com/FOTD/> The temperature rose to 88F 31C in the early afternoon on Monday here at Fractal Central. At 4pm however a thunder-storm moved in with a gust of wind and a brief downpour of rain. By 5pm the temperature was a comfortable 73F 23C. The storm dropped 1.5cm or just under 1/2 inch of rain, much to FL's satisfaction, but the rain here is still about 25cm or 10 inches below normal for the year. The fractal cats braved the storm without dashing for cover. The next FOTD will be posted in 24 hours. Until then, take care, and every fractal should exceed the one before. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= GalaxialAttraction { ; time=0:01:33.41-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=+0.4069265102167707/+0.1836836593039934\ /2.5e+013/1/-55/0 params=-1.5/0.6/-0.25/6.4/0/0/0/0 maxiter=1800 inside=255 logmap=394 periodicity=6 mathtolerance=0.05/1 colors=00000500A00F00K00P00U00Z00c00h00m00r00w00zA\ JAFMAPPPSTSWWW_Z_bbbfefjhjmkmiijfhgbfd_eaXcZTbWQ`T\ N_RM`UMaWMbZMc`LdcLdeLehTchLfjKgmKhoKirVToSYqParMe\ shgnchpZhqUirPisej`Ca2EcDGeOHfZJhiO`nNborzzowzlvzi\ uzfszcqz`ozfnymmwrrrvvvzzzzzzhjrcjrZjsUisPityhxsiw\ niwiivdivZiuUiuPitVNRTQUSSXRU_QXbPZeO`hNckMenLgqai\ 1YiDUiORiZNii2D54HB6KG8NLARQBUVDX`F`eHcjJfoIBUJFXJ\ I_JMbJPdJTgKWjK_lKboKfrN`1McKLfbLBEKEIKHMKKPKNTKQW\ KT_KWcKZfKajKdmKgqK3eJ6eJ9eJCjNFoNIrNLtMOtMQtMTtLW\ tLZtLatKdtKgtnzgkxhiwifvjdtkbsl_rmYpnVooTnpRlqOkrM\ jsAKuBMtCOtDQtDStEUtFWtFXtGZtH`tIbtIdtJftKhtSbUPeb\ MgkWKoVMpUOpTQqaSslUzQWrPYrO_sNasMcsLetKgt7HN9KQAM\ TBPWCRZDUaEWcFYfG`iHblIeoJgrPMJOOMOQPNSSNTUNVXMX_M\ YaM_dLagLcjLdlKfoKhrrmKomOlmRimzfmzcmz`mzYmzVmzSmz\ PmzMmzjmzamzTmzgmzdmzbmz_mzYzzWzzTzzRzzOzzMzzyzzuz\ zrzzozzlzzhzzezzbzz_zzzzZ } 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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A Weave Effect
by Roger Alexander 12 Jul '10

12 Jul '10

Knock knock... Who's there? Orange. Orange who? Orange you glad I didn't say "Today's minibrot..." Today's posting is not a minibrot it's a fractal with a metallic weave effect from the Liar family of formulas. Use an outside coloring with a higher than usual proximity value, calculate with low maximum iteration value and you get today's fractal. Go to the old reliable http://maxitersfractalfollies.blogspot.com for the pre-calculated fractal. And now for the local weather report.Calgary had a hailstorm today with some large hailstones but not of the bigger than a golf ball type. No significant damage but with this latest down pour the weather remains unseasonably wet and cold and the farmers are worried. fract310.gif { ; metallic weave ; blank ; calctime 0:01:21.67 ; created Jul 12, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=fract001.frm formulaname=F'Liar1 function=ident center-mag=3.41766/-2.62175/0.8266842 params=0.9479354228339488/0.30405590990936 float=y maxiter=15 inside=0 proximity=2 outside=fmod invert=0.791558580278939/-0.0923184911648915/-0.439802240058596 colors=000CGUBET9DS8BR7AQ69P57O36N24M13L02K02K13L25M36N47O69P7AQ8CR9DSAE\ TBGUCHVDIWFKXGLYHMZIO_JP`KRaLSbMTcOVePWfQXgRZhS_iTajUbkVclXemYfnZgo_ip`j\ qakrbmscntepufqvgrwhtxiuyjvzjvziuyhsxgrwfqvdoucntblsakr`jq_hpZgoYfnWdmVc\ lUbkT`jS_iRYhQXgPWfNUdMTcLSbKQaJP`IN_HMZGLYEJXDIWCHVBFUAET9DS8BR7AQ58P47\ O36N24M13L02K02K13L25M36N47O69P7AQ8CR9DSAETBGUCHVDIWFKXGLYHMZIO_JP`KRaLS\ bMTcOVePWfQXgRZhS_iTajUbkVclXemYfnZgo_ip`jqakrbmscntepufqvgrwhtxiuyjvzjv\ ziuyhsxgrwfqvdoucntblsakr`jq_hpZgoYfnWdmVclUbkT`jS_iRYhQXgPWfNUdMTcLSbKQ\ aJP`IN_HMZGLYEJXDIWCHVBFUAET9DS8BR7AQ58P47O36N24M13L02K02K13L25M36N47O69\ P7AQ8CR9DSAETBGUCHVDIWFKXGLYHNZIO_JP`KRaLSbMTcOVePWfQYgRZhS_iTajUbkVclXe\ mYfnZho_ip`jqalrbmscntepufqvgswhtxhtxiuyhtxgrwfqveoucntbmsakr`jq_ipZgoYf\ nXdmWclVbkT`iS_hRZgQXfPWeOUdNTcMSbLQaKP`IO_HMZGLYFJXEIW } frm:F'Liar1 {; Generalization by Jon Horner of Chuck Ebbert formula. ; X: X is as true as Y ; Y: Y is as true as X is false ; Calculate new x and y values simultaneously. ; y(n+1)=abs((1-x(n) )-y(n) ), x(n+1)=1-abs(y(n)-x(n) ) z = pixel: z = 1 - abs(imag(z)-real(z) ) + flip(1 - abs(1-real(z)-imag(z) ) ) fn1(abs(z))<p1 ;SOURCE: fractint.frm } Roger Alexander _________________________________________________________________ Game on: Challenge friends to great games on Messenger http://go.microsoft.com/?linkid=9734387

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FOTD 12-07-10 (Arc-Tangent Does It [8])
by Jim Muth 11 Jul '10

11 Jul '10

FOTD -- July 12, 2010 (Rating 8) Fractal visionaries and enthusiasts: Today's image is located in the middle of nowhere. Well, it's actually located in a parent fractal resembling a Mandelbrot set starting to split apart along its negative X-axis. The scene lies in the apparently empty space between the two spread- apart branches of the parent's Scepter Valley. When I first rendered today's image in the usual manner, it was a total flop. But thanks to Fractint's various rendering options, I raised the total flop to a rating of an impressive 8. The delicate and decorative fern-like features jutting in from the edges consist of 'outside' stuff exaggerated by the 'atan' option; the soft, gently colored aura surrounding the order-3.5 minibrot is 'inside' stuff made visible by the 'fmod' option. Put all of this together and the image honestly earns its 8. The name "Arc-Tangent Does It" came to mind when I tried the 'atan' feature on the original near-hopeless image and saw the unexpected improvement. Re-rendering the scene with the 'fmod' inside was an afterthought. The calculation time of 1-1/4 minutes will pass swiftly once the full glory of the scene becomes apparent. It will take even less time to view the image already calculated on the FOTD web site at: <http://www.Nahee.com/FOTD/> According to the fractal cats, a splendid day prevailed here at Fractal Central on Sunday. The humidity was quite low and the sky was completely cloud-free all day. True, the temperature of 88F 31C was on the warm side, but the dry air kept things quite comfortable. With the work caught up after a hectic week, my day was spent trying to relax. My next task is to stay caught up and relaxed so I can finish a logo for the FOTD web site. I have the design, which includes some 4-D stuff, worked out, but I have not yet done the footwork. FL spent the day Sunday giving hints that it was her XX'th birthday. (I had not forgotten.) If all goes well, and even if it does not, the next FOTD is quite likely to be posted in 24 hours. Until then, take care, and iterate wildly. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Arc-TangentDoes_It { ; time=0:01:13.71-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip inside=fmod center-mag=-1.267991618657123/-0.0061887110744204\ /199069.8 params=3.5/-99/0/0 float=y maxiter=2500 proximity=0.0003 outside=atan periodicity=6 colors=000000000000000000000000000000000000000000Z\ 7O_7O`7OXAPTDPQFPMIPGLOJKPLKQNKQPKRSKSUKSWKTYKU`KU\ bKVdKWeJXfKWfLVfMVfNUfOTfPTfQSfRRfRRfSQfTPfUPfVOfW\ NfXNfYMfZLgZLg_Kg`JgaJgbIgcHgdHgeGgfFgfFggEghDgiDg\ jCgkBglBgmAgmAhkBhjBhiBhhChgChfCheChdDhcDhbDhaDh`E\ h_EhZEiYFiXFiWFiVFiUGiTGiSGiRGiQHiPHiOHiNIiMIiLIiK\ KjJMjIOjHQjGSjFUjFWjGYjH_jIaiJchKegLgfMieNkdOlcOmb\ PmbQnaRn`So`To_Up`UpaUq_UpaVqbWqcXqdYqfZqh`qkbrmdr\ ofrqhrsjrulrwmrpimiemcbmXZmRWnKSjEPf7Lb0HZ1IZ2IZ2I\ Z3IZ3IZ4I_5I`5Ia6Ib6Ic7Id8Ie8If9Ig9IhAIiBJjCKkDLmE\ MoFNqGOsHPtIQuJRvKSwLTwLTwLTwLTxKTyKTzKTzKTzJTzJTz\ JTzITzITzITzITzHTzHTzHTzGTzGTzGUzGUzFTzFTyFTxETwET\ vETuETtDTsDTrDTqCTpCToCTnDUmCTlCSkCRjCRiBQhBPgBOfB\ OeANdAMcAMbALa9K`9J_9JZ9IY8HX8HW8GV8FU7ET7ES7DR7CQ\ 6CP6BO6AN69M59L58K57J36I57H67G56F45E34D23C12B01A00\ 9008007006005004003002001 } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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A Maximum of Minibrots
by Roger Alexander 10 Jul '10

10 Jul '10

Another minibrot. You know what they say, repetition is the sincerest form of flattery. Well actually they don't say it I just made it up and to be truthful I really don't know what it means, although it has a nice ring to it. More cool wet weather in Calgary but on parts of the eastern side of Canada there is a mini heat wave. Rather fractalish, a chaotic divergence of outputs. Go to http://maxitersfractalfollies.blogspot.com for not only the pre-calculated gif but a post-processed jpg. fract299.gif { ; repetition is the sincerest form of flattery ; blank ; calctime 0:03:35.91 ; created Jul 10, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_d.frm formulaname=D-ROCK function=sin passes=1 center-mag=-0.43612715894868200/+0.00000000000000000/274914.1/1/90/3.885\ 78058618804789e-016 params=0/0 float=y maxiter=1500 inside=0 outside=atan colors=00100100100100100100100200200200200200200300300300300300300400400\ 400400400400500500500500500500600600600600600600700700700700700700800800\ 800800800800900900900900900900A00A00A00A00A00A00B00B00B00B00B00B00C00C00\ C00C00C00C00D00E00F00G00I00J00K00L00M00N00P00Q00R00S00T00U00W00X00Y00Z00\ _00a00b00c00d00e00f00h00i00j00k00l00m00o00p00q00r00s00t00v00w00x00z01z02\ z03z04z06z07z08z09z0Az0Bz0Dz0Ez0Fz0Gz0Hz0Iz0Jz0Lz0Mz0Nz0Oz0Oz0Pz0Pz0Qz0R\ z0Rz0Sz0Sz0Tz0Uz0Uz0Vz0Vz0Wz0Xz0Xz0Yz0Yz0Zz0_z0_z0`z0az0az0bz0bz0cz0dz0d\ z0ez0ez0fz0gz0gz0hz0hz0iz0jz0jz0kz0kz0lz0mz0mz0nz0oz0oz0pz0pz0qz0rz0rz0s\ z0sz0tz0uz0uz0vz0vz0wz0xz0xz0yz0zz0zz0zz0yz0yz0yz0xz0xz0xz0wz0wz0vz0vz0v\ z0uz0uz0uz0tz0tz0tz0sz0sz0rz0rz0rz0qz0qz0qz0pz0pz0pz0oz0oz0nz0nz0nz0mz0m\ z0mz0lz0lz0lz0kz0kz0jz0jz0jz0iz0iz0iz0hz0hz0hz0gz0gz0fz } frm: D-ROCK { z = 0, c = pixel: z = sqr(z) + c c = c + p1 * z z = fn1(z)/c |z| <= 4 ;SOURCE: d-rock.frm Roger Alexander _________________________________________________________________ MSN Dating: Find someone special. Start now. http://go.microsoft.com/?linkid=9734384

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FOTD 11-07-10 (Quick Mandy Test [6])
by Jim Muth 10 Jul '10

10 Jul '10

FOTD -- July 11, 2010 (6) Fractal visionaries and enthusiasts: On Saturday, with the end of the backup rush here at FC in sight, FL was a victim of an uncontrollable urge to set out on an antiquing trip. By the time we returned to FC, the sun was sinking beneath the western ridge, leaving me only a short time to come up with a worthy FOTD image. Luckily, the Mandelbrot set has no end of worthy images, and it runs extremely fast on the 2000mhz fractal-dedicated machine. I found today's worthy image hiding in the fourth valley out the main stem of the largest minibrot on the main stem of the parent Mandelbrot set. The magnitude of the image is past the point of perfect resolu- tion with conventional math. But if anyone wishes to eliminate the nearly invisible (at 640x480 resolution) slight trace of jagginess, they may shift to arbitrary math and wait a half hour instead of 6 seconds to see the image. The name "Quick Mandy Test" describes how I found the scene. The rating of a 6 is what I think the image is worth. The finished image is posted as usual on the FOTD web site at: <http://www.Nahee.com/FOTD/> About 2cm of rain fell here at Fractal Central Friday night. It hardly erased the 25cm rainfall deficit for the year, but FL's flowers do appear a bit perkier. The afternoon temperature reached 88F 31C, still very warm, but with the lower humidity, the day's weather felt much more comfortable than Friday's. The fractal cats spent the day sleeping, but sprang to life when we returned around 8pm. The next FOTD will be posted in about 24 hours. Until then, take care, and save mankind. Stop crying about the trouble the earth is in and face the real problem. The earth will survive its infection of human viruses by developing a fever and killing them off. It's the future of humanity we're really worried about, not the temperature of the third planet from a mediocre star. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Quick_Mandy_Test { ; time=0:00:06.43-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.7797007392746\ 13/+0.00003354724215589/1.15e+013/1/-175/0 float=y params=0/0 maxiter=20000 mathtolerance=0.05/1 colors=000000`XIZVJYULWTMWROVSNUSNTSNTSMSSMRSMRSLQ\ SLPSLOSLOSKNSKMSKMSJLSJKSJAbHFXIKSJONKTHLYCMc1Nb4M\ a7MaAM`DL_GL_JLZMKYPKYSKXVJWYJW`JVcIUfITmKUkJUiIUg\ HUeGUcFPZAS`DUbFWcHYeJ_gLahNcjPelRgmTioVkqXmrZot`q\ vbswduyfwzhvxfuvetucssbrqaqp_qnZplYokWniVmgUlfSkdR\ qpNkcQeRSV2P`EUfQZnXhlackeZjiUinPhrKfyGgvGgsGhqGhn\ GilGiiGjfGjdGkaGk_GlXGlUGmSGmPGnNGnKGoHGoFGpCGq4Bp\ 7EpAGpDJoFLoINoLQnOSnQUnTXmWzmZzm`zlczlfzmizrjzviz\ zgzzczz_zzWzzSzzNzzJzzFzzBzz7zz5zz3zz7zkAlhDkeHjbK\ iZNgWRfTUeQXdPYdOZeN_cM_aL`_K`YJaXIaVHaTGbRFbQEcOD\ cMCcKBdIAdH9eF8eD7eB6fA5f84g63g42g35d87aDA_ICXNFVR\ HSWKP`MNePKjPGsQHpRInRJlSKiSLgTLeTMcUN`UOZVPXVPUWQ\ SWRQXSOXTLYTJYUHZVEZWC_XAVV1YW5_X8bYBdZFf_Ii`LkaPn\ bSpcVqcXrcYpdZne_lf_jg`hh`fhadiabjb`kcZlcXmdVmdTne\ RoePpfNqgLrgJrhHshFtiDuiBvj8xlAvjCuiDthFsgGrfIqeoi\ 4mg6lf7je9icAgbBfaDd`EcZF } END PARAMETER FILE=========================================

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FOTD 10-07-10 (Diamond Festival [6])
by Jim Muth 10 Jul '10

10 Jul '10

FOTD -- July 10, 2010 (Rating 6) Fractal visionaries and enthusiasts: Well, the cool air is up and running again here at FC, and in a day or two, things should be back to normal. Until then, we will have a couple undistinguished but still pleasant fractal images to enjoy. The parent fractal of today's image is a strange thing that came about when I combined 3 parts of Z^(-3) with 7 parts of Z^(-1.5) and added (1/C). It is best described as a single large rectangular bay with rounded corners, surrounded by a cloud of satellite minibrots. Today's image is located in the Seahorse Valley of one of these satellites on the east side of the main bay. The name "Diamond Festival" is one of those phrases that seems to have a deep between-the-lines meaning. Actually, it has no inner meaning at all. I chose it simply because, like the old song 'Stairway to Heaven' it causes the ears to perk up and the mind to exercise itself searching for a deep meaning that does not exist. The rating of a 6 is not too bad considering that we're still struggling here at FC to get caught up in the work that backed up while the cool air was down. The calculation time of 3-3/4 minutes will pass in somewhat less than a flash. The full flash may be experienced by viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> With a high temperature of 95F 35C here at Fractal Central on Friday, and more clouds obscuring the sun, I guess one might say the heat wave was broken. But the higher humidity made it every bit as uncomfortable as Thursday, when the official high was 104F 40C. The only good news was the high humidity, which makes rain more likely. (We have a pretty serious drought in progress here at FC in Central Pennsylvania, and the farmers are praying.) The fractal cats spent the morning on the cool tile floor in the kitchen. When the air conditioning finally came on in the afternoon, they shifted to the cool air vent. My day was quite busy getting caught up in the work. The next FOTD will be posted in 24 hours. Until then, take care, and if reality is not real, then what is it? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Diamond_Festival { ; time=0:03:46.35-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip inside=0 center-mag=+1.075320540484659/+0.4639328126579238/\ 4.546794e+012/1 params=3/-3/7/-1.5/0/0/0/0 float=y maxiter=3500 logmap=757 mathtolerance=0.05/1 colors=000000KOJE16F42909K86CA3UO9zpGulEqhDmeCiaBe\ ZA`V9XR8TN7PK6LG5GE4CA3872451r_YnYXjWVfUUaTSYRRUPP\ QNOMMNONOPOPRPQUQRXRS`SScTTfUUjVVmWWpXWVyRXzPZzN_z\ LazJczHdzFfzDgzBctC_oDWjDTdEP_ELVFHQFEKGAFG6AH35H9\ 7IE9JJAKOCLTEMYFMUIIRKFONCLP9IR6JT8KU9LWBMXCNZEO_F\ PaHQbIRdKSeLTfM4asGbrScrcdroermRekCTuHQsIPrJOpKNoL\ MmMLlNKkOK_NLONMKJIHGFDDC679A99666333fJxaGqXEjSCcN\ AXJ8RE6K94D4265ga4ZU3QM2HF1877sq5gf4XW2ML1BAh2wd1r\ a1nZ1jW1eS1aP1YM1UJ0PG0LC0H90C6083040T80Q70O60M60K\ 50H40F40D30B3082061041020cqzirzenvbjm_gkXciU_WRX`O\ TPLPMIMJFIGCEC9B9676333jhXZXONMGBB8eNS`KOWHLSFINCF\ IACE79956423pw8jp7di6Zc5TX4NQ3HK2BD1560_pAOZ6CK3pK\ mkKzgUUcUR_cOWcMScJOcGKmDGmBCm88m54m2QmDNmBLmAIm9G\ m8Em7Bz59z47z34z22z1PzQGzH8z8zzzzzvzzrzznzzjzzfzzb\ zzZzzVzzRzzNzzJzzFzzBzz7zz3zz3zz2zz2zz2zz2zz1zz1zz\ 1zz1zz1zz0zz0zz0zz0zzPzzQ } 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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Minibrots Comin' at Ya!
by Roger Alexander 09 Jul '10

09 Jul '10

Another day, another minibrot today's specimen in bright summery colors. This one is a bit of a slow poke, go to the usual http://maxitersfractalfollies.blogspot.com for the completed gif. fract298.gif { ; minibrot ; blank ; calctime 1:13:11.20 ; created Jul 09, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_w.frm formulaname=Waves center-mag=-1.75832257989310900/-0.01637659723394863/1558932 params=2/50/2/1 float=y maxiter=12000 inside=0 logmap=264 colors=w0dv0bt0ar0_q0Zo0Xm0Wl0Uj0Ti0Rg0Qe0Pd0Nb0M`0K_0JY0HX0GV0ET0DS0BQ0\ AO08P08Q08R08S18U18V18W18X28Y28_28`28a38b38d38e38f48g48h48j48k58l58m58o5\ 8p68q68r68s68u78v78w78x78z88z98zA8zB8zC8zD8zE8yF8yG7yH7yI7yJ7yK7xL7xM7xN\ 7xO6xP6xQ6wR6wS6wT6wU6wV6wW5vX5vY5vZ5v_5v`5va5ub5uc4ud4ue4uf4ug4th4ti4tj\ 4tk3tl3tm3sn3so3sp3sq3sr3rs2qs2os3ns3mr4lr4kr5jr5hr6gr6fr6er7dr7cq8aq8`q\ 9_q9ZqAYqAXqBVqBUpCTpCSpDRpDQpDOpENpEMpFLpFKoGJoGHoHGoHFoIEoIDoJCoJAnK8q\ L5tN3wP0zR0wQ0sO0pN0lL0hJ0eI0aG0YE0VD0RB0N90K80G60C40H90MF0RL0WR0`X0eb0j\ h0on0tt0zz0xx0vv0st0qr0no0lm0jk0gi0ef0bd0`b0Y`0WY0UW0RU0PS0MP0KN0HL0FJ1C\ G2CL4DP5DU7DZ8EbAEgBElDFpEFuGGzGGxFFvEEtDDrCCpBBnBBlAAj99h88f77d66b66`55\ Z44X33V22T11R00O53SA6XG9aLCfQFkWIp`LufOzfNyfMweLveKtdJsdIqdHpcGncFmbEkbD\ jaChaBgaAe`9d`8b_7a_6__5ZZ4XZ3WY2UY1TX0Rc0Vk0Zr0bz0fy0e } frm:Waves (XAXIS) {; Try params=2/50/2/1 c=z=pixel: z=z^Real(p1)+c |Real(z)*Real(p2)|+|Imag(z)*Imag(p2)|<=Imag(p1) ; "She canna take this much longer Cap'n!" ;SOURCE: fractfun.frm } Roger Alexander _________________________________________________________________ Game on: Challenge friends to great games on Messenger http://go.microsoft.com/?linkid=9734387

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FOTD 09-07-10 (Oddball Minibrot [No Rating])
by Jim Muth 09 Jul '10

09 Jul '10

FOTD -- July 09, 2010 (No Rating) Fractal visionaries and enthusiasts: With the outdoor heat still on and the indoor cool air still off, things were rather stifling here at Fractal Central on Thursday. We worked around the problem by limiting the time we ran the computers to periods of 30 minutes. In the fractal department, I grabbed the first image I came up with, added a dash of color, and declared it FOTD for July 09. The image is a close-up of a curious little minibrot with its main stem cut off. Very little of the usual symmetry is in evidence around the minibrot, though traces are clearly visible. The fiery effect was created intentionally in an effort to make something of nothing.. The generating expression mixes Z^2.5 with 1/2 part of Z^5 and adds straight C. The parent fractal resembles nothing as much as a flying wing. Today's scene is located on the southern shore line of the 'East Valley' of the parent. Of course, I could give the image no rating. The name "Oddball Minibrot" fairly describes the scene. The calculation time of 1-3/4 minutes will pass in a flash, especially if the image is viewed already calculated on the FOTD web site at: <http://www.Nahee.com/FOTD/> Total heat prevailed here at Fractal Central on Thursday, with the outside temperature at 104F 40C and the air conditioning still down inside. The fractal cats spent the day in the breeze stirred up by two emergency fans we picked up at the dollar store. If the fractal computer keeps working, the next FOTD will be posted in 24 hours. Until them, take care, and why is the fourth dimension so hard to visualize? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Oddball_Minibrot { ; time=0:01:42.73-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident center-mag=+0.313868105791/-0.000439415919/3196675\ /1/-172.5/0 params=1/2.5/0.5/5/0/0/0/0 float=y maxiter=2500 inside=0 logmap=202 periodicity=6 colors=000P2KPIC1LP0_c0RU0IK09AhAd`8YU6RM5KF3DzzzU\ Jxio8UY5FH2ScqIQ_9DIHr5Cd38R24D1scmeU`SKPEACHoCEhA\ Cb9AW78Q66J44D3261UxEFU77Ms6Jl5Ge4DZ3BS28L15E027LO\ JILGFIEDFBAC9797564232NI8PEQKGUFJXAL`5Od0QgGafWmej\ yeimghaigQjfElf3ma4nX4oS3g970N2`I2TE1M91E4074Y53T4\ 2O32J21E2191040NM7BB3ZHUSDOLAIE6C736VxCKc8AK4rNtBk\ v5OT4Xb3SY3OT2KO2GJ1CE189044VdzRZrNUjJPbFKVBFN7AF3\ 57C73842421pIzZCeH6LZKLHAAylOlbJ`TEOJ9C94cQKZMHUJF\ PGCKDAF97A65532nUkaM_PFOC7CcEUK7Fe72_c8IK4Ik48HY6E\ S5BM48H25B125Q4yK3lF2`A1O50CyJW1k50a40S30J2091tLZj\ HTaENSAHJ7B9358uSLTuHOkEJaAET79J349Hj5Ed4CZ3AT38N2\ 6H14B1250jTtbOjVJaNESF9J749aEkJ7OU39M26F14702ayRPd\ ICK9IKFEGCAC9786343QFHHAB855WHCOC9G86843n2Pe1KY1Gz\ 1CH08804z62441m20`EzTBmM8`E5Pz2CXEGnVMaNGzFBz75kJA\ zE7z95z42bx6zJ3zF2zC2z91F617z09z36z23z1QzKMzHIzEEz\ Bzz8zz5zz2zz0zzzzzzzzzzzz } 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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Frequent Minibrot Sightings (It's Their Annual Migration)
by Roger Alexander 08 Jul '10

08 Jul '10

A familiar face- a minibrot (from Fractint's built in magnet2m formula) with a dark blue twilight map. Ready made at http://maxitersfractalfollies.blogspot.com fract297.gif { ; magnetic minibrot ; blank ; calctime 0:31:40.80 ; created Jul 08, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=magnet2m center-mag=+1.94263374043111200/-0.89721570294892640/136460.1/1/-84.9999\ 99999779817/4.51270208701171072e-010 params=0/0 float=y maxiter=1500 inside=0 colors=0Qk0Qj0Pj0Oi0Oi0Ni0Nh0Mh0Lg0Lg0Kg0Jf0Jf0Ie0Ie0He0Gd0Gd0Fc0Fc0Eb0D\ b0Db0Ca0Ca0B`0A`0A`09_08_08Z07Z07Z06Y05Y05X04X04X03W02W02V01V00U01V03W05\ X07Y09Z0A_0C`0Ea0Gb0Ic0Kd0Le0Nf0Pg0Rh0Ti0Vj0Wk0Yl0_m0an0co0ep0fq0hr0js0l\ t0nu0pv0rw0qw0ov0mu0lt0js0hr0fq0ep0co0an0`m0Zl0Xk0Vj0Ui0Sh0Qh0Pg0Nf0Le0J\ d0Ic0Gb0Ea0D`0B_09Z07Y06X04W02V00U00U00T00S00R00Q00P00O00O00N00M00L00K00\ J00I00H00H00G00F00E00D00C00B00A00A00B00C00D00E00F00F00G00H00I00J00K00K00\ L00M00N00O00P00P00Q00R00S00T00U01V03W05X06Y08Z0A_0B`0Da0Fc0Gd0Ie0Kf0Lg0N\ h0Pi0Qj0Sk0Um0Vm0Xn0Zo0`o0bp0cq0er0gr0is0kt0mt0nu0pv0rw0tw0vx0xy0zz0zz0y\ z0yz0xz0xy0wy0wy0vy0vy0ux0ux0tx0tx0sx0sw0rw0qw0qw0pw0pv0ov0ov0nv0nu0mu0m\ u0lu0lu0kt0kt0jt0it0it0hs0hs0gs0gs0fs0fr0er0er0dr0dq0cq0cq0bq0aq0ap0`p0`\ p0_p0_p0Zo0Zo0Yo0Yo0Xo0Xn0Wn0Wn0Vn0Um0Um0Tm0Tl0Sl0Rk0Rk } Roger Alexander _________________________________________________________________

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FOTD 08-07-10 (Back-up Special [No Rating])
by Jim Muth 08 Jul '10

08 Jul '10

FOTD -- July 08, 2010 (No Rating) Fractal visionaries and enthusiasts: Everyone knows that the air conditioning always breaks down on the hottest day of the year. It's an evil plot. Well, that's what happened here at F.C. on Wednesday, which was actually only the second hottest day. But the breakdown meant that the computers could be run only for a half hour or so before they overheated, and this cut into my fractal time. But, being resourceful, I still managed to find a fractal in cold storage, which I present as today's image. The name "Back-up Special" indicates that I had today's image in storage in case of just such an emergency as arose here at FC on Wednesday. The image has no rating and it runs in a fast 36 seconds. The parent fractal was created by combining 2 parts of Z^2 with 0.1 part of Z^10 and adding straight C on every iteration. Today's scene is located near a cut-off satellite minibrot of the near- shapeless main fractal. The completely finished image is posted on the FOTD web site at: <http://www.Nahee.com/FOTD/> The heat remained in full force here at Fractal Central on Wednesday as the temperature reached 102F 39C. The increased humidity simply added to the discomfort. The fractal cats were so warm that they had to be scraped from the cool tile floor. With the cool air on the bust, my day was hot. Luckily, the work was not too heavy, letting us run the computers in short bursts to avoid overheating. If all goes well, which is never guaranteed, the cool air will be running and the next FOTD will be posted in 24 hours. Until then, take care, and when the heat strikes, take a cold shower. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Back-up_Special { ; time=0:00:36.23-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident float=y center-mag=-1.014400360567347/-0.4204233759208762/\ 2.95728e+011/1/50/0. params=0.1/10/2/2/-0.5/0/0/0 maxiter=1500 inside=0 logmap=127 periodicity=6 colors=000Q9KRAKSBKTCKUDKVFKWHKXJKYLK_NKaPKcRLeTMg\ VNhXOh_PgbQgeRfhRfkSfmSRVNBDJLXEmtASmEPkHMiLJfOHdS\ EbVB_Z8Ya5We3Hh8JgCMZGMeKLdONcSQbXSa`Z`dZ_h_ZcPQz`\ Xt`XqaYoaYlaZjaZgaZea_ba_`a`Ya`Wa`TaaRaaOabMabKabP\ XaTSaY0`a0`X0YS0VNUzIYzDaz8ez4iz9gzDfzHezMdzQczUbn\ YasWbqVboUcmTckRciQdgPdeOddMebLe`KfZJfXHfVGgTFgREg\ QDcTC_WCWZBTaAPdALf9Hi8El8Ao76r73tAKvC_wEoxFkvGgtH\ csI_qJWpKSnLOlMKkNGiNChXGgeJfnMewPduOesOeqOeoNfmNf\ kNfiNfhMgfMgdMgbMg`LhZLhXLhWLhXOiXQjYSkYUlZWmZYn__\ o_ap`cq`eq_goZhnYimXjlWkkVliUmhUngTofSpeRqcQrbPszO\ tzOuzRszTqzWpzYnz_m_bk_dj_fh_if_ke_mc_pb_r`_t__qZY\ nZWkZVhZTeYScYQ`YPYYNVXLSXKQXINXHKWFPWEUWCZWBcYDh_\ EmaFrcGveHzgIziJzkKzmLzoMzqNzsOzuPzwQzyRzzSzzVzzXz\ zZzz`zzbzzdzzfzzhzzjzzlzznzzYFzIFz2Jz5Nz7Rz9VzBZzD\ bzGfzIjzKnzMrzOuzQszKrzEqz8pz3nz8mzDlzIkzMjzRizWhz\ `gzdfziezndzsrzJrzJqzJpzJ } 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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Re: [Fractint] climate change
by JackOfTradeZ＠comcast.net 07 Jul '10

07 Jul '10

. I've always been a fervent believer in climate change; I witness it personally all the time - there can be no doubt it is real! I see Winter->Spring->Summer->Autumn happen every year! There is always a marked warming trend as Winter proceeds into Summer! People just gotta open their eyes and be more open minded! Cheers .

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FOTD 07-07-10 (What Is It? [No Rating])
by Jim Muth 07 Jul '10

07 Jul '10

FOTD -- July 07, 2010 (No Rating) Fractal visionaries and enthusiasts: Due to a work rush here at FC, today's image is both late and fast, which means I could give it no rating. Its name is a question -- "What Is It?". The answer is a Julia set. The way to see the image is to run the included parameter file and wait 23 seconds. Another way to see the image is to visit the FOTD web site at: <http://www.Nahee.com/FOTD/> Things were really cooking here at Fractal Central on Tuesday as the temperature reached 104F 40C. The fractal cats passed the time stretched on the cool tile floor. I passed the time working. The next FOTD will be posted in 24 hours. Until then, take care, and be ready for anything. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= What_Is_It? { ; time=0:00:23.45-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2J function=recip inside=0 center-mag=0.311146/0/0.45/1/-90/0 periodicity=6 params=-0.5/5/0/0/-0.716/0 float=y maxiter=1500 colors=0000OJ5FB964G86N97TA9_CAeDClEDrFEoMKlSQiYWf\ dacjgapmdohgodjo`moXpoSsoOvoKyoGd4nLDp1Mr1Ri1W`1`S\ 1eJ3aG4YD5UB6R87N68J39G1xd2rg1mj1hl1co0Zq0Ut0Pv0Uw\ 1Yw1ax1ex1iy2my2qz2uz2or3ij4cc5YW6SP7MH8GA8GC8GE8G\ G8EG8CG8AG88G88GA8GC8GE8GG8EG8CG8AGBBGCBGDBGFBGGBG\ GBFGBDGBCGBBGCBGDBGFBGGBFGBDGBCGBBGBBGCBGDBGFBGGBF\ GBDGBCG00000000000000000000000000e0e00eee00e0eeL0e\ eeLLLLLzLzLLzzzLLzLzzzLzzz000555888BBBEEEHHHKKKOOO\ SSSWWW___ccchhhmmmssszzz00zG0zV0zj0zz0zz0jz0Vz0Gz0\ 0zG0zV0zj0zz0jz0Vz0Gz00z00zG0zV0zj0zz0jz0Vz0GzVVzb\ VzjVzrVzzVzzVrzVjzVbzVVzbVzjVzrVzzVrzVjzVbzVVzVVzb\ VzjVzrVzzVrzVjzVbzhhzlhzqhzuhzzhzzhuzhqzhlzhhzlhzq\ hzuhzzhuzhqzhlzhhzhhzlhzqhzuhzzhuzhqzhlz00S70SE0SL\ 0SS0SS0LS0ES07S00S70SE0SL0SS0LS0ES07S00S00S70SE0SL\ 0SS0LS0ES07SEESHESLESOESSESSEOSELSEHSEESHESLESOESS\ EOSELSEHSEESEESHESLESO8PP } frm:FinDivBrot-2J { ; Jim Muth z=pixel, c=(p3), a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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Minibrot Ice
by Roger Alexander 06 Jul '10

06 Jul '10

Yesterday fire, today a minibrot surrounded by ice crystals. That's what my imagination says anyway. Completed fractal posted at the old standby http://maxitersfractalfollies.blogspot.com fract295.gif { ; minibrot ; blank ; calctime 0:19:51.00 ; created Jul 06, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=frac_ml.frm formulaname=Nuclear_M_k_0 center-mag=+0.28877190200636940/+0.71021293639915940/2637.932/1/-155.000\ 000000016087/1.17175505409683467e-011 params=-0.423688467055269/-0.4882045960875271/-0.1990722373119297/-0.987\ 1822260200812 float=y maxiter=1200 inside=0 colors=000M0fL0eL0dK0cK0bJ0aJ0`I0_I0ZH0YH0XG0WG0VF0UF0TE0SE0RD0QD0PC0OC0\ NB0MB0LA0KA0J90I90H80G80F70E70D60C60B50A50940840730630520420310210100000\ 200400600800A00C00E00G00I00K00M00O00Q00S00U00W00Y00_00a00c00e00g00i00k00\ m00o00q00s00u00w00z01z03z05z07z09z0Bz0Dz0Fz0Hz0Jz0Lz0Nz0Pz0Rz0Tz0Vz0Xz0Z\ z0`z0bz0dz0fz0hz0jz0lz0nz0pz0rz0tz0vz0xz0zz0zz0yz0xz0wz0vz0uz0tz0sz0rz0q\ z0pz0oz0nz0mz0lz0kz0jz0iz0hz0gz0fz0ez0dz0cz0bz0az0`z0_z0Zz0Yz0Xz0Wz0Vz0U\ z0Tz0Sz0Rz0Qz0Pz0Oz0Nz0Mz0Lz0Kz0Jz0Iz0Hz0Gz0Fz0Ez0Dz0Cz0Bz0Az09z08z07z06\ z05z04z03z02z01z00z00z03z07z0Bz0Fz0Jz0Nz0Rz0Vz0Zz0bz0fz0jz0nz0rz0vz0uz1t\ z1sz2rz3pz3oz4nz5mz5kz6jz7iz7hz8gz9ez9dzAczBbzB`zC_zDZzDYzEWzFVzFUzGTzHS\ zHQzIPzJOzJNzKLzLKzLJzMIzNGzNFzOEzPDzPCzQAzR9zR8zS7zT5zT4zU3zV2zW0zW0zV0\ yV0xU0wU0vT0uT0tS0sS0rR0qR0pQ0oQ0nP0mP0lO0kO0jN0iN0hM0g } frm:Nuclear_M_k_0 { ; p1, p2 parameters. Use float=y. k is Mandel parameter, ; critical point 0. a=p1, c=p2, k=pixel, a2=a*a, ac=a*c, r3=sqrt(3), r3a2=r3*a2 a6=3*a2, r3ac=r3*ac, ack=k*ac z=0: z2=sqr(z) z3=z*z2 z=(r3a2*z3-a6*z2-r3ac*z-ac)/(r3*z+1)+ack, lastsqr<=1000000 } Roger Alexander _________________________________________________________________ Learn more ways to connect with your buddies now http://go.microsoft.com/?linkid=9734388

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Subject? It's a Tad Volcanic
by Roger Alexander 05 Jul '10

05 Jul '10

Today's fractal might make good wallpaper if you're in a volcanic state of mind. Look-fractal lava! Before and after versions at - you guessed it - http://maxitersfractalfollies.blogspot.com fract293.gif { ; wallpaper ; blank ; calctime 0:07:39.70 ; created Jul 05, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_b.frm formulaname=BEES corners=1.730718/3.511423/-0.4553519/0.8801776 params=-0.1692159794915616/-1.652272103030488/2.886104922635579/0.705648\ 9761040071 float=y maxiter=1200 fillcolor=0 periodicity=0 colors=000000000000000000000000000000000100100200400500700900B00D00G00I0\ 0L00O10Q10T10W10Z10a10e10h20k20o20r20v20y20z30z50z60z80z90zB0zC0zE0zF0zH\ 0zI0zK0zL0zN0zO0zQ0zR0zT0zU0zW0zX0zZ0z_0za0zb0zd0ze0zg0zh0zj0zk0zm0zn0zp\ 0zq0zs0zt0zv0zw0zy0zz1zz3zz4zz6zz7zz7zy7zx7zx7zw7zv7zv7zu7yt7ys7ys7yr7yq\ 6yq6yp6yo6yo6xn6xm6xl6xl6xk6xj6xj6xi5xh5wh5wg5wf5we5we5wd5wc5wc5vb5va5va\ 5v`4v_4vZ4vZ4vY4vX4uX4uW4uV4uV4uU4uT4uS3uS3uR3tQ3tQ3tP3tO3tO3tN3tM3tL3sL\ 3sK3sJ2sJ2sI2sH2sH2sG2sF2rE2rE2rD2rC2rC2rB1rA1rA1r91q81q71q71q61q51q51q4\ 1q31p20p20o20n20m20m20l20k20j20j20i20h20g20g20f20e20d20d20c20b20a20a20`2\ 0_20Z20Z20Y20X20W20W20V20U20T20T20S20R20Q20Q20P20O20N20N20M20L20K20K20J2\ 0I20H20H20G20F20E20E20E20D20D20C20C20C20B20B20A20A20A2092092092082082072\ 0720720620620520520520420420420320320220220220120120010 } frm:BEES {; Ray Girvan ; Newton variant giving biomorphs ; z -> sin(z)-k before Newton iteration ; use floating point, periodicity=no ; and smooth colour palette ; p1 controls twist of spirals ; p2 controls number of lobes ; try p1=0.1, p2=3 for 'bees' ; p1=0.1, p2=6 for 'scorpions' z=pixel: z1=sin(z)-p1 z2=z1^p2-1 ; any function f(z) z3=p2*(z1^(p2-1)) ; its derivative f'(z) z=z-(z2/z3) |z2| >= 0.00001 ;SOURCE: 97msg.frm } Roger Alexander _________________________________________________________________ MSN Dating: Find someone special. Start now. http://go.microsoft.com/?linkid=9734384

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FOTD 06-07-10 (Total Discrimination [6])
by Jim Muth 05 Jul '10

05 Jul '10

FOTD -- July 06, 2010 (Rating 6) Fractal visionaries and enthusiasts: After 3 days in the (near) pristine wilderness, it's good to be back at the fractal desk. At least the cats must think so. I have never seen them demanding so much attention. Today's image is a quickie, and as such, can rate no more than a 6. The parent fractal is a near-shapeless thing that at first glance appears totally non-critical. Today's scene is located in a debris-filled hole lying a short distance northwest of the main body. Much of the image consists of holes, which cause the swiss- cheese effect. The rating of a 6 equals just the slightest above average. The name "Total Discrimination" once meant something, but the meaning has long since been forgotten. The calculation time of 3 minutes may be saved by viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> The 3 days' vacation went reasonably well, even though I almost got into a dispute with FL. While watching a soaring eagle, she commented how enjoyable it was to get away from the hectic every- day world, and said she hoped we soon do something about climate change. I saved the day by remaining silent. The heat wave remained in full force here at Fractal Central on Monday, with blazing hot sun, little wind and a temperature of 97F 36C. The fractal cats were so glad to see us return that they forgot about the heat. The next FOTD will be posted in 24 hours. Until then, take care, and do your part to fight climate change. (IMO, 'climate change' is real, the climate always changes, but the danger is grossly exaggerated by the media, which is motiva- ted by profit and politics. And I doubt that the planet would obey any laws we might pass to fight the change.) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= TotalDiscriminaton { ; time=0:03:09.93-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritMinZ function=ident float=y center-mag=+0.0000091918653/+0.0028961512608/8.880\ 02e+008/1/-27/0 params=1/3/0.05/13/0/0/0/0 passes=1 maxiter=1500 inside=0 logmap=258 periodicity=6 colors=000_MqZJkZGfYDaYAWX7RX5MSELXMKUVJcbImkHzsG6\ rzzqL6pzzoPzoR6nT6mV7lY7k_7ka7jc7ie7hz7mz7qzCuzHqz\ LmzQkqVgsZgt_ju_mv_pw`nsampblmbkicjfdicdh_egXfeUfd\ QgcNhbKhaGi`Dj_AjZ7k_9k`BlaClbEmcGmcHndJneKofMogOp\ gPphRqiTqjUrkWrkXnjYkjYhjZejZbj__j_Xi`Ui`RiaOiaLib\ IibFibJjdMjfPjhVjjcjkmjmvkozkqzkrvktskvpkxskymgthc\ pc_kZWgTTbOPZJLUEHQ9EMECQJBTNAWS8ZX7a`6d_8aZ9ZYAWX\ BUWCRVDOUEMTGJSHGRIDQJBPK8OL5NM3PN2QO2RP2VN5YL8`JA\ cIDfGFiEIlDKkERjEYiEdiEkpLUvRCuTGtVJtWMsYQr_Tr`Wt`\ Xv_Yx_Zy__tZdzfytbqoZiiVadRUZNK_OM`OO`PQaPSbPUbQWc\ QYdR_dRaeRcfSdfSfgShhTjhTliUnjUpjUrkVtlVvlVwlctllq\ ovpluojunhtmetlctkasjZsiXrhVrhSrgQqfOqeLpdJpcHpbEo\ aCo`2wV5tX8rZAo`DmbFkdIhfKfhNcjPalS_nUXpXVr`Qt_SsZ\ TsYUsXWrWXrWZrVcqUhqTmqSrpSvpzzpzzozzozzoNznNznMzn\ LzmKzmzzUzzVzzWzzYzzZzz_zz`lzbnzcpzdqzelzdhzcdzc`z\ bzzSzzPzzMzzJzzGzzDzzAzzW } frm:MandAutoCritMinZ {; 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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Self-Similar, Looks Like Worms
by Roger Alexander 04 Jul '10

04 Jul '10

Happy July 4th! Bits and pieces of self-similarity all over the place. Go to http://maxitersfractalfollies.blogspot.com for the ready made version. To the dark imagination it might look like worms. fract292.gif { ; blank ; blank ; calctime 0:09:31.38 ; created Jul 04, 2010 ; Fractint Version 2004 Patchlevel 9 reset=1900 type=formula formulafile=fract002.frm formulaname=mask function=asin/atan/tan center-mag=+0.06954360169420207/-0.10547296438733110/190405.8/1/90/3.885\ 78058618804789e-016 params=-0.125/2.125/2.125/-0.125 float=y maxiter=1200 inside=0 cyclerange=0/255 colors=000430320220210110000000100200310310420520620730730840940A40B50B5\ 0C60D60E60E70F70G80H80I80I90J90KA0LA0MA0MB0NB0OC0PC0QC0QD0RD0SE0TE0UE0UF\ 0VF0WG0XG0XH0YH0ZH0_I0`I0`J0aJ0bJ0cK0dK0dL0eL0fL0gM0hM0hN0iN0jN0kO0lO0lP\ 0mP0nP0oQ0oQ0pR0qR0rR0sS0sS0tT0uT0vT0wU0wU0xV0yV0zW0zW0zX0zY0zZ0z_0z`0za\ 0zb0zc0zd0ze0zf0zg0zh0zi0zj0zk0zl0zm0zn0zo0zp0zq0zr0zs0zt0zu0zv0zw0zx0zy\ 0zz0zz4zz8zzCzzGzzKzzOzzSzzWzzZzzbzzfzzjzznzzrzzvzzzzzvzzrzznzzjzzfzzbzz\ ZzzWzzSzzOzzKzzGzzCzz8zz4zz0zy0zx0zw0zv0zu0zt0zs0zr0zq0zp0zo0zn0zm0zl0zk\ 0zk0zj0zi0zh0zg0zf0ze0zd0zc0zb0za0z`0z_0zZ0zY0zX0zW0zW0yW0xW0wV0wV0vU0uU\ 0tU0sT0sT0rS0qS0pS0oR0oR0nQ0mQ0lP0kP0kP0jO0iO0hN0gN0gN0fM0eM0dL0cL0cL0bK\ 0aK0`J0_J0_J0ZI0YI0XH0WH0VG0VG0UG0TF0SF0RE0RE0QE0PD0OD0NC0NC0MC0LB0KB0JA\ 0JA0IA0H90G90F80F80E70D70C70B60B60A50950850740740630530 } frm:Mask = {; Ron Barnett [70153,1233] ; try fn1 = log, fn2 = sinh, fn3 = cosh ;P1 = (0,1), P2 = (0,1) ;Use floating point z = fn1(pixel): z = P1*fn2(z)^2 + P2*fn3(z)^2 + pixel, |z| <= 4 } Roger Alexander _________________________________________________________________ Look 'em in the eye: FREE Messenger video chat http://go.microsoft.com/?linkid=9734386

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Ferns and Fronds
by Roger Alexander 03 Jul '10

03 Jul '10

Another plant inspired fractal. Do I need a policy on giving posts names? I could say "the description is swirling ferns" which is analogous to giving it a title but I could also use the terms "caption" or "tag". Just can't make up my mind I suppose. Looking at the color of the dark green I could have also used "a plate of spinach" but that doesn't sound dignified enough. fract291.gif { ; ferns ; blank ; calctime 0:28:53.39 ; created Jul 03, 2010 ; Fractint Version 2004 Patchlevel 9 reset=1960 type=formula formulafile=frac_ml.frm formulaname=tri-fn+fn function=sqrt/sqr center-mag=0.55523/1.10691/2.73224 params=1000.235145115513/1.456831568346202/0.3772087771233253/0.02272103\ 030487991 float=y maxiter=12000 inside=0 outside=atan periodicity=0 cyclerange=0/255 colors=0R00Q00P00O00N00M00L00K00J00I00H00G00F00E00D00C00B00A009008007006\ 00500400300000200000000000200300500600800A00B00D00E00G00I00J00L00M00O00Q\ 00R00T00U00W00Y00Z00`00a00c00e00f00h00i00k00m01m03m04n06n07o09o0Ao0Cp0Ep\ 0Fq0Hq0Iq0Kr0Lr0Ns0Ps0Qs0St0Tt0Vu0Wu0Yu0Zv0`v0bw0cw0ew0fx0hx0iy0ky0mz0mz\ 1mz3nz5nz7oz9ozBpzDpzFpzHqzJqzLrzNrzPrzRszTszVtzXtzZuz`uzbuzdvzfvzhwzjwz\ lwznxzpxzryztyzvzzxzzzzzyzzwzzvzzuzztzzrzzqzzpzznzzmzzlzzkzzizzhzzgzzezz\ dzzczzbzz`zz_zzZzzXzzWzzVzzTzzSzzRzzQzzOzzNzzMzzKzzJzzIzzHzzFzzEzzDzzBzz\ Azz9zz8zz6zz5zz3zz2zz0yz0xz0vz0uz0tz0sz0qz0pz0oz0mz0lz0kz0iz0hz0gz0fz0dz\ 0cz0bz0`z0_z0Zz0Yz0Wz0Vz0Uz0Sz0Rz0Qz0Oz0Nz0Mz0Lz0Jz0Iz0Hz0Fz0Ez0Dz0Bz0Az\ 09z08z06z05z03z02z00z00y00x00w00v00u00t00s00r00q00p00o00n00m00l00k00j00i\ 00h00g00f00e00d00c00b00a00`00_00Z00Y00X00W00V00U00T00S0 } frm:tri-fn+fn { ; Sylvie Gallet ; Thanks to Kerry Mitchell for the idea! ; real(p1) = bailout ; imag(p1) must be different from 0 (>=1 recommended) ; z=fn1(z) + p2*fn2(z) ; This formula must be used with decomp = 256 and periodicity = 0 ; z1 = pixel , mz1 = cabs(z1) , summ = iter = 0 b1 = abs(real(p1)) , f = b1^0.1 b2 = b1*f , b3 = b2*f , b4 = b3*f , b5 = b4*f , b6 = b5*f b7 = b6*f , b8 = b7*f , b9 = b8*f , b10 = b9*f , b11 = b10*f iter1 = iter2 = iter3 = iter4 = iter5 = iter6 = iter7 \ = iter8 = iter9 = iter10 = summ_tot = iter_tot = 0 k = imag(p1) * (0.0,6.28319530718) : iter = iter + 1 , za = fn1(z1) , a = cabs(za) zb = p2*fn2(z1) , b = cabs(zb) z1 = za + zb , mz1 = cabs(z1) , a_b = abs(a - b) summ = summ + (mz1 - a_b) / (a+b - a_b) IF (mz1 > b1) IF (iter1==0) iter1 = iter iter_tot = iter_tot + iter1 , summ_tot = summ_tot + summ ENDIF IF (mz1 > b2) IF (iter2==0) iter2 = iter iter_tot = iter_tot + iter2 , summ_tot = summ_tot + summ ENDIF IF (mz1 > b3) IF (iter3==0) iter3 = iter iter_tot = iter_tot + iter3 , summ_tot = summ_tot + summ ENDIF IF (mz1 > b4) IF (iter4==0) iter4 = iter iter_tot = iter_tot + iter4 , summ_tot = summ_tot + summ ENDIF IF (mz1 > b5) IF (iter5==0) iter5 = iter iter_tot = iter_tot + iter5 , summ_tot = summ_tot + summ ENDIF IF (mz1 > b6) IF (iter6==0) iter6 = iter iter_tot = iter_tot + iter6 , summ_tot = summ_tot + summ ENDIF IF (mz1 > b7) IF (iter7==0) iter7 = iter iter_tot = iter_tot + iter7 , summ_tot = summ_tot + summ ENDIF IF (mz1 > b8) IF (iter8==0) iter8 = iter iter_tot = iter_tot + iter8 , summ_tot = summ_tot + summ ENDIF IF (mz1 > b9) IF (iter9==0) iter9 = iter iter_tot = iter_tot + iter9 , summ_tot = summ_tot + summ ENDIF IF (mz1 > b10) IF (iter10==0) iter10 = iter iter_tot = iter_tot + iter10 , summ_tot = summ_tot + summ ENDIF IF (mz1 > b11) iter_tot = iter_tot + iter , summ_tot = summ_tot + summ z = exp (summ_tot * k / iter_tot) ENDIF ENDIF ENDIF ENDIF ENDIF ENDIF ENDIF ENDIF ENDIF ENDIF ENDIF mz1 <= b11 } Roger Alexander _________________________________________________________________ Look 'em in the eye: FREE Messenger video chat http://go.microsoft.com/?linkid=9734386

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Re: [Fractint] Jim's Blunder
by JackOfTradeZ＠comcast.net 03 Jul '10

03 Jul '10

. Hey Jim - you just discover the negative exponents ?!? I have known about them for some time; I even made an animation of the default MSet with exponent -7 -> +7 a while back. A few years ago I was investigating these, and most of the images are very similar to yours - characterized by all sorts of roundish blobs and very complex patterns. You should look into it more - should come up with some interesting FOTD images in the future. BTW, in science we don't call things like this "blunders"; we use the word "serendipity", that is, a good result or discovery resulting from chance error. .

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A Fractal and Some Mustard Talk
by Roger Alexander 03 Jul '10

03 Jul '10

More before and after wispiness at Action Central. Yowwzaa look at the difference! The weather report for Calgary (actually the whole prairies)-wet wet wet. This place is described as semi-arid. Who thought that one up? Nature being contrary I suppose. If I had a speculative nature I would invest in mustard futures-seriously (almost seriously). Canada is the worlds largest grower of mustard seeds and there has been so much rain farmers have had trouble getting crops of any type in. But I'm not a big risk taker. For some non-mustard related graphics go to http://maxitersfractalfollies.blogspot.com and have a gander. fract288.gif { ; filaments not nematodes ; blank ; calctime 0:02:14.35 ; created Jul 02, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=kerrym.frm formulaname=star_dup_rjr passes=1 center-mag=-0.177622/0.591426/7.251421 params=33/0/0.5/-0.375 float=y maxiter=1500 inside=atan decomp=256 periodicity=0 cyclerange=0/255 colors=05F05F05F16G16G16G16G16G27H27H27H27H27H38I38I38I38I38I49J49J49J49\ J49J5AK5AK5AK5AK5AK6BL6BL6BL6BL7CM7CM7CM7CM7CM8DN8DN8DN8DN8DN9EO9EO9EO9E\ O9EOAFPAFPAFPAFPAFPBGQBGQBGQBGQBGQCHRCHRCHRCHRCHRDISDISDISDISDISEISEJTFJ\ TFKTGKUGLUHLVHMVIMVINWJNWJOWKOXKPXLPYLQYMQYMRZNRZNSZOS_OT_PT_PT`QU`QUaRV\ aRVaSWbSWbTXbTXcUYcUYcVZdVZdW_eW_eX`eX`fYafYafZbgZbg_ch_ch`ch`diadiaeibe\ jbfjcfjcgkdgkdhlehleilfimfjmgjmgknhknhlniloimojmpjmpknpknqloqloqmprmprnq\ snqsorsortpstpstqtuqturuuruvsvvsvwtwwtwwuxxuxxuxxvyyvyywzzvyyvyyuxxtxxtw\ wsvwsvvruvquuqtupstostorsnqsnqrmprlpqloqknpjnpjmoimohlnhkngkmgjmfjleileh\ kdhkcgjcfjbfibeiaeh`dh`cg_cgZbfZbfYaeX`eX`dW_dW_cVZcUYbUYbTXaSWaSW`RV`RV\ _QU_PTZPTZOSYNSYNRXMQXLQWLPWKPVKOVJNUINUIMTHLTGLSGKSFKRFJREIQDIQDHPCHPBG\ OBFOAFN9EN9EM8DM8CL7CL6BK6AK5AJ49J49I38I37H27H16G16G05F } frm:star_dup_rjr {; Kerry Mitchell ; renamed to distinguish from ; other frm called star ; also p2 added so user can directly input ; julia parms previously hard coded to .439,.493 ; p1 appears to specify degrees zc=pixel, c=p2, r=1e30 t=real(p1)/180*pi, ct=cos(t), st=sin(t), qmin=99: zc=sqr(zc)+c, q=|ct*real(zc)+st*imag(zc)| IF (q<qmin) qmin=q t=log(q) z=cos(t)+flip(sin(t)) ENDIF |zc| < r ;SOURCE: frac_ml.frm } Roger Alexander _________________________________________________________________ Game on: Challenge friends to great games on Messenger http://go.microsoft.com/?linkid=9734387

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No FOTD for July 2,3,4,5
by Jim Muth 02 Jul '10

02 Jul '10

Fractal visionaries and enthusiasts: We have decided to take a grossly overdue holiday here at Fractal Central. The next FOTD will be posted on July 6. The fractal cats will be well cared for while we are away. Until the next FOTD, take care, and be environmentally alert. Jim Muth

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Blue Minibrots
by Roger Alexander 01 Jul '10

01 Jul '10

It's busy at Action Central and this post is short. It's a minibrot today, check it out at http://maxitersfractalfollies.blogspot.com and as a bonus there is an intriguing video from You Tube on manipulating statistics. fract284.gif { ; minibrot appears to be slightly perturbed ; blank ; calctime 0:06:15.14 ; created Jul 01, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=kerrym.frm formulaname=hermanm_man-cart center-mag=1.79491/1.13844/14.97396/1/60.0000000000000995/-1.26836041669\ 520228e-013 params=3/2/0.5/0.5/2/0 float=y maxiter=1500 inside=0 outside=atan colors=00000000200400600800A00C00E00G00I00K00M00O00Q00S00U00W00Y00_00a00\ c00e00g00i00k00m00o00q00s00u00w00z01z03z05z07z09z0Bz0Dz0Fz0Hz0Jz0Lz0Nz0P\ z0Rz0Tz0Vz0Xz0Zz0`z0bz0dz0fz0hz0jz0lz0nz0pz0rz0tz0vz0xz0zz0zz0yz0xz0wz0v\ z0uz0tz0sz0rz0qz0pz0oz0nz0mz0lz0kz0jz0iz0hz0gz0fz0ez0dz0cz0bz0az0`z0_z0Z\ z0Yz0Xz0Wz0Vz0Uz0Tz0Sz0Rz0Qz0Pz0Oz0Nz0Mz0Lz0Kz0Jz0Iz0Hz0Gz0Fz0Ez0Dz0Cz0B\ z0Az09z08z07z06z05z04z03z02z01z00z00z03z07z0Bz0Fz0Jz0Nz0Rz0Vz0Zz0bz0fz0j\ z0nz0rz0vz0uz1tz1sz2rz3pz3oz4nz5mz5kz6jz7iz7hz8gz9ez9dzAczBbzB`zC_zDZzDY\ zEWzFVzFUzGTzHSzHQzIPzJOzJNzKLzLKzLJzMIzNGzNFzOEzPDzPCzQAzR9zR8zS7zT5zT4\ zU3zV2zW0zW0zV0yV0xU0wU0vT0uT0tS0sS0rR0qR0pQ0oQ0nP0mP0lO0kO0jN0iN0hM0gM0\ fL0eL0dK0cK0bJ0aJ0`I0_I0ZH0YH0XG0WG0VF0UF0TE0SE0RD0QD0PC0OC0NB0MB0LA0KA0\ J90I90H80G80F70E70D60C60B50A509408407306305204203102101 } frm:hermanm_man-cart { ; Kerry Mitchell 16feb98 ; ; real(p1) = z exponent (use integer >= 2; m=n-1) ; imag(p1) = g exponent (integers) ; p2 = alpha ; real(p3) = critical point selector (>0 for positive root) ; imag(p3) = unused (<0 for negative root) ; use decomp=256 ; zero and infinity bailouts hardcoded to 1e-6, 1e6 ; coloring speed hardcoded to 4 ; c=pixel, iter=1, n=real(p1), m=imag(p1), nfac=2*n-1 maxr=1e6, minr=1/maxr, speed=4*pi/128, alpha=p2 oln=1/log(n), fac=log(0.5*log(maxr)) c2=sqr(c), hypnum=sqr(n)+sqr(m), pn=1 hypden=sqr(n-m), hypfac=hypnum/hypden if (real(p3)<0) pn=-1 end if if (real(c2)>hypfac) pn=-pn end if if (imag(c)<0) pn=-pn end if afac=c*n, bfac=c2*(n-m)+(n+m), cfac=c*n d=sqrt(bfac*bfac-4*afac*cfac) z=(bfac+pn*d)/(2*afac) : g=(z-c)/(1-c*z), z=alpha*z^n*g^m iter=iter+1, r=|z| ; ; orbit trap around 0 ; renormalize iteration count via decomp angle ; set "iteration done" flag (iter=-1) ; if (r<minr) angle=(iter+oln*(fac-log(log(cabs(z)))))*speed z=cos(angle)+flip(sin(angle)) iter=-1 end if ; ; orbit trap around infinity ; renormalize iteration count via decomp angle ; add pi to angle to separate from 0 orbit trap ; set "iteration done" flag (iter=-1) ; if (r>maxr) angle=(iter+oln*(fac-log(log(cabs(z)))))*speed angle=angle+pi z=cos(angle)+flip(sin(angle)) iter=-1 end if iter>0 } Roger Alexander _________________________________________________________________ Look 'em in the eye: FREE Messenger video chat http://go.microsoft.com/?linkid=9734386

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FOTD 01-07-10 (Jim's Blunder [No Rating])
by Jim Muth 01 Jul '10

01 Jul '10

FOTD -- July 01, 2010 (No Rating) Fractal visionaries and enthusiasts: Have no concern about today's parameter file, which includes no color information. The program will automatically pick up the default color palette, which works quite well with this image. How can a person rate a mistake? They cannot! So how could I give a rating to today's image? It is an error. With the type=julzpower formula on the screen I decided to try some- thing with the Julia set of Seahorse Valley of the Mandelbrot set. But instead of entering 2 as the exponent, I entered minus-2, and look what happened. I have no idea how I could have missed such an obvious fractal for such a long time, but I did. Anyway, I post the image as today's FOTD. It will never set any world record, but it is interesting and it calculates in a faster-than-light 4 seconds. The name "Jim's Blunder" says it all. The result may be seen by running the included parameter file or by going to the FOTD web site at: <http://www.Nahee.com/FOTD/> where the finished image is posted for instant if not total gratification. Absolutely perfect weather here in the Fractal Central area on Wednesday made for an enjoyable day in the outdoors for FL and myself. The total sun, low humidity and high temperature of 77F 25C that marked the day could hardly be improved upon. The fractal cats showed their approval by getting into trouble while FL and I were traversing a local hiking trail. When we returned, we found a lamp overturned and two totally innocent looking cats. The next FOTD will be posted in around 12 hours. Until then, take care, and do what the doctor says. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Jim's_Blunder { ; time=0:00:04.01-SF5 on P4-2000 reset=2004 type=julzpower center-mag=0/0/0.17425/1\ /90/0 params=-0.75/0/-2/0 float=y maxiter=1500 bailout=1000 inside=0 } END PARAMETER FILE=========================================

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Another Before and After
by Roger Alexander 30 Jun '10

30 Jun '10

Today's post is another fractal with a thread like structure. Maybe I should start a thread on threads. Again I posted a before and after pair of graphics on my blog. With resampling the visibility of thread like form is significantly enhanced. If you want to see threads that don't say tailor go to http://maxitersfractalfollies.blogspot.com for a gander. fract281.gif { ; before anti-aliasing ; blank ; calctime 0:03:43.78 ; created Jun 29, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_f.frm formulaname=field4_man center-mag=-0.29661890258823510/-0.65850594286477460/81.3497 params=1000000/8 float=y maxiter=1500 inside=0 proximity=1 outside=fmod decomp=256 periodicity=0 colors=05F05F05F16G16G16G16G16G27H27H27H27H27H38I38I38I38I38I49J49J49J49\ J49J5AK5AK5AK5AK5AK6BL6BL6BL6BL7CM7CM7CM7CM7CM8DN8DN8DN8DN8DN9EO9EO9EO9E\ O9EOAFPAFPAFPAFPAFPBGQBGQBGQBGQBGQCHRCHRCHRCHRCHRDISDISDISDISDISEISEJTFJ\ TFKTGKUGLUHLVHMVIMVINWJNWJOWKOXKPXLPYLQYMQYMRZNRZNSZOS_OT_PT_PT`QU`QUaRV\ aRVaSWbSWbTXbTXcUYcUYcVZdVZdW_eW_eX`eX`fYafYafZbgZbg_ch_ch`ch`diadiaeibe\ jbfjcfjcgkdgkdhlehleilfimfjmgjmgknhknhlniloimojmpjmpknpknqloqloqmprmprnq\ snqsorsortpstpstqtuqturuuruvsvvsvwtwwtwwuxxuxxuxxvyyvyywzzvyyvyyuxxtxxtw\ wsvwsvvruvquuqtupstostorsnqsnqrmprlpqloqknpjnpjmoimohlnhkngkmgjmfjleileh\ kdhkcgjcfjbfibeiaeh`dh`cg_cgZbfZbfYaeX`eX`dW_dW_cVZcUYbUYbTXaSWaSW`RV`RV\ _QU_PTZPTZOSYNSYNRXMQXLQWLPWKPVKOVJNUINUIMTHLTGLSGKSFKRFJREIQDIQDHPCHPBG\ OBFOAFN9EN9EM8DM8CL7CL6BK6AK5AJ49J49I38I37H27H16G16G05F } frm:field4_man { ; Kerry Mitchell 20jan98 ; ; Colors Mandelbrot set by nearest approach to ; period 4 field lines ; ; use decomp=256 ; real(p1) = bailout (try 1e12) ; imag(p1) = number of field line to use: 0 - 15 ; 4 iterations per pixel ; variable zc used for calculation, z for coloring ; zc=0, c=pixel, maxr=real(p1), minr=maxr, iter=1 fieldangle=tan(imag(p1)*2*pi/15): ; ; iteration ; compare tangent of polar angle with desired ; field line angle, update minimum if needed ; iter=iter+4, zc=sqr(zc)+c, zc=sqr(zc)+c, zc=sqr(zc)+c zc=sqr(zc)+c, rzc=|zc|, tanangle=imag(zc)/real(zc), r=cabs(fieldangle-tanangle) if (r<minr) minr=r end if ; ; bailout ; set "iteration done" flag (iter=-1) ; use log of minimum difference of angles as ; decomposition angle ; if ((rzc>maxr)||(iter>=maxit)) iter=-1 angle=log(minr) z=cos(angle)+flip(sin(angle)) end if iter>0 } Roger Alexander _________________________________________________________________ Look 'em in the eye: FREE Messenger video chat http://go.microsoft.com/?linkid=9734386

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FOTD 29-06-10 (So Bad It's Good [8])
by Jim Muth 29 Jun '10

29 Jun '10

FOTD -- June 30, 2010 (Rating 8) Fractal visionaries and enthusiasts: Today's image is so bad it's good, and this is what I named it. The image was generated by combining 3 parts of an unlikely Z^(0.03) with one serving of Z^3 and adding straight C. The parent fractal vaguely resembles a Mandelbrot set, but the large negative bud is missing, replaced by an unbroken, curving west shore line of the main bay, while the large north and south buds are grossly distorted. Today's scene is located in a small, out of place valley on the northwest shore line of the main bay. The image is one riotous mass of shapes and colors. Most of it consists of 'inside' stuff that was brought to life by rendering the scene with the inside set to 'fmod'. The image is really total chaos with no organizing theme, but there are so many fractal nooks and crannies to explore that it has kind of a fascinating effect on the viewer. All this fascination earns the image a rating of an 8. The calculation time of over 7 minutes is well above FOTD average, but instant relief may be found on the FOTD web site at: <http://www.Nahee.com/FOTD/> where the finished image is posted for instant viewing. Lots of sun, lower humidity and a temperature of 84F 29C made conditions near ideal here at Fractal Central on Monday. The fractal cats actually gave up their sleeping spots on the tile floor and came out to let us know they are still here. My day was near normal; tomorrow looks so slow that FL and I might decide to take the day off. If the next FOTD is late, you will know we did. Until whenever, take care, and I'm tired of everyone talking about the threat of climate change, but doing nothing about it. Let's tell our representatives to stop the blather and pass a law banning global warming. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= So_Bad_It's_Good { ; time=0:07:18.47-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-3.3291178822/+0.2735827664/74216/1/57\ /0 params=3/0.03/1/3/0/0/0/0 float=y maxiter=1800 inside=fmod proximity=0.1 periodicity=6 colors=000aFlbFkdFkfFkgFkiFkkFkoJjmHklFkkDkjBki9kg\ 6nh7lh8kh9ii9hiAfiBeiBdjCbjDajD_jEZkFYkFWkGVlHTlHS\ lIRlJPmJOmKMmLLpGFmLKjPPhUTeYYbab`ffYjkXrsWpqWnoWl\ mVjkVhiVfgVdeUbcU`aUZ_UXZTVXTTVTRTSPRSNPSLNSJLRHJR\ FHRDFSBDRCERDFRDGREHRFIQFJQGJQHKQHLQIMPJNPJOPKPPLP\ PLQOMRONSONTOOUJ2VMDUOOUQZTPnSSiTUdTX_TZVUaQUcLUfG\ VhBVf4Kj6Vn7dr9nuAxpDvlFtgIrcKp_NnVPmRSkNUiIXgEZe5\ aeA`dE_dJZdNYcSXcWWc`VbdUbiTbmSarRavQazQayS`xT_xUZ\ wVYwWXvXWvZVu_Uu`TtaTtbSscRseQrfPrgOqhNqiMpjLwmLsl\ LpkLmjLjiLghLdgLafLZfLYeJXeHWdGVdEUcDTcBcqCYjBScAN\ X9HQ8BJ72B44C56D68E6AF7CG8DH8FI9HI9JJALKBNLBOMCQND\ SODUPEWPEYQFZRG`SGbTHdUIfVIhWJl`NjYLiWJhUHfRFePDdN\ BbK9aI7fK8cI6`G5ZE3WC2UA1T93T95T87S89S8BS7DS7FR6GR\ 6IR6KR5MQ5OQ4QQ4SQ5TUBVXGX`MZcR_fWajacmfdqlftqhvti\ xulwuivtfurbppfiph_om000000000000000000000Gh`HhaIh\ aJhbKhbLhcMidNidOiePifQif } 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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Nostalgia
by Roger Alexander 29 Jun '10

29 Jun '10

Blast from the past! Anybody remember Fracxtr6?. It was zip of oodles of support files for Fractint. Here in its original form is one of my favorite entrys from overkill.par (by Bradley Beacham) that was in the collection. He wrote the formula tutor file frmtutor.txt which is included in the Fractint distribution zip. For those who not nostalgic and don't want togenerate a fractal the old fashioned way go to http://maxitersfractalfollies.blogspot.com for instant viewing. Primate_Skull { ; A big steamin' heap o' profundity. Yow! (ok-20) ; (c) 1994 Bradley Beacham 74223,2745(a)compuserve.com reset=1820 type=formula formulafile=overkill.frm formulaname=ok-20 function=sqr/sqr corners=0.755474/-1.596526/-1.574358/1.561642/-1.596526/1.561642 params=-3.1000000000000001 float=y potential=256/175/0 colors=000zzz00110001011120221212222232132323342443243453353554354564464\ 6654656755757765767866868876878977887889989A8899899AA9AB99AA9AABBABCAACA\ CBBCACBBCBDBDCCDBDCCDCECEDDECEDDEDDEFEEFDFEEFEEFGFFGEGFGFHFGHGGHHGGHGIHH\ FHHHIHHIHJIIGIIIJIIJIKJJHJJJJJLKJLKKIKKKKKMKLJMKLLLLLLNLMKNLMMMMMMOMNLOM\ NNNNNNPNOMNOOOOONPNOPNOPPPPPOQOOQQ<2>RQPPRRQRRRRQQSQSRSRSSSSRRTRRTTSTTTT\ SSUSSUUVTTUUTUUVTVVWUUVVUVVWUWWXVVWWVWWXVXXYWWYWYXXYYXXXYXZXZYYZZYYYZY_Y\ _ZZ__ZZZ_ZZ_`__``___`__`a``aa``a`b`abaaa`babacbb`bbbacbcbdccacccbdcdcedd\ bdddddfedfeeceeeeegefdgeffffffhfgehfggggggighfighhhhhhjhighiiiiijihijhij\ jjjikjikjkjkkkkjjljlklkllllkkmkkmmlmmmmllnllnnommnnmnnomoopnnoonoopnppqo\ oppoppqoqqrpprprqqrrqqsqqsqsrrssrrrsrtrtssttssstsstuttuutttuttuvuuvvuuvu\ wuvwvvvuwvwvxwwuwwwvxwxwyxxvxxxwyxyxzyywyyyxzyyzxzzx } frm:OK-20 { a = b = c = z = pixel: a = fn1(b) + c^z b = fn2(a+c) z = z + (a * b * c) |z| <= (5 + p1) ;SOURCE: overkill.frm } Roger Alexander _________________________________________________________________ Game on: Challenge friends to great games on Messenger http://go.microsoft.com/?linkid=9734387

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Re: [Fractint] The works of Héctor Garrido
by Roger Alexander 29 Jun '10

29 Jun '10

Subject: [Fractint] The works of Héctor Garrido If you wish to see some really amazing examples of Fractals in Nature, then you should head over to the "Armonia fractal de Doñana y las marismas" web site. (My Spanish is not too great, but I believe this means Harmony fractal of Doñana and the salt marshes.) http://www.ArmoniaFractal.com/ snip For other examples try "fractals in nature" as a search term in Google or Flickr. The appreciation of self-similarity of form at different scales is unexpectedly widespread. Roger Alexander _________________________________________________________________ Learn more ways to connect with your buddies now http://go.microsoft.com/?linkid=9734388

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FOTD 29-06-10 (Forever Nameless [6])
by Jim Muth 29 Jun '10

29 Jun '10

FOTD -- June 29, 2010 (Rating 6) Fractal visionaries and enthusiasts: Today's image rates a 6. So far, so good. Its parent fractal is one of the largest I have ever found, needing the maximum possible outzoom before it fits onto the screen. No problem here either. I named the image "Forever Nameless", which is paradoxical because this is actually a name. OK, but fractals are meant to be observed with the eyes, not to be given clever names. Today's image is evaporated. I raised the escape radius to one googol, which caused all the 'outside' parts to vanish, leaving an image consisting totally of 'inside' stuff. This left-over inside stuff was then brought to life by the 'bof61' inside fill. The generating expression combines various negative portions of Z^(-1.2) and Z^(-4.4) then adds (1/C). The calculation time of 54 seconds is quite fast, I admit it. But the image can be seen instantly on the FOTD web site at: <http://www.Nahee.com/FOTD/> assuming Paul has already posted it there, that is. Heavy clouds, high humidity and sporadic rain showers spoiled Monday here at Fractal Central. The temperature of 86F 30C felt very sultry -- like an afternoon on the banks of the Panama Canal rather than the Susquehanna River. The fractal cats, who have never been to Panama, spent the day stretched on the cool tile floor. My day was average. FL, who was beginning to worry that it might never rain again, felt much relieved when the showers fell, even though the day's rain amounted to only 1cm. The next FOTD will be posted in 24 hours. Until then, take care, and be on the alert for alien invaders from space. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Forever_Nameless { ; time=0:00:54.41-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=-6.396910880855549/+1.12547947073241/\ 1.606963e+011/1/-17.5/0 params=-4/-1.2/-0.2/-4.4/0\ /1e+100/0/0 maxiter=1600 inside=bof61 periodicity=6 colors=000SFaVFZYFXaEUdERgEPjEMmEJpEHsEEwDBqLGkUMe\ bR_kXUtbZkYYl_Xl`VmbUncTneRofQphPpiOqkMrlLrnKsoItq\ KrmKqjJpgJodJnbIm_IlXHkUHjSHiPGhMGgJGfHFeEFdBEc8Jd\ CNdDSeEWeF_fGdfHhgIlgJqhKuhLziMzfOzcQy`SyXUxUWxRYw\ N_wKawHcvEevAgu7iu4kt0ms2mq4no7om9okBpiEqgGreIrcLs\ aNt_QuYOsTQqPSoKUmFWkFaYEgJDm4EcMEZPFUSFPVFKZGFaGA\ dG5gH0kN0`T0QZ0Fd03RPRDnnDlkEjhJd_OZRTTIZM8aIJeDVh\ 8fl3rrQ`xmIkpHZsFod0atMeuUhv`lwhpxppqppjoqbnqWmqPl\ rHkrAjs2in2fi3cd3`_4YV4VQ5SL6PJGRBSQNIOSKLWNI`PFeS\ CdWBc`Abe8aj7`o6_t4Vp4Ql4Kh4Fd4A`44X38Z6C`9GbCLdFP\ fIThLYjPBkeAcd8Wb7O`5G_48Y20WGC_VPciagxnltlmpjnlho\ hfpddq`brX`sSYuXSraMogFlbOlcQieSffUbhW_iYXk_TeWQ_S\ NUNKOJHHEERHJUFLXCN_APb7Re5Ti2Wd8W_EXVKYPQZNRSLTKJ\ VCDca4ntCcdAdh8dl6ep7TY6HJ544GA9RGEbMJmSOyYTmSQmSS\ mSUlSXlSZlS`kTclRamP_nNXoLVpJTqGQpINnLJlNFjQBhT7fQ\ BaRAXRASS9l2Kd6HXADPE94Qn } 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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Fractal Spiral of Spirals
by Roger Alexander 28 Jun '10

28 Jun '10

What says fractal more than a spiral of self-similar spiral? Well if I get pedantic "fractal" says "fractal" more than anything else but I'm talking rhetorically here. This post has two graphics, a Fractint compatible gif and an anti-aliased jpg. I used my usual technique to anti-alias. The original 800x600 gif was regenerated to 3200x2400 resized to 800x600 in Gimp 2.6.8 sharpened a bit and saved as a 800x600 low compression jpg. To compare the two you'll have to go to http://maxitersfractalfollies.blogspot.com. fract279.gif { ; yas ; yet another spiral ; calctime 0:21:31.64 ; created Jun 27, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_f.frm formulaname=F'ULI_8 function=sin/sqr center-mag=-1.09735/0.702671/14.63015 params=-0.09854426709799494/-0.3008209479049043/-0.8890957365642262/0.38\ 54182561723685 float=y maxiter=1500 inside=0 colors=000rC2rB1rA1rA1r91q81q71q71q61q51q51q41q31p20p20o20n20m20m20l20k2\ 0j20j20i20h20g20g20f20e20d20d20c20b20a20a20`20_20Z20Z20Y20X20W20W20V20U2\ 0T20T20S20R20Q20Q20P20O20N20N20M20L20K20K20J20I20H20H20G20F20E20E20E20D2\ 0D20C20C20C20B20B20A20A20A2092092092082082072072072062062052052052042042\ 042032032022022022012012001000000000000000000000000000000010010020040050\ 0700900B00D00G00I00L00O10Q10T10W10Z10a10e10h20k20o20r20v20y20z30z50z60z8\ 0z90zB0zC0zE0zF0zH0zI0zK0zL0zN0zO0zQ0zR0zT0zU0zW0zX0zZ0z_0za0zb0zd0ze0zg\ 0zh0zj0zk0zm0zn0zp0zq0zs0zt0zv0zw0zy0zz1zz3zz4zz6zz7zz7zy7zx7zx7zw7zv7zv\ 7zu7yt7ys7ys7yr7yq6yq6yp6yo6yo6xn6xm6xl6xl6xk6xj6xj6xi5xh5wh5wg5wf5we5we\ 5wd5wc5wc5vb5va5va5v`4v_4vZ4vZ4vY4vX4uX4uW4uV4uV4uU4uT4uS3uS3uR3tQ3tQ3tP\ 3tO3tO3tN3tM3tL3sL3sK3sJ2sJ2sI2sH2sH2sG2sF2rE2rE2rD2rC2 } frm:F'ULI_8 {; by Jon Horner - 100112,1700 - FRAC'Cetera z = pixel : z = fn1 (p1+z) + fn2(p2-z) |z| <= 16 ;SOURCE: uli.frm } Roger Alexander _________________________________________________________________ Learn more ways to connect with your buddies now http://go.microsoft.com/?linkid=9734388

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FOTD 28-06-10 (Eructating Julia Set [5])
by Jim Muth 28 Jun '10

28 Jun '10

FOTD -- June 28, 2010 (Rating 5) Fractal visionaries and enthusiasts: Today's image is one of the laziest in FOTD history. My energy totally wilted in the outside heat on Sunday, so I took up resi- dence in front of the TV and passed the afternoon watching baseball. (The good old Baltimore Orioles are doing abysmally terrible this year!) Despite the laziness attack, I still managed to find a fractal. True, it's only a Julia set of the northeast shore line of the Mandelbrot set, but the image is just unusual enough to earn FOTD status. The way I achieved the effect is obvious enough, as is the cor- responding point of the Mandelbrot set. The rating of a 5 says the image is average. The name "Eructating Julia Set" pretty well describes the image. The calculation time of 4-1/2 minutes is brief enough, though even this brief time may be saved by viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> A temperature of 95F 35C made Sunday the hottest day so far this summer here at Fractal Central, with a sky so hazy that it was hard to tell if the sun was shining or not. The fractal cats, who do not care about sun in the summer, claimed the cool tile floor early and stayed there all day. My day was average, while FL busied herself in the garden. The next FOTD will be posted in 24 hours. Until then, take care, and if it makes no sense, how can it be untrue? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= EructatingJuliaSet { ; time=0:04:32.65-SF5 on P4-2000 reset=2004 type=julia passes=1 center-mag=0/0/0.851 params=0.3241498435054749/-0.05196490083507214 float=y maxiter=15000 bailout=6 inside=bof60 symmetry=origin periodicity=6 colors=000OVcQVaQW_TWZWXZYZY__Ya`YcaYebXgcXidXkeXl\ gWmhWniWojWpkWqlXrmXsnXtoYupYvqYwrZxsZytZyu_yv_zw_\ zx`zyczzhzzmzzrzzvzzzmpbmqbnqcnqcnqcmoblnbklajkaij\ `hh`gg`fe_ed_dcZcaZb`YaZY`YY_XXZVXYUWXTWWRWVQVUOVT\ NUSMURKTQJTPHTOGSNFSMDRLCRKBRMATNAUP9WQ9XR8YT8_U7`\ V7a_9`cA_gCZlDYpFXtGWtHXtIYtJZtK`tMatNbtOctPetQftR\ gtThtUjtVktWltXmtYnjUk`QiSMgVPeXSdZUbaXac_`eaZgdYj\ gWliVnlUpoSsqRutPwwOyyNwvOutOsrPqpPpnQnkQliRjgRieS\ gcSeaScZTaXT`VUZTUXRVVOVUMWSKWQIXOGXF7_JBYNEXRIWVL\ UZPTbSSfWQjZPnbOsgOreNrdMrcLrbKqaJq`Jq_IqZHqYGpWFp\ VEpUEpTDoSCoRBoQAoP9uQ8oO9jMAeLB_JCVHDQGEKEFFCGABH\ GJQLQZRXgWcp`eYYg_ViaShhTjcUlZVnUWpPXqLYsGZuB_w6_x\ 2`r4al6bf7c`9dVBePCfJEgDGe6Fh7Hk7In7KFgYq7Lo6On6Qm\ 6Sl5Uk5Wj5Yi4`h4bg4df3fe3hd3j`FhXQfZRd`RcaRbcR`eR_\ fRZhRYjSWkSVmSUoSSpSRrSQsSPqPMX8kYAjZCj_Ej`GjaIjbK\ jcMjdOjeQjfSjgUjhWjiYjj_j } END PARAMETER FILE=========================================

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More Orbit Trap Stuff
by Roger Alexander 27 Jun '10

27 Jun '10

You can't keep a good formula down! Today's fractal was generated from Paul Carlson's Zf_ang formula which had been mindlessly mutated by myself. For the formula modification I used the monkey-at-keyboard approach rather than any algorithmic insight Today's post at http://maxitersfractalfollies.blogspot.com has a bonus feature- a photo of Tipsy our almost fractal cat. fract276.gif { ; another orbit trap ; blank ; calctime 0:04:24.79 ; created Jun 26, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_z.frm formulaname=Zf_Ang_rjr3 function=sin/sqr center-mag=0/0/0.6666667 params=0.1/-0.9/0.5/-12/2/128 float=y maxiter=1500 inside=0 outside=summ colors=zffzffzeezddzccyccybbyaay``x``x__xZZxYYwYYwXXwWWwVVwUUvUUvTTvSSvR\ RuRRuQQuPPuOOtOOtNNtMMtLLtKKsKKsJJsIIsHHrHHrGGrFFrEEqEEqDDqCCqBBqAApAAp9\ 9p88p77o77o66o55o44n44n33n22n11m00m00l00l00k00j00j00i00h00h00g00g00f00e0\ 0e00d00c00c00b00a00a00`00`00_00Z00Z00Y00X00X00W00V00V00U00U00T00S00S00R0\ 0Q00Q00P00P00O00N00N00M00L00L00K00J00J00I00I00H00G00G00F00E00E00D00C00C0\ 0B00B00A00900900800700700600500ffzffzeezddzcczcczbbzaaz``y``y__yZZyYYyYY\ yXXyWWxVVxUUxUUxTTxSSxRRxRRwQQwPPwOOwOOwNNwMMwLLvKKvKKvJJvIIvHHvHHvGGuFF\ uEEuEEuDDuCCuBBuAAtAAt99t88t77t77t66t55s44s44s33s22s11s00r00r00q00p00p00\ o00n00n00m00l00l00k00j00j00i00h00h00g00f00f00e00d00d00c00b00b00a00`00`00\ _00Z00Z00Y00X00X00W00V00U00U00T00S00S00R00Q00Q00P00O00O00N00M00M00L00K00\ K00J00I00I00H00G00G00F00E00E00D00C00C00B00A00A009008007 } frm:Zf_Ang_rjr3 {; Copyright (c) Paul W. Carlson, 1998 ; p1 = Julia set coordinates ; real(p2) = controls size of the elements ; imag(p2) = number of iterations to skip ; real(p3) = number of color ranges ; imag(p3) = number of colors in a range ; modded rjr z = k = iter = range_num = bailout = 0 w = pixel c = p1 prev_modw2 = 1.0e20 size = real(p2) skip_iters = imag(p2) num_ranges = real(p3) colors_in_range = imag(p3) factor = (colors_in_range - 1) / size : w = c * (w - 1 / w) a = 2 * atan(imag(w) / real(w)) a = a * a + c a = fn1(1 - a) /fn2(a) ; dist = abs(|w| - |a|) IF (dist < size) bailout = 1 IF (iter > skip_iters) k = 1 ENDIF z = (factor * dist + range_num * colors_in_range + 1) * k ENDIF range_num = range_num + 1 IF (range_num == num_ranges) range_num = 0 ENDIF iter = iter + 1 z = z - iter bailout == 0 && |w| < 1.0e20 ;SOURCE: 98msg.frm } Roger Alexander _________________________________________________________________ Learn more ways to connect with your buddies now http://go.microsoft.com/?linkid=9734388

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FOTD 27-06-10 (Thoughtful Fractal [7])
by Jim Muth 27 Jun '10

27 Jun '10

FOTD -- June 27, 2010 (Rating 7) Fractal visionaries and enthusiasts: To create the parent of today's image I combined 4 negative parts of Z^(-1.56) with 0.8 negative part of Z^(-3.3) and added (1/C). This parent is little more than a series of 4 large bays stacked one on top of the other, with today's scene located on the southwest shore line of the northernmost bay. I found the image in an unpromising valley that I almost passed by. Luckily, I got a certain 'feeling' before I abandoned the area, and was rewarded by today's image, which IMO rates a solid seven. I named the image "Thoughtful Fractal" in recognition of the second thought I had before turning to some of the other interesting sites in the parent. The calculation time of almost 14 minutes is actually more than the image is worth, but in this case at least patience will be rewarded. If no reward is sought, the pre-calculated image may be viewed in its full clory on the FOTD web site at: <http://www.Nahee.com/FOTD/> The temperature reached 86F 30C here at Fractal Central on Saturday, while the humidity was high enough to make things muggy. A few drops of rain tried to get started in the after- noon, but never wet the ground. The fractal cats spent the day sleeping and watching their window TV. My day was uneventful; FL kept busy in her garden. The next FOTD will be posted in 24 hours. Until then, take care, and things are darkest just before the fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Thoughtful_Fractal { ; time=0:13:53.83-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=-0.54924649445/+1.72612640297/2.26e+007\ /1/-37.5/0 params=-4/-1.56/-0.8/-3.3/0/0/0/0 maxiter=15000 inside=0 outside=tdis periodicity=6 colors=000ZZZYOcYP_XQ_XR_XS_WT`WU`VV`VW`UX`UY`UZaT\ _aT`aSaaSbaPclQbhRbeSbaTbZUaWVaSWaPWcOXbNXaNXaMX`M\ X`LX_LX_KYZKYZKYYJYYJYXIYXIYWHZWHZVGZVGZUGZTFZTFZS\ E_SE_RD_RD_QC_QC_PC_PB`OBXL6TO7WQ7YT7`W7cZ7ea7hd7k\ gAmjFpmKspPusUxvZzzczwZzuUzsPzqKzoFzmAzkAziBzgBzeB\ zcCzaCz_CzYCzZF`_I``LXbOTcRQdUMfXIg_FhbBjeZRX_SW_S\ W_TW`TV`UVaUUaVUaVUbWTbWTcXTcXSdYSdYSdZReZRe_Qf_Qf\ `Qf`PgaPgaPhbOhbOhbOgaNgaNfaNfaNfaNeaNeaNdaNdaNdaN\ caNcaMbaMbaMbaMa`Ma`M``M``M``M_`M_`M_`MZ`LZ`LY`LY`\ LY`LX`LX`LW_LW_LW_LV_LV_KU_KU_KU_KT_KT_KS_KS_KS_KR\ _KR_KR_KQZJQYJQYJQXJQWIQWIQVIPUIPUHPTHPSHPSHPRGPQG\ PQGOPGOOGOOFONFOMFOMFOLEOKENKENJENIDNIDNHDNGDNGCNF\ CMECMECMDCMCBMCBMBBMABMAAL9AL8AL8AL79L69L69L59L59J\ 49H49F39E39C29A2982971951930910900911A12A12A23A23A\ 24A24A35B35B36B36B47B47B48B48C59C59C5AC5AC6BC6BC6C\ C6CD7DD7DD7ED7ED8FD8FD8GE } 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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FOTD 23-06-10 (Gear World) and Today's Filamentous
by Roger Alexander 25 Jun '10

25 Jun '10

FOTD 23-06-10 (Gear World) - Great fractal Jim, you give it a 6, I give it a 10. I like it not just because of the design which is quite eye pleasing but also the understanding that it was generated by a fractal algorithm and that particular form is new to me. Keep up the good work. Now for today's post. Another before and after pair. The original gif in Fractint format the second an anti-aliased jpg. Filamentous - Having the form of threads or filaments. Good ole Wiktionary your 24/7 online source of authorative definitions. Both gifs and jpgs are waiting for you at http://maxitersfractalfollies.blogspot.com fract274.gif { ; wispy mandel ; blank ; calctime 0:07:09.02 ; created Jun 25, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=kerrym.frm formulaname=conic-near_man center-mag=-1.00836445556946200/+0.32038397328881490/192.4113/1/79.99999\ 99999997584/2.92994795092482718e-013 params=-0.125/0.7444380016479996/-0.1335795159764397/0.2538834803308206/\ -0.1776482436597797/-0.0489211706900235 float=y maxiter=1500 inside=0 decomp=256 periodicity=0 colors=05F05F05F16G16G16G16G16G27H27H27H27H27H38I38I38I38I38I49J49J49J49\ J49J5AK5AK5AK5AK5AK6BL6BL6BL6BL7CM7CM7CM7CM7CM8DN8DN8DN8DN8DN9EO9EO9EO9E\ O9EOAFPAFPAFPAFPAFPBGQBGQBGQBGQBGQCHRCHRCHRCHRCHRDISDISDISDISDISEISEJTFJ\ TFKTGKUGLUHLVHMVIMVINWJNWJOWKOXKPXLPYLQYMQYMRZNRZNSZOS_OT_PT_PT`QU`QUaRV\ aRVaSWbSWbTXbTXcUYcUYcVZdVZdW_eW_eX`eX`fYafYafZbgZbg_ch_ch`ch`diadiaeibe\ jbfjcfjcgkdgkdhlehleilfimfjmgjmgknhknhlniloimojmpjmpknpknqloqloqmprmprnq\ snqsorsortpstpstqtuqturuuruvsvvsvwtwwtwwuxxuxxuxxvyyvyywzzvyyvyyuxxtxxtw\ wsvwsvvruvquuqtupstostorsnqsnqrmprlpqloqknpjnpjmoimohlnhkngkmgjmfjleileh\ kdhkcgjcfjbfibeiaeh`dh`cg_cgZbfZbfYaeX`eX`dW_dW_cVZcUYbUYbTXaSWaSW`RV`RV\ _QU_PTZPTZOSYNSYNRXMQXLQWLPWKPVKOVJNUINUIMTHLTGLSGKSFKRFJREIQDIQDHPCHPBG\ OBFOAFN9EN9EM8DM8CL7CL6BK6AK5AJ49J49I38I37H27H16G16G05F } frm:conic-near_man { ; Kerry Mitchell 11may98 zc=0, cc=pixel, maxr=1e12, minr=maxr, iter=1 a=real(p1), b=imag(p1), c=real(p2), d=imag(p2) e=real(p3), f=imag(p3): iter=iter+1, zc=sqr(zc)+cc, x=real(zc), y=imag(zc) conic=|x*(a*x+b)+y*(c*y+d)+e*x*y+f| if (conic<minr) minr=conic end if if ((|zc|>maxr)||(iter==maxit)) iter=-1 t=log(minr) z=cos(t)+flip(sin(t)) end if iter>0 } Roger Alexander _________________________________________________________________ Look 'em in the eye: FREE Messenger video chat http://go.microsoft.com/?linkid=9734386

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FOTD 26-06-10 (A Near-Oblate Set [No Rating])
by Jim Muth 25 Jun '10

25 Jun '10

FOTD -- (No Rating) Fractal visionaries and enthusiasts: Today's image lies near a small minibrot on the main stem of the Mandelbrot set, quite near the main body of the set itself. It is neither a Mandelbrot nor a Julia fractal. It is oriented at an angle 16 degrees from the Oblate plane of the Julibrot. The orientation explains the name "A Near-Oblate Set". Since I put almost no effort into the image, I gave it no rating. And the calculation time of 13 minutes is far too slow for the un- impressive result. The cure of all these shortcomings is a trip to the FOTD web site at: <http://www.Nahee.com/FOTD/> to see the finished image there. Lots of sun, reasonable humidity and a temperature of 86F 30C kept the fractal cats of Fractal Central subdued on Friday. The lazy conditions kept me subdued also, while FL still worried about the lack of rain on her garden. The next FOTD will be posted in 24 hours. Until then, take care, and where are the multiple universes? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Near_Oblate_Set { ; time=0:13:01.86-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=1 symmetry=none center-mag=+0.64407582162/-0.00000162218/704047.3/\ 0.183/180 params=0/0/90/16/-1.4013068817/0/0/0/2/0 float=y maxiter=10000 inside=0 logmap=534 colors=000L9qF6s93uC4nE5hH6bJ7XM8RO9LQAFODGMGHLJIJ\ LJIOJGRKFULDWMCZNAaN9dO7fP6iQ4lR3nR2RL13F24I25K26M\ 26O27R28T28V29X2A_2Aa2Bc2Ce2Cg4Z`5uV8sWBrWEqWGpWJo\ XMnXOmXRlXUkXXjYZiYahYdgYffYdfWbfU`fSZfQXfOVfMTfKR\ fIPfGOfFPWOPMXQPWRSWSVVTYVU`UUcUVfUWiTXlTYoSZrSZuS\ YtOYsLXsIXrFXrCZtD`vEbwFdyGezGcyJaxL`wNZvQYvSWuUVt\ XTsZSs`QrcPqeNpgMpiPqhSqgVrfXre_rebsddscgsbjtamtao\ t`ru_uuZwuZpgYjUXdGWZ3V_7X_BY`FZ`I_aMaaQbbUcbXdc`f\ cdgdhhdkicgjbckb_laWm`Sn`Oo_KpZGqZCqVGmSJjPMgLPdIS\ aFVZBYW8`T5cQ2fN1_I1TD1N91G41A05E38H5BL7EOAISCLVEO\ ZHRaJUdLWZHYUE_OBaJ7cD4d81eB5eD8eGBeIEeLHeNLeQOeSR\ fVUfXXf_`facfdfffifilfkoghkhehhcdi`aiYZjWVjTSkQOkO\ LlLIlIEmGBmD7nA4n81i84e86a88Y8AUmDQmFMmHImJEmMAmO6\ mQ2mSBmQKmPTmN`mMWmQSmTOmWJm_zmbzmezmhzmezmbzm`zmY\ zmVzmTzmQzmOzmLzmIzmGzmDzmAgz8jz5lz3IzMDzK8zJ3zI6z\ J8zJBzJDzJGzJIzKLzKNzKPzK } frm:SliceJulibrot4 {; draws all 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=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 25-06-10 (Cometary Residue [7])
by Jim Muth 24 Jun '10

24 Jun '10

FOTD -- June 25, 2010 (Rating 7) Fractal visionaries and enthusiasts: NEW FORMULA ALERT! Today's formula, FinDivBrot-2J, is a new one. Actually it's simply a Julia version of the FinDivBrot-2 formula. Today's image is the first one I found with the new formula, and it rates FOTD status. I cannot recall this ever happening before. The 'comet' with the long, long tail that streaks across the entire frame is actually a complete Julia set, one of the most unlikely Julia sets I have yet stumbled upon. The corresponding Mandelbrot fractal is a Mandeloid with everything scrunched around toward the main stem, and the east side of the main bay cut off by a straight wall. Today's image corresponds to the point where the curving north shore line meets the straight wall. The image resembles a comet zooming across the sky. (In fact, comets do not zoom across the sky except in the movies.) I rated the image at a 7, which is above average. The colors are quite smooth, and it has some math interest, all of which add to its worth. The name "Cometary Residue" came about when I turned the image upside down. It originally was rotated 180 degrees from its present orientation. The coloring smoothness was achieved by rendering the image with the outside set to 'tdis', which colors the points according to how far they travel before escaping. The calculation time of under 2 minutes is not too high a price for the result, but all calculation may be avoided by viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> Partly cloudy skies, a temperature of 88F 31C, lower humidity and a refreshing breeze made Thursday quite an acceptable day here at Fractal Central. The fractal cats came out of hiding long enough to get into a squabble over who would spend the afternoon on the foot stool. My day was satisfactory, as far as that goes. And if all goes well, tomorrow will be a repeat. With the drought growing worse here in Pennsylvania, FL is concerned with her garden, but so far, with generous watering, the plants appear to be holding up rather well. The next FOTD will be posted in 24 hours. Until then, take care, and be satisfied. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Cometary_Residue { ; time=0:01:50.09-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2J function=recip center-mag=10.892/-14.7808/0.052083/1/90/0 float=y params=1/1/10000/0/0.79606/0.19699 periodicity=0 maxiter=5000 inside=255 outside=tdis symmetry=none colors=000zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzMzzNzzNzzOzzOzzPzzPzzQzzQzzRzzRzzSzzSzzTzzT\ zzUzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzbzzbzzczzczzdzzdzzezzezzfzzfzzgzzgzzhzzizzizzjz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzASsASsBSrBSrBSqCSqCSpCSpDSoDSoDSnDS\ nESmESmESlFSlFSkFSjGSjGSiGSiHShHShHSgHSgISfISfISeJ\ SeJSdJSdKScKScKSbLSaLSaLS`LS`MS_MS_MSZNSZNSYNSYOSX\ OSXOSWPSWPSVPSVPSUQSTQSTQSSRSSRSRRSRSSQSSQSSPTSPTS\ OTSOTSNUSNUSMUSMVSLVSKVSKWSJzzJzzIzzIzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz9zz8zz8zz7zz7\ zz6zz6zzzzzzzzzzzzzzzzzzzzzzzzzzzzz4zz4zz5zz5zz6zz\ 6zz7zz7zz8zz8zz9zz9zzAzzBzzBzzCzzzzzzzzzzzzzzzzzzz\ zzzzzzzGzzHzzHzzIzzJzzJzzKzzKzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzTzzUzzUzzVzzVzzWzzWzz\ XzzXzzXzzWzzVzzUzzTzzSzzz } frm:FinDivBrot-2J { ; Jim Muth z=pixel, c=(p3), a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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Floral
by Roger Alexander 24 Jun '10

24 Jun '10

Now open to the public my colorful fractal garden a product of the versatile orbit trap algorithm. Ready made at http://maxitersfractalfollies.blogspot.com fract273.gif { ; my fractal garden ; blank ; calctime 0:27:53.20 ; created Jun 24, 2010 ; Fractint Version 2004 Patchlevel 9 reset=1960 type=formula formulafile=frac_ml.frm formulaname=gallet-10-02 center-mag=+0.58981458500000010/+1.17073695700000000/112.4031/1/-5.00000\ 044121758425/5.02228108135993612e-007 params=0.25/1000/0.005/0.005/3/85 float=y maxiter=1023 inside=atan outside=summ periodicity=0 cyclerange=1/250 colors=mz0mz0lz0ky0jy0iy0hx0gx0fx0ew0dw0dv0cv0bv0au0`u0_u0Zt0Yt0Xt0Ws0Ws\ 0Vr0Ur0Tr0Sq0Rq0Qq0Pp0Op0Np0No0Mo0Ln0Kn0Jn0Im0Hm0Gm0Fl0El0Dk0Ck0Cj0Cj0Bj\ 0Bi0Bi0Bh0Ah0Ah0Ag0Ag09f09f09f09e09d08d08c08b07a07a07`07_06Z06Z06Y05X05W\ 05W05V04U04T04T03S03R03Q03Q02P02O02N01N01M01L00K0zKkzKkzKkzJkzJjzIjzIjzI\ izHizHizGhzGhzGhzFhzFgzEgzEgzEfzDfzDfzCezCezCezBdzBdzAdzAdz9cz9cz9cz8bz8\ bz7bz7az7az6az6`z5`z5`z5`z4_z4_z3_z3Zz3Zz2Zz2Yz1Yz1Yz0Xz0Xz0Wz0Vz0Uz0Tz0\ Sz0Rz0Qz0Pz0Oz0Nz0Mz0Lz0Kz0Jz0Iz0Hz0Hz0Gz0Fz0Ez0Dz0Cz0Bz0Az09z08z07z06z0\ 5z04z03z02z01z00u0zt0zr0yq0yo0xn0xl0wk0wi0vh0vf0ue0tc0tb0s`0s_0rY0rX0qV0\ qU0pS0pR0oP0nO0nM0mL0mJ0lI0lG0kF0kD0jB0iB0iB0hB0gB0gA0fA0eA0eA0dA0c90c90\ b90a90a90`80_80_80Z80Y80Y70X70W70W70V70U60U60T60S60R50R50Q50P50P50O40N40\ N40M40L40L30K30J30J30I30H20H20G20F20F20E10D10D10C10B00A } frm:Gallet-10-02 {; Modified Paul W. Carlson formula ( Petals_Mset) ;**************************************************** ; Always use floating point math and outside=summ. ; ; Parameters: ; p1 = radius of the circles ; p2 = circle offset factor ; real(p3) = number of color ranges ; imag(p3) = number of colors in each color range ; ; Note that the equation variable is w, not z. Always ; initialize z to zero. ;**************************************************** w = 0 c = pixel r = real(p1), bailout = imag(p1) r2 = r * r ro = r + r * p2 f = 1 - (2 + p2) * p2 k = r * (p2 + sqrt(f)) ;abs val of petal center (k,k) k1 = k*(1,1), k2 = conj(k1) plsqd = 2 * r2 * f ;petal length squared z = 0 num_ranges = real(p3) colors_in_range = imag(p3) range_num = 0 iter = 0: ; w = 1 / (w*w + c) ;**************************************************** ; Determine which pair of overlapping circles the ; orbit point falls in, if any. ;**************************************************** c1 = (|w - ro| < r2) c2 = (|w + flip(ro)| < r2) c3 = (|w + ro| < r2) c4 = (|w - flip(ro)| < r2) IF (c1 && c4) d = |w-k1| ELSEIF (c1 && c2) d = |w-k2| ELSEIF (c2 && c3) d = |w+k1| ELSEIF (c3 && c4) d = |w+k2| ELSE d = 0 ENDIF ; IF (d > 0) ;************************************************ ; Set z equal to the index into the colormap. ;************************************************ index = colors_in_range * d / plsqd z = index + range_num * colors_in_range + 1 ENDIF ; range_num = range_num + 1 IF (range_num == num_ranges) range_num = 0 ENDIF iter = iter + 1 z = z - iter d == 0 && |w| < bailout ;SOURCE: 98msg.frm } Roger Alexander _________________________________________________________________ MSN Dating: Find someone special. Start now. http://go.microsoft.com/?linkid=9734384

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Sparklies Before and After
by Roger Alexander 23 Jun '10

23 Jun '10

A before and after duo today. The chaotic nature of the coloring of the included par generates a sparkly image. After anti-aliasing the wispy structure produced by the formula is clearly visible. Because the anti-aliased version is a jpg you will have to go to http://maxitersfractalfollies.blogspot.com to compare the two versions. fract271.gif { ; wispy ; blank ; calctime 0:06:41.50 ; created Jun 23, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=kerrym.frm formulaname=conic-near_jul16 center-mag=-2.22045e-016/2.22045e-016/0.8130081/1/-77.4999999999999858/3\ .88578058618804789e-016 params=0.8/0.7361369670705282/0.2491225928525651/-0.6531876583147679/-0.\ 1228370006408887/-0.3843806268501846 float=y maxiter=1500 inside=0 outside=atan decomp=256 periodicity=0 colors=05F05F05F16G16G16G16G16G27H27H27H27H27H38I38I38I38I38I49J49J49J49\ J49J5AK5AK5AK5AK5AK6BL6BL6BL6BL7CM7CM7CM7CM7CM8DN8DN8DN8DN8DN9EO9EO9EO9E\ O9EOAFPAFPAFPAFPAFPBGQBGQBGQBGQBGQCHRCHRCHRCHRCHRDISDISDISDISDISEISEJTFJ\ TFKTGKUGLUHLVHMVIMVINWJNWJOWKOXKPXLPYLQYMQYMRZNRZNSZOS_OT_PT_PT`QU`QUaRV\ aRVaSWbSWbTXbTXcUYcUYcVZdVZdW_eW_eX`eX`fYafYafZbgZbg_ch_ch`ch`diadiaeibe\ jbfjcfjcgkdgkdhlehleilfimfjmgjmgknhknhlniloimojmpjmpknpknqloqloqmprmprnq\ snqsorsortpstpstqtuqturuuruvsvvsvwtwwtwwuxxuxxuxxvyyvyywzzvyyvyyuxxtxxtw\ wsvwsvvruvquuqtupstostorsnqsnqrmprlpqloqknpjnpjmoimohlnhkngkmgjmfjleileh\ kdhkcgjcfjbfibeiaeh`dh`cg_cgZbfZbfYaeX`eX`dW_dW_cVZcUYbUYbTXaSWaSW`RV`RV\ _QU_PTZPTZOSYNSYNRXMQXLQWLPWKPVKOVJNUINUIMTHLTGLSGKSFKRFJREIQDIQDHPCHPBG\ OBFOAFN9EN9EM8DM8CL7CL6BK6AK5AJ49J49I38I37H27H16G16G05F } frm:conic-near_jul16 { ; Kerry Mitchell 11may98 cc=(0.2882,0.0106), zc=pixel, maxr=1e12, minr=maxr, iter=1 a=real(p1), b=imag(p1), c=real(p2), d=imag(p2) e=real(p3), f=imag(p3): iter=iter+1, zc=sqr(zc)+cc, x=real(zc), y=imag(zc) conic=|x*(a*x+b)+y*(c*y+d)+e*x*y+f| if (conic<minr) minr=conic end if if ((|zc|>maxr)||(iter==maxit)) iter=-1 t=log(minr) z=cos(t)+flip(sin(t)) end if iter>0 } Roger Alexander _________________________________________________________________ MSN Dating: Find someone special. Start now. http://go.microsoft.com/?linkid=9734384

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FOTD 24-06-10 (Double-Scepter Scene [5])
by Jim Muth 23 Jun '10

23 Jun '10

FOTD -- June 24, 2010 (Rating 5) Fractal visionaries and enthusiasts: Most likely due to the hot weather, I never did work up the usual enthusiasm for fractal work on Tuesday. But once again the work-horse Mandelbrot set came to the rescue with an acceptable if not outstanding image. The image takes us to the third valley out the negative X-axis of the M-set. The first valley is the well-known Seahorse Valley; the second valley is Scepter Valley. I'm not sure if the third valley has an official name, though I call it 'Double Scepter Valley'. Today's image is named "Double-Scepter Scene" because IMO that's what it is. Most of the effect was achieved by setting the logmap to an artificially high 10250, which creates the brilliant flat areas that make the central minibrot stand out. The rating of a 5 says that the image is just another scene in the Mandelbrot set. The calculation time of 1 minute says that the type=mandel fractals run very fast on a P4-2000mhz machine. The URL listed below says that calculation may be totally avoided by viewing the finished image there. <http://www.Nahee.com/FOTD/> The fractal cats wilted when the temperature reached 95F 35C here at Fractal Central on Wednesday. The fractalist also wilted. FL was busy however, watering her wilting flowers. The rest of the day was under control. The next FOTD will be posted in 24 hours. Until then, take care, and be with it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= DoubleScepterScene { ; time=0:01:01.36-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.3680989308005\ 03/+0.00047736474376778/1.7e+011/1/-7.5/0 passes=1 params=0/0 float=y maxiter=125000 bailout=5 inside=0 logmap=10250 periodicity=6 mathtolerance=0.05/1 colors=000szzBW`9Ub7Sd6Rf8QdAQbCQ`DQZFPXHPVIPTKPRM\ PPNONPOLROJSOHUOFWNDXNBZN987n44p77nA9mDBlGDkJGjMIi\ PKgSMfVOeYRd`TccVbfX`iZ_laZocYreXugWwiVuhTshSqhRog\ QmgOlgNjfMhfLffJdfIbeHaeG_eEYdDWdCUdBVc9TdASdAQdAP\ eANeAMeAKfAJfAIfBGgBFgBDgBChBAhB9hB6j88hB9gEAfGBeJ\ DdLEcOFbQGaTI_WJZYKY`LXbNWeOVgPUjOTkQTlRTmTTnUToWT\ oXTpYTq_Tr`TrbTscTtdTufTugTviTwjTxkTxhUteVpbVl_WhX\ XdUX`RYXOZTGWNLZPQ`RVbT_eVdgXql_iiYafXUcVNcTMaUL`U\ K_VJZVJYWIXWHWWGVXGUXFTYESYDQYCPZCOZBN_AM_9L_9K`8J\ `7Ia6Ha69Y6Ga6Nd6Ug6`k6gn0kv6mqBnmGoiLpeQq`VrX_sTd\ tPiuKnvGswCyz3xx8wvCwtGvsLuqPuoTtmXslasjerhirgmphm\ oimnimmjmlkmkkmjlmimmhmmgnmfomeomdpmcpmbnjblhbkfbi\ cagaaf_adXabV`aT`_R`YO`XM_VK_TH_SF_QDbM8_PBXREVTHS\ WKQYNN_QLaTIdVGfYDh`Bjc8mf6oizqlzsnzskzsizsfzsdzsa\ zs_GszIszLszNszPszRszTszVszXszZszbuz`szZqzXozVmzTk\ zRmzPmzNmzLmzJmzHmzFmzDmz } END PARAMETER FILE=========================================

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FOTD 23-06-10 (Gear World [6])
by Jim Muth 22 Jun '10

22 Jun '10

FOTD -- June 23, 2010 (Rating 6) Fractal visionaries and enthusiasts: On its outer edges, today's image is a Julia set of Seahorse Valley of the Mandelbrot set. But it is not a Julia set; it is a Mandelbrot set. And it is hardly quadratic. Those circular objects in the center have 32 lobes, which makes them of order-33. So I leave it to the viewer to decide what to call the image. As for me, I took it for what it is, rated it at a 6 and named it "Gear World". I had a quick impression of a gear train as I searched for a name. The calculation time of 6-1/2 minutes is not the briefest ever, but it is not the longest either. To see what all the excite- ment is about, run the included parameter file or hurry to the FOTD web site at: <http://www.Nahee.com/FOTD/> and enjoy the finished image there. I wisely avoided another meaningless discussion at lunch time on Tuesday, when FL asked me if I think the end of the world is coming. "Of course it's coming," I told her. The only ques- tions are when it's coming and what will cause it. I did not tell her that I believe our current obsession with technology is pathological, and is probably the beginning of the end. Now for some news that is more immediate. Lots of clouds prevailed all morning here at Fractal Central on Tuesday. At noontime a short but heavy shower fell, followed by heavy clouds most of the afternoon. The sky cleared around 5pm, but the air was so hazy that the clearing was almost invisible. The high humidity and temperature of 84F 29C merely added to the unpleasantness. The fractal cats spent the day doing what cats do best. They slept. Cassie chose the foot stool, while Nico stretched on the cool floor. My day was about as peaceful as days ever get. The next FOTD will be posted in 24 hours, give or take a few. Until then, take care, and what will we do when the world ends? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Gear_World { ; time=0:06:31.77-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-1.780919193881258/+0.00000021348863863\ /4.538402e+010/1/-20/0 params=33/1e+118/0/0 float=y maxiter=3200 inside=0 logmap=680 periodicity=6 colors=000GxsHwrEvqIupMtoQsnTrmUqlUqkUpkUpjUojUoiU\ niUnhUmgUmgUlfUlfUkeWkeUkeSibRh_PfWOeTMcQLbMJ`JI_G\ GYCFX9DV6CU3FT6HT9JSCMSFORIQRLSQOVQRXPUZPXcNb`P_YR\ XVTVSVSQWQNYNK_LHaICgKFbGHYDHR9JUALWBMYCO_DQaERcFT\ fGUhHWjIYlJZnK`pLarLcoMemMgkNiiNkgOmeOocPqaPs_QuYQ\ zbOvWQrQSnKUjEWM2RX5Vg8Yq5dr8brB`rDZrGYsJWsLUsOTsQ\ RtTPtWOtYMt`KwdGtbJq`LoZNlXQiVSgTUdRWaQZ_O`XMbUKdS\ IgPGiMEkK1lKDmKPnK_oKkpMxrLwqKvqJupItpIspHroGqoFpo\ EonEnnDmnClmBkmBkmKmlTnk`ojiqirrhzsgxqfvoetndsldqk\ coibnhblfaje`ic`gb_e`ZaZVc_Xd_Ze``g`ah`ciaekaflbhm\ bjobkpcmqcougtrcpo`mlXjjUfgQcdN`aJY_GUXCRU9OM1HP4J\ S6LU8MXAO_CQzCfmDZaERPFJ893DFBILJMRRRXZOXjS_gVbeYd\ bag`diYglWkocnqmzzzzzzzzzoumjscerVapYXo`SmcNmfJmiE\ ml9mo4mr0mu5mq9mnDmjHmgMmcQm`UzXYzUbzQfzNjzJnzGrzD\ kzKezQ_zWTzbNzhHznBztEzqGzoJzmLzkNziQzfSzdVzbXz`Zz\ ZazWczUfzShzQjzOjzO9z89z7 } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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Zf_ang Again!
by Roger Alexander 21 Jun '10

21 Jun '10

Another pair of fractals demonstrating the effect of positive and negative skipped iteration values on the Zf_ang formula.What this shows about the math I couldn't tell you, Jim Muth knows more on this subject than I do.I have posted only one par. To recreate both fractals use imag(p2) values of +1 and -1. Also the link for yesterdays blog posting appeared to be broken. It's now fixed, hope I didn't disappoint anybody. Go to http://maxitersfractalfollies.blogspot.com and download two fractals for the price of one. fract267.gif { ; zf_ang blue and red ; negative(-1) skipped iteration value ; calctime 0:05:40.76 ; created Jun 21, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_z.frm formulaname=Zf_Ang function=sqr center-mag=0.296636/0.0627236/1.173709 params=0.5/0.5/0.5/-1/2/128 float=y maxiter=1500 inside=0 outside=summ colors=zffzffzeezddzccyccybbyaay``x``x__xZZxYYwYYwXXwWWwVVwUUvUUvTTvSSvR\ RuRRuQQuPPuOOtOOtNNtMMtLLtKKsKKsJJsIIsHHrHHrGGrFFrEEqEEqDDqCCqBBqAApAAp9\ 9p88p77o77o66o55o44n44n33n22n11m00m00l00l00k00j00j00i00h00h00g00g00f00e0\ 0e00d00c00c00b00a00a00`00`00_00Z00Z00Y00X00X00W00V00V00U00U00T00S00S00R0\ 0Q00Q00P00P00O00N00N00M00L00L00K00J00J00I00I00H00G00G00F00E00E00D00C00C0\ 0B00B00A00900900800700700600500ffzffzeezddzcczcczbbzaaz``y``y__yZZyYYyYY\ yXXyWWxVVxUUxUUxTTxSSxRRxRRwQQwPPwOOwOOwNNwMMwLLvKKvKKvJJvIIvHHvHHvGGuFF\ uEEuEEuDDuCCuBBuAAtAAt99t88t77t77t66t55s44s44s33s22s11s00r00r00q00p00p00\ o00n00n00m00l00l00k00j00j00i00h00h00g00f00f00e00d00d00c00b00b00a00`00`00\ _00Z00Z00Y00X00X00W00V00U00U00T00S00S00R00Q00Q00P00O00O00N00M00M00L00K00\ K00J00I00I00H00G00G00F00E00E00D00C00C00B00A00A009008007 } frm:Zf_Ang {; Copyright (c) Paul W. Carlson, 1998 ; p1 = Julia set coordinates ; real(p2) = controls size of the elements ; imag(p2) = number of iterations to skip ; real(p3) = number of color ranges ; imag(p3) = number of colors in a range ; z = k = iter = range_num = bailout = 0 w = pixel c = p1 prev_modw2 = 1.0e20 size = real(p2) skip_iters = imag(p2) num_ranges = real(p3) colors_in_range = imag(p3) factor = (colors_in_range - 1) / size : w = c * (w - 1 / w) a = 2 * atan(imag(w) / real(w)) a = a * a + c a = fn1(1 - a) / a ; dist = abs(|w| - |a|) IF (dist < size) bailout = 1 IF (iter > skip_iters) k = 1 ENDIF z = (factor * dist + range_num * colors_in_range + 1) * k ENDIF range_num = range_num + 1 IF (range_num == num_ranges) range_num = 0 ENDIF iter = iter + 1 z = z - iter bailout == 0 && |w| < 1.0e20 ;SOURCE: 98msg.frm } Roger Alexander _________________________________________________________________ Look 'em in the eye: FREE Messenger video chat http://go.microsoft.com/?linkid=9734386

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FOTD 22-06-10 (Negative Minibrot [7])
by Jim Muth 21 Jun '10

21 Jun '10

FOTD -- June 22, 2010 (Rating 7) Fractal visionaries and enthusiasts: Yesterday's image was a true-to-life antiminibrot. Today's image is a negative minibrot, which is not quite true to life, since the negative effect was totally created by the coloring. The minibrot itself is nothing more than an everyday run-of-the- mill minibrot given interest by rendering the entire scene with the outside set to 'tdis'. The negative effect gives a rather ominous feeling to the image. I have occasionally seen this effect used in Japanese 'anime' cartoons. The name "Negative Minibrot" is self explanatory. The calculation time of 39 seconds is no error. The parameter file really runs this fast. But running parameter files involves a bit of hassle. This small hassle may be avoided by checking the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> and forgetting about running the parameter file. The parent fractal came about when I combined 0.1 part of Z^10 with one part of Z^1.5 and added straight C. This parent is a mis-shapen Mandelbrot set rotated about 180 degrees, with a large open area extending beyond its east (west) valley and a curled-up main stem. Today's scene lies on a kind of figure-8 shaped hole on this curled stem. The weather here at Fractal Central on Monday was almost perfect. Only a too-warm temperature of 88F 31C kept it from being totally perfect. The fractal cats spent the day relaxing, though at one point Nicholas ducked briefly under the bed when he thought we were getting out the cat-carrying box to take him to the doctor again. My day was about average; FL is concerned about the unusually dry weather we have had so far this year, and the effect it is having on her garden, (and the farmers' crops also). The next FOTD will be posted in 24 hours. Until next time, take care, and does anyone know how to get more water to fall from the sky? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Negative_Minibrot { ; time=0:00:39.66-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident inside=0 center-mag=+0.5547669664716627/-0.0077870219432185\ /1.259273e+011/1/-120/0 params=0.1/10/1/1.5/0/0/0/0 float=y maxiter=1500 outside=tdis periodicity=6 mathtolerance=0.05/1 colors=000XiXXiXXjXXjXXkXXkX_lWamVdnVfoUipTkqTloSm\ nRnmRolQpkPqjPriOrhNsgNtfMueLvdLwcKxbJxaJudOrfTpiY\ mkbjnghplesqbuv`wzbvvcvseuofulhuiitektblt_cpUWlONh\ IZyEGiDFeCEbCE_CDXCDTCCQCBNBBKBAGBADB00042797BFFIK\ IMMMMRQPVVT__Wcd_nplklkhijeehbbg__eYXeXVeVSfTQfROg\ PLgNJhMHhLPYKXNKcDJdHIeKIfNHgRHgUGhXFi_FjcEkfEkiDl\ lCmpCnsBovBoy_dkYaiW_gUXfSVdQSbOQaMN_KLYIIXGGVEDTc\ BSc8Qc6PcANcDMcGLmJKmMJmPImSGmVFmYEm`DecCzfBzS0z`5\ ziAz0yzSazrFzlDzfBz`9zP4zT6zW7zZ8zbAzeBzhCzkDzoFzr\ GzuHzxIzvKctMdsOfqPgpRhnTilVkkWliYmh_nzapzbqzdrzfs\ zgTzDWzGYzJ_zMazPdzRfzUhzXjz_ozamzalzakzaizahzagza\ fzadzaczabza`za_zaZzaYzaTzdPzfLziHzkEzoDzmCzlCzkBz\ iBzhAzgAze9zd9zc8za8z`7z_7zZCz_Hz`MzaJzvNzkQzaTzRX\ wDWzHWzLWzPWzSWzWWz_VzbVzfVzjVzmVzqVzuVzxYzw_zvazu\ cztezsgzsizrjzqkzpjznjzmizlizjhzihzhgzfgzefzdfzbez\ aez`dzZdzYczXAzxXzXXzXXzX } 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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Celery of the Gods
by Roger Alexander 21 Jun '10

21 Jun '10

Busy busy today but not so busy I don't have time to post this par "Celery of the Gods". If you're busy as I am go to http://maxitersfractalfollies.blogspot.com and save some precious calculating moments by viewing the finished fractal. fract265.gif { ; fractal chlorophyll ; blank ; calctime 0:04:40.40 ; created Jun 20, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2000 type=formula formulafile=_t.frm formulaname=tri-julia-2 center-mag=-0.338785/-0.449154/4.341378/1/47.5000000000000711/5.12714870\ 559705105e-014 params=1025.653340250862/1.891872920926542/-0.4537186803796504/0.4264961\ 699270607 float=y maxiter=1200 outside=atan periodicity=0 cyclerange=0/255 colors=0000200000000000200300500600800A00B00D00E00G00I00J00L00M00O00Q00R\ 00T00U00W00Y00Z00`00a00c00e00f00h00i00k00m01m03m04n06n07o09o0Ao0Cp0Ep0Fq\ 0Hq0Iq0Kr0Lr0Ns0Ps0Qs0St0Tt0Vu0Wu0Yu0Zv0`v0bw0cw0ew0fx0hx0iy0ky0mz0mz1mz\ 3mz3lz3kz3jy3iy3hy3gy2fx2ex2dx2cx2bw2aw1`w1_w1Zv1Yv1Xv1Wu0Wu0Xu0Yu0Zu1_u\ 1`u1av2bv2cv2dv3ev3fv3gw4hw4iw4jw5jw5kw5lw5mx6nx6ox6px7qx7rx7sy8sy8ry8qy\ 7py7py7oy6ny6my6my5ly5ky4jy4iy4iy3hy3gy3fy2fy2ey2dy1cy1bz0cz0dz0ez0fz0gz\ 0hz0iz0jz0kz0lz0mz0nz0oz0pz0qz0rz0sz0qz0pz0oz0mz0lz0kz0iz0hz0gz0fz0dz0cz\ 0bz0`z0_z0Zz0Yz0Wz0Vz0Uz0Sz0Rz0Qz0Oz0Nz0Mz0Lz0Jz0Iz0Hz0Fz0Ez0Dz0Bz0Az09z\ 08z06z05z03z02z00z00y00x00w00v00u00t00s00r00q00p00o00n00m00l00k00j00i00h\ 00g00f00e00d00c00b00a00`00_00Z00Y00X00W00V00U00T00S00R00Q00P00O00N00M00L\ 00K00J00I00H00G00F00E00D00C00B00A0090080070060050040030 } frm:tri-julia-2 {; Sylvie Gallet <sylvie_gallet(a)compuserve.com>, May 1997 ; Thanks to Kerry Mitchell for the idea! ; real(p1) = bailout (1024 recommended) ; imag(p1) must be different from 0 (>=1 recommended) ; p2 = parameter for the Julia set ; This formula must be used with decomp = 256 and periodicity = 0 ; z1 = pixel, mz1 = cabs(z1), b = cabs(p2), summ = iter = 0 b1 = abs(real(p1)), f = b1^0.1 b2 = b1*f, b3 = b2*f, b4 = b3*f, b5 = b4*f, b6 = b5*f b7 = b6*f, b8 = b7*f, b9 = b8*f, b10 = b9*f, b11 = b10*f iter1 = iter2 = iter3 = iter4 = iter5 = iter6 = iter7 \ = iter8 = iter9 = iter10 = summ_tot = iter_tot = 0 k = imag(p1) * (0.0,6.28319530718) : iter = iter + 1, a = mz1 * mz1 z1 = z1 * z1 + p2, mz1 = cabs(z1), a_b = abs(a - b) summ = summ + (mz1 - a_b) / (a+b - a_b) IF (mz1 > b1) IF (iter1==0) iter1 = iter iter_tot = iter_tot + iter1 summ_tot = summ_tot + summ ENDIF IF (mz1 > b2) IF (iter2==0) iter2 = iter iter_tot = iter_tot + iter2 summ_tot = summ_tot + summ ENDIF IF (mz1 > b3) IF (iter3==0) iter3 = iter iter_tot = iter_tot + iter3 summ_tot = summ_tot + summ ENDIF IF (mz1 > b4) IF (iter4==0) iter4 = iter iter_tot = iter_tot + iter4 summ_tot = summ_tot + summ ENDIF IF (mz1 > b5) IF (iter5==0) iter5 = iter iter_tot = iter_tot + iter5 summ_tot = summ_tot + summ ENDIF IF (mz1 > b6) IF (iter6==0) iter6 = iter iter_tot = iter_tot + iter6 summ_tot = summ_tot + summ ENDIF IF (mz1 > b7) IF (iter7==0) iter7 = iter iter_tot = iter_tot + iter7 summ_tot = summ_tot + summ ENDIF IF (mz1 > b8) IF (iter8==0) iter8 = iter iter_tot = iter_tot + iter8 summ_tot = summ_tot + summ ENDIF IF (mz1 > b9) IF (iter9==0) iter9 = iter iter_tot = iter_tot + iter9 summ_tot = summ_tot + summ ENDIF IF (mz1 > b10) IF (iter10==0) iter10 = iter iter_tot = iter_tot + iter10 summ_tot = summ_tot + summ ENDIF IF (mz1 > b11) iter_tot = iter_tot + iter summ_tot = summ_tot + summ z = exp (summ_tot * k / iter_tot) ENDIF ENDIF ENDIF ENDIF ENDIF ENDIF ENDIF ENDIF ENDIF ENDIF ENDIF mz1 <= b11 ;SOURCE: triangl.frm } Roger Alexander _________________________________________________________________ Look 'em in the eye: FREE Messenger video chat http://go.microsoft.com/?linkid=9734386

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FOTD 21-06-10 (Great AntiMinibrot [10])
by Jim Muth 20 Jun '10

20 Jun '10

FOTD -- June 21, 2010 (Rating 10) Fractal visionaries and enthusiasts: Minibrots in fractals are easy to find and very widely known, but much less known are antiminibrots, which are quite difficult to find. Minibrots lie at the center of a basin where the iteration count increases as the center is neared, and reaches infinity at the edge of minibrot itself. Antiminibrots are peaks with an area of lowest iteration count at the center. In today's image the center is beyond resolution, so I cannot give the iteration count at the central peak. But the count need not be as low as 1. In a minibrot basin, the number of elements surrounding the central minibrot bifurcates in a 2,4,8,16... series as the 'brot is approached. In an antiminibrot such as the one in today's image, the number antibifurcates in a 16,8,4,2 series. In everyday minibrot images, the lowest iteration bands lie around the edges of the frame, and the automatic logmap feature (setting the logmap to 2) works very well, but in antiminibrot images such as today's, where the lowest count is at the center, the automatic logmap is useless. Luckily, turning off the log- map in today's image works just as well as the automatic feature. Today's image rates an honest 10. Its mathematical and coloring values are both well above average. And its cauculation time of 59 seconds can hardly be beat. BTW, 95-percent of the coloring was created by the Fractint program. I tweaked only 10 or so color registers. The name "Great AntiMinibrot" says it all. The image cauculates in less than a minute, but it still takes some time to set up the parameter file. To avoid this small hassle, the finished image may be seen already calculated on the FOTD web site at: <http://www.Nahee.com/FOTD/> Partly cloudy skies with slightly lower temperatures and notice- ably lower humidity prevailed here at Fractal Central on Sunday. Nicholas, the fractal cat who dislikes heat, spent most of the day stretched on the cool tile floor. Cassie, who likes it warmer, passed the day curled on the foot stool. FL and I spent the day taking it easy. The next FOTD, probably not as great as today but hopefully still quite good, will be posted in 24 hours. Until then, take care, and get a new angle on things. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Great_AntiMinibrot { ; time=0:00:59.09-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip center-mag=-0.2382764653067911/+0.6598651051332169\ /1.26548e+013/1/-15/0 params=6/1e+023/0/0 float=y maxiter=2250 periodicity=6 mathtolerance=0.05/1 colors=000T_IXWMGELHFMIGMJGMKHMKHMLIMMINNJNNJNOKNP\ KNQLNRLNRMOSMOTNOUNOUOOVOOWPOXPPYQPYQPZRP_RP`SPF8_\ QIUT3gU5fU6eV7dV8cV9bWBaWC`XD_XEZXFYYHYYIXYJWZKVZL\ U_NT_OS_PR`QQ`RPmg4ke7jc9ibBg`Df_FeYHcWJbVLaTNvZkt\ YisYhrXgqXfpXdoWcmWblWakV`jVZiUYhUXfUWeTVdTTcTSbSR\ aSQAC_NVgOVfPVePVdQUbRUaSU`TU_TUZUTYVTXWTWXTVXTUYS\ T_SPZSS_SR`SQXubYsaYr`Yp`Yo_YnZZlZZkYZjXZhXZgWZfW_\ dV_cU_aU_`T__S`YS`XR0mz0kz0iz2gz4ez5cz6az7_z9YzAWz\ BUzCSzDQzFOvGMrHLmILhJMcLM_MNZNNYOOYOOXNPWNPVMQUMR\ TLRSLSRKTQKUPJXOI_MKbKMeIOhGQkETnCVqAXt8Zw6ay3ax3`\ u3_r4Zo4Yl5Xi5Wf6Vc6U`6TY7SV7RS8QP8PM9OJ9NGAMMGLTM\ K_Szczzazv_wtYtrWqpUnnSklPhjNehKbeH_cEXaCU_9RY6OV3\ KTAMRHOPORNVTKbWNaXQ_YUZZXX`_VacUbfSciQemPfpNgtLir\ MioNilOijPigQidRhVKVLCHB42B42B52B52B62B72B72B82B82\ B92BA2BA2BB2BC2FE8KHFPKMTNTYQ_bTfaTe_TcZTaXT_WTYUT\ WSTVRTT`SP`SPDp3Hk7LgBPcE } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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Orbit Trap Oddness
by Roger Alexander 20 Jun '10

20 Jun '10

Two par files today illustrating a pecularity of the Zf_Ang formula, one of Paul Carlson's orbit trap formulas. With a postive "number of iterations to skip" value (imag p2) there is blank space and truncated stalks (which give some of the orbit trap formulas their name). With a negative imag p2 value the blank space is filled in. However I have gotten this techique to work only with this one formula. Another quirk of these formulas is the requirement of using outside=summ to generate high banding count images. Bypass the calculation process and go to http://maxitersfractalfollies.blogspot.com for immediate viewing and put the serve back in web server. fract263.gif { ; Carlson stalks positive skipped iterations value ; blank ; calctime 0:03:50.63 ; created Jun 19, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=frac_ml.frm formulaname=Zf_Ang function=sqr center-mag=0/0/0.6666667 params=-0.2551805169835505/1.054979094821009/3/1/2/128 float=y maxiter=1500 inside=0 outside=summ invert=0.5/0/0 cyclerange=0/255 colors=zffzffzeezddzccyccybbyaay``x``x__xZZxYYwYYwXXwWWwVVwUUvUUvTTvSSvR\ RuRRuQQuPPuOOtOOtNNtMMtLLtKKsKKsJJsIIsHHrHHrGGrFFrEEqEEqDDqCCqBBqAApAAp9\ 9p88p77o77o66o55o44n44n33n22n11m00m00l00l00k00j00j00i00h00h00g00g00f00e0\ 0e00d00c00c00b00a00a00`00`00_00Z00Z00Y00X00X00W00V00V00U00U00T00S00S00R0\ 0Q00Q00P00P00O00N00N00M00L00L00K00J00J00I00I00H00G00G00F00E00E00D00C00C0\ 0B00B00A00900900800700700600500ffzffzeezddzcczcczbbzaaz``y``y__yZZyYYyYY\ yXXyWWxVVxUUxUUxTTxSSxRRxRRwQQwPPwOOwOOwNNwMMwLLvKKvKKvJJvIIvHHvHHvGGuFF\ uEEuEEuDDuCCuBBuAAtAAt99t88t77t77t66t55s44s44s33s22s11s00r00r00q00p00p00\ o00n00n00m00l00l00k00j00j00i00h00h00g00f00f00e00d00d00c00b00b00a00`00`00\ _00Z00Z00Y00X00X00W00V00U00U00T00S00S00R00Q00Q00P00O00O00N00M00M00L00K00\ K00J00I00I00H00G00G00F00E00E00D00C00C00B00A00A009008007 } fract264.gif { ; Carlson stalks with negative skipped iterations value ; blank ; calctime 0:05:06.60 ; created Jun 19, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=frac_ml.frm formulaname=Zf_Ang function=sqr center-mag=0/0/0.6666667 params=-0.2551805169835505/1.054979094821009/3/-1/2/128 float=y maxiter=1500 inside=0 outside=summ invert=0.5/0/0 cyclerange=0/255 colors=zffzffzeezddzccyccybbyaay``x``x__xZZxYYwYYwXXwWWwVVwUUvUUvTTvSSvR\ RuRRuQQuPPuOOtOOtNNtMMtLLtKKsKKsJJsIIsHHrHHrGGrFFrEEqEEqDDqCCqBBqAApAAp9\ 9p88p77o77o66o55o44n44n33n22n11m00m00l00l00k00j00j00i00h00h00g00g00f00e0\ 0e00d00c00c00b00a00a00`00`00_00Z00Z00Y00X00X00W00V00V00U00U00T00S00S00R0\ 0Q00Q00P00P00O00N00N00M00L00L00K00J00J00I00I00H00G00G00F00E00E00D00C00C0\ 0B00B00A00900900800700700600500ffzffzeezddzcczcczbbzaaz``y``y__yZZyYYyYY\ yXXyWWxVVxUUxUUxTTxSSxRRxRRwQQwPPwOOwOOwNNwMMwLLvKKvKKvJJvIIvHHvHHvGGuFF\ uEEuEEuDDuCCuBBuAAtAAt99t88t77t77t66t55s44s44s33s22s11s00r00r00q00p00p00\ o00n00n00m00l00l00k00j00j00i00h00h00g00f00f00e00d00d00c00b00b00a00`00`00\ _00Z00Z00Y00X00X00W00V00U00U00T00S00S00R00Q00Q00P00O00O00N00M00M00L00K00\ K00J00I00I00H00G00G00F00E00E00D00C00C00B00A00A009008007 } frm:Zf_Ang {; Copyright (c) Paul W. Carlson, 1998 ; p1 = Julia set coordinates ; real(p2) = controls size of the elements ; imag(p2) = number of iterations to skip ; real(p3) = number of color ranges ; imag(p3) = number of colors in a range ; z = k = iter = range_num = bailout = 0 w = pixel c = p1 prev_modw2 = 1.0e20 size = real(p2) skip_iters = imag(p2) num_ranges = real(p3) colors_in_range = imag(p3) factor = (colors_in_range - 1) / size : w = c * (w - 1 / w) a = 2 * atan(imag(w) / real(w)) a = a * a + c a = fn1(1 - a) / a ; dist = abs(|w| - |a|) IF (dist < size) bailout = 1 IF (iter > skip_iters) k = 1 ENDIF z = (factor * dist + range_num * colors_in_range + 1) * k ENDIF range_num = range_num + 1 IF (range_num == num_ranges) range_num = 0 ENDIF iter = iter + 1 z = z - iter bailout == 0 && |w| < 1.0e20 ; } Roger Alexander _________________________________________________________________ Turn down-time into play-time with Messenger games http://go.microsoft.com/?linkid=9734385

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FOTD 20-06-10 (Break a Leg [5])
by Jim Muth 19 Jun '10

19 Jun '10

FOTD -- June 20, 2010 (Rating 5) Fractal visionaries and enthusiasts: The calculation time of today's image is no mistake. It finishes in a little over 1 second. The parent fractal is the Mandelbrot set, and the image is located on the north shore line of the main bay, just west of the large bud. I named the image "Break a Leg". The phrase came to mind of its own accord. I think it means something like 'good luck', which I hope the fractal has. But how much luck can another image in the Mandelbrot set have? The rating of a 5 means I am neither pleased nor displeased with the image, the likes of which has been seen countless times before. To see the image copy this letter with a .par extension to your Fractint directory and run it like any parameter file. If the image does not appear in a few seconds, something is wrong. If something does go wrong or your machine has forgotten how to run DOS programs, see the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> Heat and humidity returned to Fractal Central on Saturday, with partly cloudy, hazy skies and a temperature of 93F 34C. The fractal cats took to the cool tile floor early in the day and slept there until evening. My day was about average, while FL spent a good part of the afternoon fretting about her flowers, which wilted in the heat. The next FOTD will be posted in 24 hours. Until then, take care, and pass the idle time with an interesting fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Break_a_Leg { ; time=0:00:01.21-SF5 on P4-2000 reset=2004 type=mandel center-mag=-0.1937408443716\ 891/+0.65434656770299990/8.5247e+012/1/-157/0 params=0/0 float=y maxiter=4200 bailout=6 inside=0 mathtolerance=0.05/1 colors=000KLjKMiKNhKOgKPfKQeKRdKScKTbKUaLV`MW_NXZO\ YYPZXL_WI_VE_UG_TI_SK_RM_QOYPQXOSVQUUJWTDYRI_PNaNS\ cLWaJ`ZHeWFiTDnQBsO9wIHoDPg8W_DYcI_gNakScnXeragvfi\ yhguierjcnkakm_gnYdoW`pVYdZbTagHdl6gq8ik9kfBmaCoXE\ pSFrNHtIIvDJw8Ls9MpANmAOiBQfBRcCS_CTXDUUDTXFS_GRaH\ RdJQfKPiLPlNOnONqPNsQUiN_`LfSJlJHrAFwN6U`X0mw8inGe\ fNaYVYQaVIZUJWTJUSJRRJOQJMPJJOJHNJEMJBLJ9KJ6JJ4IJE\ ELNAMOFPOJSPNUPRXQVZQZaRcdRgfSkiSokTsnTwpUtoVqoVoo\ WloXioXgoYdoYboZ_o_Xo_Vo`So`QobShdTbfVWgWQiXJkZDnZ\ 6oZ0pZ4qY8rXBsWFtVIuTMvTPwTTxSWyR_zQbwR`tSZqSXnSVk\ SThUSeUQbUO_TMXTKVSJTQERP9PO5NM8LLBJAEHAHFAKEANCAP\ BCSAEV9GY8I`7Kc6MhCOmIQrOSvUUzZVzcZzcczchzcmzcrzcv\ zeHUbGX`FZYEaWEcTDfRChOBkMBmPGkRLiTPgVUeXYcZba`f_b\ kYdoXamYZkZXi_Ug`SeaPcdR`hUcmchrmmvtrzzvzzzzzzz6zU\ IzGNzHRzIWzJ_zLdzMhzNmzOqzPvzQzzRxzTwzUvzVuzXtzYsz\ Zrz`qzapzbozdnzemzflzhkzi } END PARAMETER FILE=========================================

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FOTD 19-06-10 (Whatever Wherever [8])
by Jim Muth 19 Jun '10

19 Jun '10

FOTD -- June 19, 2010 (Rating 8) Fractal visionaries and enthusiasts: The expression behnd the parent fractal of today's image subtracts 1.4 parts of Z^1.5 from one part of Z^3.5 then adds straight C. This parent fractal consists of one large bay with four prominent lobes. Today's scene is located in a valley jutting into the interior of the northern lobe. A good part of the image consists of 'inside' stuff brought to life by the 'fmod' inside fill. The rest is made of the usual equal-iteration bands. In my opinion the image is well worth the rating of an 8. The name "Whatever Wherever" came to mind when I slipped into a spell of pondering the nature of reality. The calculation time of a little over 4 minutes is slightly slow, but the wait may be avoided by surfing out to the FOTD web site at: <http://www.Nahee.com/FOTD/> and viewing the finished image there. Lots of sun, reasonable humidity and a temperature of 84F 29C kept both cats and humans content here at Fractal Central on Friday. With the increasing heat, the cats returned to the coolness of the kitchen floor. The humans had more important things to do. The next FOTD will be posted in 24 hours. Until then, take care, and when I close my eyes, the world vanishes. Or is it only my mental image of the world that vanishes. If this is so, then all I have ever observed is a mere mental image of some- thing that can never be experienced directly and may bear no resemblance at all to my interior mental image of it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Whatever_Wherever { ; time=0:04:23.79-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident float=y center-mag=+0.59214677143/+0.289726274064/3.6e+007\ /1/82.5/0 params=1/3.5/-1.4/1.5/0/0/0/0 logmap=205 maxiter=1600 inside=fmod periodicity=6 colors=000000HR`JPKKN3MOFOPRQQbRQmSTnSVoTXoT_pTapU\ cqUerVhrVjsVlsWntWquXsuXuvXwzSzzNvzIrzDmz8hvDcrIZm\ MUhMTcMSZMRUMQUMPUMOUMNYMM_MLaLK_KJYJIWKIUMJSNMQPP\ OccMSVKccIV`GWcGYfGZiG`lGaoGVjFOfFIaEBYE5UE7XJ9ZOB\ `TDcYFebHgfLecKd`McYObVQ`SS_PUZNWYKYWH_VEaUBcT8cS6\ aVD_XKY_QPaXGcbJd`Me_PfZSgYVhXYiW`jVcjUeeSfaQhXPiT\ NjOLlKKmFInBHlFJjJLhNMfROdVQcZRabT_fVYjWWnYUr_Tv`V\ qaWmaXhbYdb__b`WcaRcbNddIdeEdf9eg5eh1ee5`c9W`DRZHM\ WLHUPCRT7PX3LYAHZGDZM9_S5`Y2`c8WYDRTIMOOHITCDY88XD\ AXICXMEXRGXVIX_KXdMXhOXmQXqRWrTVrUUsWTsXStZRt_QtaP\ ubOudNveMvgMvhSsgXqfbnegldmicrgbwebcvGirLnoQslVNm_\ 5HoJPkXWgjbcuXVvaXweZotPXQ6j_LgsTpnXQaTZcVgeXpgZ63\ tKEnYPik_d2isWiiPKx`Tolag9XoM`kZcgkfcbeCGLVATP5_Kc\ u9lstgercTq_GoW3nO9hGFc8LZ0RUATcKUmUVw8QUCOLGMCJL4\ aFLs9`6iCJaBVVAgO9sH8hKIYMRdYPkYWR`i6UbP_afd`PNufZ\ jWn3clCjkKqjS5`2JjPXiTH_d } 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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Slow Minibrots
by Roger Alexander 18 Jun '10

18 Jun '10

Another good ole boy of a minibrot. This little fella is sloooow so check out http://maxitersfractalfollies.blogspot.com for instant viewing. fract258.gif { ; your friendly neighbourhood minibrot ; blank ; calctime 1:59:08.22 ; created Jun 18, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=fotdv1.frm formulaname=fatlog center-mag=+1.15314064744049000/+0.73129742549128560/1380112/1/159.99999\ 9995470858/2.05330125749303427e-008 float=y maxiter=5000 logmap=209 cyclerange=0/255 colors=0vz0tz0rz0pz0nz0lz0jz0hz0fz0dz0bz0`z0Zz0Xz0Wz0Uz0Sz0Qz0Oz0Mz0Kz0I\ z0Gz0Ez0Cz0Az08z06z04z02z00z00y10x20v20u30s40r50p50o61n71l81k91i91hA1gB1\ eC1dC1bD1aE1_F1ZF1YG1WH1VI1TJ2SJ2RK2PL2OM2MM2LN2JO2IM2GJ2EH1CE1AC1891661\ 4312000201302504705806A07C19D19E1AF1AF1BG1BH1CI1DI1DJ1EK1FL1FL1GM1GN1HN1\ HO2IO2JQ2IT2HV2GY2E_2Da2Cd2Bf1Ai19k18m17p15r14u13w12z00z20z50z70zA0zC0zF\ 0zH0zK0zM0zP0zR0zU0zX0zZ0za0zc0zf0zh0zk0zm0zp0zr0zu0zw0zz0zw0zu0zr0zo0zl\ 0zj0zg0zd0za0z_0zX0zU0zS0zP0zM0zJ0zH0zE0zB0z80z60z30z00x01v02s03q04n06l0\ 7i08g19e1Ab1B`1CY1EW1FT1GR1HO2JN2IM2HK2GJ2FH2DG2CE2BD2AB19A1881771551441\ 3212000000101201202302403504604605705806906A07A08B08C19D19D1AE1BF1BG1CH1\ CH1DI1DJ1EK1FL1FL1GM1GN1HO2IN2KM2NK2QJ2TH2VG2YE2`D2cB1fA1i81l71n51q41t21\ w00z03z07z0Bz0Fz0Jz0Nz0Rz0Vz0Zz0bz0fz0jz0nz0rz0vz0zz0xz } frm:fatlog { ; by Jay Hill, 1998 c=log(pixel),z=0: z=sqr(z)+c |z|<=100 } Roger Alexander _________________________________________________________________ Turn down-time into play-time with Messenger games http://go.microsoft.com/?linkid=9734385

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FOTD 18-06-10 (Zippy the Minibrot [No Rating])
by Jim Muth 17 Jun '10

17 Jun '10

FOTD -- June 18, 2010 (No Rating) Fractal visionaries and enthusiasts: I spent almost no time on today's image. Most all day I was occupied with optimizing the fractal computer for the internet. But I did find a moment to dredge up an image that is just good enough to reach FOTD status. The parent fractal came about when I combined 0.1 part of Z^10 with 1 part of Z^1.5 and added straight C. This parent resem- bles a Mandelbrot set rotated about 180 degrees, with a large open area beyond its East Valley (in this case, West Valley) and a curly filament serving as its main stem. The image is located on this curly stem. The name "Zippy the Minibrot" refers to the extreme speed of the image, which at a mere 6 seconds, is one of the fastest of all time. Once again, I could not give the image an honest rating. The finished image is posted for all to see on the FOTD web site at: <http://www.Nahee.com/FOTD/> Partly cloudy skies, lower humidity and a temperature of 77F 25C made Thursday an ideal day here at Fractal Central. At least the fractal cats must have thought so. They deserted their cool spot on the kitchen floor and set up residence on the living room carpet. My day was average. Unless I get totally involved with the new computer arrangement, the next FOTD will be posted in 24 hours. Until then, take care, and see you soon. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Zippy_the_Minibrot { ; time=0:00:06.97-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident center-mag=+0.5547630297/-0.0077854361/190441/1/55\ /0 params=0.1/10/1/1.5/0/0/0/0 float=y maxiter=272 inside=0 logmap=17 periodicity=6 colors=000KH7GGmDFkAEh6De3Cb0BZ4EV7HRBJNEMHchBvz9m\ v8cr7dm7hh6mc6qZ5vU5zc5zeEeZMVRVLKbEPf7Ui1Zl9aeGc_\ NfTVhNakGhmAoo4rQ9tVMuZZvbktZerV_pRUoOPgIN_CLS6KQJ\ bOWuRYqU_nW`jZbg`ccce`efY_e`VdcQcfLbhRcfWce`cdedcj\ dbodahZdbTfWNhQHjJG`DGS7FI1F9EUHQgPauXxeljkiXpgJud\ 5zb4u_4pY3kV3gT2bQ2YO2UM9SPFRSLPUROXYM_cLaiJdoIfkO\ ggTgcYh_bhWgiSliOqjLvjXfOgR1OSD5SOARYEQgIPqMPzROrV\ NkZMdbLXfKQjJJhIPgIUfIZdHdcHibHndIofJohKojLplMpnNp\ oOpiG`c8LY05U14R13O12K22H21E20B20A61A919C19F18I28L\ 27O27R24IG29UBBQJDMRFIZHE`FCbEAdD8eC6FSvITpKUjNVdP\ WZRXTUYNWZHY_CUUDQPEMJFIEGHUIGiJGxKLwPQvTVuX_t`dsd\ hrhUqkFpm0oo8RdG3UK3XO3_S3bW3d_3gc3jg3mj3olGfmSYnc\ QphDrl1ifB``KTVTj9OV6GF38rUdRFK8x86h64U42F2CUg6FMz\ FKeADL56oOmbI`QCPD6Catav`ogRbTIQE9D`6DO48C24DDxSdD\ _izOUeCFLnqd8HP6CI48C24629t16e14S02EARp7Kb5DQ26DkG\ 6NmdayjSiZJVN9FB63U42M31F } 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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RSS feed added for FOTD script
by Richard 17 Jun '10

17 Jun '10

I added an RSS feed for my nightly FOTD script that's been running for a while now. Sometimes the newest images added aren't the ones that have the most recent FOTD date. Now you can use the RSS feed to see what's been added over the past 30 days. <http://www.xmission.com/~legalize/fractals/fotd/fotd-rss.xml> -- "The Direct3D Graphics Pipeline" -- DirectX 9 draft available for download <http://legalizeadulthood.wordpress.com/the-direct3d-graphics-pipeline/> Legalize Adulthood! <http://legalizeadulthood.wordpress.com>

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Symmetrically Hot
by Roger Alexander 16 Jun '10

16 Jun '10

Contrasting with the June 13 post this fractal is symmetrical both inside and outside. The hot-hot-hot palette itself contrasts with the cold wet weather we're having up here. And speaking of contrasts go to http://maxitersfractalfollies.blogspot.com to compare the satisfaction of instant viewing with the delay of calculation from a par file. fract255.gif { ; symmetrical all over ; blank ; calctime 0:06:50.51 ; created Jun 16, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_t.frm formulaname=tsept_rjr_3 function=floor/cotan center-mag=-1.19904e-014/6.21725e-015/0.1712413 params=0.7978453932309947/-0.6339609973448898/-1.157170323801386/0.98809\ 7781304361 float=y maxiter=1500 inside=0 invert=4.23167500735944/0/0 periodicity=0 cyclerange=0/255 colors=000000000000000000000000000000000100100200400500700900B00D00G00I0\ 0L00O10Q10T10W10Z10a10e10h20k20o20r20v20y20z30z50z60z80z90zB0zC0zE0zF0zH\ 0zI0zK0zL0zN0zO0zQ0zR0zT0zU0zW0zX0zZ0z_0za0zb0zd0ze0zg0zh0zj0zk0zm0zn0zp\ 0zq0zs0zt0zv0zw0zy0zz1zz3zz4zz6zz7zz7zy7zx7zx7zw7zv7zv7zu7yt7ys7ys7yr7yq\ 6yq6yp6yo6yo6xn6xm6xl6xl6xk6xj6xj6xi5xh5wh5wg5wf5we5we5wd5wc5wc5vb5va5va\ 5v`4v_4vZ4vZ4vY4vX4uX4uW4uV4uV4uU4uT4uS3uS3uR3tQ3tQ3tP3tO3tO3tN3tM3tL3sL\ 3sK3sJ2sJ2sI2sH2sH2sG2sF2rE2rE2rD2rC2rC2rB1rA1rA1r91q81q71q71q61q51q51q4\ 1q31p20p20o20n20m20m20l20k20j20j20i20h20g20g20f20e20d20d20c20b20a20a20`2\ 0_20Z20Z20Y20X20W20W20V20U20T20T20S20R20Q20Q20P20O20N20N20M20L20K20K20J2\ 0I20H20H20G20F20E20E20E20D20D20C20C20C20B20B20A20A20A2092092092082082072\ 0720720620620520520520420420420320320220220220120120010 } frm:tsept_rjr_3 {; blank ; Mutated rjr y2k04 z = fn2(p2)/pixel, zp1 = zp2 = (0,0), huge = 1.0e32: temp = z+pixel z = z*z - zp2 zp2 = zp1 zp1 = p1/fn1(p2) (|zp1| <= 64) && (|z| <= huge) ;SOURCE: noel.frm } Roger Alexander _________________________________________________________________ Look 'em in the eye: FREE Messenger video chat http://go.microsoft.com/?linkid=9734386

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FOTD 17-06-10 (Undekatic Mystery [6.5])
by Jim Muth 16 Jun '10

16 Jun '10

FOTD -- June 17, 2010 (Rating 6.5) Fractal visionaries and enthusiasts: I think the end is near for my 15-year association with AOL. I have had it with the unending flood of trendy pop stuff that slows things down to a crawl with a dial-up connection. Earlier today I tried accessing Earthlink through the built-in network- ing ability of XP. It worked great. What a pleasure it was to go directly to the destination, be it e-mail or web site, even on dial-up, without passing by the countless ads etc. the ISP throws at you. Today's image lies rather deep in a kind of East Valley of its parent fractal. This parent fractal is little more than a cluster of overlapping order-11 Mandeloids, arranges with a vague resemblance to the Mandelbrot set. I named the image "Undekatic_Mystery", assuming that this is the proper term for order-11 stuff. I rated it at a 6.5, not a little bit of which is earned by the extra effort I put into the coloring. I could just as easily have named the image something like 'missing elephants'. Though the image lies right in the center of the East Valley area of its parent, no elephants at all are visible in the scene. Nothing remains but their merging spiral- ling trunks. The calculation time of 1-5/6 minutes is speedy enough for near- instant gratification. For totally instant gratification, see the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> Clouds hung tough here at Fractal Central on Wednesday, while the temperature remained around a very humid 75F 24C. Cassie, the small gray fractal cat, had a good day. Nicholas, the over- sized 17-pound black cat, had a bad day. It was the day for his visit to the doctor, and both FL and I are sporting various and sundry cuts and scratches from the battle to get him into the carrying box. He passed inspection with flying colors however. Otherwise, the day went reasonably well. It's looking more and more like I'll soon have the fractal dedicated machine on a DSL line. The next FOTD will be posted in 24 hours. Until then, take care, and start each day with a clean slate. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Undekatic_Mystery { ; time=0:01:50.88-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=+0.46128270044467/-0.00113594365883053/\ 3.806838e+011/1/97.5/0 params=11/111/1111/0 float=y maxiter=1500 inside=0 logmap=163 symmetry=none periodicity=6 mathtolerance=0.05/1 colors=000rIgqKepMdoOcnQamS`lU_kWYjYXi_WhaUgcTfeSe\ gRdiUchWbgVbfUaeU`dU_cU_bUZaUY_UXYUXWUWUUVSUVQUXOU\ YMUZJU_IU`HUaGUbFUcEUcDUcCUdBUdAUdAUdAUeCPeEKeGFeI\ AgKAiMDjPEkSGlVImYKi`LfcMbfO_iQWlSTmU`nVhoWjpXkpXl\ nXmlXojWphWqeWrcWtaVu_VvYVwWVxUVvVUuWTtXSrYRqZQp_P\ o_Pm`OlaNkbMicLhdKgeJeeJdcIbaH`_HYYGVWFSUFPSEMQDKO\ DFMCAKC7IDALECOFFRGHUHKXIN_JPbJSeKUhLXkM_nNaqOdtPf\ vPdsQcnQbhQadQ`_Q_WQYSRXNRWJRVERUART6RR8NQ9KOBGNCD\ MDAKF6JG3IH0HL5HO9HRDHVHGYLG`PGdUGgYFjaFneFqiFtmFw\ qMksT_t_PufDvl2wd5qY8lQBgJEbCGeFKhHOmKSrMYvOczRizT\ lzVozcrzcvzczzczzczzczzczzczzczzczz`yhYufWqdTmbQi`\ NeZLcXIaVF_TCYRAWQ9VR8US7UT7TT6SU5SV4SW4SW9RVDQVHQ\ VLQUPRUTRUXRT`STdRThRTjRTlRTnRTpRTrRTtRTuRTqVZnYdk\ aigdodhuakzbnybqxcswcuvdwudytezsezrfzqfzpgzogzoizl\ jzikzflzdmzanzZozXpzUqzRrzOszMtzJuzGvzEYzRAzcBzbBz\ bBzbBzatzsuzuuzpuzktziszh } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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experimental fotd feed
by Richard 16 Jun '10

16 Jun '10

<http://www.xmission.com/~legalize/fractals/fotd/test/index.html> Yes, there are gaps. xfractint doesn't always succeed in rendering. Comments? -- "The Direct3D Graphics Pipeline" -- DirectX 9 draft available for download <http://www.xmission.com/~legalize/book/download/index.html> Legalize Adulthood! <http://blogs.xmission.com/legalize/>

7 15

FOTD 16-06-10 (Things and Things [?])
by Jim Muth 15 Jun '10

15 Jun '10

FOTD -- June 16, 2010 (Rating ?) Fractal visionaries and enthusiasts: After seeing what AOL did to the 2 FOTD's that I tried to send in text format, I have decided to forget that has-been and over- priced ISP, and stick with Earthlink (aka Mindspring). I am currently having problems getting the Earthlink software, which I downloaded, to run properly on the new machine, but if I have no luck in a day or so, I'll forget the software and access Earthlink directly through the built-in networking ability of Windows XP. I might do this anyway. I think I would appreciate not seeing all the advertising. As for today's image, it's a quick one, though no bargain. Not wanting to embarrass myself, I declined to give it a rating. The name "Things and Things" is the best I could think of. I might also have intended a comment about the names of several unbearably trendy 'country gift' shops in town. When I first saw today's image, I saw only a sea of featureless chaos. But a bit of color tweaking brought out vague shapes in the chaos. Today's subtle, pastel-tinted image shows every bit of stuff the image has in it. The calculation time of 1-1/2 minutes is brief enough so that nothing will have been wasted if the image disappoints. And even this brief calculation time may be avoided by viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> Near-normal mid-June weather was the rule here at Fractal Central on Tuesday. Normal conditions mean partly-cloudy skies with a temperature of 82F 28C, which is exactly what we had. The fractal cats were also near normal, which means they spent most of the day stretched out on the kitchen floor. With the computer situation coming under control, but not yet quite there, my day was a bit hectic, but another day or so should see peace once more prevailing. The next FOTD will be posted in 24 hours. Until then, take care, and walk on the trendy side. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Things_and_Things { ; time=0:01:31.67-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-1.124216189194/-0.018694435832/1100000\ /1/32.5/0 params=-2.5/25/0/0 float=y maxiter=1500 inside=0 logmap=123 periodicity=6 colors=000gYIgYIfYHeYHdYGdYGcYFbYFaZEaZE`ZD_ZDZZCZ\ ZCYZBXcBWcAUbBWcAXcAYcAZcA_d9ad9bd9cd9de8ee8fe8he8\ ie8zzzzz7zzzzz7zzzzz6zzzzz6zz5zzzzz7zz8zzzzzAzzAzz\ zzrAzrAzrAzrFzrFzrGzmHzmIzmJzgKzgKzgLzgMwfNzfOzfPm\ ePmeQmeRmdSmdTmdUmdUmcVmcWmcXmbYmbZmUKmUKmUKmUKmUb\ 0UKmUc0UKmUe0UKmUgmUK0UfmUK0Ue0UKmUd0UKmUc0UKcYbcX\ KcXacXKcX_cXKcWZcWKcWYcWKUWXUVXUVWUVWUVVUVVUUUUUTU\ UTUUSmTmUTRUTRUTQUTQUSPUSPeSOeSNdSNcRMcRMbRLaRLaRK\ `QK_QJ_QJZQIZQIYRHYRHYSHYSHYSGXTGXTGXTGXUGXUFXVFWV\ FWVFWWEWWEWWEWXEVXEVYDVYDVYDVZDVZDUZCU_CU_CU_CU`BT\ `BTaBTaBTaBTbATbASbAScASc9Sd9Sd9Sd9Rz9ze8Rz8zf8Rz8\ zf8Qz7ze7Qz7zd7Pz7zc7Oz7zb7Oz7za7za7Na7M`7z`7M_7L_\ 6z_6LZ6KZ6zY6KY6JY6zX6JX6JW6zW6nPPoOQpNRqWTrWUsWVt\ WXuWYvWZvW`weaxebyedzeezefzehzrizrjzrizrhzrgzrfzre\ zrdzrdzrczrbzrazr`zr_zr_zrZzrYzrXzrWzrVzrVzrUzrTzr\ SzrRzrQzrQzrPzrOzrNzrMzrL } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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Return of Tdis - The Sequel (Part 2)
by Roger Alexander 15 Jun '10

15 Jun '10

More scaly veggieness. Well if not exactly veggie it's certainly green which brings me to my final point - three cheers for tdis! Speaking of three cheers celebrate the convenience of the internet and view the completed fractal at http://maxitersfractalfollies.blogspot.com fract256.gif { ; tdis scales ; blank ; calctime 0:13:08.23 ; created Jun 15, 2010 ; Fractint Version 2004 Patchlevel 9( reset=2004 type=formula formulafile=_m.frm formulaname=mand2_zdif center-mag=+0.08868716627491702/+0.63494407427012580/245.142 params=0/0/3000/0 float=y maxiter=1500 inside=0 outside=tdis colors=000lz5lz5kz5kz5kz4jz4jz4iz4iz4iz4hz3hz3hz3gz3gz3gz3fz2fz2fz2ez2ez\ 2dz1dz1cz1bz1ay1`y1_y1_x1Zx1Yx1Xw1Ww1Vw1Uv1Uv1Tv1Su1Ru1Qu1Pt1Ot1Ot1Nt1Ms\ 1Ls1Ks1Jr1Ir1Ir1Hq1Gq1Fq1Ep1Dp1Cp1Co1Co1Cn1Cn1Cm1Cm1Cl1Bk1Bk1Bj1Bj1Bi1Bi\ 1Ah1Ag1Ag1Af1Af1Ae19e19d19c19c19b19b18a18a18`18_18_18Z17Z17Y17Y17X17W17W\ 16V16V16U16U16T16S15S15R15R15Q15Q15P14O14O14N14N14M13L03L03M03M03N04N04O\ 04O04P05Q05Q05R05R06S06S06T06T07U07V07V07W07W08X08X08Y08Y09Z09_09_09`0A`\ 0Aa0Aa0Ab0Bc0Bc0Bd0Bd0Ce0Ce0Cf0Cf0Cg0Dh0Dh0Di0Di0Ej0Ej0Ek0Ek0Fl0Fm0Fm0Fn\ 0Gn0Go0Go0Gp0Hq0Iq0Jr0Kr0Lr0Ms0Ns0Ns0Ot0Pt0Qt0Ru0Su0Tu0Tu0Uv0Vv0Wv0Xw0Yw\ 0Zw0Zx0_x0`x0ay0by0cy0dz1dz1ez1ez1fz2fz2gz2gz2hz3hz3iz3iz3jz4jz4kz4kz4lz\ 5mz5mz5nz5nz6oz6oz6pz6pz7qz7qz7rz7rz8sz8sz8tz8uz9uz9uz9tz9tz9tz9sz9sz8sz\ 8rz8rz8rz8qz8qz7qz7pz7pz7oz7oz7oz6nz6nz6nz6mz6mz6mz5lz5 } frm:mand2_zdif(XAXIS_NOIMAG) { ;p2 is the bailout (default=127) b=p2,b=b+(b==0)*127 z=j=c=pixel: k=z z=z*z+j*c-p1 j=z-k |z|<b ;SOURCE: mandhack.frm } Roger Alexander _________________________________________________________________ Look 'em in the eye: FREE Messenger video chat http://go.microsoft.com/?linkid=9734386

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FOTD 14-06-10 (Pint-Sized Quartic [8])
by JimMuth＠aol.com 15 Jun '10

15 Jun '10

FOTD -- June 14, 2010 (Rating 8) Fractal visionaries and enthusiasts: This is a test to see how well AOL works with the FOTD. Today's blindingly fast image is surprisingly simple, yet it delivers more than seems possible in a mere 10 seconds. In fact it is one of the best quartic minibrots I have ever seen. The parent fractal is a Mandelbrot set caught well along the way of morphing into the Z^4+C Mandeloid. Today's image lies quite deep on the negative X-axis of the parent fractal. The rating of an 8 is justified. Though the image is little more than a quartic minibrot with radiating arms, it has a certain something that sets it apart from the crowd. The name "Pint-Sized Quartic" is a play on words that refers to the unusually large magnitude of the image and the corresponding small size of the minibrot. The calculation time of 10 seconds hardly seems possible, but this is how fast the image runs on my optimized, fractal-dedica- ted 2000mhz computer. The trip to see the finished image on the FOTD web site at: <_http://www.Nahee.com/FOTD/_ (http://www.Nahee.com/FOTD/) > will take a bit longer, but the minor hassle of setting up and running the parameter file will be eliminated. A mix of clouds and sun, oppressive humidity and a temperature of 88F 31C made things pretty uncomfortable here at Fractal Central on Sunday. A brief but heavy rain shower just after noon added to the unpleasantness. The fractal cats suffered no unpleasantness however as they passed the day sleeping on the cool floor. My day was about average; the same is true for FL. Unless something goes wrong, the next FOTD will be posted in 24 hours. Until then, take care, and after the world ends, will the Mandel- brot set still exist? Jim Muth _jamth(a)mindspring.com_ (mailto:jamth@mindspring.com) _jimmuth(a)aol.com_ (mailto:jimmuth@aol.com) START PARAMETER FILE======================================= Pint-Sized_Quartic { ; time=0:00:10.26-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip center-mag=-1.188028881200462/0/4.56327e+011/1/180 params=4/-4/0/0 float=y maxiter=1500 inside=0 symmetry=xaxis periodicity=6 mathtolerance=0.05/1 colors=000dKdoMzlKoiIdgGUdEJnZvbD8_IAYNBVSCTWEQ`FO\ eGDj1MiHZvaXq_WmYUiW7Ni7V2WfRTeVQdZNcbLcfIbjFanC`r\ 4cyA`vGZtMXrSVoYTmmOPiPXfQcbRkdSxbRvaRt8BaAEcCGeEI\ gGKiKMkOOmSRoWWo_`qcfsgoulyzzzzyszuovqirncmjYhfRcc\ La_F_U2LU6SX9YTCUU7UUBcQFiGJoRPz8Uz7Zz7cz7hz7mzNYh\ KYeaZeKZdaZdKUdaUdKUcaUcKUcaUcKUbaUbKUbaUbKUammamm\ ammamm`mm`mm`mm`mm_mm_mm_mm_mmZmmZmmZmmZmmYaeYaeYa\ eYaeXafXafXafXafWagWagWagWagVagEahVahVahVzhUziUziU\ ziUziTzjTzjTzjTzjSzkSzkSzkSzkRzkRzlRzlRzlQzmVzmWzm\ WzmWzmYzmRzmKzmPzmUzmZzmczmwzmrzmmzmh_mz_mz_mz_mza\ mzbmzcmzdmzemzfmzumzgmzUmzGmz2mz3mz4mz5mz6mz7mzomz\ omz5mz7mz9mzBmzDmzFmzHmzMmzKmzImzGzPCzIDzNEzSFzXGz\ a5ztHzeSzSoz4hz9bzEXzJRzOIzRKzTNzVPzWSzYUz_5z8EzIN\ zRWz`jzegzgezhczi`zjZzkTzwXzl_zaczRozJfzHZzGRzFGza\ JzEPzGUzI_zKdzMjzOozQiz4tzRlzTezVmzmZzXEzTHzPJzLLz\ HNzEPzARz6Tz3WzGYzTUzf_ze } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

3 2

Blue Scales
by Roger Alexander 14 Jun '10

14 Jun '10

What to call these structures? I call 'em scales, Jim Muth calls 'em terraces. It is my suggestion that someone go to the expense and bother of convening an international conference on standardizing fractal graphic nomenclature. I'd volunteer but I'm quite busy at the moment. Until then I'll have to make it up as I go along. As I am a creature of habit I have posted the completed fractal at http://maxitersfractalfollies.blogspot.com fract257.gif { ; remix ; blank ; calctime 0:12:34.07 ; created Jun 14, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=fotdv1.frm formulaname=contest4a center-mag=-1.45759282649133000/+0.00712563729151517/5934.286/1/90/3.885\ 78058618804789e-016 params=-1.194830164494766/-0.1142918179876095/4000/0 float=y maxiter=4000 inside=0 outside=tdis colors=00048F49F59G5AH5AI5BJ6BK6CK6CL6DM7DN7EO7EP7FP8FQ8GR8GS9HT9HU9IUAI\ VAJWAJXBKXBKYBLYCLZCMZCM_DN`DN`DOaDOaEPbEPbEQcFQcFRdFReGReGSfGSfHTgHTgHU\ hIUiIViIVjIWjJWkJXkJXlKYlKYmLZnLZnM_oM_oM`oN`pNapOaqObqPbrPcrPcrQdsQdsRe\ tRetRftSftSgtTguThuUhuUivVivVjvVjvWkwXkwYlwYlwZmxZmx_nx_nx`ox`oxapyapybq\ ybqycrydryesyeszftzgtzhuzhuzivzjvzkwzmwznxzpxzqyzryzuzzuzzryzqyzoxznxzmw\ zkwzjvzivziuzhuzgtzftzfszesydrycrybqybqyapyapy`ox_ox_nxZnxZmxYmwYlwXlwXk\ wWkwVjvVjvVivVivUhvUhuTguTguSfuSftRetQesQdsQdrPcrPcrObqObqOapNapN`oN`oM_\ nM_nMZmLZmLYlLYlKYlKXkJXkJWjJWjIViIViIUhHUhHTgHTgGSfGSfFRfFReFQdFQcEPcEP\ bEObDOaDNaDN`CM_CM_BLZBLZBKYAKYAJXAJWAIV9IU9HU9HT8GS8GR8FR8FQ7EP7EO7DN7D\ M6CL6CL6BK6BJ5AI5AH59G59G48F48E47D37C36B36A35A25924824723613512412411301\ 200100000101211312412413523624724825935936A36B37C47D48E } frm:contest4a {; Kerry Mitchell (variable bailout by JM) ; formulaname appended to "a" to differentiate from ; previously posted contest4 formula ; slightly optimized version of Contest formula z=p1, c=pixel: z2=sqr(z), z=z*z2+c*(1+z-z2), |z| <= p2 } Roger Alexander _________________________________________________________________ Game on: Challenge friends to great games on Messenger http://go.microsoft.com/?linkid=9734387

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FOTD 15-06-10 (Cranky Calculation [No Rating])
by JimMuth＠aol.com 14 Jun '10

14 Jun '10

FOTD -- June 15, 2010 (No Rating) Fractal visionaries and enthusiasts: Things were rather disorganized here at FC on Monday, as we shifted things to different machines. For some reason, the new fractal machine will not connect to mindspring, which explains why I am sending this through my AOL address. The problems are being solved one at a time however, and within a day or two, we should be up and running on the same old schedule. But another big change is not far off. I am putting the fractal dedicated unit on a DSL line, most likely with a new URL address. As for today's fractal, I doubt that it's worth a rating. The image is a simple minibrot in a valley of one of the Z^(1.7)+C parent fractals. I named it "Crabby Calculation", which rather describes my mood after fighting with disobedient computers all day. The image, for all its worth, fails to earn a rating, but with its calculation time of 2-1/2 minutes, not much will be lost if the image fails to satisfy. Calculation may be avoided by viewing the finished image on the FOTD web site at: <_http://www.Nahee.com/FOTD/_ (http://www.Nahee.com/FOTD/) > With a temperature of 84F 29C and reasonable humidity, Monday was fairly pleasant here at Fractal Central. Too many clouds kept it from being an outstanding day however. The next FOTD will be posted in 24 hours. Hopefully, by then I'll be back in the familiar fractal routine. But if no image appears, it will be a sign that we ran into more computer problems. P.S. The fractal cats had a sulky day. They didn't like all the disorganization. Jim Muth _jamth(a)mindspring.com_ (mailto:jamth@mindspring.com) _jimmuth(a)aol.com_ (mailto:jimmuth@aol.com) START PARAMETER FILE======================================= Crabby_Calculation { ; time=0:02:34.77-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=floor center-mag=-0.058531449501/+0.648142658462/2264403 params=1.7/0/19/0 float=y maxiter=7500 inside=0 logmap=206 periodicity=6 colors=000yFYwJWvKVuKUtKSrKRqKQpKOoKNnKPmKSlKVkKYk\ L`kNckPckRbkSakU_kWZkXYjXXjXVjWUjVTjUSjTQhSPfRSdQT\ bPU`QVZRWXSXVUYTVZRW_PX`NYaLZbJ_cKaeKbfKcgKdhKeiKf\ jKgkKhlKimJjlIjlHkkHkkGkjFljFliEliDmhDmhCmhBngBngA\ oh9om9or8pv7pz7pv6qr5qm5qh6od7me8lf9jfAigBghCfhDdi\ EcjFajG`jHZkIXlJWmKYnL_nMaoNcpOepNgqMirLjrKkm_jhXi\ cUhZRgUOfPLeKQdFTgBXjC_lEcmF_mGWlYYmV_mTalRbkPdjNf\ iLhhKigKjfKkeKldKmcOmbNlaMl`Nl_NkZMkYMkXMjYLjXKkWK\ kVJlUIlTHmSOlRNlQMlTMkWLkZLkaKjeJjhJjkIinIhmKglKfk\ KejKdiKchKcgKcfKceKccKZZKUUKPPKKLJ90EB3FD6FF9FHBFI\ EFKHFMJFOMGPPGRSGTUGVXGW_GYaG_dHagHbjHdlHfoHhrHl7M\ QHzTMtVQoXVjZZeac`cgWelRgpMJdyMnxOouPosQopSpnTpkUp\ iWqfXqdYqb_r_`rYarVcsTdsQesOgtLhtJltZktYktXktWktVk\ tVktUktTjtSjtRjtRjtQjtPjtOjtOjtNiuMivLiwKixKiyJizI\ izH8z9AzACzADzAFzBGzBIzBKzCLzCNzCOzDQzDRzDTzEVzEWz\ EYzFZzF`zFbzGczGezGfzHhzH } 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=========================================

1 0

Six Fold Almost Symmetry
by Roger Alexander 13 Jun '10

13 Jun '10

Symmetrical on the outside, asymmetrical on the inside. I'm sure there is some profound meaning in that observation.If I try hard enough I'm sure I can work in "duality" or "dichotomy". Ready for viewing at the usual suspect http://maxitersfractalfollies.blogspot.com frac254.gif { ; symmetrical,not symmetrical ; blank ; calctime 0:07:26.43 ; created Jun 13, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_rc2.frm formulaname=Carr2075 center-mag=-4.44089e-016/2.22045e-016/0.8912656 params=0/0/0/0/0/0 float=y maxiter=1000 colors=000000000000000000000000000000000100100200400500700900B00D00G00I0\ 0L00O10Q10T10W10Z10a10e10h20k20o20r20v20y20z30z50z60z80z90zB0zC0zE0zF0zH\ 0zI0zK0zL0zN0zO0zQ0zR0zT0zU0zW0zX0zZ0z_0za0zb0zd0ze0zg0zh0zj0zk0zm0zn0zp\ 0zq0zs0zt0zv0zw0zy0zz1zz3zz4zz6zz7zz7zy7zx7zx7zw7zv7zv7zu7yt7ys7ys7yr7yq\ 6yq6yp6yo6yo6xn6xm6xl6xl6xk6xj6xj6xi5xh5wh5wg5wf5we5we5wd5wc5wc5vb5va5va\ 5v`4v_4vZ4vZ4vY4vX4uX4uW4uV4uV4uU4uT4uS3uS3uR3tQ3tQ3tP3tO3tO3tN3tM3tL3sL\ 3sK3sJ2sJ2sI2sH2sH2sG2sF2rE2rE2rD2rC2rC2rB1rA1rA1r91q81q71q71q61q51q51q4\ 1q31p20p20o20n20m20m20l20k20j20j20i20h20g20g20f20e20d20d20c20b20a20a20`2\ 0_20Z20Z20Y20X20W20W20V20U20T20T20S20R20Q20Q20P20O20N20N20M20L20K20K20J2\ 0I20H20H20G20F20E20E20E20D20D20C20C20C20B20B20A20A20A2092092092082082072\ 0720720620620520520520420420420320320220220220120120010 } frm:Carr2075 {; Modified Sylvie Gallet frm. c=pixel-conj(0.10/pixel)-flip(0.010/pixel) z=pixel*sqr(pixel)-sqr(conj(0.10/pixel))-(flip(0.010/pixel)) compt=0, limit=real(p1/(1/cos(pixel/5))), bailout=4 cinv=p2/(z+p3) p=(-0.743380900000982,-0.131850030300002): test=(compt<limit) c=c*test+p*(1-test) z=z*z+c compt=(compt+1) |z|<=bailout ;SOURCE: 42bcarr.frm } Roger Alexander _________________________________________________________________ Game on: Challenge friends to great games on Messenger http://go.microsoft.com/?linkid=9734387

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FOTD 23-05-10 (Wretchedly Colorful [7])
by Jim Muth 13 Jun '10

13 Jun '10

FOTD -- May 23, 2010 (Rating 7) Fractal visionaries and enthusiasts: Today's super brilliant image is also super fast, calculating in an unbelievable 8 seconds. It is also a rather good image, well worth the minor task of setting up this letter as a parameter file and running it in Fractint. The parent fractal was created with the FinDivBrot-2 formula. It appears as a Mandelbrot set surrounded by rings of rather interesting extra stuff, which were created by the Z^(-10) in the iterated expression. Today's scene lies at -6.2 on the negative X-axis, rather deep in some of the rather interesting extra stuff. The rating of a 7 is not bad, especially for an image that comes about with almost no effort. I thought of the name "Wretchedly Colorful", while I was still working on the colors. Since then I have gotten the colors good enough to meet FOTD standards, but the name shall remain forever. Viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> will eliminate a bit of computer work, but it could hardly shorten the 8-second wait to see the finished image. Lots of clouds marred the sky here at Fractal Central on Saturday. But the temperature reached 73F 23C and it stayed dry all day, so I guess the day ended up a success. The most mentionable event here at FC on Saturday was when FL suggested that we go on Facebook and I disagreed. When she replied that everyone is doing it, I told her that this is a good reason not to. People get ahead in the world when they do what everyone else is NOT doing, not when they join the crowd like a flock of sheep. Then she told me that with all the stuff I write in my FOTD discussions, we might as well be on Facebook. This might be true, but not nearly as many on Facebook have been writing daily discussions about fractals for over 13 years. The fractal cats purred agreement. The next FOTD will be posted in 24 hours. Until then, take care, and the cognitive scientist tells me that I have a brain. The priest tells me that I have a soul. The mystic tells me that I have a spirit. But what is the "I" that possesses all these things? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= WretchedlyColorful { ; time=0:00:08.30-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip inside=255 center-mag=-6.238184136922903/0/1.7683e+011 float=y params=-10/1000000000/100/0 maxiter=300 logmap=35 symmetry=xaxis periodicity=6 mathtolerance=0.05/1 colors=000TelYjqdvxmzzporjfdngVlXLdQJWTH3IFZHD7EOA\ 00CKQENWGQbIThKWoMYuLTtLOsLJrLEqL9qPDpSGpWJoZMobQo\ eTniWnlZniZmfZldZkaZj_Zi`ah`dgaggajfbmeboeOgfA_gNg\ g_ogkwgzskkpozmskjvzmobpizscUuYzuYUuXzuXUuXzuWUuWz\ uWUuWzuVUuVzuVUuUzuUUuUzuUUuTzuTTuJzuTUuSzuSUuSzuS\ UuRUuRUuRUuQUuQUuQUuQUuPUuPUuPUuOUuOUuOUuOUuNUuNUu\ NUuMUuMUuMUuMUuLUuLUuLUuKUuKUuKqzNpzMpzMpzMozMozMo\ zMnzMnzMnzMmzMmzMmzMlzMlzMlzMkzMkzMkzMjzMjzMjzMizM\ izMizMizMhzLhzLhzLgzLgzLgzLfzLfzLfzLezLezLezLdzLdz\ LdzLczLczLczLbzLbzLbzLazLazLazLazL`zK`zK`zKhzJizOi\ zSjzWjz_hzXgzUezSdzPbzNazK`zI2zuAzpIzlQzhXzcdz_lzW\ szSrzVrzXqz_qzapzdyzgtzfpzflzfhzfcze_zeWzeFzhMzfSz\ eZzddzbkzaqz`MzfZzckzawz_xzIszLnzNjzQezShzZdzWazUZ\ zSWzQSzOPzMMzKpz8_zDJzIAzk7zb4zU2zM3zP4zR4zT5zV6zX\ xzuXzi6zZDzSKzL`z9RzE3zE8zGDzIIzJNzLSzNbzEXzOSzYMz\ gHzqCzzHzrMzkRzdWzY8zjzzz } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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The Friendly Minibrot
by Roger Alexander 12 Jun '10

12 Jun '10

Today's fractal is another nomadic minibrot, waiting to be adopted at http://maxitersfractalfollies.blogspot.com. fract253.gif { ; the wandering minibrot ; blank ; calctime 0:17:54.18 ; created Jun 12, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_m.frm formulaname=Mandel_alt passes=1 center-mag=-1.41413466833541900/+0.00000000000000000/1666667 float=y maxiter=1500 inside=0 proximity=1 outside=fmod colors=000000000000000000000000jvzivziuzhuzgtzftzfszesydrycrybqybqyapyap\ y`ox_ox_nxZnxZmxYmwYlwXlwXkwWkwVjvVjvVivVivUhvUhuTguTguSfuSftRetQesQdsQd\ rPcrPcrObqObqOapNapN`oN`oM_nM_nMZmLZmLYlLYlKYlKXkJXkJWjJWjIViIViIUhHUhHT\ gHTgGSfGSfFRfFReFQdFQcEPcEPbEObDOaDNaDN`CM_CM_BLZBLZBKYAKYAJXAJWAIV9IU9H\ U9HT8GS8GR8FR8FQ7EP7EO7DN7DM6CL6CL6BK6BJ5AI5AH59G59G48F48E47D37C36B36A35\ A25924824723613512412411301200100000101211312412413523624724825935936A36\ B37C47D48E48F49F59G5AH5AI5BJ6BK6CK6CL6DM7DN7EO7EP7FP8FQ8GR8GS9HT9HU9IUAI\ VAJWAJXBKXBKYBLYCLZCMZCM_DN`DN`DOaDOaEPbEPbEQcFQcFRdFReGReGSfGSfHTgHTgHU\ hIUiIViIVjIWjJWkJXkJXlKYlKYmLZnLZnM_oM_oM`oN`pNapOaqObqPbrPcrPcrQdsQdsRe\ tRetRftSftSgtTguThuUhuUivVivVjvVjvWkwXkwYlwYlwZmxZmx_nx_nx`ox`oxapyapybq\ ybqycrydryesyeszftzgtzhuzhuzivzjvzkwzmwznxzpxzqyzryzuzz } frm:Mandel_alt { ;(c) 1993 by: ; ; LRCMIKE(a)LRC.OLDSCOLLEGE.AB.CA ; ; Michael G. Wareman ; P.O. Box 1856 ; Olds, Alberta, Canada ; T0M 1P0 z = c = pixel: z = z * z + c |z - pixel| < 4 ;SOURCE: frame.frm } Roger Alexander _________________________________________________________________ Look 'em in the eye: FREE Messenger video chat http://go.microsoft.com/?linkid=9734386

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FOTD 13-06-10 (Least Likely Fractal [6])
by Jim Muth 12 Jun '10

12 Jun '10

FOTD -- June 13, 2010 (Rating 6) Fractal visionaries and enthusiasts: Today's image takes us back to the tiny parent fractal of the FOTD image for June 7, where we check into a valley in the degen- erate bud on the northeast shore line of the main bay. Like the minibrots in that image of 6 days ago, the order of the minibrot at the center of today's image is ambiguous. At first glance, the elements around the minibrot appear to be arranged in the expected quadratic 2,4,8... series, but the image is filled with discontinuities, which totally confuse things. The rating of a 6 means I consider the image to be just a little above FOTD average. The name "Least Likely Fractal" means nothing at all, since it gives no hint of what the fractal is least likely to be. The calculation time of 10-1/2 minutes is somewhat slow by FOTD standards, but the wait may be avoided by viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> Things turned a bit too warm here at Fractal Central on Satur- day, as the temperature reached 91F 33C. The fractal cats ignored the heat and passed the day on the cool floor in the kitchen. My day was another uneventful one. The next FOTD will be posted in 24 hours. Until then, take care, and keep cool. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= LeastLikelyFractal { ; time=0:10:37.74-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=+0.00994432744737835/+0.010338677909109\ /1.384924e+012/1/-150/0 params=1.99/-0.95/1000/0 float=y maxiter=22500 inside=0 logmap=960 periodicity=6 mathtolerance=0.05/1 colors=000K`IK`HKaHKaIKbJKbKKcKKdLKeMKfMKgNKhOKiOH\ jPEkQBhQ8fR5dS2bS9`PGZNNXKWVIaSFgQDfSHgUKgVNhXQhZT\ i_Wia_jbbjdekfhkgjlilljmjhmhfjgdgebdc``bZY`YVZWSYU\ PWSLUQITOFRMCQL9PK8NJ8LJ8JI8HH8FH8EG8EG8DF8CE8BE8A\ D89C88C87B87B8BF8EI8HL8JO8LR8OU8QX8TWCUWGWWKXVNZVR\ _VV`UZbUacUeeTifTmgTpdRmaPjZNgWMdTKaQIZNHWKFTHDQEC\ ONFKWIHcLElOBmR8nV7hZ6ba5Xe4Rh3Ll2Fo2Ek5Eh7DdADaCC\ YECVHBRJBOMAKOAHQ9DT9AV86Y83_80aC1cF2eJ3fM3hP4iT5k\ W5lZ6nb7pe8qh8sl9toAvrAwsCssEptFmtHjtIguKduLauNZvP\ VvQSwSPwTMwVJxWGxYDxZAklOZza_pW`fRYdUWcWTaZR_`OYbM\ WeJUgHTiJRmLPmNNmOMmQKmSImUGrVFvXDwZBz`9za8zc6ze4z\ g2zh1zi5zi9zjCzjGzkJzkNzlQzlUzmYzm`4nd3ng3ok2on2pr\ 1pu1ot4ns7nrAmqDlpGloJknMkmPlmNmmmnmmnmmommpmmpmmo\ mmnmmmmmlmmkmmjmmimmhmmgmmfmmemxZmzSmzMmzFmz8mz2mz\ 8mzEmzKmzPmzNmzLmzJmzHmzGmzHmzImzJmzJmzKmzLmzLmzMm\ zNmzNmzOmzPmzPmzMmzKmzkmz } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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Three Fold
by Roger Alexander 11 Jun '10

11 Jun '10

The irregularity of the natural world reflected by the fractal algortithm-almost but not quite perfect tri-radial symmetry. Tri-radial,I learned that word from Wikipedia today. Don't hesitate go to http://maxitersfractalfollies.blogspot.com for the finished product. There are plenty of photons for everbody. fract251.gif { ; a three armed something ; blank ; calctime 0:06:07.94 ; created Jun 11, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2003 type=formula formulafile=_p.frm formulaname=Phoenix2-1_rjr_c center-mag=-0.00351492/-0.0175803/1.598307 params=0.9733878597369304/0.1380352183599352 float=y maxiter=1600 bailout=360 inside=0 outside=atan invert=0.0841253791708796/0/0 periodicity=0 colors=0FNyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyxxxxxxxxxxxxxxxxxxxxxxx\ xxxxwwwwwwwwwwwwwwwwwwwwwwwwvvvvvvvvvvvvvvvvvvuuuuuuuuuuuuuuuuuuuuuttttt\ ttttttttttssssssssssssssssssrrrrrrrrrrrrrrrqqqqqqqqqqqqqqqqqqppppppppppp\ ppppoooooooooooonnnnnnnnnnnnnnnmmmmmmmmmmmmmmmllllllllllllkkkkkkkkkkkkkk\ kjjjjjjjjjjjjiiiiiiiiiiiihhhhhhhhhhhhggggggggggggffffffffffffeeeeeeeeeee\ eddddddddddddccccccccccccbbbbbbbbbbbbaaaaaaaaaaaa`````````____________ZZ\ ZZZZZZZYYYYYYYYYYYYXXXXXXXXXXXXWWWWWWWWWVVVVVVVVVVVVUUUUUUUUUTTTTTTTTTSS\ SSSSSSSSSSRRRRRRRRRQQQQQQQQQPPPPPPPPPPPPOOOOOOOOONNNNNNNNNMMMMMMMMMMMMLL\ LLLLLLLKKKKKKKKKJJJJJJJJJIIIIIIIIIHHHHHHHHHGGGGGGGGGFFFFFFFFFEEEEEEEEEEE\ EDDDDDDDDDCCCCCCCCCBBBBBBBBBAAAAAAAAA99999999988888877777777766666666655\ 5555555444444444333333333222222222111111111000000000000 } frm:Phoenix2-1_rjr_c { ; This is the Phoenix formula as described by ; Shigehiro Ushiki. mutated by rjr z = pixel zold = (0.0, 0.0): zt = z * z + (p1 * zold) zold = z z = zt |z| < 4 ;SOURCE: phoenix2.frm } Roger Alexander _________________________________________________________________ Look 'em in the eye: FREE Messenger video chat http://go.microsoft.com/?linkid=9734386

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FOTD 12-06-10 (Pits and Bieces [7])
by Jim Muth 11 Jun '10

11 Jun '10

FOTD -- June 12, 2010 (Rating 7) Fractal visionaries and enthusiasts: Today's image is named "Pits and Bieces", which is a play on the words 'bits and pieces'. The reason for the name will be obvious as soon as the image is seen, and with a calculation time of 1-1/4 minutes, the wait will not be long. The parent fractal is a degenerate Mandelbrot set. Today's scene is located some distance east of the remains of the East Valley of the parent. Little East Valley stuff remains in the image, though a few hints appear here and there. Surprisingly, the image is extremely sensitive to changes in the escape radius, imag(p3), which in the image is the formula default of 100. As the escape radius is increased or decreased, the image changes dramatically. It evaporates and vanishes entirely when the value of imag(p3) is increased to about 8500. When imag(p3) is set to -13.92, the image takes the shape of a Maltese cross. Any negative value greater than this gives a blank screen. Before experimenting with the escape radius however, be warned that the calculation time increases dramatically as the ER is increased. When imag(p3) is set to substantially greater values, the calculation time increases to more than 15 minutes. At an escape radius of over 8500 or so, the result is a blank screen consisting totally of 'inside' stuff. But even here all hope is not lost. Using an active inside fill such as 'bof61' brings the blank screen to life. But here again, the calcula- tion time grows even longer. The rating of a 7 seems about right. Calculation may be avoided entirely by viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> Near perfect outside conditions kept the fractal cats happy here at Fractal Central on Friday, even though they are inside cats. Partly cloudy skies, low humidity and a temperature of 79F 26C are near perfect by any human's or any cat's standards. In my area, the rush died out in the morning, followed by a slow afternoon. The next FOTD will be posted in 24 hours. Until then, take care, and don't be caught with your fractals down. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Pits_and_Bieces { ; time=0:01:15.73-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritMinZ function=recip center-mag=+0.2794802820587657/+0.0280646118234618\ /6.298586e+008/1/180 params=1/1/3/-1/0/0/0/0 float=y maxiter=1500 inside=0 periodicity=6 colors=000mVHsPGxHCzCAz68z06``P0ze4zkGsoRks`dvkXzv\ PzzHzzAzzAvzAizAVzAHxA2vA0o00i00b00X000Eu0AmA6eP4Z\ HLeAbk2ss0zx0zzJzskzgzuZCXz6Xz2Xz0Xz0Xz0Xz0Xz0RzCN\ zPJzbGziPzqXzvdqzeezgVzgJzi8zi0zk0zk0zb0kT0VJ0EC0C\ C4ACNACe2Eg0Ei0Gk0Gm0Gm0Ag06d00`00V00R00N00T00Z00b\ 42gA6mGAqLEvRGzzzvzsuqdugPuZ8uP0uG0uoLo0LV0RX4VXH`\ ZTdZegZsm`zq`zu`mxiJzq0zxkxqdovZezRXzLNzGGzdPzzZzz\ gzzixiiqPki6kb8bXAVRALNCEHE6CE08G02G00N0C000`0Ze0i\ k0ui0mg4ggXbebXedRdeLdgGXiERkEJiEEgE6eE0dETbC0bk0L\ T0C8026006004004000000400E00N00X00e00o0Tq0Tz00z0Tz\ PTz8TzUTvRTs`Tzd0zf0zh0zjCzpEzsExuEzz0izE`zTKuzLzz\ XuzezzouzxzzzzzzzzzzzzzzzzzzzzzzzgzzdzzNzz8mT0ZT0J\ TTPTzzzzkzxgzqeziizbmzv`ozP`zXdodebkgPszCzk0zm0zo0\ mk0Pg00d00b00gH0mb0sv0xz0zz0sz0iz0`z8RzGHzN8xV0v`0\ 4z0Cz0JuARmJZeTeZbmRkuJuzEzqkZgz2izEkzPmzZoziqzusz\ zuzzZv4XsAVqGToLTmP`eLe`J } frm:MandAutoCritMinZ {; 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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FOTD 11-06-10 (Smooth Nothings [4])
by Jim Muth 11 Jun '10

11 Jun '10

FOTD -- June 11, 2010 (Rating 4) Fractal visionaries and enthusiasts: A late FOTD usually means a busy day, and so it was here at FC on Thursday. We have another merely average FOTD fractal. How humiliating! But nobody is perfect, and with no time to find a good fractal, today's image is the best I could do. Basically, the image is a smoothly-colored spiral with most of the frills left out. Perhaps the most interesting part is the series of similarly-shaped holes along the spiral arms. The parent fractal is little more than a large area of chaos, with the remains of one large Mandelbrot set, and minibrots of various shapes and sizes scattered throughout. Today's scene is located in the remains of the East Valley of the large M-set. I rated the image at a 4 and named it "Smooth Nothings". The calculation time of 1-1/3 minutes is brief enough to cause no one to be impatient. The trip to view the finished image at: <http://www.Nahee.com/FOTD/> is far less work. After Wednesday's all-day rain, near perfect weather prevailed here at Fractal Central on Thursday, with partly cloudy skies, low humidity, and a temperature of 84F 29C. The fractal cats sincerely approved all of this. My day was very busy, but otherwise pretty good. The one annoyance was a wet spot that I noticed on the third floor ceiling when I went up there to find some old files. I guess the FC roof needs work. I'll put it on the list of things to be done. The next FOTD will be posted in 24 hours. Until then, take care, and what do the big-time thinkers think about when they do their big-time thinking? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Smooth_Nothings { ; time=0:01:21.17-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident center-mag=+1.84163644868959/-0.3001059371524035/\ 7.86298e+010/1/-40/0 params=0.4/2/-1.1/-0.5/0/0/0/0 float=y maxiter=1500 inside=0 periodicity=6 mathtolerance=0.05/1 colors=000ZVZWYXTaUQdRNgPKkMHnJEqHHmJJjLLfMNcOP`PR\ XRTUTWQUYNW_KXaGZcD`e9ag6ci3dg5ee7fc9gaBh_DiYFjWHk\ VJlTLmRNnPPoNRpLTqJVrHXsGYsJXhMWYPVNSUCUT2MgVFuvGr\ tHprHmqIkoIhmJflJcjKaiL_gLXeMVdMSbNQ`NN_OLYOJXNLRN\ MLNNFNO9NP3OR6OS9PTCPUFQWIQXLRYORZRS`USaXTb_TcbTdd\ ZcWdbNjaEp`6nY7lV7jS7hP7fM7dJ7bG7`D7_45Z76ZA7ZD8ZG\ 8ZJ9ZMAZPAZSBYVCYYCY`DYcEYfEYiFYlG`qAYnGWlMUjSShYP\ fcNdiLbonalZ`qJ`uMZrOXpRVnTUlVSjYQh_PfaNcdLafJ_hIY\ kGWmEUyHHoDSfAbX7mO4wDKBBeG_pLaqOcrQesSgtUiuWkvYmw\ _oxaqyetxhtwgtvftuestdqtcosamq_koZimXgkVeiTchR`gQY\ fOXeLVdKWcIXbDYbF_cHcdJgeKkfMohOsjPvlRznTvoTrnUmlU\ hiVcfVZcWU`WRYXRWXSTXSQYTNYTKZUHZUE_VB_V9_PBMIA7JD\ 8KG8LJ8MM8NPANSFOVKPYPU`UccZmfcrihzlmzorzrvzzztnvm\ hrebmbXhVRcSLZOBULDTLFTLHTMJTMLTMNTNPSNRSNTSOVSOXS\ OZSKXQO_SRaUUcWYfY`h_bhZcj`dkadmbencfodfqegrfhsghu\ hiviiwjkFlmEljIigLfdOdaSa } 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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More Summer Colors
by Roger Alexander 10 Jun '10

10 Jun '10

The color map goes well with the outline of the fractal structure.The effect is enhanced by the network of filaments which adds a degree of complexity which breaks up the potential monotony of a simple gradient. To make good use of my Flickr account go to http://maxitersfractalfollies.blogspot.com and view the completed fractal. fract248.gif { ; I like the colors ; blank ; calctime 1:12:54.31 ; blank ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=specials.frm formulaname=newtonmand1 center-mag=+0.34643437485131020/+0.00012503403917515/1865306/1/-122.5000\ 00001580091/1.70223325018925564e-009 params=7/0/1/0 float=y maxiter=3200 inside=0 logmap=108 cyclerange=0/255 colors=000v0bt0ar0_q0Zo0Xm0Wl0Uj0Ti0Rg0Qe0Pd0Nb0M`0K_0JY0HX0GV0ET0DS0BQ0\ AO08P08Q08R08S18U18V18W18X28Y28_28`28a38b38d38e38f48g48h48j48k58l58m58o5\ 8p68q68r68s68u78v78w78x78z88z98zA8zB8zC8zD8zE8yF8yG7yH7yI7yJ7yK7xL7xM7xN\ 7xO6xP6xQ6wR6wS6wT6wU6wV6wW5vX5vY5vZ5v_5v`5va5ub5uc4ud4ue4uf4ug4th4ti4tj\ 4tk3tl3tm3sn3so3sp3sq3sr3rs2qs2os3ns3mr4lr4kr5jr5hr6gr6fr6er7dr7cq8aq8`q\ 9_q9ZqAYqAXqBVqBUpCTpCSpDRpDQpDOpENpEMpFLpFKoGJoGHoHGoHFoIEoIDoJCoJAnK8q\ L5tN3wP0zR0wQ0sO0pN0lL0hJ0eI0aG0YE0VD0RB0N90K80G60C40H90MF0RL0WR0`X0eb0j\ h0on0tt0zz0xx0vv0st0qr0no0lm0jk0gi0ef0bd0`b0Y`0WY0UW0RU0PS0MP0KN0HL0FJ1C\ G2CL4DP5DU7DZ8EbAEgBElDFpEFuGGzGGxFFvEEtDDrCCpBBnBBlAAj99h88f77d66b66`55\ Z44X33V22T11R00O53SA6XG9aLCfQFkWIp`LufOzfNyfMweLveKtdJsdIqdHpcGncFmbEkbD\ jaChaBgaAe`9d`8b_7a_6__5ZZ4XZ3WY2UY1TX0Rc0Vk0Zr0bz0fy0e } frm:newtonmand1(XAXIS_NOIMAG) { ;combination of a Newton-like ("a") ;and Mandelbrot ("b") formula ;needs floating point! ;p1 (the Newton exponent) should be 3 or more, default=7 ;best with 7 or more ;if p2 (the Mandelbrot exponent) is not specified, it will be p1 z=c=pixel,nx=p1,nx=nx+(nx==0)*7,mx=p2,mx=mx+(mx==0)*nx: a=b=z a=a-(a^nx-1)/(nx*a^2) b=b^mx+c z=a*b |z|<4 ;SOURCE: specials.frm } Roger Alexander _________________________________________________________________ MSN Dating: Find someone special. Start now. http://go.microsoft.com/?linkid=9734384

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FOTD 10-06-10 (Passing the Time [5])
by Jim Muth 09 Jun '10

09 Jun '10

FOTD -- June 10, 2010 (Rating 5) Fractal visionaries and enthusiasts: With an unexpected rush job suddenly arriving on Thursday, I had little time to devote to fractals. But I did manage to produce an acceptable if not exceptional image, which appears as today's FOTD. The name "Passing the Time" might have some vague connection to the image, but if so, I fail to recognize it. The rating of a 5 indicates that I consider the image to be average. The 7-1/2 minute job of calculating the image may be escaped by viewing the image in finished form on the FOTD web site at: <http://www.Nahee.com/FOTD/> Heavy clouds and a steady chilly rain kept a damper on things here at Fractal Central. The temperature of 61F 16C was more like April than June, and the fractal cats didn't like it. As stated above, my day was very busy. Tomorrow will likely be a repeat, so I cannot guarantee the FOTD will appear on time. Until whenever, take care, and be watchful. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Passing_the_Time { ; time=0:07:31.10-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=+0.2732344319114242/+0.0006059468366376\ /1.487367e+012/1/-170/0 params=0/4/0/0 float=y maxiter=4200 inside=0 logmap=770 periodicity=6 mathtolerance=0.05/1 colors=000HZlJYkKYkLXjMWiOViPVhQUhRTgSTfUSfVReWQdX\ QdZPc_Oc`ObaNabMadL`eL_fK_gJZjI_hJZgJYfJXeJWdJVcJU\ bJTaJS`JR_JQZKPYKOXKNWKMVKLTKKSKJRKIQKHPKGOLFNLEML\ DLLCKLBJLAIL9HL8GL7FL6EL6GM7HN8IO9KPALPBMQCNRDPSEQ\ TFRTGTUHUVIVWJWWKYXLZYL_ZMa_Nb_Oc`PdaQfbRgbShcTjdU\ keVlfWmfXogYphZqi_ri_qhZphYpgXogXnfWnfVmeVleUleTkd\ TjdSjcRicRhbQhbPgbPfaOfaNe`Nd`Md_Lc_Lc_KbZJaZJaYI`\ YH_XH_XGZWFYWFYWEXVDWVDWUCVUBUTBUTATT9SS9SS8RR7QR7\ QQ6PQ5PQ5XSHdUTlWdtXosXnsXnrXmrXmqXmqXlpXlpXloXkoX\ knXknXjmXjmXjlXilXikXikXhjXhjXgiXgiXghXfhXfgXfgXef\ XefXeeXdeXddXddXccXccXcbXbbXbdZbbXbaWb`Vb_UbZTbYRb\ XQbWPbVObVKcUNbUQaUT`UV_UYZU`YUbXUeWUfVTgVUhUUiTUj\ SUkRUlQUmPUnOVoNVpMWqLYrK_sJatIcuHdvIewIfxJgyJhzKi\ zKjzLkzLlzMmzMozNqzNszOuzOwzPzzPzzQzzQzzRzzRzzUzzX\ zz_zzbzzezzhzzkzznzzqzztzzwzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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If This Thing had a Personality it Would be Magnetic
by Roger Alexander 08 Jun '10

08 Jun '10

Today's fractal is one of Fractint's built-in magnetic types. I remember generating these things on my second hand 486-66. Those were literally overnight calculations. Ahh memories... Speaking of calculation time you can save some by visiting http://maxitersfractalfollies.blogspot.com for a ready made specimen. fract242.gif { ; a magnetic,tdis ; blank ; calctime 0:11:58.75 ; created Jun 06, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=magnet1m center-mag=+1.78360967709637100/+1.76573408414023400/310077.5 params=0/0 float=y maxiter=1500 bailout=320 inside=0 outside=tdis cyclerange=0/255 colors=7Yo9et8Zp6Sk4Lg2Eb06Y06W07U08R09P0AM0BK0CH0EI0GJ0IK0KM0MN0PP0RP0T\ P0VP0XP0_P0aP0cP0eP0hP0iO0jN0kM0mL0nK0oJ0pI1rH1sG1tF1uE1vD1xC1xC1wC1vD1v\ D2uD2tE2tE2sF3rF3rF3qG3pG4pG4oH4nH4nI4mI5lI5lJ5kJ5jJ6jK6iK6hL6hL7gL7fM7f\ M7eM8dN8dN8cO8bO8bO9aP9`P9`P9_QAZQAZRAYRAXRBXSBWSBVSBVTCUTCTUCTUCSUCRVDR\ VDQVDPWDPWEOXENXENXEMYFLYFLYFKZFJZGI_EGXCFTAEQ8CN6BK4AG28D58D97DD7EH6EL6\ EO5FS5FW4G_4Gc3Gf3Hj2Hn2Hr1Iv1Iz0Jw0Jt0Iq0Hm1Gj1Fg1Fd1E`2DY2CV2BS2BO3AL3\ 9I38F37B46824935A46C46D46F46G46I46J46L46M46O46P46R46S46U46W45X57Z68_7Aa8\ Bb9DdAEfBGgCHiDJkEKlFMnGNoHPqIQsKSsKQsKOsLMtLKtLHtMFtMDtMBtN9uN7uN4uO2uO\ 0uR0uV0uY0ua0ud0ug0uk0un0ur0uu0tr1so3rm4qj5pg6od8nb9m_AlXCkUDiSEhPFgMHfJ\ IeHJdELcBMb8Na6O`3Q_0RW0VT0WR0XO0YL0ZK0YK0XJ0WJ0VI0UI0TH0SH0SG0RF0QF0PE0\ OE0ND0MD0LC0KB0LA1M91N82P72Q63R53S44U34V25W06Y1Da3Kf5Rj } Roger Alexander _________________________________________________________________ Learn more ways to connect with your buddies now http://go.microsoft.com/?linkid=9734388

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FOTD 09-06-10 (Beyond the Horizon [7])
by Jim Muth 08 Jun '10

08 Jun '10

FOTD -- June 09, 2010 (Rating 7) Fractal visionaries and enthusiasts: Today's formula, the FinDivBrot-2, certainly creates some interesting and unexpected parent fractals -- and it's only 4 lines long. (I have always avoided those overblown formulas with 40 or 50 lines, most of which are devoted to coloring tricks. I much prefer the coloring tricks to come from the fractal math, not the fractal artist.) Today's formula, along with the type=Mandel, MandAutoCritInZ, MandelbrotBC3, and SliceJulibrot4 formulas (formulae) are the ones I turn to almost automatically when I boot the Fractint program. They rarely disappoint me. In today's FOTD, the FinDivBrot-2 formula produced a parent fractal that resembles a Mandelbrot set pretty closely until its main stem is examined. Instead of one main stem, this parent has two main stems, both of them infinitely divided into ever- smaller curled stems. Today's image is located in the East Valley area of the minibrot on the northern main stem. I named the image "Beyond the Horizon" because I did go a bit beyond the limit of perfect definition to find the scene. The rating of a 7 means the image is kind of good, but nothing to get excited about. The calculation time of just under 4 minutes may be avoided by viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> Another picture perfect day prevailed here at Fractal Central on Tuesday, an exact repeat of Monday. The fractal cats, now convinced that the unwanted intruder cat has moved on, spent most of the day sleeping. My day was busier than Monday, but still left lots of time for fractal diversions. The next FOTD will be posted in 24 hours. Until then, take care, and pass the time pleasantly. P.S. If a Klein bottle is given an extra twist, the result is a surface known as a 'projective plane', which needs a full five dimensions to be seen in its full unsquashed, non-intersecting glory. But don't ask me to describe the shape of this surface. Describing the Klein bottle is hard enough. And unless I'm mistaken, a projective plane may also be created by widening a Mobius strip until the single edge closes on itself to form a single-sided edgeless surface. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Beyond_the_Horizon { ; time=0:03:54.18-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip logmap=506 center-mag=-1.418212964957334/+0.03225319123708284\ /1.626e+013/1/167.5/-0 params=-0.05/-10/0/0 float=y maxiter=1500 inside=0 mathtolerance=0.05/1 colors=000L1UK1SK1QJ1OJ1MI1KH1IH1GG1EG1CF1AE19E18D\ 07D06C05B04B03A02001A00900800800700700600500500400\ 40030020020010010000000000000000000000000000000000\ 0000000000000000000000000000000000000000000000IwzF\ zxCzw9yv6xu3wsGuqEsnDojCjfBfbAbZ9YV8UR6QN5LJ4HF3DB\ 207hhZzzhrrZmoPhkFci5Zf0Ud0Sa0Q_0OY0NV0LT0JQ0HO0GL\ 0EJ0CH0AE08C0790570340120BqVAmT9jR9gP8dN7aL7YK6VI5\ SG5PE4MC3JA3F92C7195163031Ave8o`7hW6bS5WN4QI3JE2D9\ 1640SO0OL0LI0IG0FD0CA098065zczw`zsZzoXzkUvhSrdQm`N\ hXLcZJhSGbMETOBWF9FB7A74z32zB5V94z73K52F31A105aZuY\ VoUSiQOcMLYJHTFENBAH77B335PvWOtVNrUNqTMoSLnRLlRKkQ\ JiPJhOIfNHeMHcMGbLG`KF_JEYIEXIDVHCUGCSFBREAPDAOD9M\ C8LB8JA7I97c96c85c75c64c53c43c42U31U21c10U0zUszUpz\ UnzUkzUizUfzUzVUzTUzRUzPUzNUzLUzJUzHUzFUzDUzBUz9Uz\ 7Uz5Uz3Uz1UzUUzTUzSUzRUzRUzzzEzzEzzEzzDzz1zz1zz0zz\ 0zz0zz0zz0zz0zz0zz0zz0zz0 } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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Re: [Fractint] Art and Numbers
by Roger Alexander 08 Jun '10

08 Jun '10

Author: Maryetta Campbell Date: 2010-06-05 14:112010-06-05 20:11 -600UTC To: fractint Subject: Re: [Fractint] Art and Numbers Roger Alexander wrote: > > One is a fractal the other is the > painting "The Great Wave".... > http://maxitersfractalfollies.blogspot.com > Nice comparison of images!! Out of the fractals you have made available lately, I like the following the best: 06_02_10_02.GIF (a Study in Green-ishness) 4662386524_2d15585e10_o.gif (Filaments or Threads) 4648709391_ee054ee135_o.gif (Life and hemoglobin) The addition of the "Men Without Hats" video was an added treat: http://www.youtube.com/watch?v=v7aGFrVSTAY&feature=player_embedded Glad you enjoyed the posts! I post two kinds of fractals. Either they might be visually appealing whether or not you the audience is familiar with fractals and those fractals illustrating some technique of fractal generation. When I feel too serious I will post something with humorous content. -Roger Alexander _________________________________________________________________ Turn down-time into play-time with Messenger games http://go.microsoft.com/?linkid=9734385

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Round and round...
by Roger Alexander 07 Jun '10

07 Jun '10

Round and round and round.... Do you have an iron will? Can you gaze upon the hypnotizing vortex of obedience and resist its siren call? For those who cannot bear the uncertainty go to http://maxitersfractalfollies.blogspot.com for immediate illumination. fract230.gif { ; swirly ; blank ; calctime 0:05:17.58 ; created May 28, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_d.frm formulaname=distortpendulumMG function=exp center-mag=-0.707336/-0.294517/12.05242 params=-0.4908230842005677/-0.7574785607470931 float=y maxiter=1500 inside=0 proximity=1 outside=fmod colors=0Qk0Qj0Pj0Oi0Oi0Ni0Nh0Mh0Lg0Lg0Kg0Jf0Jf0Ie0Ie0He0Gd0Gd0Fc0Fc0Eb0D\ b0Db0Ca0Ca0B`0A`0A`09_08_08Z07Z07Z06Y05Y05X04X04X03W02W02V01V00U01V03W05\ X07Y09Z0A_0C`0Ea0Gb0Ic0Kd0Le0Nf0Pg0Rh0Ti0Vj0Wk0Yl0_m0an0co0ep0fq0hr0js0l\ t0nu0pv0rw0qw0ov0mu0lt0js0hr0fq0ep0co0an0`m0Zl0Xk0Vj0Ui0Sh0Qh0Pg0Nf0Le0J\ d0Ic0Gb0Ea0D`0B_09Z07Y06X04W02V00U00U00T00S00R00Q00P00O00O00N00M00L00K00\ J00I00H00H00G00F00E00D00C00B00A00A00B00C00D00E00F00F00G00H00I00J00K00K00\ L00M00N00O00P00P00Q00R00S00T00U01V03W05X06Y08Z0A_0B`0Da0Fc0Gd0Ie0Kf0Lg0N\ h0Pi0Qj0Sk0Um0Vm0Xn0Zo0`o0bp0cq0er0gr0is0kt0mt0nu0pv0rw0tw0vx0xy0zz0zz0y\ z0yz0xz0xy0wy0wy0vy0vy0ux0ux0tx0tx0sx0sw0rw0qw0qw0pw0pv0ov0ov0nv0nu0mu0m\ u0lu0lu0kt0kt0jt0it0it0hs0hs0gs0gs0fs0fr0er0er0dr0dq0cq0cq0bq0aq0ap0`p0`\ p0_p0_p0Zo0Zo0Yo0Yo0Xo0Xn0Wn0Wn0Vn0Um0Um0Tm0Tl0Sl0Rk0Rk } frm:distortpendulumMG { ; Morgan L. Owens <packrat(a)nznet.gen.nz> ; Tue, 14 Jan 2003 19:54:33 bailout=4 dt=real(p1) a=imag(p1) b=real(pixel) c=imag(pixel) time=0 z=pixel: x=real(z) y=imag(z) z=x+dt*y+flip(y+(dt*fn1(b*x-c*time)-x)*a) time=time+dt |z|<=bailout ;SOURCE: morgan~1.frm } Roger Alexander _________________________________________________________________ Turn down-time into play-time with Messenger games http://go.microsoft.com/?linkid=9734385

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FOTD 08-06-10 (One Froggy Fractal [7])
by Jim Muth 07 Jun '10

07 Jun '10

FOTD -- June 08, 2010 (Rating 7) Fractal visionaries and enthusiasts: The Klein bottle comment at the end of a recent FOTD discussion was totally in jest, as are most of my closing comments, with a few exceptions. Since the true Klein bottle is an abstraction, it would hold zero gallons of presumably 3-D water, which itself would be an abstraction in 4-D space. The familiar 3-D Klein-bottle model could hold water, but the water would not be enclosed. It would merely be a puddle sloshing around in a basin of the single- sided surface. The Klein bottle is actually mis-named. It is not at all a bottle with an inside that could be sealed. It is actually a two-dimensional surface with no edges or breaks, which twists in 4-D space in such a manner that its apparent two sides are actually different parts of the one and only side. A way to almost picture the true Klein bottle is to imagine a cylinder like a length of garden hose bent into a circle, with the ends joined to form a donut (torus). All we need to do is find a way to gradually turn the hose inside-out without making cuts, so that halfway around the loop the inside of the hose finds itself on the outside. It's impossible in 3-D space but simple in 4-D space, where the 2-D surface may rotate in place on itself. To see an analog of the problem, take a broad, short rubber band, cut it, twist it, and rejoin the edges so that it forms a flexible Mobius strip. Then squash the strip between two panes of glass in an effort to flatten it into two dimensions. It will become apparent that a true Mobius strip must intersect itself when it is squeezed into its model in 2-D space, just as a 4-D Klein bottle must intersect itself when squeezed into its model in 3-D space. There is also a 'figure-8' model of the Klein bottle, which is less well known but actually a bit closer to the real thing. The FOTD is about fractal geometry and not topolgy. So let's get on to today's 7-rated image. I named today's image "One Froggy Fractal" because of the vague frog-like shape near the center. The whole image is a close up of the area where the two prominent minibrots in yesterday's image almost merge. In addition to reminding me of a frog, the image bears a striking resemblance to a dwarf galaxy such as what one might see in a deep sky photograph taken by the space telescope. The calculation time of over 10 minutes might seem a bit slow. The way to save time is to visit the FOTD web site at: <http://www.Nahee.com/FOTD/> and view the finished image there. Cooler weather moved into Fractal Central on Monday, much to the fractal cats' appreciation. The partly cloudy skies, lower humidity and temperature of 73F 23C made things pleasant for all concerned. My day was acceptable, as was FL's day also. The fractal cats were happy that no intruding tomcats tried to break in. The next FOTD will be posted in 24 hours. Until then, take care, and what results in 5-D space when a Klein bottle is given an extra twist in 4-D space? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= One_Froggy_Fractal { ; time=0:10:43.29-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=+0.004236797608/-0.000422139251/2104673\ /1/85/0 params=1.99/-0.95/1000/0 float=y maxiter=2000 inside=255 logmap=9 colors=000Xzz_zzbzzezzczzazz`zzZzzXzzYzzqdUnbRk`Oh\ ZMeXKbVI_THXRHVPITMJQLLOLMQLKRLIUMGWOE_QCbSAeT8hU6\ kU4nU2oU5qU8rUBrUEsUHtUKuUNuUQqUSmAUiBWeBYcC_cDacE\ ccEecFgcGicHkcHmzzzzznzzcxyUvxOuwNswNrvMpuLouLpsKq\ pJrnJskIthItfHucGv`GwZFxWFyTEySEp_ZoZZnZZnZZmZZmZZ\ lYZkYZkYZjYZjYZeVW`SUXPScMQcKccHccEccBcc9cf3uh6qiB\ njGkkLhmOenSboWZp_WraTsdQtgPujUvlZogchchacmVcrOcvH\ czBczCczCczCczCczCczCczDczDczDczDczDczDcz5uz7sz8qz\ 9ozAmzCkzDizEgzFezGdzHezHfzHgzHhzHizHjzHkzHlzImzIn\ zIozIpzIqzIrzIszItzGqzFnzEmzDmzBmzAmz9mz8mz7mz5mz4\ mz3mz2mz1mz9mzHmzPhzWqzVrzVrzVrzVrzVrzVrzVrzVszVsz\ VszVszVszVszVszSqzQozOmzMmzKmzImzFmzDmzBzz9zz7zz5z\ z3zzHzzVzzhzzvzlwzkwzjwziwzhwzgwzgwzfwzewzdwzcwzcw\ zbwzawz`wz_wzzkzz`zzbzzczzezzfzzhzzizzjzzlzzmzzozz\ pzzqzzkzzfzz`zzWzzQzzLzzGzzIzzKzzMzzOzzQzzRzz3zz4z\ z8zzBzzEzzHzzKzzNzzRzzH0P } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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Brite Colors
by Roger Alexander 06 Jun '10

06 Jun '10

It's been a busy weekend so I have to be brief. The palette and design of this fractal is intended to suggest garden colors and a bright summer day. Perhaps the next floral fractal will feature a minibrot. As usual click a path to http://maxitersfractalfollies.blogspot.com to sample the finished product. fract132.gif { ; florals and spirals ; blank ; calctime 0:15:36.93 ; created May 01, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_e.frm formulaname=Extend function=abs/ident/sin center-mag=-0.59068576520650990/-0.43241933088480660/493.826/1/90/3.8857\ 8058618804789e-016 params=64/0 float=y maxiter=1500 inside=0 logmap=40 periodicity=0 colors=w0dv0bt0ar0_q0Zo0Xm0Wl0Uj0Ti0Rg0Qe0Pd0Nb0M`0K_0JY0HX0GV0ET0DS0BQ0\ AO08P08Q08R08S18U18V18W18X28Y28_28`28a38b38d38e38f48g48h48j48k58l58m58o5\ 8p68q68r68s68u78v78w78x78z88z98zA8zB8zC8zD8zE8yF8yG7yH7yI7yJ7yK7xL7xM7xN\ 7xO6xP6xQ6wR6wS6wT6wU6wV6wW5vX5vY5vZ5v_5v`5va5ub5uc4ud4ue4uf4ug4th4ti4tj\ 4tk3tl3tm3sn3so3sp3sq3sr3rs2qs2os3ns3mr4lr4kr5jr5hr6gr6fr6er7dr7cq8aq8`q\ 9_q9ZqAYqAXqBVqBUpCTpCSpDRpDQpDOpENpEMpFLpFKoGJoGHoHGoHFoIEoIDoJCoJAnK8q\ L5tN3wP0zR0wQ0sO0pN0lL0hJ0eI0aG0YE0VD0RB0N90K80G60C40H90MF0RL0WR0`X0eb0j\ h0on0tt0zz0xx0vv0st0qr0no0lm0jk0gi0ef0bd0`b0Y`0WY0UW0RU0PS0MP0KN0HL0FJ1C\ G2CL4DP5DU7DZ8EbAEgBElDFpEFuGGzGGxFFvEEtDDrCCpBBnBBlAAj99h88f77d66b66`55\ Z44X33V22T11R00O53SA6XG9aLCfQFkWIp`LufOzfNyfMweLveKtdJsdIqdHpcGncFmbEkbD\ jaChaBgaAe`9d`8b_7a_6__5ZZ4XZ3WY2UY1TX0Rc0Vk0Zr0bz0fy0e } frm:Extend { ; SherLok Merfy <brewhaha(a)freenet.edmonton.ab.ca> ; Sun, 4 Apr 2004 10:28:36 ; z=fn1(pixel), c=fn2(pixel): z= z*z +fn3(z) +c |z| <= real(P1) ;SOURCE: sherlo~1.frm } Roger Alexander _________________________________________________________________ Turn down-time into play-time with Messenger games http://go.microsoft.com/?linkid=9734385

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FOTD 07-06-10 (Midgets Without End [6])
by Jim Muth 06 Jun '10

06 Jun '10

FOTD -- June 07, 2010 (Rating 6) Fractal visionaries and enthusiasts: Today's image is a mess! It obviously shows a nest of mini- brots, but of what order is hard to say. My best guess is that the minibrots are of order 1.99, since this is the exponent of Z. When I look closer however, I see things that look more like order 2.5 minibrots, which makes no sense at all. I named the image "Midgets Without End" because the more I searched for minibrots in the image, the more I found. Most of the smaller ones are nothing at all like those in today's image, and appear to be distortions of the classic quadratic Mandelbrot set. The parent fractal is a shrunken thing, so shrunken in fact that it is almost out of sight at the default magnitude of 0.67. But an inzoom will reveal that this parent fractal is quite an inter- esting thing, caught on the verge of flipping left to right. Today's scene is located in a large mass of debris floating in the eastern part of the main bay. The most striking thing in the image may be the character of the scenery surrounding the nest of minibrots. The assorted blobs bring a hint of a third dimension to the image, while the colors give hints of things happening just beneath the surface, especi- ally near the nest of minibrots. The rating of a 6 is a comedown from recent images. The calcu- lation time of a fireball 31 seconds will take most of the sting from the disappointment however. As always, the finished image is available on the FOTD web site at: <http://www.Nahee.com/FOTD/> Muggy conditions in the morning, with lots of clouds and a few showers, gave way to crystal blue skies, puffy white clouds and brilliant sunshine in the afternoon here at Fractal Central on Sunday. The temperature reached a high of 86F 30C early in the afternoon, then dropped to 70F 21C by sunset. A warning of tor- nadoes on the morning news report proved to be a false alarm when nothing more than a mild rain squall arrived. The fractal cats had a relaxing day, but the relaxation ended in the evening when a stray tomcat leaped onto the outside window sill and started a shouting match with Nicholas, who fought back from inside with vicious growls, hisses, and a thrashing tail that stirred up more wind than the threatened tornadoes. Cassie gave moral support from her resting place on the foot stool, and rewarded Nicholas with an ear washing when he eventually chased the other cat away. My day was average, though I think FL is still bothered that I am not more of an environmentalist. The next FOTD will be posted in 24 hours. Until then, take care, and do what you think is right. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= MidgetsWithoutEnd { ; time=0:00:31.66-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip float=y center-mag=+0.0042215/-0.00042237/4504 params=1.99\ /-0.95/1000/0 maxiter=2000 inside=0 logmap=9 colors=000qdUnbRk`OhZMeXKbVI_THXRHVPITMJQLLOLMQLKR\ LIUMGWOE_QCbSAeT8hU6kU4nU2oU5qU8rUBrUEsUHtUKuUNuUQ\ qUSmAUiBWeBYcC_cDacEccEecFgcGicHkcHmcTfcc`lnVxyPvx\ OuwNswNrvMpuLouLpsKqqJrpJsnItlItkHuiGvgGwfFxdFybEy\ aEpiZohZnhZnhZmhZmhZlgZkgZkgZjgZjgZedW`aUXZScWQcUc\ cRccOccLccJcfDuhGqiJnjMkkPhmRenUboXZp_WraTsdQtgPuj\ UvlZogchchacmVcrOcvHczBczCczCczCczCczCczCczDczDczD\ czDczDczDcz5uz7sz8qz9ozAmzCkzDizEgzFezGdzHezHfzHgz\ HhzHizHjzHkzHlzImzInzIozIpzIqzIrzIszItzGqzFnzEmzDm\ zBmzAmz9mz8mz7mz5mz4mz3mz2mz1mz9mzHmzPhzWqzVrzVrzV\ rzVrzVrzVrzVrzVszVszVszVszVszVszVszSqzQozOmzMmzKmz\ ImzFmzDmzBzz9zz7zz5zz3zzHzzVzzhzzvzlwzkwzjwziwzhwz\ gwzgwzfwzewzdwzcwzcwzbwzawz`wz_wzzkzz`zzbzzczzezzf\ zzhzzizzjzzlzzmzzozzpzzqzzkzzfzz`zzWzzQzzLzzGzzIzz\ KzzMzzOzzQzzRzz3zz4zz8zzBzzEzzHzzKzzNzzRzzUzzXzz_z\ zbzzezzczzazz`zzZzzXzzYzz } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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

06 Jun '10

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

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Two Arthopods Today
by Roger Alexander 05 Jun '10

05 Jun '10

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

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Art and Numbers
by Roger Alexander 05 Jun '10

05 Jun '10

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

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FOTD 05-06-10 (Pleasant Patterns [8])
by Jim Muth 04 Jun '10

04 Jun '10

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

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FOTD 04-06-10 (Marshmallow Design [9.5])
by Jim Muth 03 Jun '10

03 Jun '10

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

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FOTD 03-06-10 (Square-Root-of-Three Minibrot [8.5])
by Jim Muth 02 Jun '10

02 Jun '10

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

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Fmod Leaves
by Roger Alexander 02 Jun '10

02 Jun '10

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

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Threads-I Like the Colors
by Roger Alexander 01 Jun '10

01 Jun '10

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

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FOTD 02-06-10 (Mandelbrot Picnic [X])
by Jim Muth 01 Jun '10

01 Jun '10

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

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Spirals
by Roger Alexander 31 May '10

31 May '10

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

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FOTD 01-06-10 (Mandy Points the Way [7.5])
by Jim Muth 31 May '10

31 May '10

FOTD -- June 01, 2010 (Rating 7.5) Fractal visionaries and enthusiasts: Today's fractal is a pleasant diversion, a non-assuming image that promises little and delivers all of what it promises. The star-like scene lies in the 'East Valley' of the parent fractal that appeared as the FOTD for May 30. But it lies much deeper in the valley than yesterday's FOTD image, which also lies in the same East Valley. I have no idea where the rating of 7-1/2 came from, but it seems about right, so why not go with it. The name "Mandy Points the Way" is an equal mystery, since today's parent fractal hardly resembles the Mandelbrot set. The calculation time of just over 1-3/4 minutes is brief by any standards, though not as brief as the lifetimes of certain sub- atomic 'resonance' particles, which exist for such infitesimal periods of time that they don't really exist at all. One thing that surely exists however is the FOTD web site. Scientific proof of its existence may be found by going online and surfing out to: <http://www.Nahee.com/FOTD/> where today's image is posted in finished form. Midsummer conditions continued here at Fractal Central on Monday, with hot but hazy sun, high humidity and a temperature of 93F 34C. Early in the day the fractal cats sought the cool- ness of the tile floor in the kitchen, and stretched out there most all afternoon. FL spent the day puttering in her garden. I spent the day watching her putter and offering occasional helpful advice. The next FOTD, a moderately deep look into the M-set, will be posted in 24 hours. Until then, take care, and those with sharp tongues often make blunt statements. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= MandyPointsTheWay { ; time=0:01:47.80-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=+0.1868775575702199/+0.0003973109476461\ /6.54e+007/1/-112.5/0 params=1.01/-1/6000/0 float=y maxiter=1500 inside=0 logmap=177 periodicity=6 colors=000KBHKBHIAHG9GE7FF8GF8HG8IG8IH9JH9KI9LI9LJ\ 9MJANKAOKAOLAPLAQMBRMBRNBSNBTOBUOCUPCVPCWQCXRBWQCX\ QCYQDZQDZQE_QE`QEaQFaQFbQGcQGcQGdQHeQHfQIfQIgQIhQJ\ iQJiQJjQHmREoQGnQImQKkPMiPOfPQdPSbOU`OWYOYWO_UNaSN\ cQNeNMgLMiJMkHMmELoCLqALs8Ns2Lr6Kp9JnCHlGIjKMhKPfK\ SdKVbKYaKaaKddIgfFjiCmk9pm7onAooCooFopHnqKnqMnrPnr\ RmsUmtWmtZmu`lvclxelzhlzjmzlnznnwpowrowtpwwpwzqwzr\ wzrwzswvswrtwmtwhrrcpnZniUlePj`KhXFfSHdOJbJLaFNcPe\ eZwWTmNNdEHWJJZOLaTNdXOgaQifSljTooVrtXuxYwqTojPhcK\ `XGURCNWIP_NRcTTgYVlbXphZtm`xravdjuSrrPpoNomLmjIlg\ GjeEibBh_9fY7eV4cS2bQ0aN4ZL7XJAVHDSFGQDJOBNL9QJ7TH\ 5WE3ZC1aA5ZB8XCBVCETDHREKPENNFQLGUJGXHH_FIbDIeBJh9\ Kk7Kn5Lq3Lr7MsAMtEMuHNvLNwONxSNyVOzZOzaOzePzhPzlPz\ oPzpSzqczrczscztczuczvczwczxczymzzmzzmzzmzzmzzmzzm\ zzmzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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FOTD 31-05-10 (Is it an Elephant? [7])
by Jim Muth 30 May '10

30 May '10

FOTD -- May 31, 2010 (Rating 7) Fractal visionaries and enthusiasts: Today's image is a dip into the East Valley area at the bottom center of yesterday's fractal. The name of the image, "Is it an Elephant?", is a question that may be answered with a resounding 'no'. The image holds nothing that even vaguely resembles an East Valley elephant. But this is what makes the image so interesting. Instead of spiralling elephant trunks, we have spidery networks strung between brilliant balls of light. The rating of a 7 might be a little conservative considering the 20 minutes I devoted to tweaking the basically program-generated color palette. The calculation time of 2 minutes can be avoided by viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> Picture an absolutely perfect day and you'll have an idea of the weather here at Fractal Central on Sunday. Well, I actually thought the cloudless skies were a bit boring, and the tempera- ture of 86F 30C was a bit too warm, but with the low humidity, things were still well within the comfort range. The fractal cats slept through most of the day, getting up only to check the outside conditions every hour or so. They sprang to total alertness however when they heard a can of tuna being opened. My day, as well as FL's day, was reasonably peaceful, even if the smoke from a neighbor's grill did occasionally waft into the yard and mix with the smell of the roses. Tomorrow will be much the same. The next FOTD, another scene in yesterday's fractal, will be posted in 24 hours. Until then, take care, and keep the negative matter contained. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Is_it_an_Elephant? { ; time=0:02:05.73-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip float=y center-mag=+0.9759553350515242/+0.1492507155382438\ /5.38467e+007/1/-151.5/0 params=1.01/-1/6000/0 maxiter=2250 inside=0 logmap=298 periodicity=6 colors=000zzz9kzAgzCbzDZzFUvHPrILmKGhKCcKDZKEUKEPK\ FLKGLKHLHGKDFK9FK5FK8FNBGQEHSHHVKGXNF_QEbTDdUCgUBi\ UAlUAnUEoUIoUMoUQpUUpSYpQ_pOamNchOecPgZPiUUkPZmKco\ Fcq8ds7dt7eu7ev7fw6gx6oy6tz6wy5zx5zw5zu4zs4zq4zo4z\ m3ym3xm3wm3vk5ug7t`9sXBrSDqOFpKHoKJnKJjPKgUKdZLacL\ ZcLWcMShMPmNMrNmvzzzzmwzArOCoPElPGiQIfQKcRM`RN_SPY\ SRXTTVTVUUXSUWORYRU_TW`VZbX`d_ceaegcgiejjhlljonntw\ tzoptghq_cnSYlKSi5SrDNgKIYRDNY8Dd43oJHyYUHqZGzXFnW\ EzUElTDzRCjQCzPBgNAzMAeK9zJ8cH8zG7`F6mD6ZC5YA4X94W\ 86U77S78R79P7AO7BM7CK7DJ7EH7FG7HE6IC6JB6K96L86M66N\ 46O36P16Q06R3AS6DT9HUBKVENVHRWJUXMXYP`ZSc_Uf_Xj`_m\ aapcctehwgmzihzkcrlZqlUqlPplPplPplQolRolSnlTnlTnlU\ msUmzVlzWlzXlzYkzZkz_kzajzcjzejahi_kiYniXqhVthUwhz\ zgzzgzzgzzfzzfKzzzzezzezzezzdCzzzzd9zzzzc6zzzzc7zz\ 8zzzz_BzzzzYEzzzzWzzVzzUzzTLzzzzROzzzzPRzzzzNUzzzz\ LXzzzzJ_zzzzHbzzzzGazzzz9 } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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Another Lacy Pattern
by Roger Alexander 30 May '10

30 May '10

Yesterday was another busy busy day and I didn't get to post. This must not become a habit! This intriguing fractal is a classic mandelbrot in julia clothing. Ready made at http://maxitersfractalfollies.blogspot.com. fract233.gif { ; a mandelbrot that looks like a julia ; blank ; calctime 0:18:14.67 ; created May 30, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=mandel center-mag=-1.18736325508505100/+0.30405228076885590/1.20289e+008/1/-38.\ 6637220782875062/-0.00548315397550004635 params=0/0 float=y maxiter=3200 inside=0 logmap=422 logmode=fly cyclerange=0/255 colors=0Az08z06z04z02z00z00y10x20v20u30s40r50p50o61n71l81k91i91hA1gB1eC1\ dC1bD1aE1_F1ZF1YG1WH1VI1TJ2SJ2RK2PL2OM2MM2LN2JO2IM2GU2EH2CE1AC1891661431\ 2000101302503605806A07C19D19E1AF1AF1BG1BH1CI1DI1DJ1EK1EL1FL1FM1GN1HO2IO2\ JQ2IS2HV2GX2F_2Da2Cd2Bf2Ah19k18m17p15r14u13w12z00z20z50z70zA0zC0zF0zH0zK\ 0zM0zP0zR0zU0zX0zZ0za0zc0zf0zh0zk0zm0zp0zr0zu0zw0zz0zw0zu0zr0zo0zl0zj0zg\ 0zd0za0z_0zX0zU0zS0zP0zM0zJ0zH0zE0zB0z80z60z30z00x01v02s03q04n06l07i08g1\ 9e1Ab1B`1CY1EW1FT1GR1HO2JN2IM2HK2GJ2FH2DG2CE2BD2AB19A1881771551441321200\ 0000101201000302403503504604705805806907A07B08B08C09D1AE1AF1BF1BG1CH1CI1\ DI1EJ1EK1FL1FL1GM1GN1HO2IN2KM2NK2QJ2TH2VG2YE2`D2cB1fA1i81l71n51q41t21w00\ z03z07z0Bz0Fz0Jz0Nz0Rz0Vz0Zz0bz0fz0jz0nz0rz0vz0zz0xz0vz0tz0rz0pz0nz0lz0j\ z0hz0fz0dz0bz0`z0Zz0Xz0Wz0Uz0Sz0Qz0Oz0Mz0Kz0Iz0Gz0Ez0Cz } Roger Alexander _________________________________________________________________ Win $10,000 from Hotmail! Enter Here. http://go.microsoft.com/?linkid=9729708

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FOTD 30-05-10 (M-set Gone Wild [8])
by Jim Muth 29 May '10

29 May '10

FOTD -- May 30, 2010 (Rating 8) Fractal visionaries and enthusiasts: The one-and-only reference-standard Mandelbrot set is created by the expression Z^2+C. Minibrots however are another story. They come in all sizes and shapes, sometimes so distorted that the Mandelbrot aspect is all but invisible. It is much less common to see a parent Mandeloid suffer such extreme distortion, but today's image, which is the parent fractal itself, is in a state of true agony. Today's image obviously has Mandelbrot characteristics, but it is quite difficult to recognize the parts of what was once a fully-formed M-set. Actually, to better fit the fractal onto the screen the entire image has been rotated 90 degrees, so that west is up and east is south. In this orientation, the main bay is the open area at bottom center of the frame. It resembles the bulb of an ear syringe. East Valley is the tiny dimple on the shore line at the bottom center of this bulb. Minibrots certainly lie in this area, though I have not yet checked their appearance. The two large bays, sprouting like Mickey Mouse's ears from the main bay are the large bud that in the true M-set lies on the negative X-axis. The bud has split into two separate buds. The narrow valley, which shoots straight up the center of the screen from the main bay, like the stem of the syringe, is something entirely new, which has no corresponding part in the true M-set. It is in this stem that the most interesting minibrots will be found, but that's a story for another FOTD. The fractal also has two separate Seahorse Valleys, located in the brilliant white area where the mouse ears join the main bay. Any minibrots in this area could be quite interesting also, but if they are actually there, they will be quite slow to calculate. The calculation time is only 23 seconds because the image has such a low magnitude. The rating of an 8 includes a generous reward for my coloring effort, which was still not quite totally successful in hiding the iteration bands but did give a pock- marked appearance to the image. The name "M-set Gone Wild" describes the image. It has nothing to do with the behavior of college kids on spring break. And as always, the finished image is posted in its full glory on the FOTD web site at: <http://www.Nahee.com/FOTD/> where it may be viewed and studied at leisure. Clearing skies and a temperature of 82F 28C graced both Fractal Central and the fractal cats on Saturday. I was graced by a day off and a worthy fractal, while FL was graced by the best show of roses I have ever seen her produce. The next FOTD will be posted in 24 hours. Until then, take care, think logically, but realize that the universe does not necessarily run by our particular rules of logic. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= M-set_Gone_Wild { ; time=0:00:23.58-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip logmap=3 center-mag=-19.2404/0/0.042/1/-90/0 params=1.01/-1\ /6000/0 float=y maxiter=1500 inside=0 periodicity=6 colors=000000JCHKDI000MFKNGLOHMPINQJOPKOSLQQKPTNSR\ LQUPUSMRVRVTNSWRXUOUXSZVPWXT_WQYYTaXR_ZUcYSa_VdZTc\ `Vf_UeaWh`VgaXiaWibXkbXkcYmcYmdZndZoeZpe_qf_rg_sf`\ sg`tg`uh`vhawhavhawhawgawgbwgbwfbwfbwfcwecwecwedwd\ dwddwcdwcewcewbewbewbfwafwafwagw`gw`gx_gx_hx_hxZix\ ZixZixYixYjxYjxXkxXjxWkxWkxWlxVkxVlxVlxUlxUlxUlxTm\ yTlzTmzSkzSlzRkzRkzRjzQjzQjzQizPizPhzPhzOhzOgzOgzN\ fzNfzNezMezMezMdzLdzLczLczKczKbzKbzJazJazIbzJazK`z\ K`zK_zKZzKZzKYzKXzKXzKWzKWzKVzKUzKUzKTzKSzKTzKUzKV\ zKWzKXzKYzKZzK_zL`zMazNbzOczPdzQezRfzSgzTgzUhzVhzW\ izXkzYlyZly_ly`mybnycnydnyenyfnygnyhoziozjozkozlpz\ mpznqzorzoszptzqtzruzsvztwzuxzvyzwzzxzzyzzzzzzzzzz\ zzzzzzzzzzyzzxzzwzzvzzuzztzzsyzsyzsyztxztxztxztwzt\ wztwzuvzuvzvvzwuzwuzxuzxtzutzrtzoszlszjszgrzdrzarz\ ZqzXqzUqzRpzOpzMpzNozOozOozPozPnzQnzQnzRnzRmzSmzSm\ zTmzTmzTmzUmzUmzUmzUmzUmz } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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Imitating the Organic
by Roger Alexander 28 May '10

28 May '10

Today's design was chosen to suggest hemoglobin and the organic although good old Wikipedia says that there is copper based blood (if you're a mollusk or arthropod) which has hemocyanin as the oxygen carrier and is blue when oxygenated. Subdivision upon subdivision similar to arteries branching and eventually become capillaries. fract232.gif { ; organic ; blank ; calctime 0:02:02.21 ; created May 28, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=*.frm formulaname=JSomethingelse center-mag=-8.27433/4.69652/0.2271338 params=-0.6334421826837977/0.03381450849940486 float=y maxiter=1200 inside=0 proximity=1 outside=fmod invert=-0.196523941770684/-0.635975218970306/-0.273964659566027 colors=zffzffzffzeezeezeezddzddzddzccyccyccybbybbyaayaayaay``y``x``x__x_\ _x__xZZxZZxYYxYYxYYwXXwXXwXXwWWwWWwWWwVVwVVwUUvUUvUUvTTvTTvTTvSSvSSvSSvR\ RuRRuRRuQQuQQuPPuPPuPPuOOuOOtOOtNNtNNtNNtMMtMMtLLtLLtLLtKKsKKsKKsJJsJJsJ\ JsIIsIIsHHsHHrHHrGGrGGrGGrFFrFFrFFrEErEEqEEqDDqDDqCCqCCqCCqBBqBBqBBpAApA\ ApAAp99p99p88p88p88p77o77o77o66o66o66o55o55o44o44n44n33n33n33n22n22n22n1\ 1n11m00m00m00m00m00m00m00m00l00l00l00l00l00l00l00l00k00k00k00k00j00j00j0\ 0j00i00i00i00i00h00h00h00h00g00g00g00g00f00f00f00f00e00e00e00e00d00d00d0\ 0d00c00c00c00c00b00b00b00b00a00a00a00a00`00`00`00`00_00_00_00_00Z00Z00Z0\ 0Z00Y00Y00Y00Y00X00X00X00X00W00W00W00W00V00V00V00V00U00U00U00U00T00T00T0\ 0T00S00S00S00R00R00R00Q00Q00Q00P00P00P00O00O00O00N00N00N00M00M00L00L00L0\ 0K00K00K00J00J00J00I00I00I00H00H00H00G00G00F00A00500000 } frm: JSomethingelse (xyaxis) { z = pixel: z = p1 * (z*z + 1/z/z) |z| <= 1000000 ;SOURCE: fract002.frm } Roger Alexander _________________________________________________________________ 30 days of prizes: Hotmail makes your day easier! Enter Now. http://go.microsoft.com/?linkid=9729710

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FOTD 29-05-10 (Two-for-One Sale [7])
by Jim Muth 28 May '10

28 May '10

FOTD -- May 29, 2010 (Rating 7) Fractal visionaries and enthusiasts: Today's image gives us two for the price of one. The upper half is partly evaporated, the lower half is not. The line of demar- cation runs right through the center of the image. The 'inside' parts of the upper half have been colored by ren- dering the image with the inside set to the color 255, which in today's palette is a brilliant blue-green. The lower half is all outside stuff rendered in the usual equal-iteration manner. The imag(p3) parameter controls the location of the edge of evaporation, but its value is quite critical. Change it at your own risk. Most of the image's value lies in its mathematical aspect, though the artistic merit adds to the worth, for a final rating of a 7. The name "Two-for-One Sale" refers to the contrasting images on the two halves of the screen. The parent fractal is little more than an amorphous oversized hole with a filament curling up and around to its west. A rather large minibrot lies on this filament. Today's image lies in the interior of the East Valley of this minibrot. The calculation time of a mere 37 seconds is cheap enough, but the trip to see the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> will eliminate all possible calculating problems, such as an over-qualified SOTA computer that can surf the WWW in a few seconds but cannot run a DOS program. Clouds and humidity ruled the weather here at Fractal Central on Friday, with occasional light showers to add variety. The temperature of 77F 25C felt much higher due to the humidity. The fractal cats, apparently unaffected by high humidity, were comfortable. The next FOTD will be posted in 24 hours. Until then, take care, and be of noble heart. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Two-for-One_Sale { ; time=0:00:37.13-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip center-mag=-6.445544478503554/+0.3276897461769029/\ 970000/1/93/0 params=-0.9/-0.9/-0.15/-9.9/0/2435\ 73570000000.0/0/0 float=y maxiter=12000 inside=255 colors=000eaTdcXde`hf_kg_nhZqiZleahaccYe_VgVRiRNlM\ JnIGpDCr98t55v98sDApGDnKFkOHhRKfVMcZO`aRZeTWiVTlYR\ p_OsaMmYSgVYbScXOhSLnMItHFyLDuOCqRAmU9jX8f_6bb5Ze4\ Wh2Sk1On0Ll2Mj3Nh5Of6Pd7Qb9RaAS_BTYDUWEVUFWSHXQIYP\ JYq1Kp6LpBMoFMoKNnPNnTOnYPmbPmfQlkQlpRltRgeZcSe_El\ FXtIVpKUlMTiOReRQbTPZVOWXMSZLOaKLcIHeHEgGAiF7gEBeE\ EdDIbDL`CO_CSYBVXBZVAaTAdS9hQ9kP9nUEiZJecOagSYdQWb\ OU_MSYLQVJOTHMQFKOEITKGJAEG8CE7BNEEHEGIKIKKKLNMMQO\ NTQPXSQ_URbWSeYUh_VkaZnccqehrfmrhrrmvrrzsvzszzszzu\ vzwrzzmzzhzzgzzfzzezzczybzxavx`ry_myZht_co`ZkaUfbP\ acMYdJTeGOfDKgAFh7Ai56j6Ai6Ah6Ag6Ag6Ff6Ke6Pe6Ud6Zc\ 6cb6hb6ma6r`6v`mz`zl`vkbczzmkekhfjchiZihUkgPleKncF\ oaAp_AkZAgZAcYA_YAVYARXANXAJYAEYVAZT6_S2YR3VR3SR3P\ R3MR3JR3GR3DR3AR37R3AS4CT4EU4GV4IW5KX5MY5OY5QZ6S_6\ U`6Wa6Yb7_c7ad7cd7de9deBdeCeeEefFefHffJffKfgMggNgg\ PggQjN5iQ9hSzgVHgXLfZPczz } 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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Re: [Fractint] FOTD 28-05-10 and a new post
by Roger Alexander 28 May '10

28 May '10

Re: FOTD 28-05-10. Jim, a great example of the inexhaustible potential of the classic mandelbrot. Yesterday was busy-busy at Action Central and I didn't get to post. Hope this fractal makes up for the delay. Another typo, well a cousin of a typo, I wrote in the post of May 26 the image resembled the Phoenix type. I meant the Manowar type. Arrrgh! Tardily posted at http://maxitersfractalfollies.blogspot.com fract229.gif { ; semi-spiralish ; blank ; calctime 0:20:21.98 ; created May 28, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_d.frm formulaname=D3_Jul center-mag=0.577524/0.161422/40.39831 params=-0.8994720297860652/-0.336527603991821/-0.01571703238013855/-0.88\ 70204779198584 float=y maxiter=1500 inside=0 logmap=81 colors=00000000200400600800A00C00E00G00I00K00M00O00Q00S00U00W00Y00_00a00\ c00e00g00i00k00m00o00q00s00u00w00z01z03z05z07z09z0Bz0Dz0Fz0Hz0Jz0Lz0Nz0P\ z0Rz0Tz0Vz0Xz0Zz0`z0bz0dz0fz0hz0jz0lz0nz0pz0rz0tz0vz0xz0zz0zz0yz0xz0wz0v\ z0uz0tz0sz0rz0qz0pz0oz0nz0mz0lz0kz0jz0iz0hz0gz0fz0ez0dz0cz0bz0az0`z0_z0Z\ z0Yz0Xz0Wz0Vz0Uz0Tz0Sz0Rz0Qz0Pz0Oz0Nz0Mz0Lz0Kz0Jz0Iz0Hz0Gz0Fz0Ez0Dz0Cz0B\ z0Az09z08z07z06z05z04z03z02z01z00z00z03z07z0Bz0Fz0Jz0Nz0Rz0Vz0Zz0bz0fz0j\ z0nz0rz0vz0uz1tz1sz2rz3pz3oz4nz5mz5kz6jz7iz7hz8gz9ez9dzAczBbzB`zC_zDZzDY\ zEWzFVzFUzGTzHSzHQzIPzJOzJNzKLzLKzLJzMIzNGzNFzOEzPDzPCzQAzR9zR8zS7zT5zT4\ zU3zV2zW0zW0zV0yV0xU0wU0vT0uT0tS0sS0rR0qR0pQ0oQ0nP0mP0lO0kO0jN0iN0hM0gM0\ fL0eL0dK0cK0bJ0aJ0`I0_I0ZH0YH0XG0WG0VF0UF0TE0SE0RD0QD0PC0OC0NB0MB0LA0KA0\ J90I90H80G80F70E70D60C60B50A509408407306305204203102101 } frm:D3_Jul { ; Morgan L. Owens <packrat(a)nznet.gen.nz> ; Sun, 19 Jan 2003 18:54:47 z1=real(pixel),z2=imag(pixel),z3=0 c1=real(p1),c2=imag(p1),c3=real(p2): nz1=z1*z1+z2*z3+z3*z2+c1 nz2=z1*z2+z2*z1+z3*z3+c2 nz3=z1*z3+z2*z2+z3*z1+c3 z1=nz1,z2=nz2,z3=nz3 z=nz1+flip(nz2) |z-pixel| < 100 ;SOURCE: morgan~1.frm } Roger Alexander _________________________________________________________________ 30 days of prizes to be won with Hotmail. Enter Here. http://go.microsoft.com/?linkid=9729709

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FOTD 28-05-10 (Seahorse Valley Scene [6])
by Jim Muth 27 May '10

27 May '10

FOTD -- May 28, 2010 (Rating 6) Fractal visionaries and enthusiasts: How about a trip to Seahorse Valley of the Mandelbrot set? Every so often I get an uncontrollable desire to return to the M-set to see what new old-stuff I can dredge up. Today I have dredged up a minibrot in a period-20 star on the west side of the north branch of the valley. Minibrots in Mandelbrot stars are nothing new, but today's image seems just far enough above average to meet FOTD standards. The name "Seahorse Valley Scene" tells it like it is. The rating of a 6 says that the image is a little above average. On my fractal dedicated machine the image finishes before the video can switch to SF5 mode. On any machine it should finish in no more than one minute. But why worry about calculation at all? The trip to the FOTD web site at: <http://www.Nahee.com/FOTD/> is effortless, and the image may be seen there in all its virtual glory. Another midsummer-like day passed without incident here at Fractal Central on Thursday. With the cool air now running at FC, the fractal cats passed the day in blissful comfort, while the outside temperature reached 91F 33C. They were disturbed only by a late-afternoon cat fight that erupted nearby. My day was acceptable, and there was no fight, of the human or cat kind. The next FOTD will be posted in 24 hours. Until then, take care, and how can anyone be naive enough to think we puny humans can halt the earth's natural warming cycle by pass- ing some meaningless laws that do nothing but make us feel good? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= SeahorseValeyScene { ; time=instantly on a P4-2000mhz reset=2004 type=mandel center-mag=-0.7579385211067\ 7/+0.07655879014348/1.791076e+010/1/173.7/0 float=y params=0/0 maxiter=12000 inside=0 colors=000FMHHLIILJKLJMKKOKKPKLRJMmJzmJzmIzYIm_Ima\ HmbHQdHRfGRhGSkHTiGShGSgGRfGReGRdGQcGQbGPaGP`GP_GO\ ZGOYGNXGNWGNVMHVRBVX5Va0U`3U`6U_9U_CUZFUZHUZKUYNUY\ QUXTUXVUXYUczUqzUnzUkzUhzUczUZzUUzUTwUTyVWxVYxV_wW\ awWcvWevXguXiuXktYmtYosYqs_nt`ktaitcftddteatf_thXu\ iUujSulPumNunKuoIugFi`CZU9ON6DY75_A6`C7aE7cH8dJ8eL\ 9fN9hQAiSAjUBkWBmZCn`CobDpdDrgEsiEtkFumFpiIkeLfbOa\ ZRXWUSSXNP_ILbDGfEIeEJdFKcFMbGNbGOaHQ`HR_IS_IUZIXY\ JYXJ_WK`WKaVLbUMcTQdTUeSYfRagQeiUilQmoNqrKuuGvtHws\ IwrJwqKwpKwoKwnKwmKwlKwkKwjKwiKwhKwgKwfKzeJydIycHy\ bGyaGy`Fx_FxZFxYFxXExXExYEwZEw_Ew_Dw`DwaDvbDvbCvcC\ vdCveCxfBveCtdCrcCpbCnaDl`Dj_DhZDfYDdXEbWE`VEZUEXT\ EVSFTRFRQFPPFNOFLNGJMGHLGFKG9LHDKGGJFJIFMHEPGESFDV\ EDYDCaCBdBBgAAj9Am89p79s68z42v58r5En5Jj6Pf6Ub6_Z7d\ V7jS7oTAnTDmTGlTJkTMjTPiTSiUVhUYgU`fBLRBLQBLOBLNAM\ MAMLAMJ9NI9NH9NG9NFBMGDMH } END PARAMETER FILE=========================================

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FOTD for 5/26/10
by Brian Prentice 27 May '10

27 May '10

While searching in vain for a midget in Jim's fractal for today I found these two details: http://linuxenvy.com/bprentice/Fractals/Set%2014/BP_14_76a.png http://linuxenvy.com/bprentice/Fractals/Set%2014/BP_14_76b.png Brian Prentice

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FOTD 27-05-10 (Squirt Minibrot [7.5])
by Jim Muth 26 May '10

26 May '10

FOTD -- May 27, 2010 (Rating 7.5) Fractal visionaries and enthusiasts: THIS VERSION WORKS!!! Today's unusually colorful image shows a minibrot in the parent fractal that comes about when the expression Z^(sqrt(2))+C is iterated 11 levels up the complex logarithmic hyperladder, and no function is applied. In this case, the series of elements around the minibrots is 1.4142, 2, 2.8284, 4, 5.6569, 8, etc. But with all the discon- tinuities in the images, this series is exceedingly difficult to discern. Despite the discontinuities, some interesting scenes sometimes pop up along the way however, and today's image is one of these scenes. The name "Squirt Minibrot" is a play on the words 'square root'. I rated the image at a 7, then added a half-point bonus for my part in the coloring, most of which was done by the program anyway. The calculation time of just under 3 minutes is about what the image is worth. Extra value may be found by surfing out to the FOTD web site at: <http://www.Nahee.com/FOTD/> and enjoying the finished image in virtual relaxed comfort there. The fractal cats complained about the hot weather here at Fractal Central on Wednesday. When the temperature reached 91F 33C, they stretched out so far on the wood floor that we had to turn on the cool air for the first time this season. With the cool air on, the rest of the day was comfortable enough, at least indoors. The next FOTD will be posted in 24 hours. Until then, take care, and take my word for it. The globe certainly *IS* getting warmer. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Squirt_Minibrot { ; time=0:02:52.20-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident inside=0 center-mag=+0.2626651480634892/+0.8900190082293845\ /3.828861e+011/1/55/0 params=1.4142/0/11/0 float=y maxiter=1800 logmap=395 mathtolerance=0.05/1 colors=000T09V0AW0AX0AZ0B_0B`0Bb0Cc0Cd0Cf0Dg0Dh0Dj\ 0Ek0Em0Em0Kn0Qo0Wq0`r0cs0gt0kl5cmA_mEYnIVnMRnQNoUJ\ oYFoaBk`Cg_Dc_E_ZFWYFSYGOXHKWIGUICSJ8RK4PL1OLazC`w\ B_tB_qBZnBZkAYgAYcAXZAXVAYWDYXGYYIYYLYZNZ_QZ`TZ`VZ\ aaZbc_cc_cc_dc_ec_ecC0LF0HF0EG0AMA7Q63U30X82cD4mI6\ VN7WR9WWBX`CzeEYjGYnHzmSzlbzllzfmh`m_VnSPiJJeBDeCG\ cDJYELVFOdGQcHTaIWeJYcK`bLbaMe_NhZOjXPmWPyVRzWSuWU\ uWziWztWYgWZfWYdZXb`W`bV_dUYfTWhSVjRTmQRoPPqOOsNMu\ MKwMJyPKsSLmULhXMbZNXaNScOMfPGhPBkQ5mQ0lT4kV8kYCj_\ GjbKidOifSeSXbE`_0d`6c`Cb`IbaOaaUaa_`be`bk_bq_STKH\ 54KBCNHJQNQTTXWZcYdjUfcQhXMiQIkJEmCAn5Dj8GfAJbCMZE\ PVGRRIUNKXJM_FObBQd7SeBTeFTeJWeMZfQcfUhfXmf`rgdvgg\ zgkzgozgrzdozbmz_jzYhzWezKzMAzOAzQAzSAzUAzWAzYAz_A\ zaAzczzezzgzzizzLzzSzzYzzdzzjzzhzzfzzdzzbzzazz_zzY\ zzWzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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 27-05-10 (Squirt Minibrot [7.5])
by Jim Muth 26 May '10

26 May '10

FOTD -- May 27, 2010 (Rating 7.5) Fractal visionaries and enthusiasts: Today's unusually colorful image shows a minibrot in the parent fractal that comes about when the expression Z^(sqrt(2))+C is iterated 11 levels up the complex logarithmic hyperladder, and no function is applied. In this case, the series of elements around the minibrots is 1.4142, 2, 2.8284, 4, 5.6569, 8, etc. But with all the discon- tinuities in the images, this series is exceedingly difficult to discern. Despite the discontinuities, some interesting scenes sometimes pop up along the way however, and today's image is one of these scenes. The name "Squirt Minibrot" is a play on the words 'square root'. I rated the image at a 7, then added a half-point bonus for my part in the coloring, most of which was done by the program anyway. The calculation time of just under 3 minutes is about what the image is worth. Extra value may be found by surfing out to the FOTD web site at: <http://www.Nahee.com/FOTD/> and enjoying the finished image in virtual relaxed comfort there. The fractal cats complained about the hot weather here at Fractal Central on Wednesday. When the temperature reached 91F 33C, they stretched out so far on the wood floor that we had to turn on the cool air for the first time this season. With the cool air on, the rest of the day was comfortable enough, at least indoors. The next FOTD will be posted in 24 hours. Until then, take care, and take my word for it. The globe certainly *IS* getting warmer. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Squirt_Minibrot { ; time=0:02:52.20-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident indide=0 center-mag=+0.2626651480634892/+0.8900190082293845\ /3.828861e+011/1/55/0 params=1.4142/0/11/0 float=y maxiter=1800 logmap=395 mathtolerance=0.05/1 colors=000T09V0AW0AX0AZ0B_0B`0Bb0Cc0Cd0Cf0Dg0Dh0Dj\ 0Ek0Em0Em0Kn0Qo0Wq0`r0cs0gt0kl5cmA_mEYnIVnMRnQNoUJ\ oYFoaBk`Cg_Dc_E_ZFWYFSYGOXHKWIGUICSJ8RK4PL1OLazC`w\ B_tB_qBZnBZkAYgAYcAXZAXVAYWDYXGYYIYYLYZNZ_QZ`TZ`VZ\ aaZbc_cc_cc_dc_ec_ecC0LF0HF0EG0AMA7Q63U30X82cD4mI6\ VN7WR9WWBX`CzeEYjGYnHzmSzlbzllzfmh`m_VnSPiJJeBDeCG\ cDJYELVFOdGQcHTaIWeJYcK`bLbaMe_NhZOjXPmWPyVRzWSuWU\ uWziWztWYgWZfWYdZXb`W`bV_dUYfTWhSVjRTmQRoPPqOOsNMu\ MKwMJyPKsSLmULhXMbZNXaNScOMfPGhPBkQ5mQ0lT4kV8kYCj_\ GjbKidOifSeSXbE`_0d`6c`Cb`IbaOaaUaa_`be`bk_bq_STKH\ 54KBCNHJQNQTTXWZcYdjUfcQhXMiQIkJEmCAn5Dj8GfAJbCMZE\ PVGRRIUNKXJM_FObBQd7SeBTeFTeJWeMZfQcfUhfXmf`rgdvgg\ zgkzgozgrzdozbmz_jzYhzWezKzMAzOAzQAzSAzUAzWAzYAz_A\ zaAzczzezzgzzizzLzzSzzYzzdzzjzzhzzfzzdzzbzzazz_zzY\ zzWzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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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Fractals and Volcanic Colors
by Roger Alexander 26 May '10

26 May '10

More fractal pyrotechnics. This similar in appearance to Fractint's built in Phoenix formula. If you want to make good use of my Flickr account download the finished product at http://maxitersfractalfollies.blogspot.com fract227.gif { ; fiery ; blank ; calctime 0:56:38.74 ; created May 26, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=jo_weber.frm formulaname=hsqr center-mag=+0.19212659824046130/-0.78326189374185100/41407.87 float=y maxiter=1500 logmap=45 invert=6.25000000000024e-005/0.195542521994135/-0.783608213820079 periodicity=0 cyclerange=0/255 colors=xo0xm0xl0xk0xj0xi0xh0xg0xf0yd0yc0yb0ya0y`0y_0yZ0yY0yW0yV0yU0yT0yS\ 0yR0yQ0yP0zN0xM0vL0tK0rI0pH0nG0lE0iD0gC0eA0c90a80_60Y50W40T20S20R30Q30P4\ 0O40N50M50L60K60J70I70H80G80F70E70D60C60B50A5094084073063052042031021000\ 0100300500700900B00D00F00H00J00L10N10P10R10T10W10Y10_10a10c10e20g20i20k2\ 0m20o20q20s20u20w20z30z40z60z70z90zB0zC0zE0zF0zH0zJ0zK0zM0zN0zP0zR0zS0zU\ 0zW0zX0zZ0z_0za0zc0zd0zf0zg0zi0zk0zl0zn0zo0zq0zs0zt0zv0zt0zr0zp0zn0zl0zj\ 0zh0zf0zd0zb0z`0zZ0zX0zV0zT0yQ0wP0tN0qM0nK0lI0iH0fF0cD0aC0ZA0W90T70R50O4\ 0L20I00H20F00F00E00D00C00C00B00A0090090080070060060050040030030020010000\ 0000200500800A00D00G00J00L00O00R00U00W00Z00a00d00f00i00l00o00q00t00w00z0\ 0z10z30z50z70z90zB0zD0zF0zH0zJ0zL0zN0zP0zR0zT0zV0zX0zZ0z`0zb0zd0zf0zh0zj\ 0zl0zn0zp0zr0zt0zv0zx0zz0zy0yx0yw0xv0xu0xt0xs0xr0xq0xp0 } frm:hsqr(XYAXIS) { ; squaring the initialized value of the hydra fractal z = pixel^2,zp=(0,0): temp = z z = z*z + zp zp = temp, |zp| <= 4 } Roger Alexander _________________________________________________________________ 30 days of prizes to be won with Hotmail. Enter Here. http://go.microsoft.com/?linkid=9729709

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Colorful Minibrot
by Roger Alexander 25 May '10

25 May '10

Today's fractal is a minibrot from Fractint's built in mandellambda formula. I like the colors. Ready,able, and willing at http://maxitersfractalfollies.blogspot.com fract219.gif { ; a lacy little minibrot ; blank ; calctime 0:19:34.09 ; created May 21, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=mandellambda corners=1.07587867636758/1.07587864489943/0.42860406873311929/0.42860406\ 907919935/1.07587866487293/0.42860408405932254 params=0/0 float=y maxiter=2400 logmap=213 colors=000302403503504604705805806907A07B08B08C09D1AE1AF1BF1BG1CH1CI1DI1\ EJ1EK1FL1FL1GM1GN1HO2IN2KM2NK2QJ2TH2VG2YE2`D2cB1fA1i81l71n51q41t21w00z03\ z07z0Bz0Fz0Jz0Nz0Rz0Vz0Zz0bz0fz0jz0nz0rz0vz0zz0xz0vz0tz0rz0pz0nz0lz0jz0h\ z0fz0dz0bz0`z0Zz0Xz0Wz0Uz0Sz0Qz0Oz0Mz0Kz0Iz0Gz0Ez0Cz0Az08z06z04z02z00z00\ y10x20v20u30s40r50p50o61n71l81k91i91hA1gB1eC1dC1bD1aE1_F1ZF1YG1WH1VI1TJ2\ SJ2RK2PL2OM2MM2LN2JO2IM2GJ2EH2CE1AC18916614312000101302503605806A07C19D1\ 9E1AF1AF1BG1BH1CI1DI1DJ1EK1EL1FL1FM1GN1HO2IO2JQ2IS2HV2GX2F_2Da2Cd2Bf2Ah1\ 9k18m17p15r14u13w12z00z20z50z70zA0zC0zF0zH0zK0zM0zP0zR0zU0zX0zZ0za0zc0zf\ 0zh0zk0zm0zp0zr0zu0zw0zz0zw0zu0zr0zo0zl0zj0zg0zd0za0z_0zX0zU0zS0zP0zM0zJ\ 0zH0zE0zB0z80z60z30z00x01v02s03q04n06l07i08g19e1Ab1B`1CY1EW1FT1GR1HO2JN2\ IM2HK2GJ2FH2DG2CE2BD2AB19A18817715514413212000000101201 } Roger Alexander _________________________________________________________________ MSN Dating: Find someone special. Start now. http://go.microsoft.com/?linkid=9729707

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FOTD 26-05-10 (More Fractal Stuff [5.5])
by Jim Muth 25 May '10

25 May '10

FOTD -- May 26, 2010 (Rating 5.5) Fractal visionaries and enthusiasts: Today's image shows a screen full of fractal stuff. When I saw the stuff, I named the image "More Fractal Stuff". The scene lies in the parent fractal that results when the formula Z^(1.025)+C is calculated 27 levels up the complex logarithmic hyper-spiral. This parent fractal resembles a stone arrowhead with the tip facing NNW. Today's image is located in debris on the western edge of the large and only open bay. The incredible thing about the image is that an expression so close to being linear can result in such detail when iterated a few thousand times. At first glance the scene looks totally chaotic, but a second look reveals tiny repeating patterns all through the frame. Unfortunately, there is no center of attention in the image, and this lack of a unifying theme costs a full rating point. The bit of extra work I put into the coloring raised the rating a half-point above an everyday 5, but do not expect the thrill of a lifetime when the image first appears. The calculation time of 6-2/3 minutes is slower than the result is worth, so I advise surfing out to see the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> Summer arrived here at Fractal Central on Tuesday, with hot sun all day and a temperature of 86F 30C. The fractal cats of FC stretched out on the carpet and looked very happy. My day was reasonable, which is well within reason. The next FOTD will be posted in 24 hours. Until then, take care, and maybe I should follow the media, which tells us what we should worry about, and be more concerned about global warming and less concerned about cell-phone radiation. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= More_Fractal_Stuff { ; time=0:06:39.91-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-0.7913597645032089/-3.065371046706491/\ 5.402604e+010/1/-125/0 params=1.025/0/27/5000 float=y maxiter=3600 inside=255 logmap=418 periodicity=6 mathtolerance=0.05/1 colors=000RJPRKQRLRSMRSMSSNSTOTTPTSQUTRUUSUVSUWTVX\ UWYVXZWY_XZ`Y_aZ`b_ac`acabcaccbdccecdfcegcfhdgmehr\ fivgjzgkzkkzmmzppzsszvvzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zhsugrugrtfqtfpteptdotdoscnscnsbmsblsalrakr`kr_jr_\ jrZiqZhqYhqYgqXgqXfpWfpVepVdpUdpUcoTcoTboSaoRaoR`n\ Q`nQ_oP_oPZoOYoOYoNXoMXpMWpLWpLVqKUqKUqJTrJTrISsHS\ sHRsGQtGQtFPtFPtEOuDPuEOuEOuENvFNvFMvFMvFLvGLwGKwG\ KwGJwHJxHIxHIxIHxIHyIGyIGyJFyJFzJEzJEzKDzKDzKCzMDz\ LCzKCzKCzJBzJBzIBzIAzHAzHAzGAzG9zF9zF9zE8zE8zD8zD8\ zC7zB7zB7mA6mA6m96m95m85m85m75m74m64m64c53c53c43c3\ 2c43c43c54c54U65X65Y66Z76Z77_87_88`88a98a99bA9bAAc\ AAdBBdBBeCCeCCfCDgDDgDEhEEhEEiEFjFFjFGkGGkGHlGHmHI\ mHInIJnIJoIJoJLnJNmJPlKRkKTkKVjLXiLZhL`gMbgMdfMfeN\ hdNjcNkcOjbOjbPjbPjbQibQibRibRibSibShbThbThbUhbUgb\ VgbVgbWgaWgaXfaXfaYfaYfaZeaZea_ea_ea`ea`daadaadabd\ adc`bda`db_dc_F__G_ZHZYIZ } 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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Fractint's Built In Newton
by Roger Alexander 25 May '10

25 May '10

I was busy yesterday and didn't get around to posting. Here it is a rootin' tootin converging newton. Take Fractint's built in newton formula add some inversion,mix with some fmod and you get today's fractal. As usual ready made at http://maxitersfractalfollies.blogspot.com. fract228.gif { ; classical newton with fmod and inversion ; blank ; calctime 0:02:13.85 ; created May 24, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=newton center-mag=42.2891/-231.357/0.007044422/-1 params=3 float=y maxiter=1200 inside=maxiter proximity=1 outside=fmod invert=23.3678395947142/-0.6718039490951/0.30027161473433 colors=05F05F05F16G16G16G16G16G27H27H27H27H27H38I38I38I38I38I49J49J49J49\ J49J5AK5AK5AK5AK5AK6BL6BL6BL6BL7CM7CM7CM7CM7CM8DN8DN8DN8DN8DN9EO9EO9EO9E\ O9EOAFPAFPAFPAFPAFPBGQBGQBGQBGQBGQCHRCHRCHRCHRCHRDISDISDISDISDISEISEJTFJ\ TFKTGKUGLUHLVHMVIMVINWJNWJOWKOXKPXLPYLQYMQYMRZNRZNSZOS_OT_PT_PT`QU`QUaRV\ aRVaSWbSWbTXbTXcUYcUYcVZdVZdW_eW_eX`eX`fYafYafZbgZbg_ch_ch`ch`diadiaeibe\ jbfjcfjcgkdgkdhlehleilfimfjmgjmgknhknhlniloimojmpjmpknpknqloqloqmprmprnq\ snqsorsortpstpstqtuqturuuruvsvvsvwtwwtwwuxxuxxuxxvyyvyywzzvyyvyyuxxtxxtw\ wsvwsvvruvquuqtupstostorsnqsnqrmprlpqloqknpjnpjmoimohlnhkngkmgjmfjleileh\ kdhkcgjcfjbfibeiaeh`dh`cg_cgZbfZbfYaeX`eX`dW_dW_cVZcUYbUYbTXaSWaSW`RV`RV\ _QU_PTZPTZOSYNSYNRXMQXLQWLPWKPVKOVJNUINUIMTHLTGLSGKSFKRFJREIQDIQDHPCHPBG\ OBFOAFN9EN9EM8DM8CL7CL6BK6AK5AJ49J49I38I37H27H16G16G05F } Roger Alexander _________________________________________________________________ Win a $10,000 shopping spree from Hotmail! Enter now. http://go.microsoft.com/?linkid=9729711

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FOTD 25-05-10 (Merging Julia Sets [8])
by Jim Muth 24 May '10

24 May '10

FOTD -- May 25, 2010 (Rating 8) Fractal visionaries and enthusiasts: Today's super quickie image is super quick only when calculated with the type=julia formula on my 2000mhz machine. When this is done, it finishes in a stunning 35 seconds. The image is a Julia set, or rather a merging of two separate Julia sets related to Seahorse Valley of the large minibtot on the west branch of the filament extending from the large north bud of the Mandelbrot set. This merging may be seen in progress by changing the initial C-value of the image. But this value is extremely critical, so change only the least significant digits. The merging of separate Julia sets was hinted at in yesterday's image, but I have never actually seen it before it appeared while I was searching for today's image. The name "Merging Julia Sets" is self explanatory. The rating of an 8 is based mostly on the mathematical interest. The artistic value is closer to a 6. And do not be surprised if the image requires quite a few minutes to calculate. The time of 35 seconds is true only on my 2000mhz fractal-optimized unit. The 200mhz machine chugs away for over 9 minutes. Of course, the finished image is available as always on the FOTD web site at: <http://www.Nahee.com/FOTD/> While reading the May 31 issue of the struggling 'Time' magazine at lunch today, I came upon a short article on page 15 about the results of the latest study of the possible connection between cell-phone use and brain damage. The study proved inconclusive. Surprise, surprise. This is exactly what would be expected from a team of investigators who cannot honestly say the phones are safe, and at the same time are under heavy political pressure not to declare them a risk. My opinion is that the continuing inability to find the phones safe for unlimited use is an implied admission of the risk of cell-phone radiation. I, for one, consider the phones to be devices mainly for emergencies. I'm also thankful I have no children worrying me for a __________. (Fill in the blank with whatever wireless on-line device is the current fad among the kiddies.) Monday turned out better than expected here at Fractal Central. There were more clouds than would have been ideal, but no rain fell and the temperature reached a very comfortable 79F 26C. The fractal cats kept their eye on the activity at the nearby hawk's nest most of the time. For me the day was about average, and with any luck, tomorrow will be the same. The next FOTD will be posted in 24 hours. Until then, take care, and maybe the cell-phone situation is a plot of the evil aliens from Arcturus who want to turn us into brain-dead zombies. But wait a minute . . . Why do we need aliens when the public schools are already doing the job? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Merging_Julia_Sets { ; time=0:00:35.37-SF5 on P4-2000 reset=2004 type=julia center-mag=0/0/36910/1/127/0 params=-0.1613440487151149/-1.036047040470627 float=y maxiter=250000 inside=0 periodicity=0 colors=000NB6NC6OC6PD6QE6QE6RF5SG5TG5TH5UI5VI5WJ4W\ K4XK4YL4ZM4YL3ZM4_N5`N6`O6aO7bP8bQ8cQ9dRAeRAeSBfSC\ gTCgUDhUEiVEjVFjWGkXGlXHlYImYInZJoZKo_Kp`Lq`MqaMra\ NsbOsbSsbQsbPsbOraMp_LoYKnWImVHkUGjUEiUDiUBhUChUCh\ UDhUDgUDgUEgWEgYEg_FfaFfcFfdGfeGffGegHehHeiIejIdkI\ dlJdmJdnJdoKcpKcqKcrLcsLft8iuDfvHcwL`xPYyTVzXRzaOz\ eLziIzmFzqCzu9zyCzvEzsHzqJznMzkOziRzfTzdWzaYzZ`zXb\ zUezRgzPjzMpzHozInzJmzKlzKkzLjzMizNhzNgzOfzPgzQhzQ\ izRjzSkzTlzTmzUnzVozWpzWqzXrzYszZtzZzz_zz`zzgzzmzz\ gzwcwtdtqdqpdnodkmchkcekbbjb_jaXiaUi`Rh`Oh_Lg_KfZK\ fZKeYKeYKdXJcXJbWJbWJaVJ`VJ_UJZUJYTIXTIWSIVSIURIUR\ IUQIUQEUSFUTGUSHTRISQJRPKQOLPNLPMMOLNNKOMJPLHQKGRK\ FRLESLDTLCULBVLAWL9XL8ZN6YN7XN7XM7WM7WM8VL8VL8UKTU\ KTTKTSKSSJRRJQRJPQIOPINPHMOHLOHKNGJNGIMGHLFGLFFKFE\ KEDJECCABEBAGCAIDAJEALFANGAH6AIAIJAAKAALAAMAAMAAMA\ AMAAMAANAANAANAANAANAANAA } END PARAMETER FILE=========================================

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Swirlies
by Roger Alexander 23 May '10

23 May '10

Today's graphic has an unexpectedly convincing 3d appearance. The swirling design could represent the root system of some silicon based vegetation. This brings me to a completely unrelated point. I run Fractint through the dos emulator D-Fend Reloaded under Vista. When generating the fractals I frequently switch between background and foreground processes which means the calctime values in the par files may longer than if generated completely in foreground mode( I use a laptop with an Intel 2 GHz T3200). To avoid the bother of having to prove this view the completed fractal at http://maxitersfractalfollies.blogspot.com fract225.gif { ; swirlies-almost 3-d ; blank ; calctime 0:05:41.86 ; created May 23, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=forum_97.frm formulaname=january_gen function=abs/cabs/exp center-mag=-1.65129/0.104802/3.370408/1/24.9990000000000165/2.5833502004\ 2466112e-014 params=6/-1/10/-1 float=y maxiter=1000 proximity=2 outside=fmod decomp=256 periodicity=0 cyclerange=0/255 colors=000000000100100200400500700900B00D00G00I00L00O10Q10T10W10Z10a10e1\ 0h20k20o20r20v20y20z30z50z60z80z90zB0zC0zE0zF0zH0zI0zK0zL0zN0zO0zQ0zR0zT\ 0zU0zW0zX0zZ0z_0za0zb0zd0ze0zg0zh0zj0zk0zm0zn0zp0zq0zs0zt0zv0zw0zy0zz1zz\ 3zz4zz6zz7zz7zy7zx7zx7zw7zv7zv7zu7yt7ys7ys7yr7yq6yq6yp6yo6yo6xn6xm6xl6xl\ 6xk6xj6xj6xi5xh5wh5wg5wf5we5we5wd5wc5wc5vb5va5va5v`4v_4vZ4vZ4vY4vX4uX4uW\ 4uV4uV4uU4uT4uS3uS3uR3tQ3tQ3tP3tO3tO3tN3tM3tL3sL3sK3sJ2sJ2sI2sH2sH2sG2sF\ 2rE2rE2rD2rC2rC2rB1rA1rA1r91q81q71q71q61q51q51q41q31p20p20o20n20m20m20l2\ 0k20j20j20i20h20g20g20f20e20d20d20c20b20a20a20`20_20Z20Z20Y20X20W20W20V2\ 0U20T20T20S20R20Q20Q20P20O20N20N20M20L20K20K20J20I20H20H20G20F20E20E20E2\ 0D20D20C20C20C20B20B20A20A20A2092092092082082072072072062062052052052042\ 0420420320320220220220120120010000000000000000000000000 } frm:January_gen { ; Modified Sylvie Gallet "january" formula ; Based on Scott Burns equation solver applied to z^3-1 = 0 ; Use decomp = 256 ; generalized by Les St Clair, Dec 1997 ; use p1(real)=6, p2(real)=10, fn1=abs, fn2=cabs & fn3=exp for default behaviour z1 = pixel , iter = 0 a = 23*(0,0.0245436) ; 23 * 2i pi / 256 mz = fn1(fn2(z1)-1) : if (mz >= 0.1) z2 = z1*z1 z1 = ((1,-1)*z2*z2 + (7,1)*z1) / (2*z1*z2 + p1) mz = fn1(fn2(z1)-1) , cont = 1 iter = iter + 1 else z = fn3((iter + p2*mz)*a) cont = 0 endif cont } Roger Alexander _________________________________________________________________ 30 days of prizes to be won with Hotmail. Enter Here. http://go.microsoft.com/?linkid=9729709

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FOTD 24-05-10 (Passing in the Night [6.5])
by Jim Muth 23 May '10

23 May '10

FOTD -- May 24, 2010 (Rating 6.5) Fractal visionaries and enthusiasts: For some strange reason, today's image reminds me of two ships passing peacefully in the night, which explains the name "Passing in the Night". But the image does not show two ships passing; it shows two almost-Julia sets arranged in a symmetri- cal pattern around an imaginary point. The image is located in the Seahorse Valley complex of the large minibrot on the main spike of the Mandelbrot set. The orienta- tion is double-rotated 0.005,0.005 degrees from the true Julia direction. As is true of many near-Julia sets, this tiny rota- tion makes a world of difference in the appearance of the inside parts of the parent fractal. The twin almost-Julia-set theme of today's image is repeated without change at ever smaller scales at the centers of the Julia sets in the image, apparently all the way to infinity, which is the way things usually go in the world of fractals. The basic image rates a 6. The extra half-point that brings the rating to 6.5 is a reward for the effort I put into coloring the scene in an effort to make the almost-Julia sets resemble real three-dimensional objects. The calculation time of 5 minutes is true on the 2000mhz unit. Surprisingly, on the 200mhz unit the same image finishes in well under 9 minutes, which is only 1.8 times the running time of the supposedly 10 times faster unit. Even more surprising, with type=mandel fractals the 10-times-faster machine runs almost 20 times as fast. But why not forget this timing confusion by visiting the FOTD web site at: <http://www.Nahee.com/FOTD/> and viewing the finishedimage there. Clouds and occasional light showers of rain marred Sunday here at Fractal Central, though the temperature of 75F 24C could hardly have been improved upon. The fractal cats showed their dis-satisfaction when they got into a spat to decide who would spend the afternoon on the ottoman foot-stool. Cassie won the minor dispute with a loud hiss and a hit to Nicholas' head. Nicholas then sulked for an hour or so. My day was about average; most likely Monday will be the same. The next FOTD will be posted in 24 hours. Until then, take care, and everything that happens above the quantum level has a probable cause, but does it have a reason? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= PassingInTheNight { ; time=0:05:08.10-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=+0.000680161\ 02056917/+0.00100690867803902/1095589/1/-2.5/0 params=89.995/0/89.995/90/-1.768531/0.0002/0/0/2/0 float=y maxiter=32767 inside=255 periodicity=0 colors=000Ok5Ok5Nk5Pl5Um5Zn5co5hp5mq5rr5vz4zz3zz2z\ z2vz4rz6my7hw9cuBZsCUqEPpGKoHInJKmLLlMNkOPjQQiRShT\ TgURfSQfRPeQOePNdOMdMLcLKcKJbJIbIHbGGaFFaEE`DD`CC_\ AB_9AZ89Z78Z69`CAbIBcOCeUDg_EhdIccM_cPWcNYdM_dLaeK\ beIdfHffGggFigDkhCmhBniApi8rj7sj6uk5wk4xk6wl8vlAum\ BtmDsmFrnGqnIpnKooLnoNmpPlpQkpSjqUiqVhqXgrZfr_frag\ nbhjdigejcgk`hlXjmUkmQmnNnoJppGqqCsr9ts5us2tp3sm3s\ k3rh3qf4qc4pa4oZ4oX5nU5mR5mP5lM6kK6kH6jF6iC7iA7h77\ H6RJ7TL8VN9XPA_RBbTCeVDhXElZFo`GrbHucIxdJzdKzeLzeM\ zeNzfOzfPzgQzgRzgSzeTzcUzbXz`Zz_azYczXeuVhuTjtSmtQ\ otPqsNrsMssItoFukBvg8wd4r`1mX0hUBcTDZSFVRHSRJQQLOP\ NMPQKOSJNUINeMMjTLrVLwYKz`JzcJzdIzcHzaHz_GzYFzWFzU\ GvSHqQInOJkMKhKKfILeGMcEKbCF`DAZEAYFAWGAVHATIASJAQ\ KAOKALKAJKAHKAJKALKANKAPLFRMGTNGROHPPINQJMRKLSKKTL\ JUMIVNHWOGXOGYNGXNHWMHVLIULIUKJUKJUJJUJKUIKUHLUHLU\ GMWGMYFM_FQaDUcBXeA`g8ci7 } frm:SliceJulibrot4 {; draws all 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=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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Fractal Mashup
by Roger Alexander 23 May '10

23 May '10

Busy yesterday didn't get time to post the Fractal Follies fractal. Well here it is, a fusion of iteration loops, with bailouts and inverse bailouts. You've got newtons in my mandelbrots-you've got mandelbrots in my newtons! While not tachyon based and faster than light instant viewing is available at http://maxitersfractalfollies.blogspot.com fract224.gif { ; newtons and mandelbrots my oh my! ; firey colors ; calctime 0:01:17.67 ; created May 22, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=bejones.frm formulaname=BJ-SG-MaNewt-001 function=recip center-mag=-0.480601/0/0.6666667 params=24/0 float=y maxiter=2400 inside=0 periodicity=0 colors=000000000000000000000000000000000100100200400500700900B00D00G00I0\ 0L00O10Q10T10W10Z10a10e10h20k20o20r20v20y20z30z50z60z80z90zB0zC0zE0zF0zH\ 0zI0zK0zL0zN0zO0zQ0zR0zT0zU0zW0zX0zZ0z_0za0zb0zd0ze0zg0zh0zj0zk0zm0zn0zp\ 0zq0zs0zt0zv0zw0zy0zz1zz3zz4zz6zz7zz7zy7zx7zx7zw7zv7zv7zu7yt7ys7ys7yr7yq\ 6yq6yp6yo6yo6xn6xm6xl6xl6xk6xj6xj6xi5xh5wh5wg5wf5we5we5wd5wc5wc5vb5va5va\ 5v`4v_4vZ4vZ4vY4vX4uX4uW4uV4uV4uU4uT4uS3uS3uR3tQ3tQ3tP3tO3tO3tN3tM3tL3sL\ 3sK3sJ2sJ2sI2sH2sH2sG2sF2rE2rE2rD2rC2rC2rB1rA1rA1r91q81q71q71q61q51q51q4\ 1q31p20p20o20n20m20m20l20k20j20j20i20h20g20g20f20e20d20d20c20b20a20a20`2\ 0_20Z20Z20Y20X20W20W20V20U20T20T20S20R20Q20Q20P20O20N20N20M20L20K20K20J2\ 0I20H20H20G20F20E20E20E20D20D20C20C20C20B20B20A20A20A2092092092082082072\ 0720720620620520520520420420420320320220220220120120010 } frm:BJ-SG-MaNewt-001 { ;Modified Sylvie Gallet [101324,3444], 1995 z = fn1(1/pixel) , c = z , iter = 1 rad = 3.1 , center = (1.0,0.1) pix = (10*pixel+(5.0,-3.4))*(-0.1,-0.95) zn = center+rad/(pix-center) limit = real(p1) , b1 = 16 , b2 = 0.0001 : test1 = (iter<limit) , test2=(iter!=limit) z = (z-zn)*test2 + zn z2 = z*z , z4 = z2*z2 , z1 = (z4*z-1)/(4*z4) z = (z2+c)*test1 + (z-z1)*(1-test1) iter = iter+1 ((|z| <= b1) * test1) || ((|z1| >= b2) * (1-test1)) } Roger Alexander _________________________________________________________________ Win a $10,000 shopping spree from Hotmail! Enter now. http://go.microsoft.com/?linkid=9729711

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FOTD 22-05-10 (Lost in Hyperspace [6])
by Jim Muth 21 May '10

21 May '10

FOTD -- May 22, 2010 (Rating 6) Fractal visionaries and enthusiasts: Today's image is a scene in an abstract four-dimensional object known as the Z^2+C Julibrot. It is not a scene in the Mandel- brot set, nor in one of the perturbed M-sets. Neither is it a part of any Julia set. True, it resembles a Julia set of the East Valleys of minibrots, but only one single line of it is part of any Julia set. Actually, today's image is a hybrid. In one direction it has Mandelbrot characteristics; in the perpendicular direction it has Julia characteristics. It lies in the orientation I have named the Rectangular, which is defined by the imag(z) and imag(c) axes. The image, which has been generously stretched and skewed, lies in the East Valley complex of the large minibrot on the main spike of the M-set, a short distance in the plus-imag(z) direc- tion from the M-set itself. The rating of a 6 is about what the image is worth, (IMO). The name "Lost in Hyperspace" might be the title of a sci-fi series, but it actually describes the location of today's scene. The calculation time of 1-5/6 minutes is brief by any standards. Equally brief is the time required to surf out to the FOTD web site at: <http://www.Nahee.com/FOTD/> where the finished image may be viewed in relaxed comfort. A hazy sun and temperature of 86F 30C made everyone happy here at Fractal Central on Friday. The fractal cats were especially happy, though they still kept a watchful eye out for any stray cats that might have wandered into the yard. The activity around a hawk's nest in a nearby tree also attracted their attention. My day, and FL's day as well, were satisfactory. There is a 90-percent chance the next FOTD will be posted in 24 hours, which means there is a 10-percent chance it will be late. Until whenever, take care, and if you want to know the meaning of existence, check your fractals. The answer might lie hidden there. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Lost_in_Hyperspace { ; time=0:01:50.17-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=+0.000000105\ 71810928/-0.09620033683075102/1.169683e+009/0.2073\ /94.7415060222973153/84.1664349416200679 params=90\ /90/0/90/-1.749996/0/0/0/2/0 float=y maxiter=3300 inside=0 periodicity=6 mathtolerance=0.05/1 colors=000DNUFMPGKLIIHKHDQF9XD5bC1iG2pK2qO2nS2kM3g\ 73d63a53b44d34f24g24h29h2Di2Hi2Mj2Qj2Uk2Yk2bl2fl2j\ n0ll2nk4mj5li7jh9igAhfCfeEedFdcHcbJaaK``M__OYZPXYR\ WXTUWUTVWSOzXUXRVYQWZPX_OY`NZaMZaL_bK`cJadIbeHcfGc\ fFdgEehDfiCgjBhkAhk9il8jm7kn6lo5mp4mp45KAFRIOYPYdW\ islfkbdcTbXJ`P9ZI0`J2aK4bL5cM7dN9eOAfPCgQDhRFiSHkT\ IlUKmVMnWNoXPpYQqZSr_Us`VtaXxdZubYsaXp`WnZVlYUiXTg\ WSeURbTQ`SPZROXTMWVLVXKTZJS`IRbHQdGOfFNhEMjDKlCJnB\ IpAHr9Ft8Kv7Px6Uy5Zw8cuBhtEmrGrpJvoMzmOzlRzjUzhWzg\ Zzeazcczbfz`iv_krblmdnhgoccNUcVUcaUciShQTmUTrYTvaU\ zeUziUzmHzpJzpKzpLzpNzpOzpP`pRcpSepTgpNWHOXKOYNPZP\ P_SQ`UQaXRbZRcaShdSmfTriTvkUznk4hi9igEjeIkcNlaSm_W\ nY`oWepZFaXNeWViVbm9ZoKdp`1CNFJQQVS_e9XkBYlCZlD_lF\ `mGamHamJbnKcnLdnNeoOeoPfoRgpShpTip_wvZvuZuuZuuYtt\ YstYstYrtXrsXqsXpsXpsWorWorWnrWmrVmqVlqVlqVkqUjpUj\ pUipdSd`Yh5Wm7Ui8SeARaCPY } frm:SliceJulibrot4 {; draws all 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=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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Minibrotism
by Roger Alexander 21 May '10

21 May '10

All dressed up in its outside=fmod finery this is my latest example of the ubiquitous minibrot. Ready for viewing at http://maxitersfractalfollies.blogspot.com fract220.gif { ; oddie brottie ; blank ; calctime 0:21:13.94 ; created May 21, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_n.frm formulaname=Nova4M passes=1 corners=-1.1854614102/-1.1822732582/0.27467439881/0.2761185895/-1.185006\ 887/0.27406836789 params=0/0/1e-007/0 float=y maxiter=1200 inside=0 proximity=1 outside=fmod colors=00000000000000000000000000000000000000000000000000000000000000000\ 000000000000000000000000000000000000000000000000000000000000000000000000\ 0000000000000000000000000000000000000000mwzmwzlwzlwzkwzkvzjvzjvzivziuzhu\ zhuzguzguzftzetzetzdtzdszcszcszbszbszarzarz`rz`rz_qzZqzZqzYqzYqzXpyXpyWp\ yWpyVoyVoyUoyUoyTnySnySnyRnyRnyQmyQmyPmyPmyOlyOlyNlyNlyMlyLkyLkyKkyKkyJj\ yJjyIjyIjyHjyHixGixGixFixEhxEhxDhxDhxCgxCgxBgxBgxAgxAfx9fx9fx8fx7ex7ex6e\ x6ex5ex5dx4dx4dx3dx3cx2cx2cx1cx0bw0aw0aw0`w0`w0`v0_v0_v0_v0Zv0Zu0Zu0Yu0Y\ u0Xu0Xu0Xt0Wt0Wt0Wt0Vt0Vs0Us0Us0Us0Ts0Tr0Tr0Sr0Sr0Rr0Rq0Rq0Qq0Qq0Qq0Pp0P\ p0Pp0Op0Op0No0No0No0Mo0Mo0Mo0Ln0Ln0Kn0Kn0Kn0Jm0Jm0Jm0Im0Im0Il0Hl0Hl0Gl0G\ l0Gk0Fk0Fk0Fk0Ek0Ej0Dj0Dj0Dj0Cj0Ci0Ci0Bi0Bi0Ai0Ai0Ah09h09h09h08h08g08g07\ g07g06g06f06f05f05f05f04e04e03e03e03e02d02d02d01d01d00c } frm:Nova4M {; Mandelbrot-like set for Nova4. ; P2 is an inverse bailout, ; set this to a small nonzero value and use ; floating point. E.g. 0.0000001. ; The Nova Formulae, discovered by PGD. ; Freely distributable but may not be sold. z=1 c=pixel: z2=z*z z3=z*z2 z4=z*z3 func=z4-1 der=4*z3 oz=z z=z-(func/der)+c |oz-z|>p2 ;SOURCE: nova.frm } Roger Alexander _________________________________________________________________ 30 days of prizes to be won with Hotmail. Enter Here. http://go.microsoft.com/?linkid=9729709

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FOTD 21-05-10 (Something for Nothing [7.5])
by Jim Muth 21 May '10

21 May '10

FOTD -- May 21, 2010 (Rating 7.5) Fractal visionaries and enthusiasts: The center coordinates of today's image are not an error. The scene of the image is actually located that far from the origin. The parent fractal is a monstrous distorted Mandeloid shaped like a figure-eight, with a magnitude of 0.00004, which is as small as the program can go. Actually, this parent fractal is only the large minibrot on the main spike of its parent Mandel- brot set, which is somewhere beyond reach, probably larger than infinity. The elements of the image resemble those of East Valley of the M-set, though the location of the image is in the detail on the western shore line of the northern lobe of the parent figure- eight fractal, which is nowhere near East Valley. The name "Something for Nothing" refers to the huge size of the parent fractal, which I once assumed would allow deeper inzooms. Unfortunately, increasing the size of the parent fractal merely shifts the decimal point. It does not create the greater preci- sion that would make greater magnification possible. After a few minutes of deep pondering, I rated the image at a 7.5, granting myself a 1/2 point bonus. I could rate it no higher, as it is really only another scene in the East Valley of a minibrot. The calculation time of 7-1/2 minutes is true on the P4-2000mhz machine. On the ancient but still working 200mhz 80586 unit, the image takes 41 minutes to finish. So why not forget the time your machine might take to run the included parameter file, if it will run the file at all. Hurry to the FOTD web site at: <http://www.Nahee.com/FOTD/> where the finished image is posted, and enjoy instant gratifica- tion. An absolutely perfect spring day (sunny and 84F 29C) here at Fractal Central on Thursday was fully enjoyed by all, including the fractal cats in particular, who spent the entire afternoon watching the world go by. With the real work finished, my day was slow, which gave lots of time for pondering fractals among other things. FL spent a lot of time pondering ways to improve her garden. The next FOTD will be posted in 24 hours. Until then, take care, and if God is unchanging, as He would have to be if He is truly eternal, why has He apparently changed his mind about performing miracles such as we read about in the scriptures? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= SomethingForNothin { ; time=0:07:36.43-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=+14554.248291498/+19127.966866476/24444\ /1/97.5/0 params=-7/2/-7/1/-0.72/0/0/0 maxiter=6400 inside=0 logmap=-1200 periodicity=0 mathtolerance=0.05/1 colors=000766A98DBAGDCIFELHGO\ JIQLKTOMWROYTQ`WScZUhcWmhTrmQvsUzpYzmazieweiuaitYi\ sUhsQgrMfqIepEdoAco7cpA`pCZpEWpGUpIRpKPlNShPUdSW`U\ YXX_TZaPacLccHfcDhm9jzAhzBgzCdzDZVEURFPNGKJKPFPUBU\ ZAZc9ch8hl6mp5rs4vw3yl2r_9fRF_KLQE0K30G40D40A50050\ r_ztbzubzwgzyhzzgzyXzxXzwXzvLkuNjtPitRhsUgrWfqYep_\ doacncbom`neanYazTzvSzrcznQzjPbfOcbNeZMfVLhRKiHlPO\ HcOIgOJjOJmOKpIJyLKvOKsQKpTLmWLjYLg`MebMbeM_hNXjNU\ mNRqLSpMRpMQoNPoNPnNOnONmOMsG9mOMgWZhltehpcemabj__\ gYXcYo9P_8zz7yuLyvQzwUzxYsyNmzDzz3ez5zz7cz8zzAazBz\ zDZzFzzGzzIzzJzzIzzIzzIzzIzzJzzJzzKzzKzzKzzLzzLzzM\ zzMzzMVzNTzNQzOOzOMzO6zoAzjDzfHzbKzZNzVRzRUzNYzJ`z\ FczBazE_zHYzKWzNUzQSzTQzWOzZMzaKzdIzg5zcBzgHzjNznT\ zqjzudztZztTzsOzsIzrCzr7zrBzmEzhHzcLz_OzVRzQhzTczQ\ ZzOUzM5zR4zQ4zP8zSCzVGzXKz_NzaRzdVzfZzibzkeznizpmz\ sqzuuzxxzzxzxxzvxztxzrxzpxznqzIszGuzEwzCxzHxzm } 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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Re: [Fractint] AOTD 5_15
by JackOfTradeZ＠comcast.net 21 May '10

21 May '10

. Animation of the Mayan Mystery (FOTD 5-15-10) is posted: http://www.fractal-animation.net/vid/mayanbrot.zip 22 Meg. WMV format, 115 sec (I think it was peyote and little smoke that influenced ancient SA indian art) .

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Triangles!
by Roger Alexander 20 May '10

20 May '10

Today's fractal is a variation of the Seirpinski triangle. I aimed for a coloring that suggested the mechanical or cybernetic. To demonstrate the awesome power of the internet go to http://maxitersfractalfollies.blogspot.com for an instant viewing. may_20_10.gif { ; seirpinski like ; blank ; calctime 0:01:27.88 ; created May 20, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2000 type=formula formulafile=esc-ifs.frm formulaname=EqTrngl center-mag=-4.44089e-016/0.0782269/0.8912656 params=2/0 float=y maxiter=1200 outside=atan cyclerange=0/255 colors=00000000200400600800A00C00E00G00I00K00M00O00Q00S00U00W00Y00_00a00\ c00e00g00i00k00m00o00q00s00u00w00z01z03z05z07z09z0Bz0Dz0Fz0Hz0Jz0Lz0Nz0P\ z0Rz0Tz0Vz0Xz0Zz0`z0bz0dz0fz0hz0jz0lz0nz0pz0rz0tz0vz0xz0zz0zz0yz0xz0wz0v\ z0uz0tz0sz0rz0qz0pz0oz0nz0mz0lz0kz0jz0iz0hz0gz0fz0ez0dz0cz0bz0az0`z0_z0Z\ z0Yz0Xz0Wz0Vz0Uz0Tz0Sz0Rz0Qz0Pz0Oz0Nz0Mz0Lz0Kz0Jz0Iz0Hz0Gz0Fz0Ez0Dz0Cz0B\ z0Az09z08z07z06z05z04z03z02z01z00z00z03z07z0Bz0Fz0Jz0Nz0Rz0Vz0Zz0bz0fz0j\ z0nz0rz0vz0uz1tz1sz2rz3pz3oz4nz5mz5kz6jz7iz7hz8gz9ez9dzAczBbzB`zC_zDZzDY\ zEWzFVzFUzGTzHSzHQzIPzJOzJNzKLzLKzLJzMIzNGzNFzOEzPDzPCzQAzR9zR8zS7zT5zT4\ zU3zV2zW0zW0zV0yV0xU0wU0vT0uT0tS0sS0rR0qR0pQ0oQ0nP0mP0lO0kO0jN0iN0hM0gM0\ fL0eL0dK0cK0bJ0aJ0`I0_I0ZH0YH0XG0WG0VF0UF0TE0SE0RD0QD0PC0OC0NB0MB0LA0KA0\ J90I90H80G80F70E70D60C60B50A509408407306305204203102101 } frm:EqTrngl{ z=pixel, j=(0, -1), k=(.8660, 0.5), l=(-0.8660, 0.5): x=real(z) y=imag(z) r=.575*x x1=(y>=r) x2=(-r<=y) x3=(x1 && x2) x4=(x3==0) a=x3*j b=(x<=0)*x4*k c=(x>0)*x4*l p=a+b+c z=p1*z+p |z|<=100 } Roger Alexander _________________________________________________________________ Win a $10,000 shopping spree from Hotmail! Enter now. http://go.microsoft.com/?linkid=9729711

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Minibrots in abundance
by Roger Alexander 20 May '10

20 May '10

A plethora I say, yes a plethora of minibrots.When I promise 'brots I deliver 'brots. Don't be shy, treat yourself to a heapin' helpin' of calculations from the complex plane. What do I mean by a plethora of brots? Save some calculation time and go to http://maxitersfractalfollies.blogspot.com to see for yourself. fract212.gif { ; brotties ; blank ; calctime 0:01:18.43 ; created May 18, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=calres.frm formulaname=TileMandel center-mag=-0.0057863/0.415756/10.40608/1/180 params=-0.5/0/0.8/4 float=y maxiter=1500 inside=0 outside=atan invert=1.75/0/0 colors=00zzzzzzzzzzzzzyyyyyyyyyyyyxxxxxxxxxxxxwwwwwwwwwwwwvvvvvvvvvvvvuu\ uuuuuuuuuuttttttttttttssssssssssssrrrrrrrrrrrrqqqqqqqqqqqqppppppppppppoo\ oooooooooonnnnnnnnnnnnmmmmmmmmmmmmllllllllllllkkkkkkkkkkkkjjjjjjjjjjjjii\ iiiiiiiiiihhhhhhhhhhhhggggggggggggffffffffffffeeeeeeeeeeeeeeeddddddddddd\ dccccccccccccbbbbbbbbbbbbaaaaaaaaaaaa````````````____________ZZZZZZZZZZZ\ ZYYYYYYYYYYYYXXXXXXXXXXXXWWWWWWWWWWWWVVVVVVVVVVVVUUUUUUUUUUUUTTTTTTTTTTT\ TSSSSSSSSSSSSRRRRRRRRRRRRQQQQQQQQQQQQPPPPPPPPPPPPOOOOOOOOOOOONNNNNNNNNNN\ NMMMMMMMMMMMMLLLLLLLLLLLLLLLKKKKKKKKKKKKJJJJJJJJJJJJIIIIIIIIIIIIHHHHHHHH\ HHHHGGGGGGGGGGGGFFFFFFFFFFFFEEEEEEEEEEEEDDDDDDDDDDDDCCCCCCCCCCCCBBBBBBBB\ BBBBAAAAAAAAAAAA99999999999988888888888877777777777766666666666655555555\ 5555444444444444333333333333222222222222111111111111000 } frm:TileMandel { ; modified by Sylvie Gallet [101324,3444] ; from FRACTINT.FRM ; p1 = center = coordinates for a good Mandel ; 0 <= real(p2) = magnification. Default for magnification is 1/3 ; 0 <= imag(p2) = numtiles. Default for numtiles is 3 center = p1 , mag = real(p2)*(p2>0) + (p2<=0)/3 numtiles = imag(p2)*(flip(p2)>0) + 3*(flip(p2)<=0) omega = numtiles*2*pi/3 x = asin(sin(omega*real(pixel))) , y = asin(sin(omega*imag(pixel))) z = c = (x+flip(y)) / mag + center : z = z*z + c |z| <= 4 } Roger Alexander _________________________________________________________________ 30 days of prizes to be won with Hotmail. Enter Here. http://go.microsoft.com/?linkid=9729709

2 1

FOTD 20-05-10 (Writhing Tentacles [7])
by Jim Muth 19 May '10

19 May '10

FOTD -- May 20, 2010 (Rating 7) Fractal visionaries and enthusiasts: Today's image, a totally graphic black-and-white, is rated at a 7. Basically, it's a study of what is possible with the pre- cooked color palettes built into Fractint. To create the image, I returned to one of the old MandNewt formulas, number 6 to be exact, entered some random whole-number parameters, and let her rip. I'm not sure what these formulas actually do, but what came up was a virtually blank screen consisting of 'inside' stuff. Never giving up on blank screens without at least a little fight, I applied the 'bof60' inside fill option to the blank screen and was surprised by the result. The first image was near total color-chaos, but when I turned on the logmap and applied one of the broad color palettes, things shaped up fast. Today's image shows the final result, which is surprisingly three-dimensional for a flat fractal. I named the image "Writhing Tentacles" since a tentacle was the first thing that came to mind when I saw the finished image. The calculation time of a zippy 49 seconds will pass in a flash. The trip to the FOTD web site at: <http://www.Nahee.com/FOTD/> to see the completed image will pass in a flash also. The skies were brighter here at Fractal Central on Wednesday, but the sun was still hidden. The temperature of 64F 18C was warmer than the past few days, but still fell short of the 72F 22C that is typical for mid-May. The fractal cats were quite alert most of the day, dashing from one window to another. I think a stray cat was prowling nearby, though I never saw one. My day was a very dull average. FL's day was a little above average. The next FOTD, also a little above average, will be posted in 24 hours. Until then, take care, and after all these years, I still don't know what a proton looks like. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Writhing_Tentacles { ; time=0:00:49.75-SF5 on P4-2000 reset=2004 type=formula formulafile=mandnewt.frm formulaname=MandNewt06 passes=1 center-mag=2.21949\ /0.923324/0.3180807/1/-140/0 params=1/6/3/8/5/6 float=y maxiter=100 inside=bof60 logmap=yes periodicity=0 colors=000zzzyyyxxxxxxwwwwwwvvvvvvuuuuuuttttttssss\ ssrrrrrrqqqqqqppppppoooooonnnnnnmmmmmmllllllkkkkkk\ jjjjjjiiiiiihhhhhhggggggffffffeeeeeeddddddccccccbb\ bbbbaaaaaa``````______ZZZZZZYYYYYYXXXXXXWWWWWWVVVV\ VVVVVUUUUUUTTTTTTSSSSSSRRRRRRQQQQQQPPPPPPOOOOOONNN\ NNNMMMMMMLLLLLLKKKKKKJJJJJJIIIIIIHHHHHHGGGGGGFFFFF\ FFFFFFFFFFDDDCCCCCCBBBBBBAAAAAA9999998888887777776\ 66666555555444444333333222222111111000000000000000\ 11111122222233333344444455555566666677777788888899\ 9999AAAAAABBBBBBCCCCCCDDDDDDEEEEEEFFFFFFGGGGGGHHHH\ HHIIIIIIJJJJJJKKKKKKLLLLLLMMMMMMNNNNNNOOOOOOPPPPPP\ QQQQQQRRRRRRSSSSSSTTTTTTUUUUUUVVVVVVVVVWWWWWWXXXXX\ XYYYYYYZZZZZZ______``````aaaaaabbbbbbccccccdddddde\ eeeeeffffffgggggghhhhhhiiiiiijjjjjjkkkkkkllllllmmm\ mmmnnnnnnooooooppppppqqqqqqrrrrrrssssssttttttuuuuu\ uvvvvvvwwwwwwxxxxxxyyyyyy } frm:MandNewt06 {; Jim Muth z=c=(pixel*p1): a=z^3+(c-p2)*z-c b=p3*z^2+c-1 z=z-1*a/b 0.000000000000000000000000000001 <= |a| } END PARAMETER FILE=========================================

1 0

Newts!
by Roger Alexander 19 May '10

19 May '10

Newtons are fractals too.This one is symmetrical but not visually monotonous with the distinguishing thread-like structure of the newton. Go to http://maxitersfractalfollies.blogspot.com to see the eager to be downloaded gif. ract213.gif { ; newts ; blank ; calctime 0:01:37.27 ; created May 19, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=crazynwt.frm formulaname=Nwtfn12rot function=sqr/asin center-mag=-8.88178e-016/0.0801336/1.253133 params=6.072603534043397/-0.08343760490737633/2.8676412244026/1.08444471\ 5720084 float=y maxiter=1500 inside=0 colors=00000000100300400600800900B00C00E00G00H00J00K00M00O00P00R00T00U00\ W00X00Z00`00a00c00d00f00h00i00k00m01m03m04n06n07o09o0Ao0Cp0Ep0Fq0Hq0Iq0K\ r0Lr0Ns0Ps0Qs0St0Tt0Vu0Wu0Yu0Zv0`v0bw0cw0ew0fx0hx0iy0ky0mz1mz3mz5nz7nz9o\ zBozDozFpzHpzJqzLqzNqzPrzRrzTszVszXszZtz`tzbuzduzfuzhvzjvzlwznwzpwzrxztx\ zvyzxyzzzzyzzxzzwzzuzztzzszzqzzpzzozzmzzlzzkzzizzhzzgzzezzdzzczzbzz`zz_z\ zZzzXzzWzzVzzTzzSzzRzzPzzOzzNzzLzzKzzJzzIzzGzzFzzEzzCzzBzzAzz8zz7zz6zz4z\ z3zz2zz0zz0yz0xz0wz0uz0tz0sz0qz0pz0oz0mz0lz0kz0iz0hz0gz0ez0dz0cz0bz0`z0_\ z0Zz0Xz0Wz0Vz0Tz0Sz0Rz0Pz0Oz0Nz0Lz0Kz0Jz0Iz0Gz0Fz0Ez0Cz0Bz0Az08z07z06z04\ z03z02z00z00y00x00w00v00u00t00s00r00q00p00o00n00m00l00k00j00i00h00g00f00\ e00d00c00b00a00`00_00Z00Y00X00W00V00U00T00S00R00Q00P00O00N00M00L00K00J00\ I00H00G00F00E00D00C00B00A009008007006005004003002000000 } frm:Nwtfn12rot { ;The factor exp(p1*...) rotates the pixels ;according to their distance from the origin if p1 is ;chosen complex. z = pixel+1/fn1(p2*pixel*exp(p1*fn2(|pixel|))) , Root = 1 : z = (4 * z^5 + Root) / (5 * z^4); .001 <= |z^5 - Root| } Roger Alexander _________________________________________________________________ 30 days of prizes: Hotmail makes your day easier! Enter Now. http://go.microsoft.com/?linkid=9729710

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Re: [Fractint] AOTD 5_15
by maxiterfractal＠hotmail.com 19 May '10

19 May '10

On 2010-05-19 14:03, JackOfTradeZ wrote: > . > > Animation of the Mayan Mystery (FOTD 5-15-10) is posted: > > > http://www.fractal-animation.net/vid/mayanbrot.zip > > > 22 Meg. WMV format, 115 sec > > > (I think it was peyote and little smoke that influenced ancient SA indian art) > > . > Great animation of a great fractal. Roger Alexander

1 0

FOTD 19-05-10 (Microistic Disorder [?])
by Jim Muth 18 May '10

18 May '10

FOTD -- May 19, 2010 (Rating ?) Fractal visionaries and enthusiasts: Today's image is not rated because it is merely a study in coloring fractals. The basic B-W color palette is a part of the Fractint program, and may be accessed by striking <ctrl-F1> while in coloring mode. In today's image I added a few pale extra colors to give a bit of sparkle. Take away the pale col- ing and the image is a true graphic. Actually, this particular color palette brings out the underlying forms of the fractal quite well. A bit of color tweaking will reveal the basic diffi- culty of coloring the fractal. The iterated line of the parent fractal subtracts 4 parts of Z^(-5) from 2 parts of Z^(-3) then adds (1/C). This parent is nothing more than an empty circle with a brilliant white spot in the center and six irregular islands of debris scattered around the perimeter. Today's scene is located in the easternmost debris island. With no idea how to accurately rate a fractal study, I left the rating a question. The name "Microistic Disorder" does not refer to some vague medical affliction characterized by an obses- sion with fractals. Like so many of my FOTD names, it has no meaning at all, other than the way it sounds. Unfortunately, the image is a slow one, which takes 13-1/2 minutes to run even on a fireball 2000mhz machine primed for fractal generation. The solution to this minor problem is to surf out to the FOTD web site at: <http://www.Nahee.com/FOTD/> and in ultimate comfort enjoy the finished image posted there. Light but steady rain set in at midnight Monday here at Fractal Central and continued through the day on Tuesday, while the temperature hovered around an un-springlike 50F 10C. The fractal cats were happy with the temperature, since it was 70F 21C inside FC the entire time, and there was no indoor rain. My day was busy but productive. If only every day could be the same... The next FOTD will be posted in 24 hours. Until then, take care, and look for the bright side, but don't be surprised if you get slugged by the dark side instead. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= MicroisticDisorder { ; time=0:13:28.18-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+0.993714689388549/+0.1300117885242976/\ 4e+009/1/-51.5/0 params=2/-3/-4/-5/0/0/0/0 float=y maxiter=10500 inside=0 outside=tdis periodicity=10 colors=000zzzJIKJIKKJKKJKLKKLKKMLKMLKNMKNMKONKONKP\ OKPOKQPNQPNRQORQOSRPSRPTSQTSQUTRUTRVUSVUSWVTWVTXWU\ XWUYXVYXVZYWZYW_ZX_ZX`_Y`_Y`_Ya`Za`Zba_ba_cb`cb`dc\ adcaedbedbfecfecgfdgfdhgehgeihfihfjigjigkjhkjhlkil\ kimljmljnmknmkonlpnlqomromspntpnuqovqowrpxrpysqzsq\ ztrztrzuszuszvtzvtzwuzwuzxvzxvzywzywzzxzzxzzyzutzu\ uzuuzuuzuuzuuzuuzuuzuuzuuzuuzuuzuuzutzutzuszzxzywz\ ywzxvzxvzwuzwuzvtzvtzuszusztrztrzsqzsqzrpyrpxqowqo\ vpnukntomsomrnlqnlpmkomknljmljlkilkikjhkjhjigjigih\ fihfhgehgegfdgbdfecfecedbedbdcadcacb`cb`ba_ba_a`Za\ `Z`_Y`_Y`_Y_ZX_ZXZYWZXWYXVYXVXWUXWU`VTWVT_USVUSZTR\ UTRYSQTSQSRPSRPRQORQOQPNQPNXPMPOMYNLONLXMKNMK`LKML\ KLKK_KKKJKUJKJIKYIKIHKXHKZGKHGKSKUTPKUEKKEUUDKUDUK\ CKUCUUBUUBKUAUKAUU9KK9UK8UK8KK7UK7KK6UT6KKPKK5KK5U\ K5KK6UK6KK7UK7KK8UK8KK9UK9KKAUKAKKBUKBKKCUKCKKDUKP\ KKEUKEKKFUKFKKGUKGKKHUKHK } 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 18-05-10 (Digging in the Dirt [8.5])
by Jim Muth 17 May '10

17 May '10

FOTD -- May 18, 2010 (Rating 8.5) Fractal visionaries and enthusiasts: The parent fractal of today's image came about when 4 parts of Z^(-1.75) were combined with Z^(-4) and (1/C) was added. This parent fractal consists of a large central 3-lobed bay, much resembling a clover, with a string of smaller disconnected ring- like features extending to the northeast. Today's scene is located in one of the smaller elements in this disconnected string. The entire effect of the image was created by half evaporating the original scene, then rendering the remaining 'outside' parts with the 'tdis' option. The newly opened 'inside' parts were then brought to life with the 'bof61' option. And let us not forget the part my coloring added to the overall effect. Add all this trickery together and the rating works out to an 8.5. The name "Digging in the Dirt" has no meaning. It simply popped into my over-stressed head when I saw the image. The calculation time of under 18 seconds will cause no grief. Even less grief will be felt at the FOTD web site, where the finished image is posted for instant and total gratification. The web site may be accessed at: <http://www.Nahee.com/FOTD/> Clouds moved in early here at Fractal Central on Monday. The rest of the day was cloudy with a temperature of 66F 19C. Rain was hinted at, but never arrived. The fractal cats occupied themselves getting into trouble in the maze of book shelves in the hallway. In my department, things were average, whatever the word average means when applied to a particular day. And if nothing out of the ordinary happens, tomorrow will be a repeat. The next FOTD will be posted in 24 hours. Until then, take care, and what is the meaning of a search for meaning? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Digging_in_theDirt { ; time=0:00:17.90-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=+2.74893763512/+1.28555993412/1188566/1\ /22.5/0 periodicity=10 params=4/-1.75/1/-4/0/20000\ /0/0 maxiter=8000 inside=bof61 outside=tdis colors=000750vwjghZTUNEFBcNpQFZD7Hz9we6cL3K3Mu1BTb\ ptTbeJQS9DElZog3I_2FT2CM19E16703zm89K8vY0cczyRzUPz\ yjzvLzuJztHzuGzuGzvGzvGzwGzwGzxGzxGztHzqHzmHzjHzfH\ zcHpZFkUEgPCcKB_GAWC7O85Gzz0Xl6Qb4JT3DJ2691YJ7LH3D\ NLDRIBOF9KC6F94A6253T5EJ39914bI6TD4J93941a54LWEAG7\ 8WU7SQ6OM5KI4GF3CB2871436d55Z44U33P33K22F11A1050LJ\ KFEFA9A545Bs5BrI8gE6XA4M72B3s1bk0Xc0RW0MKJKKJK805Y\ `JMrzTmzRjtL`hGSYAIM59Bz00nMMcGGWBB000_e7UZ5OS4IL3\ 000000zzUunXfgS9_N1TJ1ME0E9074000YZJHH9zzzOzqIWmCL\ I6A9GCgA8T54EfQzYKYPFPHAH85824F13C12A1280160140026\ Oz5Kz4HZ3DS2AL16E037S47O36L35H24E23A127113006Rr5Nk\ 4Kd3GY3DR2AK16D036cnFXeCQYAKP7DH5682WS3OL2GE1870vv\ aKWfETftVmlXgeZaZ`WRbQKdKDfE6h88fAAdCBbED`GFZIGXKI\ VMJTNO4VL3RI3NF2JC2F91B617303xQYUDH71I309OC0YmlRcb\ KUTDKJ6A9QutYuOSkKMaGHTCBJ8594KSnAEP9Ib6CQ36DyNElI\ B`D8O95C42gX3_R2TM2MG1EB1 } 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

Yet Another Metallic Spiral
by Roger Alexander 17 May '10

17 May '10

Fractint and fractals=minibrots and spirals. So I have parametric tunnel vision. They see me iteratin' they be hatin'. To experience possibly instant vertigo from the hypnotic power of the classical spiral go to http://maxitersfractalfollies.blogspot.com fract204.gif { ; yams ; blank ; calctime 0:38:10.05 ; created May 16, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_m.frm formulaname=MandMix-x center-mag=-0.17019135519399270/-0.56709074644407300/2771.311 params=0.6370128482924894/0.9864497817926573/0.6011841181676687/0.356975\ 0053407392 float=y maxiter=1500 inside=0 proximity=1 outside=fmod colors=ELLFLLFMMGMMGNNHNNHOOIOOIPPJPPJPPKQQKQQLRRLRRMSSMSSNTTNTTOTTOUUPU\ UPVVQVVQWWRWWRXXSXXSXXTYYTYYUZZUZZV__V__W``W``W``XaaXaaYaaYaaYbbYbbZbbZb\ b_cc_cc`dd`ddaddaeebeebffcffcffdggdggehhehhfiifiigiigjjhjjhkkikkikkjlljl\ lkmmkmmlnnlnnmnnmoonoonppoppopppqqpqqqrrqrrrrrrssssssttttttuuuuuuuuvvvvv\ vwwwwwwwwwxxxxxxyyyyyyyyyxxxxxxwwwwwwvvvvvvuvvuuutuutttsttsttrssrssqrrqr\ rprrpqqoqqoppnppnoomoomoolnnlnnlmmkmmkmmjlljllikkikkhkkhjjgjjgiifiifiieh\ hehhdggdggcggcffbffbeeaeeaeeadd`dd`cc_cc_ccZbbZbbYaaYaaXaaX``W``W__V__VZ\ ZUZZUZZTYYTYYSXXSXXRXXRWWQWWQVVQVVPVVPUUOUUOTTNTTNTTMSSMSSLRRLRRKRRKQQJQ\ QJPPIPPIPPHOOHOOGNNGNNFNNFMMFMMELLELLDLLDKKCKKCJJBJJBIIAIIAII9HH9HH8GG8G\ G7GG7FF6FF6EE5EE5EE4DD4DD3CC3CC3CC2BB1BB1AA0AA0AA1BB1BB2CC2CC3DD3DD4DD4E\ E5EE5FF6FF6FF7GG7GG8HH8HH9HH9IIAIIAJJBJJBJJCKKCKKDLLDLL } frm:MandMix-x {; Jay Hill u=real(p1), v=imag(p1), w=real(p2), b=4+imag(p2) c=pixel/w, x=v-u, z=(-u/v/w)^(1/x): z=z^u + w*z^v + c |z| <= b ;SOURCE: 98msg.frm } Roger Alexander _________________________________________________________________ Win $10,000 from Hotmail! Enter Here. http://go.microsoft.com/?linkid=9729708

1 0

Re: [Fractint] What is the point of hiding a formula from FRACTINT?
by Roger Alexander 17 May '10

17 May '10

On 2010-05-07 05:50, Jay Litwyn wrote: > Re: [Fractint] What is the point of hiding a formula from FRACTINT? Why am I hiding formulas from Fractint? I am confused. I have checked my mailing list posts and it appears the formula information was included if needed. For Fractints built in formulas no formula information is necessary. As for my blog(http://maxitersfractalfollies.blogspot.com) I don't include formula or parameter information because at the moment the blog serves as a supplement to my mailing list posts and used mainly as a stash to display the pre-calculated fractals and give list members a chance to decide whether to generate the fractals themselves. This is a similar arrangement to Jim Muth's FOTD being hosted at http://www.nahee.com/FOTD/. If asked I will be glad to include par and frm information on my blog. The main reason I post to the mailing list to begin with is to completely share the fractal generating information. Roger Alexander _________________________________________________________________ MSN Dating: Find someone special. Start now. http://go.microsoft.com/?linkid=9729707

8 18

Minibrots
by Roger Alexander 16 May '10

16 May '10

Minibrots everywhere-they almost define the escape time fractal. I chose this little fella because he is sorrounded by dotties rather than the filaments and lobes of the classical Mandelbrot. Finding a conventional minibrot in an unconventional context is one of my major Fractinting satisfactions. Go to http://maxitersfractalfollies.blogspot.com for your immediate download satisfaction. fract197.gif { ; a study in minibrots and pebbles ; blank ; calctime 0:14:37.21 ; created May 15, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_q.frm formulaname=Quotient center-mag=+7.54497038581824600/+0.15081442711555390/109.5866/1/-160.000\ 000000002728/2.83743861739793601e-012 float=y maxiter=1500 inside=0 colors=A00A00B00B00C00D00D00E00F00F00G00G00H00I00I00J00K00K00K00L00L11M1\ 1M11N11N11O11O11P11P11Q11Q11R11S00S00T00T00U00V00V00W00X00X00Y00Z00Z00_0\ 0`00`00a00b00b00c00d00e00f00g00g00h00i00i00j00k00k00l00m00m00n00o00o00p0\ 0q00q10q20q40q50q70q80qA0qB0qC0qE0qF0rH0rI0rK0rL0rN0rO0rP0rR0rS0rU0rV0sX\ 0sY0s_0s`0sa0sc0sd0sf0sg0si0sj0tl0tl0tm0un0uo0up0vq0vr0ws0ws0wt0xu0xv0xw\ 0yx0yy0zz0zz0zy0yx0yw0yv0xu0xt0ws0ws0wr0vq0vp0vo0un0um0tl0tl0tk0tj0tj0ti\ 0th0uh0ug0uf0ue0ue0ud0uc0vc0vb0va0v`0v`0v_0vZ0wZ0wY0wX0wX0wW0wV0wU0xU0xT\ 0xS0xS0xR0xQ0yP0xP0wO0vO0uN0uN0tM0sM0rL0qL0pK0oK0oJ0nJ0mI0lI0kH0jH0iG0iG\ 0hF0gF0fE0eD0dD0cC0cC0bB0aB0`A0_A0Z90Y90Y80X80W70V70U60T60S50S50R40Q40P3\ 0O30N20M11M11M11M11L11L11L11L11K11K11K11K11J11J11J11J11I11I11I11I11H11H1\ 1H11H11G11G11G11G11F11F11F11F11E11E11E11E11D11D11D11C00 } frm:Quotient (XAXIS) { z = pixel: z = (sqr(z) + pixel) / (sqr(z) - pixel) |z| <= 42 ;SOURCE: hubert.frm } Roger Alexander _________________________________________________________________ Win a $10,000 shopping spree from Hotmail! Enter now. http://go.microsoft.com/?linkid=9729711

1 0

FOTD 17-05-10 (Breaking the Rules [5])
by Jim Muth 16 May '10

16 May '10

FOTD -- May 17, 2010 (Rating 5) Fractal visionaries and enthusiasts: To create today's unexceptional, 5-rated image I subtracted 0.6 part of Z^5 from Z^3 and added straight C. The image is located on the positive X-axis of the parent fractal, which is far easier to see than to describe. The name "Breaking the Rules" refers to the lack of any kind of 2,4,8... symmetry in the elements surrounding the obviously quadratic minibrot at the center. Quadratic minibrots are not always found by searching for 2-way symmetry. The calculation time of the image is a surprisingly brief 38 seconds, which is about half the time needed to view the image on the FOTD web site at: <http://www.Nahee.com/FOTD/> but viewing the already finished image avoids the hassle of setting up and running the included parameter file. The Sunday weather here at Fractal central was a repeat of Saturday's, minus the morning cat fight in the yard. The sky was partly cloudy, while the temperature reached a high of 70F 21C. The fractal cats were far more relaxed with no shouting tomcats squared off outside. The next in the apparently endless string of FOTD's will be posted in 24 hours. Until then, take care, and one day there will be a final FOTD, but not for some considerable time, I presume. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Breaking_the_Rules { ; time=0:00:38.28-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident inside=0 center-mag=+1.081611773/0/4800/1/90/0 logmap=36 params=1/3/-0.6/5/0/0/0/0 float=y maxiter=750 colors=000demcfmbgmahm`im_jmZkmYlmXmmWnmVomOpmIqmB\ rmCsmDtmLumTvm`wmhxnpyoxzpzzzzzzzzzzzzznnmUUmUJmU8\ mUDhW8cTDZRHUOMWNQYMU_MSaLRcKPeIOgFMiDLkBJm9Ii7OX5\ YK3c72hG8cODZWNUcSPkXLjVHjWDkWAnU6qS3tQ0wO0zQ0zS9z\ TAmVBjXCjYDj_Ej`FjbGkdIkeJkgKkgQkhLkjMklNkmOkoP5D4\ 8G6BI7DL8GNAIQBLSCNUEQXFSZGVaHXcJ_eKahLdjNfmOioPiS\ qhUohVngWmgXkgYjf_if`geafebeeccdebdfadg_hhZc_YbaWb\ bVbcUadSaoR2nBCpELqHUsKboNHo_JpZKpZLpYMpYNqYPqXQqX\ RqWSrWTrWVrVWrVXrVYsUZsU`sTasTbtTctSdtSftRguRhuRiu\ QjuQ3tx5sv7st9ssBsqDspFrnHrmJrmLrmNrmPmmRlmTlmVlmX\ lmZlm`lmbkmdkmfkmhkmjkmRmmSlmSlmTlmUlmWlmYlm_lmalm\ clmelmglmimmkmmmnmonmqomtomwpmxpmzqzzqzzqzzqzzpzzp\ zzpzzpzzpzzpzzpzzpzzpzzpzzpzzpzzuzzuzzuzzuzzuzzuzz\ uzzuzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ 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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FOTD 16-05-10 (Test Test [No Rating])
by Jim Muth 16 May '10

16 May '10

FOTD -- May 16, 2010 (No Rating) Fractal visionaries and enthusiasts: Since time is of the essence, there will be only a very short discussion with today's image. The trip to Old Fractal Central on Saturday went well enough, though there was a half-hour delay on the way down due to an accident on Route I-83. While I was at OFC, my sister expressed thoughts of getting two new cats to take the place of Thomas and Tippy, the original fractal cats, who went to the next cat world not too long ago. If she actually does get the cats, they will be called the all-new fractal cats of Old Fractal Central. Today's image has no rating. I could give it no rating because I put almost no effort into creating it. But it's still margin- ally worth the time of exactly 5 minutes required to run the parameter file. (I wonder if such calculation-time exactness has ever happened previously?) The name "Test Test" came about when I doubled the default name that appeared in the parameter file. Four of the 5 minutes required to calculate the image may be salvaged by going to the FOTD web site at: <http://www.Nahee.com/FOTD/> and viewing the finished image there. Partly cloudy skies and temperatures of 70F 21C made Saturday an ideal day here at Fractal Central. The fractal cats big thrill came early in the day, when two stray tomcats got into a fight in the yard. Otherwise, I assume all went well enough. The next FOTD, if I have one ready, will be posted in 6 hours. Until whenever, take care, and put your trust in the unseen metaphysical. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Test_Test { ; time=0:05:00.00-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-0.75213769500977/+0.05134481676682934/\ 4.93002e+007/1/-70/0 params=-100/1e+046/0/0 float=y maxiter=1500 inside=0 outside=tdis periodicity=6 colors=0007RY9QOBQFyZwgVpQSiG6TEBWCGZAK`8Pc6Te4YhG\ CACJK9PT6Wa3aj9bhEcfKdders_mmVihPdcK`YEWTO`yKYoGWf\ DUX9SO5QEfSLYRHQQEIPBAO82O5JSLentcjobfkabg`Zc_V_j7\ keTAbSI`RPjxhkOXZRWMTW3Tb5U`6U_7VZ8VYAVWBWVCWUArRB\ lSCfSC`TDWTDQUEKUG0jF4eF8aFCYEFUEJQENMmcGWXH0V07S9\ EQILNRayn_pkYhhW`eUTbSL_QDX5yuAjnFXgKJ`R0PO5UMAYKE\ aIJeFOiDSmBXq9`uA_pAZkUAcc9gPMd1UUAYaI`iQcq6exDfyK\ fyRfyYfydfykfyrfyhwkqnr9GByfyjikqxYluZhsZdpZ`nZWkZ\ SiZOfZZ4G5xoAqiFkcKdZzUTzZFzcHzhJzmLzmMzcOzUQDj9Ee\ DF`GGWKGSNHNRIIUJDYwzHllMb_RTMWJK`NUXRcTVhPZmMbrIf\ wEjzBfzJbmRZiZ5kAYnhWjgVffUbeSZdRVczRzzHzzKlPNbNQ`\ LTZJWX1Pd7T`CWYIZVNaSc26_FDWSJCtRKlQSdPvkUrhTnfSjd\ RgbQOdFIbHDaI7`J2_K2`U2`b2ak2atKPfaCTs0GaINKZU2o`D\ zzOm_Zl_ik_sj_thZtgZufZueZucZvbZvaZv`ZGVAGZFGaKGeP\ GhUGkZGocGrhGumLpaPlQTgEXc3b`ChZKnXTsV`pXWnZRk_Mia\ HgbD``KUZRNYYGWd9Uk2Tq5Sg } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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More Spirals
by Roger Alexander 15 May '10

15 May '10

I will never forget Prof. Phogbound`s comment when I showed him this fractal ``This figure bears a striking resemblance to a self-similar object`` His expertise was profound. I remember asking him questions on nomenclature. ``Professor are these structures called embedded recursive spirals?" His educated reply "No they are called fairy dust curly-swirlies" has remained with me all these years. Prof. Phineas T. Phogbound, one of the major influences in my life. fract193.gif { ; spirals and spirals ; blank ; calctime 0:42:09.49 ; created May 14, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_o.frm formulaname=okJ_05 passes=1 center-mag=-0.47305175469336680/-1.03833369616026600/691.7064 params=0.9318216498306223/-0.3567918942838832/0.1708731345561083/-0.4616\ 534928434095/138.7748954741051/-0.5227515488143559 float=y maxiter=1500 inside=0 colors=0Kdv0bt0ar0_q0Zo0Xm0Wl0Uj0Ti0Rg0Qe0Pd0Nb0M`0K_0JY0HX0GV0ET0DS0BQ0\ AO08P08Q08R08S18U18V18W18X28Y28_28`28a38b38d38e38f48g48h48j48k58l58m58o5\ 8p68q68r68s68u78v78w78x78z88z98zA8zB8zC8zD8zE8yF8yG7yH7yI7yJ7yK7xL7xM7xN\ 7xO6xP6xQ6wR6wS6wT6wU6wV6wW5vX5vY5vZ5v_5v`5va5ub5uc4ud4ue4uf4ug4th4ti4tj\ 4tk3tl3tm3sn3so3sp3sq3sr3rs2qs2os3ns3mr4lr4kr5jr5hr6gr6fr6er7dr7cq8aq8`q\ 9_q9ZqAYqAXqBVqBUpCTpCSpDRpDQpDOpENpEMpFLpFKoGJoGHoHGoHFoIEoIDoJCoJAnK8q\ L5tN3wP0zR0wQ0sO0pN0lL0hJ0eI0aG0YE0VD0RB0N90K80G60C40H90MF0RL0WR0`X0eb0j\ h0on0tt0zz0xx0vv0st0qr0no0lm0jk0gi0ef0bd0`b0Y`0WY0UW0RU0PS0MP0KN0HL0FJ1C\ G2CL4DP5DU7DZ8EbAEgBElDFpEFuGGzGGxFFvEEtDDrCCpBBnBBlAAj99h88f77d66b66`55\ Z44X33V22T11R00O53SA6XG9aLCfQFkWIp`LufOzfNyfMweLveKtdJsdIqdHpcGncFmbEkbD\ jaChaBgaAe`9d`8b_7a_6__5ZZ4XZ3WY2UY1TX0Rc0Vk0Zr0bz0fy0e } frm:okJ_05 {; Perturbed Julia set ; Julia parameter p1 is perturbed by p2*pixel ; p2=0 -> no perturbation ; p3 = bailout z=pixel c=p1+p2*pixel: z=z*z+c |z|<=p3 ;SOURCE: 98msg.frm } Roger Alexander _________________________________________________________________ 30 days of prizes: Hotmail makes your day easier! Enter Now. http://go.microsoft.com/?linkid=9729710

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FOTD 15-05-10 Mayan Mystery
by Roger Alexander 15 May '10

15 May '10

Great fractal Jim! Roger Alexander _________________________________________________________________ Win a $10,000 shopping spree from Hotmail! Enter now. http://go.microsoft.com/?linkid=9729711

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FOTD 15-05-10 (Mayan Mystery [7.5])
by Jim Muth 14 May '10

14 May '10

FOTD -- May 15, 2010 (Rating 7.5) Fractal visionaries and enthusiasts: Friday turned unexpectedly busy here at FC, so the day's fractal is a quick one. The parent fractal, which was created with the FinDivBrot-2 formula, consists of a Mandelbrot set surrounded by much extra detail. Today's image is located in some of this extra detail on the positive X-axis. I named the image "Mayan Mystery". Something about it reminds me of the symbolic art of the ancient Mayans of Central America. Since so much of the image's worth is in the coloring, I gave myself a half-point bonus for my color work, bringing the final rating to 7.5. The calculation time of 19 seconds will pass in a flash, or at least as close as is possible to get to a flash. And the finished image is posted on the FOTD web site at: <http://www.Nahee.com/FOTD/> Friday turned surprisingly warm here at Fractal Central, with a high temperature of 82F 28C and partly cloudy skies. Showers were in the area during the afternoon, though none fell at FC. The fractal cats enjoyed chasing a fly that got inside. One of them, probably the more agile Cassie, must have caught the fly. It disappeared as fast as today's fractal appeared. My day was acceptable. I'll be going back to old FC on Saturday to take care of a few details, so don't be surprised if the FOTD for May 16 is a day late. Until whenever, take care, and be fortunate. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mayan_Mystery { ; time=0:00:19.27-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=+1.29914424038879/0/2.932468e+011 params=-13/-5000000/0/0 float=y maxiter=450 inside=0 logmap=68 symmetry=xaxis periodicity=6 mathtolerance=0.05/1 colors=000000c0000c0U0000TST800V1cA0N50BzzcEgz9RPz\ sBjc8RA5FD2z00cIPK9CZg8zjfhXUUMKFBAm3rz2_61IUNpFBQ\ zFzEAY75HEiT9UJ4F9PChI9XC6M63BkBPYOqPIcHCR86DMK5BA\ 2afvYhzVi`RjROkGLl6cAZaCV`DSZFPYGMWHJVJGTKDSLAXJD`\ HGeFJiDMmBPr9Sv7Vz6XzHzvEsrBln8ej5Zf2Sc0MW9POISGRV\ 8_YBSUEKQGNSHPTIRUJTVUVTcWRmXQZkbLzoMqqNirN`tzTuzK\ wzCxz4yz5sz5nz6hz6cz7Zz7Tz8Oz8JzRKzhLzeMzcNzaNz_Oz\ YOzZMz_Kz`Jz`HzaFzbEzcCzcBzk5zr0zi6z`BzSHzJzzAzz2z\ zCzzMzzWzzezzozzlzzjzzhzzezzczzazzczzdzzfizgeziazj\ YzkUz`UzQUzFUzLVzQWzWWz`XzfYzkYzqZzvZzwVzxRzyOzzMz\ zKzzJzzHzzGzzFzzFzzEzzEzzDzzDzzCzzCOzJLzQIzWEzbBzi\ 8zoDzlIziNzfSzcXz`azYfzVlzhqzulzpgzlczgZzcVz_bzWiz\ SbzNWzIPzEOzGOzINzJNzLMzNMzOLzQLzRKzUJzXIz_HzbGzeF\ zhEzjLzrSzzTzyTzxTzxnzYUzTWzGXz4Mz3Bz1wzzUzVKzRPzH\ GzB8z5wzpczZKzHBzl8z_5zO2zCbzRQzIQzIazKJzABzV7zK3z\ Azz5jz3Vz2Fz1rzCdz9Rz6Dz3 } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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Newton; Escape Time
by Roger Alexander 14 May '10

14 May '10

Looks like a cross between a newton and an escape time fractal. It has the filament structure that can be found in both. The ready made image is a mouse click away at http://maxitersfractalfollies.blogspot.com fract194.gif { ;blue threads ; blank ; calctime 0:05:00.75 ; created May 14, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_e.frm formulaname=ex1csecdav center-mag=1.8676/-0.433119/0.7014088/1/62.5000000000000071/-5.050126983\ 26368081e-014 params=0.749687185277871/0.337137974181341/-0.533616138187811/0.05874813\ 074129459 float=y maxiter=1500 inside=0 logmap=4 periodicity=0 colors=00000000200400600800A00C00E00G00I00K00M00O00Q00S00U00W00Y00_00a00\ c00e00g00i00k00m00o00q00s00u00w00z01z03z05z07z09z0Bz0Dz0Fz0Hz0Jz0Lz0Nz0P\ z0Rz0Tz0Vz0Xz0Zz0`z0bz0dz0fz0hz0jz0lz0nz0pz0rz0tz0vz0xz0zz0zz0yz0xz0wz0v\ z0uz0tz0sz0rz0qz0pz0oz0nz0mz0lz0kz0jz0iz0hz0gz0fz0ez0dz0cz0bz0az0`z0_z0Z\ z0Yz0Xz0Wz0Vz0Uz0Tz0Sz0Rz0Qz0Pz0Oz0Nz0Mz0Lz0Kz0Jz0Iz0Hz0Gz0Fz0Ez0Dz0Cz0B\ z0Az09z08z07z06z05z04z03z02z01z00z00z03z07z0Bz0Fz0Jz0Nz0Rz0Vz0Zz0bz0fz0j\ z0nz0rz0vz0uz1tz1sz2rz3pz3oz4nz5mz5kz6jz7iz7hz8gz9ez9dzAczBbzB`zC_zDZzDY\ zEWzFVzFUzGTzHSzHQzIPzJOzJNzKLzLKzLJzMIzNGzNFzOEzPDzPCzQAzR9zR8zS7zT5zT4\ zU3zV2zW0zW0zV0yV0xU0wU0vT0uT0tS0sS0rR0qR0pQ0oQ0nP0mP0lO0kO0jN0iN0hM0gM0\ fL0eL0dK0cK0bJ0aJ0`I0_I0ZH0YH0XG0WG0VF0UF0TE0SE0RD0QD0PC0OC0NB0MB0LA0KA0\ J90I90H80G80F70E70D60C60B50A509408407306305204203102101 } frm:ex1csecdav { del = P1 + 0.0001 z = pixel: n = z - cos(z) d = (n - (z -del - cos(z - del)))/del z = z - n/(d+P2) 0.0001 <= |n| ;SOURCE: davweird.frm } Roger Alexander _________________________________________________________________ 30 days of prizes: Hotmail makes your day easier! Enter Now. http://go.microsoft.com/?linkid=9729710

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FOTD 14-05-10 (Where is the Stem? [7])
by Jim Muth 13 May '10

13 May '10

FOTD -- May 14, 2010 (Rating 7) Fractal visionaries and enthusiasts: In today's image we return briefly, or perhaps not so briefly, to the FinDivBrot-2 formula and the strange things that happen in the vicinity of the East Valley of large minibrots on the X-axes of parent fractals, which on the surface are everyday Mandelbrot sets. The exponent in today's image is 1.05, while the added constant is 2,000,000. These parameters resulted in an image that is far more broken up than previous images. The discontinuities might be due to the unusually small value of the exponent, or maybe I simply missed such scenes in earlier images. Whatever the reason for the break-up, the feature that caught my attention in today's image is the main stem of the minibrot on the left. The stem has become detached from its minibrot and sits alone and forlorn some distance to the left of where it should be. This curious discrepancy led to the name "Where is the Stem?". The rating of a 7 is a come-down from recent images, but still quite good enough to achieve FOTD standards. The calculation time of 2-5/6 minutes may be ignored by surfing to the FOTD web site at: <http://www.Nahee.com/FOTD/> and viewing the finished image there in leisurely comfort. A mixture of sun and clouds made Thursday interesting here at Fractal Central, but the temperature of 66F 19C fell a bit short of mid-May expectations. The fractal cat duo couldn't have cared less about the weather. They were too busy getting into trouble on the maze of bookshelves in the hallway, squeezing behind the books and spilling books all over the floor. My day was near average. Unless something goes wrong, tomorrow will be the same. FL kept busy working on some kind of word- search puzzles, which I think someone has agreed to publish in one of those puzzle booklets that are found by every check-out. The next FOTD will be posted in about 24 hours. Until then, take care, and be alert for metaphysical reality. It's not an oxymoron. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Where_is_the_Stem? { ; time=0:02:50.82-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-1.749586853573996/+0.0000001972431811/\ 5.168354e+012/1/-155/0 params=1.05/-2000000/0/0 float=y maxiter=2400 inside=0 logmap=339 periodicity=6 mathtolerance=0.05/1 colors=000lnnkmmjllikkhjjgiifhheggdffceebddacc`bb_\ aaZ``Y_`XZ_WYZVXYUWYSVXRUWQTVPTUOSTNRSMQRLPQKOPINO\ HMNGLMFKLEJKDJJCIIBHHAGH8FG7EF6DE5CD4BC3AB29A19908\ 8077066055044033022011000000000000000000000000000E\ 9HG8MIBJKEFMHCOK9QN8SQ8VT7YW7`Z7ca7fd7hg7jjClmGnqL\ prPrsTtqPvmLxiIzbEwXByR7zM4vK6rI8mGAhECcCEZAGX8IU7\ KR8GO8CK980940RRI_WMb`QddTfhXil_kpcmtfoxahfXbQ1kcN\ pVLD_QE`UF`YGaaHaeIaiJbmKbqLbjHacE`XA_Q7ZJ4ZI7SH9M\ GBFFD9GHAGLBHOCHSDIWEIZFN`JSbMXcQaeTfgXkh_pjctkfqd\ eoYelRejKdgDde6dc0de1cf2bh3bi4ak5`l6`n7_o7_j9ZeBZa\ CYXEYTFXOHXKIXLNWLzzLzzMvzMrzMmmLhcJcQIZOGUMFSKDPI\ CNGAKE9HC7EA6B848635U12ZLDhKCuJCzJKzIPzHVzUWzURzUW\ zFdzKezPezUezZezcfzhfzmfzrfzvtxzfmzcczcUzcdzcozZiz\ cczhazm`zr_zvZzzYzzXzzVzzUzzTzzSzzRzzQzzZzzPzzFzzG\ zzGzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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Warm and Huggy
by Roger Alexander 12 May '10

12 May '10

A muted rather than dramatic mood. Glowing embers instead of a volcanic eruption. Go to http://maxitersfractalfollies.blogspot.com for express delivery no extra charge. fract159.gif { ; warm and huggy ; blank ; calctime 0:12:10.22 ; created May 05, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_c.frm formulaname=C09-12 center-mag=-0.02028120430538174/+0.17270063439065110/540.3957 params=0.7356486709189123/0.1425519577623829 float=y maxiter=1500 inside=0 colors=000000000000000000000000000000000100100200400500700900B00D00G00I0\ 0L00O10Q10T10W10Z10a10e10h20k20o20r20v20y20z30z50z60z80z90zB0zC0zE0zF0zH\ 0zI0zK0zL0zN0zO0zQ0zR0zT0zU0zW0zX0zZ0z_0za0zb0zd0ze0zg0zh0zj0zk0zm0zn0zp\ 0zq0zs0zt0zv0zw0zy0zz1zz3zz4zz6zz7zz7zy7zx7zx7zw7zv7zv7zu7yt7ys7ys7yr7yq\ 6yq6yp6yo6yo6xn6xm6xl6xl6xk6xj6xj6xi5xh5wh5wg5wf5we5we5wd5wc5wc5vb5va5va\ 5v`4v_4vZ4vZ4vY4vX4uX4uW4uV4uV4uU4uT4uS3uS3uR3tQ3tQ3tP3tO3tO3tN3tM3tL3sL\ 3sK3sJ2sJ2sI2sH2sH2sG2sF2rE2rE2rD2rC2rC2rB1rA1rA1r91q81q71q71q61q51q51q4\ 1q31p20p20o20n20m20m20l20k20j20j20i20h20g20g20f20e20d20d20c20b20a20a20`2\ 0_20Z20Z20Y20X20W20W20V20U20T20T20S20R20Q20Q20P20O20N20N20M20L20K20K20J2\ 0I20H20H20G20F20E20E20E20D20D20C20C20C20B20B20A20A20A2092092092082082072\ 0720720620620520520520420420420320320220220220120120010 } C09-12 {; V.1.1 - earlier versions may be discarded ; Copyright (c)1998,1999 Morgan L. Owens ; = zC08-C07 const=pixel, z=p1: zz=z*z z=z*(zz*(zz*(zz*(zz-9)+25)-24)+7)*const |z|<100 ;SOURCE: chby12.frm } Roger Alexander _________________________________________________________________ 30 days of prizes: Hotmail makes your day easier! Enter Now. http://go.microsoft.com/?linkid=9729710

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FOTD 13-05-10 (Not Quite so Deep [8.5])
by Jim Muth 12 May '10

12 May '10

FOTD -- May 13, 2010 (Rating 8.5) Fractal visionaries and enthusiasts: Today's image takes us from the East Valleys of large minibrots into totally uncharted territory. The parent fractal of the new world came about when I combined Z^(-3) with 2 parts of Z^(-1.2) and added (1/C). This parent fractal is indescribable, but it basically consists of an over-sized figure-eight and a smaller Mandeloid with no East Valley. The whole works is surrounded on its south side by an even larger sinuous loop. Today's scene is located somewhere between the figure eight and the Mandeloid. At first glance, the image resembles a very deep one, with a magnitude somewhere around 10^25. Actually, the magnitude is only 10^10, which means no arbitrary math is needed. (Actually, arbitrary math is not available with type=formula fractals.) This deceptive appearance explains the name "Not Quite so Deep". Most of the image's worth is a result of the coloring, which is why I rewarded myself with an extra half-point added to the already high rating of an 8. The parameter file runs in a very reasonable 1-3/4 minutes, at least on my fractal-dedicated 2000mhz unit. On the old but still cooking P5-200mhz unit the image takes over 9 minutes to finish. But all concern about running time may be avoided by viewing the completed image on the FOTD web site at: <http://www.Nahee.com/FOTD/> where immediate gratification is the rule rather than the exception. The weather was dry, but the heavy clouds kept things suppressed here at Fractal Central on Wednesday. Strangely enough, the sky completely cleared for an hour just after noon, then, after an hour of bright warm sun, the clouds returned as quickly as they had cleared away. The temperature reached 64F 18C while the sun was shining, the rest of the time it hung around 57F 14C. The fractal cats were rather sulky most all day, keeping themselves occupied by actively ignoring each other. My day was fair enough. Tomorrow will probably be the same. The next FOTD will be posted in 24 hours. Until then, take care, and stand in awe of your world image. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Not_Quite_so_Deep { ; time=0:01:44.32-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+3.010986478661356/+0.0682987406306285/\ 1.616741e+010/1/-107.5/0 params=1/-3/2/-1.2/0/0/0/0 float=y maxiter=1500 inside=0 logmap=185 colors=00000D00F00H00J00Q00H00_00XQ0RX0OO0dX0ecccc\ cc009000zR8zR8000000Xz7Oz92Eh5FbczzzzS000EGGyzsF`z\ 4`y7Wn9SdCOVEKLzm1NY4LS6IA9CDV000EFL000zJzzIzRHOM_\ oKTaISOTcHMVELTr7dk9beAe`BhWbtVzzVzzzzzVziQz`LxTGx\ KBxC6nGBeKFWNJNRNDVR4YRM_QbaMscIjeOagUUiZLkdDliUbz\ Hkz4sz9ozElzIizNezRbzW_p_XpheiqnbywWreTkOQe7O`EPXK\ PSQQOWQJaRFgRE`YDVcCPzBJzADz9Hz9LzFRzMYVTcP_jI_eK_\ _M_UOZPQZJSZDUY7WVCZSHbPMfLSj`o8VfCPXHJNLDDQIDONDM\ SDKXDHaDFfDDkEAlDGnBNp9Tr7_t5ev3ln7mfBoYFpQJrINs9S\ uFYhLcVSjHPmELzAJpAGzADpAAzA7pA4zB4nB5zB5jB6zB7gB7\ zB8cB9zCxnuozqejlWhgNfcDdZ3aUNZ1LS1IL1FE0HI8JMGMQO\ OVWRZcTbkWgtP_`HXHCUU6Ug0UuKUkHWgD`c9cZ5cV1cQ3cz6c\ BCczJcBQczXcAbZziUzpPzxQ9rNzmKChcEccGZcITcKVcLXcMZ\ cNacODkQEnLFqGTtsQwkOzdMzXKzQzzIzzMzzKzzJzzHzzGzzF\ zzDzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ 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=========================================

1 0

Metallic Blues
by Roger Alexander 11 May '10

11 May '10

A design with a mechanical quality.The exact self-similarity of the artifact or the approximate self-similarity of the natural. Both have their attractions. Go to http://maxitersfractalfollies.blogspot.com and helpful internet electrons will spare you the delay of generating the image. fract187.gif { ; metallic blues ; blank ; calctime 0:00:48.33 ; created May 11, 2010 ; Fractint Version 2004 Patchlevel 9 reset=1920 type=formula formulafile=*.frm formulaname=f'liar1 function=conj center-mag=-0.000459145/1.0119/1.865037/1/-45.0000045336336569/3.0224224\ 0114020122e-006 params=0.8806070131534777/-0.9629505294961395 float=y maxiter=1200 inside=maxiter proximity=2 outside=fmod cyclerange=0/255 colors=00101211312412413523624724825935936A36B37C47D48E48F49F59G5AH5AI5B\ J6BK6CK6CL6DM7DN7EO7EP7FP8FQ8GR8GS9HT9HU9IUAIVAJWAJXBKXBKYBLYCLZCMZCM_DN\ `DN`DOaDOaEPbEPbEQcFQcFRdFReGReGSfGSfHTgHTgHUhIUiIViIVjIWjJWkJXkJXlKYlKY\ mLZnLZnM_oM_oM`oN`pNapOaqObqPbrPcrPcrQdrQdsResRetRftSftSgtTguThuUhuUivVi\ vVjvVjvWkwXkwYlwYlwZmxZmx_nx_nx`ox`oxapyapybqybqycrydryesyeszftzgtzhuzhu\ zivzjvzkwzmwznxzpxzqyzryzuzzuzzuzzryzqyzoxznxzmwzkwzjvzivziuzhuzgtzftzfs\ zesydrycrybqybqyapyapy`ox_ox_nxZnxZmxYmwYlwXlwXkwWkwVjvVjvVivVivUhvUhuTg\ uTguSfuSftRetQesQdsQdrPcrPcrObqObqOapNapN`oN`oM_nM_nMZmLZmLYlLYlKYlKXkJX\ kJWjJWjIViIViIUhHUhHTgHTgGSfGSfFRfFReFQdFQcEPcEPbEObDOaDNaDN`CM_CM_BLZBL\ ZBKYAKYAJXAJWAIV9IU9HU9HT8GS8GR8FR8FQ7EP7EO7DN7DM6CL6CL6BK6BJ5AI5AH59G59\ G48F48E47D37C36B36A35A259248247236135124124113012001000 } frm:F'Liar1 {; Generalization by Jon Horner of Chuck Ebbert formula. ; X: X is as true as Y ; Y: Y is as true as X is false ; Calculate new x and y values simultaneously. ; y(n+1)=abs((1-x(n) )-y(n) ), x(n+1)=1-abs(y(n)-x(n) ) z = pixel: z = 1 - abs(imag(z)-real(z) ) + flip(1 - abs(1-real(z)-imag(z) ) ) fn1(abs(z))<p1 ;SOURCE: fractint.frm } Roger Alexander _________________________________________________________________ 30 days of prizes: Hotmail makes your day easier! Enter Now. http://go.microsoft.com/?linkid=9729710

2 1

FOTD 12-05-10 (Last of the Series [9])
by Jim Muth 11 May '10

11 May '10

FOTD -- May 12, 2010 (Rating 9) Fractal visionaries and enthusiasts: Today's image, which rates a very honorable 9, is the last in the series of minibrots in East Valley areas of large minibrots on fractalized main stems of apparent Mandelbrot sets. The image, good as it is, pretty much exhausts, (an over-statement), the immediate potential of such areas, and it is now time to move on. The exponent of today's image is 1.5 and the iterative added constant is negative 20,000. The change of values sems to have made little difference. The images in the East Valley of the large minibrot are still very good. Tomorrow's FOTD will feature something new, hopefully as good as the most recent 4 or 5 images. The name of today's image, "Last of the Series", simply tells it like it is. The calculation time of 3-3/4 minutes is fast enough; the trip to the FOTD web site at: <http://www.Nahee.com/FOTD/> to see the finished image is equally fast if not faster. Tuesday here at Fractal Central began with a splendid sunrise, but by 8am a dull gray overcast had set in, and just after noon a steady cold rain began, while the temperature hovered around 46F +8C, making it hardly a perfect spring day. The fractal cats found comfort by the heat of the hall radiator. My day was active but not too hectic. The next FOTD will be posted in 24 hours. Until then, take care, and be happy like a fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Last_of_the_Series { ; time=0:03:45.69-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-1.749760219999033/+0.00009565363837257\ /8.149523e+012/1/35/0 params=1.5/-20000/0/0 float=y maxiter=1500 inside=0 mathtolerance=0.05/1 colors=000JTJLUJOVJRWJUXJXYJ_ZJb_Je`JhaJk_KnaJqcIt\ dHwfHzgGziFzjEzlEzmDzoCzpBzrBzsAzu9zv9ztAzsBzrCzqC\ zpDzoEznFznEynDxnDxnCwnCvnBunAunAtn9sn9rn8rn7qn7pm\ 6pk6oi7ng7me8lc8ka9j_9jYAiVAhSBgPBeNCcKC`FAYICWKEU\ NFSPHUSJXUK_XMbZOeaPecRffTfhUfkWek_fmXgnVgoThpRhrO\ isMitKjuIjvGetI`sKXqMSpONnQJmSEkU9jW6l`5iY5gV4eS4c\ P4`M3ZJ3XH2VE2SB2Q81O51M21K04O86SG8WOAZWCbcEfkGjsI\ mzJhvKcsKZpLUmMPiMKfNFcNA`I7YD4VB2U81T76W7BY7G_7Lb\ 7Qdzz0zz0zz0zzzzzzzzzzzzzzzzzwzzrzzmzzhwyctxZrwUpv\ PnuFlt9jsAgqBepCcoCanD_mEYlFWkFXjGYiHZhI_gI`fJaeKa\ dKbcLcbMdaMe`Nf_OdrJfZOq6VgFTZOSQWQHdP8lOAkRCjUEiW\ GiZIh`KgcMffOfhQekSdmUcpWcrY_oZWl`SiaPfbLcdH`eEYgA\ Vh6Si3Pk5Qm6Ro7Rp8Sr9StBTuCUwDUyEVzFVAxDBvHBtKBrNC\ pQCnTCkkDjlDjmDknCloCmpBnqBorBpsAqtAruAqvDnwGixIdy\ L_zOVzQQvTLrWGmYBh`6cf0Zb1U_2PW3JT4LP5NM6PI7RF8TC9\ VNJTXSRgaPqjNjfMccLX_KQXJ } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

1 0

Electric Fern
by Roger Alexander 10 May '10

10 May '10

The unfurling of a cyber fern. Inorganic life with every atom in place and no dislocations in the crystal structure. Respect your humanity. Carbon is master, silicon is servant. I am intermittently humanistic. On display at http://maxitersfractalfollies.blogspot.com. fract172.gif { ; a mandelbrotmix4 spiral ; blank ; calctime 0:08:01.36 ; created May 08, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_m.frm formulaname=MandelbrotMix4 function=ident center-mag=-1.98681686364739400/+0.34376514647650340/183.6534 params=2.25/0.75/0.738990447706534/-1.375/-0.125/0.7961363567003388 float=y maxiter=1500 inside=0 proximity=2.5 outside=fmod colors=00z000111222333333444555666777777888999AAAAAABBBCCCDDDDDDEEEFFFGG\ GHHHHHHIIIJJJJJJKKKLLLMMMMMMNNNOOOPPPPPPQQQRRRRRRSSSTTTUUUUUUVVVWWWWWWXX\ XYYYYYYZZZ______``````aaabbbbbbcccddddddeeeeeeffffffggghhhhhhiiiiiijjjjj\ jkkkkkkllllllmmmmmmnnnnnnoooooopppppppppqqqqqqrrrrrrrrrssssssssstttttttt\ tuuuuuuuuuvvvvvvvvvwwwwwwwwwwwwxxxxxxxxxxxxxxxyyyyyyyyyyyyyyyyyyyyyzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzyy\ yyyyyyyyyyyyyyyyyyyxxxxxxxxxxxxxxxwwwwwwwwwwwwvvvvvvvvvuuuuuuuuutttttttt\ tsssssssssrrrrrrrrrqqqqqqpppppppppoooooonnnnnnmmmmmmllllllkkkkkkjjjjjjii\ iiiihhhhhhggggggfffeeeeeeddddddccccccbbbaaaaaa``````______ZZZYYYYYYXXXXX\ XWWWWWWVVVUUUUUUTTTTTTSSSRRRRRRQQQQQQPPPPPPOOONNNNNNMMMMMMLLLLLLKKKJJJJJ\ JIIIIIIHHHHHHGGGFFFFFFEEEEEEDDDDDDCCCBBBBBBAAAAAA999888 } 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 ;SOURCE: 99msg.frm } Roger Alexander _________________________________________________________________ 30 days of prizes: Hotmail makes your day easier! Enter Now. http://go.microsoft.com/?linkid=9729710

1 0

FOTD 11-05-10 (The Wind Blows Gentle [9])
by Jim Muth 10 May '10

10 May '10

FOTD -- May 11, 2010 (Rating 9) Fractal visionaries and enthusiasts: I saw two letters of interest on the list today. The first letter told me to find the hidden C, 6, and N, then read some mis-spelled text, and forward the letter on. I did all these very simple tasks with ease. I guess that means I'm pretty smart, which my modesty has always prevented me from admitting outright. A second letter asked me which FOTD images are my favorites. Actually, I haven't the slightest idea. My favorite fractal images change from day to day, even from hour to hour. It would take a lot of comparison and contemplation before I could answer this question honestly, if an honest answer even exists. As for today's image, it continues the theme of the past 2 days, this time with an exponent of 1.9 and added iterated value of negative 1000. This negative number opens the negative X-axis and infinitely divides it. Today's scene is another one on the edge of the infinitely divided X-axis, in the East Valley area of the large minibrot. The rating of a 9 seems about right. It's a pretty impressive image, but I never got the feeling that it's the best of all time. The name "The Wind Blows Gentle" can mean anything that comes to mind. It's a metaphor that could refer to anything. The calculation time of just under 10 minutes is slower that I would like, but the result of the effort is worth the wait. And as always, those who have no time to waste or have new-fangled DOS-challenged computers may see the image without the job of calculating it by visiting the FOTD web site at: <http://www.Nahee.com/FOTD/> where the finished image is posted for instant and effortless gratification. Lots of sun and a closer-to-normal temperature of 61F 16C made Monday quite liveable here at Fractal Central. But the forecast is for rain every day the rest of this week. We'll see how it goes. The fractal cats had an active day, viciously attacking the two fresh catnip mice we gave them. In my department, the work went smoothly. FL is worried about her garden and possible frost late tonight, though I doubt that it will get that cold. The next FOTD will be posted in 24 hours. Perhaps I'll continue the fractal roll I'm on. Until then, take care, and find the hidden fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= TheWindBlowsGentle { ; time=0:09:54.73-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-1.748168094567843/+0.00047373380185646\ /2.19017e+012/1/-102/0 params=1.9/-1000/0/0 float=y maxiter=18000 inside=0 mathtolerance=0.05/1 colors=000R82S95TA8TAAUBDUBFVCIVCKWDOWDQXETXEWYFZZ\ GaZGd_Hg_Hj`Im`IpaJsaJubKxcGzbKz`NzZQyXTyVWxTZxRax\ PewNhwLkvJnvHquFtuCvwDwuEvsEtqFsoGqnGplHnjHmhIkfJj\ eJhcKgaLf_LdYMcXMaVN`TOZROYPPWOQVMQTKRSIPSGRRCSRCT\ QDUQDVQEWPEXPFZPF_OG`OGaOGbNHcNHdMIfMIgMJhLJiLKjLK\ kKLlKLmIMmKLjMKhOKeQJcSI`TIZVHWXHUZGR`FPaFMcEKeDHg\ DFiCHjCKlBPnASpAUr9Ws9YrB_qCapDcoEfoFinGlmHolIpkJm\ jKhi3ch4ag5_f5Ye6Wd6Uc7Sb7Qa8O`8M_9KZ9I`AGaBFcBEdC\ DeCCgDBhDAiE9kE8lF6nD8mF9lGAkHCjIDiKEhLGgMHfNIeOKd\ QLcRMbSOaTP`VQ_WSZXTYYWVXUXZSY`Q_aO`cMbdKcfIdhGfiE\ gkCilAjn0ko9koIatRSxUUwWVvZXv`Yuc_ue`thbtjcsmesofr\ piwqgrqenqciqaeq`aqZXrXTsVOtUKuSGvQBzS7zT3zS4yR5vS\ 6rU7mV7hX8cY9__AX`9U`ARZBOXBKVCFTDARDAQEAOFAMFAKG9\ IH9GH9EI9DJ9BJ99K97L95L93M91N90NA1LB1KC1JD1IE1GF1F\ G1EH1DI1BJ1AK19L18P67SB7VG7YL7aQ6dV6g_6jd6lk4mi6L9\ EM9DN9CO9BO9AP99Q98R97S96 } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

1 0

Makes good wallpaper
by Roger Alexander 10 May '10

10 May '10

Today's fractal is intended as a background or wallpaper. The design suggestive of plants and leaves does not have have an immediate visual focus- detail without distraction. Go to the usual suspect at http://maxitersfractalfollies.blogspot.com for the completed image. fract162.gif { ;leaf like ; blank ; calctime 0:34:52.90 ; created May 05, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_m-cop~1.frm formulaname=mask1 function=sin/trunc/ident center-mag=-0.68400781971651980/+0.26225554106910050/266.6667 params=-0.4204840235602892/-0.6564531388286996/0.4740134891811884/1.0123\ 59996337779/1199.452345347453/-0.8937345500045778 float=y maxiter=2400 outside=tdis rseed=3141 cyclerange=0/255 colors=0l00l00m00m00n00o00o00p00p00q00q00r00r00s00s00t00u00u00v00v00w00w\ 00x00x00y00z00z00y00x00w00v00u00t00s00r00q00p00p00o00n00m00l00k00j00i00h\ 00g00f00f00e00d00c00b00a00`00_00Z00Y00X00W00W00V00U00T00S00R00Q00P00O00N\ 00M00M00L00K00J00I00H00G00F00E00D00C00B00B00A009008007006005004003002001\ 00000000000100100200200300300400400500500600600700700800800900900A00A00B\ 00B00C00C00C00D00D00E00E00F00F00G00G00H00H00I00I00J00J00K00K00L00L00M00M\ 00N00N00O00O00P00P00P00Q00Q00R00R00S00S00T00T00U00U00V00V00W00W00X00X00Y\ 00Y00Z00Z00_00_00`00`00`00a00a00b00b00c00c00d00d00e00e00f00f00g00g00h00h\ 00i00i00j00j00k00k00l00l00m00m00m00n00n00o00o00p00p00q00q00r00r00s00s00t\ 00t00u00u00v00v00w00w00x00x00y00y00z00X00X00Y00Y00Z00Z00_00_00`00`00a00a\ 00b00c00c00d00d00e00e00f00f00g00g00h00i00i00j00j00k00k0 } frm:Mask1 { ; Ron Barnett, 1993 ; try fn1 = log, fn2 = sinh, fn3 = cosh ;P1 = (0,1), P2 = (0,1) ;Use floating point z = fn1(pixel): z = P1*fn2(z)^2 + P2*fn3(z)^2 + pixel |z| <= p3 + 4 } Roger Alexander _________________________________________________________________ 30 days of prizes to be won with Hotmail. Enter Here. http://go.microsoft.com/?linkid=9729709

3 5

Electric Monster
by Roger Alexander 09 May '10

09 May '10

When I first saw this I thought of a monster from some grade B movie-" Attack of the Electricity Monster" perhaps and this was its footprint. How good is modern psychiatry and what can be learned about personality from the projected meaning given to abstract patterns like clouds and fractals? Go to http://maxitersfractalfollies.blogspot.com to project your own meaning. fract182.gif { ; corona discharge ; blank ; calctime 0:02:50.66 ; created May 09, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=mandel(fn||fn) function=tanh/sqr corners=-1.33022634/-1.28179889/0.0323067967/-0.0322631412/-1.28179889/-\ 0.0322631412 params=0/0/0.01 float=y maxiter=1200 cyclerange=2/255 colors=00000000100300400600800900B00C00E00G00H00J00K00M00O00P00R00T00U00\ W00X00Z00`00a00c00d00f00h00i00k00m01m03m04n06n07o09o0Ao0Cp0Ep0Fq0Hq0Iq0K\ r0Lr0Ns0Ps0Qs0St0Tt0Vu0Wu0Yu0Zv0`v0bw0cw0ew0fx0hx0iy0ky0mz1mz3mz5nz7nz9o\ zBozDozFpzHpzJqzLqzNqzPrzRrzTszVszXszZtz`tzbuzduzfuzhvzjvzlwznwzpwzrxztx\ zvyzxyzzzzyzzxzzwzzuzztzzszzqzzpzzozzmzzlzzkzzizzhzzgzzezzdzzczzbzz`zz_z\ zZzzXzzWzzVzzTzzSzzRzzPzzOzzNzzLzzKzzJzzIzzGzzFzzEzzCzzBzzAzz8zz7zz6zz4z\ z3zz2zz0zz0yz0xz0wz0uz0tz0sz0qz0pz0oz0mz0lz0kz0iz0hz0gz0ez0dz0cz0bz0`z0_\ z0Zz0Xz0Wz0Vz0Tz0Sz0Rz0Pz0Oz0Nz0Lz0Kz0Jz0Iz0Gz0Fz0Ez0Cz0Bz0Az08z07z06z04\ z03z02z00z00y00x00w00v00u00t00s00r00q00p00o00n00m00l00k00j00i00h00g00f00\ e00d00c00b00a00`00_00Z00Y00X00W00V00U00T00S00R00Q00P00O00N00M00L00K00J00\ I00H00G00F00E00D00C00B00A009008007006005004003002000000 } Roger Alexander _________________________________________________________________ 30 days of prizes to be won with Hotmail. Enter Here. http://go.microsoft.com/?linkid=9729709

1 0

FOTD 09-05-10 (Just Beyond Infinity [10])
by Jim Muth 09 May '10

09 May '10

FOTD -- May 09, 2010 (Rating 10) Fractal visionaries and enthusiasts: For a brief moment on Saturday I thought today's FOTD image was the best I have ever produced. Even though the moment did not last, this earned the image a rating of a supercalifragilistic- expialidocious 10. At least IMO, what makes the image so good is its resemblance to an actual physical object. And why should this be so surpris- ing? Physical objects are made of atoms, and read any serious book on quantum theory and you will see that atoms are made of sub-atomic particles, which in turn are mere mental models best described in the abstract language of mathematics. Both the real world and the world of fractals are made of numbers! With the exponent of Z being 2.5, one would expect the image to be filled with discontinuities. And actually, it is. But the discontinuities are arranged in so orderly a manner that they are barely noticeable. I have no idea why the central minibrot is purely quadratic in nature however. One would expect a mini- brot at such a depth to be of order-2.5. The name "Just beyond Infinity" means nothing. It merely has a kind of sci-fi feeling to it. The calculation time of 6-3/4 minutes is cheap for such a worthy image, and those who run the included parameter file will be well rewarded. This leaves only those with over-qualified compu- ters stricken with dosophobia, who may view the already calcula- ted image on the FOTD web site at: <http://www.Nahee.com/FOTD/> Saturday brought high winds accompanied by tortured clouds and afternoon showers of rain to Fractal Central. The day began with sun and a summer-like temperature of 68F 20C, but by mid afternoon it had fallen to 50F 10C and the wind gusts were near 50mph 80kph. The fractal cats showed little concern about the outdoor conditions. My day was uneventful. The next FOTD, for all it is worth, will be posted in 24 hours. Until then, take care, and physicists tell us that substantial physical objects are made of the activities of non-substantial atoms, while neurologists say that non-sunstantial thought is made of the activities of substantial physical neurons. Would the real reality please stand up? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= JustBeyondInfinity { ; time=0:06:43.70-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-1.749591043614323/+0.0000449504726666/\ 1e+12/1/-55/0 params=2.5/25000/0/0 float=y inside=0 maxiter=4600 logmap=716 mathtolerance=0.05/1 colors=000UViUVhUVgUVfUVeUUeUUeTUeRUePUeMUdKTcISaG\ R_EQYCPWBOU9NS7NS6NP9PTBRVEUXGYZIaaLfcPjfUnfZrgcvg\ hzhnyhtymzxvzxzvwzrwzmvzhvzcszZpzUmzQjzNgzKdzMazPZ\ zRWWTTXUVYUWZUX_UY`UZaU_bU`cUadUbeVadVadWacWacW`bX\ `bX`aX`aY_a__`a_`c__eZ_gZZiZZkZZm`ZpaZsbZvdZzeZzfZ\ wfZufZtfYsgXrgWqgVphUohTnhSmiRmiQmjPmjOmkNmkMmgKmc\ JmZHmVGmREmNDmRHmVLmZOmbSkfWijZcnbUrfKui2pg3lf3he4\ dd5`c5Xb6Ta6P`HS_SU_aXZlZZv`Zs_WpZUmZSjYQgYNeXLU_Y\ NWQGSJ9PCNcX_qpmYczFRqJThMU_PWSTXJWZAZ_2a`2Sd2Ig0R\ LSwAQp9Oi8Nb7LW6JP5II4GB3F53K47P3BU2FZ1J_1M_AKXIJ`\ PFeVCi`8nf5zj2uf7sYBqQGqIKqAPq3TgAUZGUQNUHTU8ZULTW\ M_YNeZOl`PraPzbNpWLiQJaJHVDzN6zG0zUDzcPaOaiQmqSysg\ jtkXpm`mediXgfPkbGn_8rX0uaJdfaPbYL_XIXYFTZBQ_8Na5K\ c2Re9XgFbiL_kOYnQWqSUtVSwXQzZMz`Izazzczzdzzfzzgzzg\ zzgzzhzzmzzrzzvzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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FOTD 10-05-10 (Patterns in Sand [7.5])
by Jim Muth 09 May '10

09 May '10

FOTD -- May 10, 2010 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image came about in almost exactly the same way as yesterday's superb image, but in today's image the exponent has been increased to 2.9 and the number added to each iteration reduced to 1000. The result is another parent fractal that on the surface appears to be a perfectly normal Mandelbrot set, but in its depths, is entirely different. And like yesterday's image, today's image lies in the East Valley of the large minibrot on the main stem of its parent. Curiously, the minibrots in yesterday's image, which has an exponent of 2.5, are quadratic, while today's image, with its exponent of 2.9, has order 2.9 minibrots in its depths. To me, this makes no sense at all, and is a reminder that there surely is a lot to learn about the way numbers work in fractals. The comb-like detail in the image is due mostly to the coloring, though something real must lie in the fractal itself, or else these patterns would not appear. The rating of a 7.5 indicates that I am satisfied with the image. The extra half point is a reward for my coloring effort. It was not easy to bring the patterns out of the 'sand'. The name "Patterns in Sand" refers to the comb patterns, which, like patterns in physical sand, totally disappear when the light or color changes. The calculation time of 2-1/3 minutes is about all the image is worth. And even this time can be saved by viewing the completed image on the FOTD web site at: <http://www.Nahee.com/FOTD/> Heavy clouds and unusually chilly winds made Sunday feel like anything but spring here at Fractal Central. When the tempera- ture failed to rise above 52F 11C, the fractal cats gave up on comfort and retired to their chosen resting places to sleep away the afternoon. My day was very close to average. The next FOTD will be posted in 24 hours . . . more or less. Until then, take care, and you can't know where you're going unless you know where you came from. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Patterns_in_Sand { ; time=0:02:18.86-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-1.74884203473413/+0.00016101734317492/\ 5.143742e+009/1/-37.5/0 params=2.9/1000/0/0 float=y maxiter=1800 inside=0 logmap=260 periodicity=6 colors=000`Rf`Rg`Rh_Qj_QkZPmZPnYOpYOqXNsXNtWMuWMuV\ LvVLu_bzZeyZgxZjxYmwboyfrzkuzowztzztwzszzmzzhwzbtz\ XqzSozRmzQizQezPaxPYvOUtNSrNQpMNmLLlLIjKGfKEaQBcSC\ _TDXVDTWEQXENZHO`IOcKOhLPmNPrOPvQPzRQzTQzUQzVRzWRz\ XRzYRzZSz_Sz`SzaSAA0CA0EA0GA0IA0JA0LA0NA0PA0R90S8F\ U7KW6PY5U_4Z`4ca7db9dbCecEecHfdJfdMgeOgeRhfThfVh`a\ mVhqQoueCp4896DC7IE8MH9RJBWLC_ODdQEhSDdUCaVCZXBWYB\ TZAP`9Ma9Jc8Gd8DeYRmwhtvmovskuzguzcuz_tzVzzRzzNzzJ\ zzFztJzvMzxPztRzqTznUWkWXhXYdZZa`_Za`WcaTdbPfcMhdJ\ ieGkfDlfFmfGmfHnfJnfKofLofMofOpfPpfQqfSqfTrfUrfVr_\ XmTYiM_eF``8bX2cT7`UCYVHVWMSXRPYWMZ`J_eH`aNbYScUXe\ QafMfhIkiEpjBie9ca7YY5ST3MP1GL4KN6NP8QRATTCWUFZWHa\ YJe_LhaNkbQndSqfUthWwjYzkTydOyZmyTmxNmzHmzBzzDzzFz\ zGzzIzzJzzLzzNzzOzzQzzRzzYzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD 09-05-10 (Just Beyond Infinity [10])
by Brian Prentice 09 May '10

09 May '10

John, take a look at this rendering: http://linuxenvy.com/bprentice/Fractals/Jim%20Muth/Just%20Beyond%20Infinity… Great image Jim, definitely one of your best! Brian Prentice

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Re: [Fractint] FOTD 09-05-10 (Just Beyond Infinity [10])
by JackOfTradeZ＠comcast.net 09 May '10

09 May '10

. Nice one Jim! It looks cool zooming back out too; I may do a zoom-in animation. .

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Magma!
by Roger Alexander 08 May '10

08 May '10

You know what they say... colors make the fractal. Well actually "they" don't say that, I just made it up. Gripped by Icelandic volcano fever I aimed for a dramatic lava effect. Hey Hollywood! Go to http://maxitersfractalfollies.blogspot.com to immediately see if I hit what I was aiming for. fract149.gif { ; magma ; blank ; calctime 0:23:38.28 ; created May 03, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=*.frm formulaname=m2v_nicespirals center-mag=+0.36785587384230370/-0.54564387045075050/1844.47 params=0/0/0/0 float=y maxiter=1500 inside=0 colors=00000000000000000000000000000000000011111111111111111111111111111\ 111111111111111111111111111111111111111111122222222222222222222222222222\ 2222222222222322422522622722822922922A22B22C22D22E22F22G22H22I22I11J11K1\ 1L11M11N11O11P11Q11R11R11S11T11U11V11W11X11Y11Z11_11_11`11a11b11c11d11e1\ 1f11g11h11h00i00j00k00l00m00n00o00p00q00q00r00s00t00u00v00w00v00u00u00t0\ 0t00s00s00r00r20r50r80sB0sE0sH0tK0tM0tP0uS0uV0uZ0vc0vh0wm0wr0xw0xw6xxCxx\ IxyOyzUyzNyyFyx8xw0ws0vo0uk0sg0rc0p_0oX0nV0mS0lQ0kN0jL0iI0hG0gD0fB0e80d6\ 0c30b00`00Y00W11T11Q22Q22P33O33O33N33N33M33L33L33K33K33J33J33I33H33H33G3\ 3G33F33E33E33D33D33C33B44B44A44A4494494484474474464464454444444444444444\ 444444444444444444444444444444444444444444444444455555555555555555555555\ 5555555555555555555555555555555555555444333222222111000 } frm:m2v_nicespirals(XAXIS_NOIMAG) { ;p2 is the bailout (default=127) b=p2,b=b+(b==0)*127 z=y=c=pixel: z=z*z*y+c-p1 y=z/y-c |z|<b ;SOURCE: mandhack.frm } Roger Alexander _________________________________________________________________ 30 days of prizes to be won with Hotmail. Enter Here. http://go.microsoft.com/?linkid=9729709

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Re: [Fractint] FOTD 08-05-10 (Mysterious East
by JackOfTradeZ＠comcast.net 08 May '10

08 May '10

. Glad to see you goin' in deep again Jim! With fractals is like we say in scuba - the deeper you go the better you feel! Interesting how the deep images in the East start to resemble those deep in the West needle (where I've done much of my exploring), with all the concentric circles getting ever more complex ..... stay amazed JoTz .

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Worms! Giant Worms!
by Roger Alexander 08 May '10

08 May '10

Looks like that giant worm in that book- what was it called? Dude? Dune? Dubious? And they had that magic powder, herb or spice or relish or whatever it was called. And under the influence of the magic powder the Kommuters could navigate the Public Transistor System. It's been ages since I read it and I can't quite remember. fract168.gif { ; a worm! ; blank ; calctime 0:02:04.63 ; created May 07, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=*.frm formulaname=zapfl4p12 center-mag=-0.827174/0.942769/9.177751 params=0.02645954771568956/-0.1608020264290292/-0.08975493636890775/-0.9\ 644154179509873 float=y maxiter=1500 inside=0 proximity=1 outside=fmod colors=zzzzzzzzzzzzzzzyyyyyyyyyyyyxxxxxxxxxxxxwwwwwwwwwwwwvvvvvvvvvvvvuu\ uuuuuuuuuuttttttttttttssssssssssssrrrrrrrrrrrrqqqqqqqqqqqqppppppppppppoo\ oooooooooonnnnnnnnnnnnmmmmmmmmmmmmllllllllllllkkkkkkkkkkkkjjjjjjjjjjjjii\ iiiiiiiiiihhhhhhhhhhhhggggggggggggffffffffffffeeeeeeeeeeeeeeeddddddddddd\ dccccccccccccbbbbbbbbbbbbaaaaaaaaaaaa````````````____________ZZZZZZZZZZZ\ ZYYYYYYYYYYYYXXXXXXXXXXXXWWWWWWWWWWWWVVVVVVVVVVVVUUUUUUUUUUUUTTTTTTTTTTT\ TSSSSSSSSSSSSRRRRRRRRRRRRQQQQQQQQQQQQPPPPPPPPPPPPOOOOOOOOOOOONNNNNNNNNNN\ NMMMMMMMMMMMMLLLLLLLLLLLLLLLLLLLLLKKKKKKKKKKKKKKKJJJJJJJJJJJJJJJIIIIIIII\ IIIIIIIHHHHHHHHHHHHHHHGGGGGGGGGGGGGGGFFFFFFFFFFFFFFFEEEEEEEEEEEEEEEDDDDD\ DDDDDDDCCCCCCCCCCCCCCCBBBBBBBBBBBBBBBAAAAAAAAAAAAAAA99999999999999988888\ 8888888888777777777777777666666666666666555555555555444 } frm:zapfl4p12 { z=pixel: z=(z*z*z*z+(pixel*p1))/(z*z*z*p2) |z|<=4 ;SOURCE: ratz.frm } Roger Alexander _________________________________________________________________ 30 days of prizes to be won with Hotmail. Enter Here. http://go.microsoft.com/?linkid=9729709

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FOTD 08-05-10 (Mysterious East [8])
by Jim Muth 07 May '10

07 May '10

FOTD -- May 08, 2010 (Rating 8) Fractal visionaries and enthusiasts: Today's image, the 8th of the month, rates an 8. It is a scene in the East Valley of a minibrot in the East Valley of a mini- brot in the East Valley of a minibrot in the East Valley of a minibrot in the East Valley of a minibrot in the East Valley of a minibrot in the East Valley of the large minibrot on the main spike of the Mandelbrot set. I think I have the number of East Valleys right, but there is no guarantee. The count of surrounding elements reset itself to a lesser number many times on the way to the minibrot at the center of the image. Perhaps the most unusual thing in the image is how it makes the normally routine East Valley scenery shine in a new light. I tried the other outside options on the image, but they produced results that were either too flat or too chaotic. The name "Mysterious East" means just about what it says. Unfortunately, the parameter file, using arbitrary precision math, runs as fast as frozen molasses, taking over 1-3/4 hours to finish even on the fractal-dedicated fireball P4-2000mhz unit. The solution is to view the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> Friday turned out to be a perfectly normal day both with the weather and the work here at Fractal Central. The weather was partly cloudy with a temperature of 70F 21C, which is just about average. The work was finished by 3pm, which is about average, and the fractal cats got into trouble, which is also average. The trouble arose when Nicholas tried to take Cassie's catnip mouse and she wanted to keep it. A loud hiss followed by a swat to Nico's ear gave him other ideas. The next FOTD will be posted in 24 hours. Until then, take care, and changing the past is the reciprocal of knowing the future. If one is possible, then the other must be possible also. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mysterious_East { ; time=1:47:46.76-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.7478\ 549044981009970872626605813389487752/-6.654476e-53\ /6.673542e+036 params=0/0 float=y maxiter=125000 bailout=9 inside=0 symmetry=xaxis periodicity=6 mathtolerance=0.05/0 colors=000IABUDOeG_pIkmMbjPVgSMfRFeTEdVEcXEbZEa`E`\ fD_mDZzDYzDmvDzzCzzCzzCzzCzz8VYaSabPebMibJmcGqcEuc\ KohPilUdpTboT`oSZnSXnSVnRUmRSmRQmQOlQMlQLlOMmNNmMN\ mKOmJOmIPmHPmFQmEQmDRmCRmEPkFNiGLhHKfIIdJGcKFaLD`z\ BZzAXz8Wz6Uz5Sz3RScPTcON1TI2XC3a73eZLczbby_axY`xW`\ wT_wR_vPZvMZuKYuIYlUgcdqWozVluUipTfkScfR`aQYXPVSOS\ NNPIMMETSJ_YNfcRmiVsnZneaiXdePf`GiX8kWRiVhhUzg_mce\ ``jPYkSZkUZkXZkZZka_kc_ke_kh_kj_km`ko`zz`zz`kv`RaL\ 605B06K06M06R06VF6YBFb8Pg0Zk0heYh_mhcpFor0zv0zx0zz\ hzzzzzzzpDzmLzmTsm`rmhqmormmrmlrmkrhjzcizZhxUgxUeu\ QduDcoBbj9aj7`j6_fA_bD__G_eJ_aN_ZQ_VT_RW_OZ_NcZNmY\ MzXLzWGzZLzVPzST`OYbLabHecEj`ArY7zZ2zW4zT5mQ6VN8NK\ 9DJ8FIAHIBJIDLIENIFOHHQHISHJUHLWHMAX9MPGXHNk0Ui5Tg\ ATfFSdKSbPRaUR_ZQYcQUfGWjLXgQYcVZ`__XdmUimUmcUmcLm\ KFPRADSCFTDGUEHUFIVGJWHKWILXJMYKNYLOZMP_NQfQKbPO_O\ RXNUUMXRL_OKbLJeIIhIFXICM } END PARAMETER FILE=========================================

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FOTD 07-05-10 (Skeletal Minibrot [6])
by Jim Muth 06 May '10

06 May '10

FOTD -- May 07, 2010 (Rating 6) Fractal visionaries and enthusiasts: Today's image is the same scene as yesterday's, with the slight difference that it was rendered with the inside set to the color number zero instead of 'bof61'. As a result, all the parts of yesterday's image that were made of 'inside' stuff have gone totally black, leaving a scattering of dots, which become the outline of a Mandelbrot set when seen from a distance. This explains the name, "Skeletal Minibrot". Though yesterday's image rated a full 8, today's image is a virtual repeat, and therefore rates no more than a 6. I don't particularly like repeats, but sometimes they do happen. The calculation time is a zippy 19 seconds, almost exactly the same as yesterday's. The trip to the FOTD web site at: <http://www.Nahee.com/FOTD/> where the finished image is posted, may not save any time, but it will avoid all the hassle that goes with setting up and run- ning the included parameter file. Thursday was a perfect day weatherwise, at least here at Fractal Central, where we had total sun and a temperature of 75F 24C. The fractal cats must have agreed, for when we gave them their morning exercise with their favorite toy, a toy bird on a string attached to a stick, they started leaping like year-old kittens. Cassie finally caught the bird in mid air and 'killed' it. My day was fair enough despite a minor flap during lunch with FL, who still feels my attitude toward the world is too negative. The next FOTD, a very deep and slow one, will be posted in 24 hours. Until then, take care, and anger solves nothing, but sometimes it sure feels right. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Skeletal_Minibrot { ; time=0:00:19.29-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-4.668/0/5.694761 params=-0.0035/-6/\ -0.014/-5/0/0/0/0 float=y maxiter=1125 inside=0 logmap=5 symmetry=xaxis periodicity=6 colors=000BD57FA5GF2HK8KMCMPIPSMRVRUYWW`_Xg`Yi_Zf_\ _h``eaagbbicckddmeeoffqhgsjhulivnjwpkxrlytmzvnzyoz\ zpzzpzzpzzpzzpzzpzzpzzqzzqzzqzzqzzqzzqzzqzzpzzozzo\ zzzKzzJzzIzzHzzGzzFzzEzzDzzCzzBzzzzzzzzzzzzzzz2zz2\ zz2zz2zz1zz1zz1zz1zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ 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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Techno!
by Roger Alexander 06 May '10

06 May '10

Techno Chunk! With its regimented spacing and perfect right angles this pseudo-blueprint is loudly and proudly a man made artifact. No mimicking the irregularity of the natural world here. To see the prefabricated structure go to http://maxitersfractalfollies.blogspot.com fract163.gif { ; boxes ; blank ; calctime 0:00:47.24 ; created May 06, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_q.frm formulaname=quadros_rjr_a function=round/round passes=t center-mag=3.66702/-8.88178e-016/0.3807356 params=-0.8998382518997772/0.6248664815210425/0.3687551499984741/0.70567\ 94946134831 float=y maxiter=1500 fillcolor=0 inside=0 logmap=6 colors=00zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz } frm:quadros_rjr_a {; bs and rjr y2k03 ; As posted in Fractal-Art, 4/28/97 z=fn1(pixel+abs(p2))/fn2(pixel): z=p1*sin(z) |z| <= 100 ;SOURCE: 97msg.frm } Roger Alexander _________________________________________________________________ Win a $10,000 shopping spree from Hotmail! Enter now. http://go.microsoft.com/?linkid=9729711

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FractalForums.com 2010 Fractal Competition
by Paul.N.Lee＠att.net 06 May '10

06 May '10

Greetings, For those that wish to view some interesting images, the "entry submittal period" for the competition ended at the first of this month. There are now around 130 entries divided unevenly amongst three different categories. And they may be viewed by going to the following location: http://www.fractalforums.com/index.php?action=gallery;cat=36 By the way, one of those categories is called "Fractal Movies", with 19 videos available for watching. These may take a bit longer to view than the typical .JPG and .PNG graphics. For those that are Members, you may also "rate" images for the current voting period, which ends June 1st. Sincerely, P.N.L. -------------------------------------- http://www.Nahee.com/PNL/Fractals.html http://www.Nahee.com/Fractals/

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FOTD 06-05-10 (Minibrot All Aglow [8])
by Jim Muth 05 May '10

05 May '10

FOTD -- May 06, 2010 (Rating 8) Fractal visionaries and enthusiasts: These minibrots keep coming. I wonder how many potential mini- brots might possibly exist in all the fractals that hold mini- brots. Before I begin counting I must admit that today's image, which is all minibrot, is indescribable. I could report that almost all of the image consists of 'inside' stuff made visible by the 'bof61' inside fill, but this gives no idea of the appearance of the image. I could state that the image is almost monochrome, but neither does this give an idea of its appearance. I could say that the parent fractal is also beyond description, but what good does this do? I named the image "Minibrot All Aglow". This might give a vague hint of its appearance. I rated it at an 8, but lots of other FOTD images have had this rating, so this is of no help at all. In the end, the only way to see today's image, one of the more unusual FOTD images, is to run the included lightning-fast para- meter file or go to the FOTD web site at: <http://www.Nahee.com/FOTD/> and view the finished image there. Another absolutely perfect day prevailed here at Fractal Central on Wednesday, this time without the brief but heavy storms. The fractal cats rejoiced when the temperature reached 77F 25C. At least, their antics seemed like rejoicing to me. My day was near average, but FL had a frustrating day when she discovered that the local rabbits have been nibbling at her newly planted flowers. The next glorious FOTD will be posted in 24 hours, and believe it or not, it is likely to be an alternate version of today's image. Until then, take care, and when rich people go bankrupt, why do they still have a lot more wealth than the average person who is in good financial shape? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Minibrot_All_Aglow { ; time=0:00:19.09-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-4.668/0/5.694761 params=-0.0035/-6/\ -0.014/-5/0/0/0/0 float=y maxiter=1125 inside=bof61 logmap=5 symmetry=xaxis periodicity=6 colors=000BD57FA5GF2HK8KMCMPIPSMRVRUYWW`_Xg`Yi_Zf_\ _h``eaagbbicckddmeeoffqhgsjhulivnjwpkxrlytmzvnzyoz\ zpzzpzzpzzpzzpzzpzzpzzqzzqzzqzzqzzqzzqzzqzzpzzozzo\ zzzKzzJzzIzzHzzGzzFzzEzzDzzCzzBzzzzzzzzzzzzzzz2zz2\ zz2zz2zz1zz1zz1zz1zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ 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=========================================

1 0

Organica
by Roger Alexander 04 May '10

04 May '10

This fractal suggests an organic nature,like a clutch of soft skinned eggs of some cold blooded creature or at the microscopic level cells. A Jim Muth formula. For immediate evaluation go to http://maxitersfractalfollies.blogspot.com fract150.gif { ;hemoglobin ; blank ; calctime 0:05:53.99 ; created May 04, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=*.frm formulaname=other_Muth center-mag=+0.24475191062229530/+0.83091743885758440/171.3281/1/-137.499\ 999999999801/-1.7772588956077584e-013 float=y maxiter=1500 inside=0 proximity=2 outside=fmod colors=zNNzNNzNNzNNzNNzMMzMMzMMzMMzMMyLLyLLyLLyLLyKKyKKyKKyKKyKKyJJxJJxJ\ JxJJxJJxIIxIIxIIxIIxHHwHHwHHwHHwHHwGGwGGwGGwGGwFFwFFvFFvFFvFFvEEvEEvEEvE\ EvEEvDDvDDuDDuDDuCCuCCuCCuCCuCCuBBuBBtBBtBBtAAtAAtAAtAAtAAt99t99t99s99s9\ 9s88s88s88s88s77s77s77s77r77r66r66r66r66r55r55r55r55q55q44q44q44q44q44q3\ 3q33q33q33p22p22p22p22p22p11p11p11p11o00o00n00n00n00m00m00m00m00l00l00l0\ 0k00k00k00k00j00j00j00j00i00i00i00h00h00h00h00g00g00g00f00f00f00f00e00e0\ 0e00e00d00d00d00c00c00c00c00b00b00b00a00a00a00a00`00`00`00`00_00_00_00Z0\ 0Z00Z00Z00Y00Y00Y00X00X00X00X00W00W00W00W00V00V00V00U00U00U00U00T00T00T0\ 0T00S00S00S00R00R00R00R00Q00Q00Q00P00P00P00P00O00O00O00O00N00N00N00M00M0\ 0M00M00L00L00L00K00K00K00K00J00J00J00J00I00I00I00H00H00H00H00G00G00G00F0\ 0F00F00F00E00E00E00E00D00D00D00C00C00C00C00B00B00B00A00 } frm:other_Muth {; Jim Muth ; As Posted in Fractal-Art, 4/97 ; Renamed from "other" because of name conflict ; Edited for Fractint v. 20 by George Martin, 10/98 z=c=pixel: z=z+(-4*(z^(-4)))+c^10+c |z| <= 100 ;SOURCE: 97msg.frm } Roger Alexander _________________________________________________________________ 30 days of prizes to be won with Hotmail. Enter Here. http://go.microsoft.com/?linkid=9729709

1 0

FOTD 05-05-10 (Way Out There [7?])
by Jim Muth 04 May '10

04 May '10

FOTD -- May 05, 2010 (Rating 7?) Fractal visionaries and enthusiasts: Today's image rates a qualified 7. IMO, it is actually worth a full unqualified 7, but how many times have we seen similar mini- brots this far out and even farther out on the negative spike of the Mandelbrot set? This is about as far out on the spike as we can go with the SF5 resolution in the search for minibrots before the number of radi- ating rays increases to the point where Moire-pattern distortion spoils the image, as is already happening near the center of today's scene. The magnitude of over 6*(10^59) means that, at the scale of today's image, the entire Mandelbrot set would be many orders of magnitude larger than the size of the entire visible universe. Yet I still wonder whether today's minibrot, which was so easy to find, has ever been pictured on a computer screen before now. At this point of the M-set, changing the bailout radius has a huge effect on the appearance of the image. To see a totally different version of today's scene, increase the bailout to 5. Decreasing the bailout to 3 obliterates the image. The name "Way Out There" refers to the position of the minibrot on the spike of the M-set. The magnitude of the image is well beyond the point where arbi- trary precision math becomes necessary. Luckily, the arbitrary math routine works quite efficiently on the negative spike, which enabled today's image to calculate in only 4-3/4 minutes. The finished image may also be seen on the FOTD web site at: <http://www.Nahee.com/FOTD/> Most of Tuesday was quite pleasant here at Fractal Central, with lots of sun, spectacular billowing clouds and a temperature of 75F 24C. But the pleasant periods came with a price. A heavy thunder-storm with hail passed over at 2pm; another passed over at 3pm, this time without the hail. Fractal cat Cassie took shelter in the closet when things got noisy, but Nicholas, taken suddenly courageous, watched the action from the window shelf. My day was otherwise uneventful. Don't be surprised if the next FOTD appears on schedule in 24 hours. Until then, take care, and let me know when we get men bearing the U.S. flag back on the moon. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Way_Out_There { ; time=0:04:47.80-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.9999999999999\ 99999999999999999270086400435940608127409894684338\ /-3.8516358e-63/6.382394e+059 params=0/0 passes=t bailout=4 maxiter=1500 float=y inside=0 logmap=292 mathtolerance=0.05/0 colors=000000zmNzkKyi0xg0wd0ua2sZ6pX9mVDjTGgQKdONa\ MR`CcWGURKFOJLKKFTQSzzzmmmcccUUUVLKXH2N880EE0EG0EI\ 0EKAEMKEOTEPSIQSLQRPRRSRRVRLM`PUUSaNe6ZaKTYXNrzUhz\ U_wUDmUJcUPUzPEzRMzSU_UaQFEMLPKQ_IV6sVQ_nbGgeH`gHr\ 15VD0VM5VU9VaD_AqYMdWYToAsakCZjEXiGwzV_ssYofWlUFcn\ FTdNaTZjCXiEWiGDyPIuNMqLRmJYffWhUs`OfeKB0EGCFLNGQZ\ HU5gVJZVXQKfCQhFFQgJV`N_URdNUtujfefgZbhTZiNcWPZbLC\ 0aRBVJBaKEVKHOKKHKMBSKE_IHgGKoFNXEEFD6KEJPEWUEhZEu\ _Lf`ST`ZFyVLqv7ImJPkIGhwLihQiVWHIVWHERLfxXn8SdRMwl\ RhjMeDoquOlpNgkMbgLUkMLoMDrMAk_BZz8dm5j`2pO0uCAnDJ\ gDT`Em44mI9mVE`nSejNigJmdFr`AvY6_ybmiKzV2rY6k`AdcD\ meHmhKmkOmr3moFmmRzXJzHBz14q7Ir6Hr6Hs5Gs5Gs5Ft4Ft4\ Et4EmcCmcAmc8mc7mc5mc3mcrmcSmc2ccDccOccZcciccwcctc\ crccocmmZmjbmhfmebmkfmgjmcnm_xuTquWkuYeu__uaUucOue\ IugQzp8zeCziFzlIzpLzsPzrTzrXzr`zrkzyczrWzlOzfGz`Hz\ JCzP8zVIzYRz__zawz0LzLlzR } END PARAMETER FILE=========================================

1 0

Minibrotiness
by Roger Alexander 03 May '10

03 May '10

Some people collect stamps I collect minibrots.Here's a recent addition to the Museum of Quadratic Iteration, on display at http://maxitersfractalfollies.blogspot.com Admission free to the first million visitors. fract141.gif { ; minibrots minibrots minibrots... ; blank ; calctime 0:05:16.33 ; created May 03, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_b.frm formulaname=bail_out05 function=tanh center-mag=-0.10519649561952480/+0.92482217028380650/277.0206/1/5.000000\ 00000009237/-1.14117049143658278e-013 params=1.318430127872555/-0.07275612659077732 float=y maxiter=1500 inside=0 proximity=2 outside=fmod colors=0kz0Qj0Pj0Oi0Oi0Ni0Nh0Mh0Lg0Lg0Kg0Jf0Jf0Ie0Ie0He0Gd0Gd0Fc0Fc0Eb0D\ b0Db0Ca0Ca0B`0A`0A`09_08_08Z07Z07Z06Y05Y05X04X04X03W02W02V01V00U01V03W05\ X07Y09Z0A_0C`0Ea0Gb0Ic0Kd0Le0Nf0Pg0Rh0Ti0Vj0Wk0Yl0_m0an0co0ep0fq0hr0js0l\ t0nu0pv0rw0qw0ov0mu0lt0js0hr0fq0ep0co0an0`m0Zl0Xk0Vj0Ui0Sh0Qh0Pg0Nf0Le0J\ d0Ic0Gb0Ea0D`0B_09Z07Y06X04W02V00U00U00T00S00R00Q00P00O00O00N00M00L00K00\ J00I00H00H00G00F00E00D00C00B00A00A00B00C00D00E00F00F00G00H00I00J00K00K00\ L00M00N00O00P00P00Q00R00S00T00U01V03W05X06Y08Z0A_0B`0Da0Fc0Gd0Ie0Kf0Lg0N\ h0Pi0Qj0Sk0Um0Vm0Xn0Zo0`o0bp0cq0er0gr0is0kt0mt0nu0pv0rw0tw0vx0xy0zz0zz0y\ z0yz0xz0xy0wy0wy0vy0vy0ux0ux0tx0tx0sx0sw0rw0qw0qw0pw0pv0ov0ov0nv0nu0mu0m\ u0lu0lu0kt0kt0jt0it0it0hs0hs0gs0gs0fs0fr0er0er0dr0dq0cq0cq0bq0aq0ap0`p0`\ p0_p0_p0Zo0Zo0Yo0Yo0Xo0Xn0Wn0Wn0Vn0Um0Um0Tm0Tl0Sl0Rk0Rk } frm:bail_out05 { z = c = pixel: z = z^2 + c imag(fn1(z)) <= p1 ;SOURCE: bailout.frm } Roger Alexander _________________________________________________________________ Hotmail & Messenger. Get them on your phone now. http://go.microsoft.com/?linkid=9724463

1 0

FOTD 04-05-10 (Bubbles of Delight [8])
by Jim Muth 03 May '10

03 May '10

FOTD -- May 04, 2010 (Rating 8) Fractal visionaries and enthusiasts: I must be on a roll, or at least on a skip. The well-above- average images seem to be coming without effort. I thought today's image would be a total loss until, out of curiosity, I applied the 'tdis' option to its outside parts and found today's bubbling basin. After a bit of color tweaking, I named it "Bubbles of Delight". The most incredible thing about today's image is that it has no parent fractal. No, the image is not the parent fractal itself; it is merely a tiny section of its invisible parent fractal. When viewed at the default magnitude of 0.67, today's image becomes nothing more than a few circular iteration bands with no open inside parts. It is only at a great magnitude that things of interest appear. The rating of an 8 seems about right. The calculation time of 33 seconds is certainly right. The trip to the FOTD web site at: <http://www.Nahee.com/FOTD/> may not be quite as fast, but it will eliminate the need to set up and run the included parameter file. Monday here at Fractal Central had a split personality. The morning brought heavy clouds and heavy rain showers. But just after noontime the rain suddenly ended, the sky magically cleared and the sun blazed forth, leading to an afternoon of gentle breezes and a temperature of 81F 27C. The fractal cats paid little attention to the outside conditions. In the summer months, they need no sun to keep them comfortable. My day was about average -- dull but average. The next FOTD will be posted in 24 hours. Until then, take care, and don't get stuck with stickers. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Bubbles_of_Delight { ; time=0:00:33.15-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip center-mag=-0.1993777649475212/+0.6939975274725773\ /4e+009/1/132.5/0 params=1/7/-1/-6/0/0/0/0 float=y maxiter=1500 inside=0 outside=tdis periodicity=6 colors=000OjHLcOJXVGP`EIgBBn94tF8mLCfRF_XJTbNMgQFc\ OG_NGWLGTKGPIHLHHHFHEEHzkzzvzzrzznzzjvzdrvZmpUhjKc\ eA`U9O0AA0BA0CAcLJwTQrUZmVfhWzdXze`zeczfgzfjzfmz_n\ zUozco`zpYmpWMmzzmWzmWzmWLmzzcXzcXzcYzcYKUYKUZKUZK\ KZKKZJK_JK_JK_JK`JK`JK`IKaIKaIKaIKbIKbIKbHKcHKcHUc\ HUdHUdHUdHUdGUeGUeGUeGUfGUfGUfFUgFUgFUgFUhFUhFchEc\ iEciEciEcjEcjEcjCclDckDckDckDckDckDckDckDckzmkzmkz\ mkzmkzmkzmkzmkzmkzmkzmkzmkzmkzmkzmkzmkzmkzwkzwjzwj\ zwjzwjzwjzwjzwjzwjzwjzwjzwjzwjzwjzwjzwjzzjzzjzzjzz\ jzzjzzjzzjzzjzzjzzezzfzzfzzfzzfzzfzzfqzfpzfpzfozfn\ zfmzfmzglzgkzgjzgizgizghzggzgfzgfzgezgdzgczhczhbzh\ azh`zh`zh_zhZzhYzhXzhXzhWzhVziUziUziTziSziRziRziQz\ iPziOziNziNziMzjLzjKzjKzjJzjIzjHzjHzjGzjFzjEzjRziQ\ zjQzjQzjPzjPzjPzjOzjOzjOzjNzjNzjNzjMzjozAnzGmzMlzS\ kzYjzcmzgpzkrzouzsxzwzzzuzqpzikzafzTazLYzDazZezs_z\ qUzpPzoJzmEzl8zk3zjAzfGzb } 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

More Imitation Brotness
by Roger Alexander 03 May '10

03 May '10

Look-it's a pseudo-brot,a wannabee brot,an impostor brot, it's the invasion of the broty snatchers! Or maybe a teensy bit of hyperbole-exaggeration for the sake of emphasis. Go to http://maxitersfractalfollies.blogspot.com for immediate delivery fract122.gif { ; close but no cigar ; where did that expression come from anyway? ; calctime 0:07:41.32 ; created Apr 30, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_m.frm formulaname=Mandel3 center-mag=-0.59611777221526870/-0.00000244343712937/19815.13/1/90/3.885\ 78058618804789e-016 float=y maxiter=3600 inside=0 logmap=67 colors=00000000200400600800A00C00E00G00I00K00M00O00Q00S00U00W00Y00_00a00\ c00e00g00i00k00m00o00q00s00u00w00z01z03z05z07z09z0Bz0Dz0Fz0Hz0Jz0Lz0Nz0P\ z0Rz0Tz0Vz0Xz0Zz0`z0bz0dz0fz0hz0jz0lz0nz0pz0rz0tz0vz0xz0zz0zz0yz0xz0wz0v\ z0uz0tz0sz0rz0qz0pz0oz0nz0mz0lz0kz0jz0iz0hz0gz0fz0ez0dz0cz0bz0az0`z0_z0Z\ z0Yz0Xz0Wz0Vz0Uz0Tz0Sz0Rz0Qz0Pz0Oz0Nz0Mz0Lz0Kz0Jz0Iz0Hz0Gz0Fz0Ez0Dz0Cz0B\ z0Az09z08z07z06z05z04z03z02z01z00z00z03z07z0Bz0Fz0Jz0Nz0Rz0Vz0Zz0bz0fz0j\ z0nz0rz0vz0uz1tz1sz2rz3pz3oz4nz5mz5kz6jz7iz7hz8gz9ez9dzAczBbzB`zC_zDZzDY\ zEWzFVzFUzGTzHSzHQzIPzJOzJNzKLzLKzLJzMIzNGzNFzOEzPDzPCzQAzR9zR8zS7zT5zT4\ zU3zV2zW0zW0zV0yV0xU0wU0vT0uT0tS0sS0rR0qR0pQ0oQ0nP0mP0lO0kO0jN0iN0hM0gM0\ fL0eL0dK0cK0bJ0aJ0`I0_I0ZH0YH0XG0WG0VF0UF0TE0SE0RD0QD0PC0OC0NB0MB0LA0KA0\ J90I90H80G80F70E70D60C60B50A509408407306305204203102101 } frm:Mandel3 {; Fractal Creations example z = pixel, c = sin(z): z = (z*z) + c z = z * 1/c |z| <= 4 ;SOURCE: fractint.frm } Roger Alexander _________________________________________________________________ Got a phone? Get Hotmail & Messenger for mobile! http://go.microsoft.com/?linkid=9724464

3 2

Galaxies
by Roger Alexander 02 May '10

02 May '10

Is this a cluster of galaxies rushing to their doom, drawn to a giga black hole with an irresistible gravitational field. Or the optical distortion caused by the temporal field distortion by traveling at warp speed? Or an eye pleasing fractal? Go to http://maxitersfractalfollies.blogspot.com to judge for yourself. fract142.gif { ; blank ; blank ; calctime 0:01:21.23 ; created May 02, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_q.frm formulaname=quadrosinq center-mag=0/0/0.6666667 params=-0.7029557176427503/0.8132145300168886 float=y maxiter=1500 inside=0 colors=00000000100300400600800900B00C00E00G00H00J00K00M00O00P00R00T00U00\ W00X00Z00`00a00c00d00f00h00i00k00m01m03m04n06n07o09o0Ao0Cp0Ep0Fq0Hq0Iq0K\ r0Lr0Ns0Ps0Qs0St0Tt0Vu0Wu0Yu0Zv0`v0bw0cw0ew0fx0hx0iy0ky0mz1mz3mz5nz7nz9o\ zBozDozFpzHpzJqzLqzNqzPrzRrzTszVszXszZtz`tzbuzduzfuzhvzjvzlwznwzpwzrxztx\ zvyzxyzzzzyzzxzzwzzuzztzzszzqzzpzzozzmzzlzzkzzizzhzzgzzezzdzzczzbzz`zz_z\ zZzzXzzWzzVzzTzzSzzRzzPzzOzzNzzLzzKzzJzzIzzGzzFzzEzzCzzBzzAzz8zz7zz6zz4z\ z3zz2zz0zz0yz0xz0wz0uz0tz0sz0qz0pz0oz0mz0lz0kz0iz0hz0gz0ez0dz0cz0bz0`z0_\ z0Zz0Xz0Wz0Vz0Tz0Sz0Rz0Pz0Oz0Nz0Lz0Kz0Jz0Iz0Gz0Fz0Ez0Cz0Bz0Az08z07z06z04\ z03z02z00z00y00x00w00v00u00t00s00r00q00p00o00n00m00l00k00j00i00h00g00f00\ e00d00c00b00a00`00_00Z00Y00X00W00V00U00T00S00R00Q00P00O00N00M00L00K00J00\ I00H00G00F00E00D00C00B00A009008007006005004003002000000 } frm:quadrosinq {; bs and rjr ; As posted in Fractal-Art, 4/28/97 z=sqr(pixel)/cabs(pixel): z=p1*sin(z) |z| <= 100 ;SOURCE: 97msg.frm } Roger Alexander _________________________________________________________________ Live connected. Get Hotmail & Messenger on your phone. http://go.microsoft.com/?linkid=9724462

1 0

FOTD 03-05-10 (Halfway There [8])
by Jim Muth 02 May '10

02 May '10

FOTD -- May 03, 2010 (Rating 8) Fractal visionaries and enthusiasts: Today's steel-blue image is rated at an 8 and named "Halfway There". The name refers to the minibrot at the center, which is of the '3-1/2' variety, and 3-1/2 is halfway between 3 and 4. The parent fractal resembles two Mandelbrot sets partially over- lapping in a north-south direction. Today's image is located just off the positive X-axis in a very tiny valley in a tiny bud at the eastern extremity of the parent fractal. The magnitude of over 8*(10^13) stretches the conventional math routine a bit, but the resolution breakdown is barely noticeable. There is little more to be said about the rather pleasant image except that to see it, run the included parameter file and wait 3 minutes or go to the FOTD web site at: <http://www.Nahee.com/FOTD/> and view it there at once. Sunday here at Fractal Central featured heavy clouds and occa- sional sprinkles of rain. The high humidity and temperature of 82 28C made it feel like midsummer and made the fractal cats feel like stretching out on the living room rug. My day was peaceful enough despite a philosophical discussion with FL in the afternoon about the world's over-population problem. There will be no problem however preparing the FOTD for May 4. It is already in the bag, and will be set free in 24 hours. Until then, take care, and the solution to the over-population problem is to eliminate the excess population now infesting the surface. Do I see anyone volunteering to be eliminated and help save the earth? The first 5-billion will be considered heroes. . . . what? . . . there are no volunteers. (Hey, don't look at me like that!) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Halfway_There { ; time=0:03:02.02-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip logmap=232 center-mag=+0.3398346291335801/+0.0000002536829285\ /8.194032e+013/1/-9.35/0 params=3.5/-4/0/0 float=y maxiter=5000 inside=0 mathtolerance=0.05/1 colors=000APjAQkARlASnAToAUqCVrFWvIXzLYzNZzGSUAMF4\ G0CM9JzIQXRXa_cfgelegrdixc_MUWSRTXOPbLMgJKfMIeOGdQ\ EcSCcUCZXCUZCP`CKbCFeCAgC5iC0kLMPORMRVJU_HWcEZhBal\ 9dq6fu4biEZYOVNXdOcnPjwPqvQcvRRuSEuS1f_QTfmbhekiZj\ vF_sZQqrInqAlpJllSlh`ldil`qlYihWadVV`TNXSGTQ8PP1MO\ 4HV7Da99gC5nE1tIAsLIrOQqRYpUeoXmn_unOTUD19zzzzzzrr\ rmmmcccUUUOOO777NNNS6WJ4LrazjXzaTzVPuNMrJLj7ZW8rU6\ cM4SF2J71ww0nn0ee0YY0PP0HH088LfwI`oFWhDQ`OvF5wI5qH\ 5kH5fG5`G5WGJQCXK9jE6x93uIAsRHq_OohVmp`dqdWrgNrkEs\ n6sqlwOiuQgsReqScoT`mVZkWXiXVhYRbTNXPJSLFMHzmC7B8N\ 3J354fhT`bPWXLQSILMEGGAAB7553z7Ez37zd5zg4zj3zm2zp2\ zs1zv0zxUzzNzzJzzGzzDzz9zz6zz3zz0zz0zz0zz0zz0zzAzz\ KzzUzzczzmzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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FOTD 02-05-10 (Pints and Quartics [8])
by Jim Muth 02 May '10

02 May '10

FOTD -- May 02, 2010 (Rating 8) Fractal visionaries and enthusiasts: Today's FOTD is late. As advised earlier, the reason is an antiquing expedition that arose on Saturday, this time to State College. Things went well enough until we were halfway back and passed a string of horse-drawn Amish buggies. When FL saw the buggies, she casually asked me what I feel is wrong with the modern world. Luckily, I said I don't know and remained quiet. If I had started to answer, I would still be talking, 15 hours later. It's a good thing fractals don't ask such tempting questions. (Or do they?) The parent fractal of today's image is a combination of quadra- tic and quartic features. It resembles a Mandelbrot set with a few extra bays. Today's image, which lies in the north branch of the valley separating the two largest bays, has lost all its quadratic features. The name "Pints and Quartics" is totally whimsical. The rating of an 8 is good enough to make the image worth the effort of the 2-minute calculation time. The already-calculated image is or soon will be posted for effortless viewing on the FOTD web site at: <http://www.Nahee.com/FOTD/> Summer arrived over a month early here at Fractal Central in Central PA on Saturday. Not only was the sun hot, but the temperature reached 88F 31C and the humidity made its first appearance of the year. The fractal cats slept through most of the early summer conditions. When we returned from the antiquing expedition, the rest of the evening was uneventful. The next FOTD will be posted in 12 hours, more or less. Until then, take care and good answers are sometimes quite elusive. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Pints_and_Quartics { ; time=0:01:53.74-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-0.1115441591768284/+0.2746767395419655\ /1.766665e+012/1/135.75/0 params=4/3/0/0 float=y maxiter=1800 inside=0 logmap=164 periodicity=6 mathtolerance=0.05/1 colors=000qhkASzA9r98gCAaEC`GEXIGHKI9MJ2V_5bp7anHa\ mQakZajgahpagy`bp`Yg`TZ_OQ_JH_E8_A0YH2XN4zc6zZ7qWS\ hXV_YYSY`JXcBVfATd9Pb8L`7EZ6XX5WV4VUDWZLWcTfg`glhh\ ppiuxjyfRpQ7gUBcYE_`IWdLShOOzkKvcGnTDeKHZGLV7HOFHe\ f9vv1zz5mz9iuDetHatLYtP6mbHm`SmZbmYmmWwmVlCVlCVlCW\ kBWkBWkBWgCXdCY`DZYD_VD`REaOEaKFbHFcEFdzzzpqzccz`a\ wYZsWXjUVdRTZPQSNOMKMGIKAGI4KN6NR8QVAUZCXbD_fFcjHf\ nJirLlvMilQgcUdVYbLa_CeY3hZ6eZ9c_Ca_F__IY`LW`OU`QS\ aTQaWObZMbaKbdIcgGcjEclCieCo_CuUCqXEn_GkaHgdJdfKai\ MYlOVnPSqROsSLvUIxVMvWQuWUsWYrW`pWdoWhmWllWokW`YcM\ Kk77s99qAApBCnDDmEFkFGjHIhIJgJLeLMdMObNPaPR_QSZRTY\ USZXSZ_SZaSZdSZgR_jR_lR_oR_rR_tR_pWVz`RidNziJbnFzr\ BYsHztMWuRzvWTw`zxeOyWzzNGzDzz4zz7azAzzDzzFzzJEzMt\ zDzzEfzBzzDcz_zzTIzMzzr9zUzz_JzUFzPBzKUzYMzRFzLUzp\ OzfJzYDzOgz7WzAKzDlzNgz0Wz5KzANzjIz_DzP1z3zzzXzmSz\ lXzq`zv3zgEzdPzbZz`qzYqzd } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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The Reliable Mandelbrot
by Roger Alexander 01 May '10

01 May '10

A busy day but even on the busiest days an exploration of the good ole mandelbrot will show something worth posting. For instant teleportation of the finished calculation go to http://maxitersfractalfollies.blogspot.com fract128.gif { ; a good ole mandel zoom ; blank ; calctime 0:02:06.94 ; created May 01, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=mandel center-mag=-0.79847407399804530/+0.16680842943050880/1168873 params=0/0 float=y maxiter=3200 logmap=195 cyclerange=0/255 colors=00100100100100100100100200200200200200200300300300300300300400400\ 400400400400500500500500500500600600600600600600700700700700700700800800\ 800800800800900900900900900900A00A00A00A00A00A00B00B00B00B00B00B00C00C00\ C00C00C00C00D00E00F00G00I00J00K00L00M00N00P00Q00R00S00T00U00W00X00Y00Z00\ _00a00b00c00d00e00f00h00i00j00k00l00m00o00p00q00r00s00t00v00w00x00z01z02\ z03z04z06z07z08z09z0Az0Bz0Dz0Ez0Fz0Gz0Hz0Iz0Jz0Lz0Mz0Nz0Oz0Pz0Qz0Sz0Tz0U\ z0Vz1Wz1Xz1Xz1Yz1Zz1_z1_z1`z1az1bz1bz1cz1dz1ez1ez1fz1gz1hz1hz1iz1jz1kz1k\ z1lz1mz1nz1nz1oz1pz1qz1qz1rz1sz1tz1tz1uz1vz1wz1wz1xz1yz0zz3zz7zzBzzEzzIz\ zMzzPzzTzzXzz_zzczzgzzjzznzzrzzvzzszzozzkzzhzzdzz`zzYzzUzzQzzNzzJzzFzzCz\ z8zz4zz0zz0zz0yz0yz0xz0xz0wz0wz0vz0vz0uz0uz0tz0tz0sz0sz0rz0rz0qz0qz0pz0p\ z0oz0oz0nz0nz0mz0mz0lz0lz0kz0kz0jz0jz0iz0iz0hz0hz0gz0fz } Roger Alexander _________________________________________________________________ Videos that have everyone talking! Now also in HD! http://go.microsoft.com/?linkid=9724465

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My Pretty, My Precious
by Roger Alexander 30 Apr '10

30 Apr '10

I choose today's fractal for it's bright colors. It is almost but not quite a mandlebrot-a pseudobrot. Immediate viewing at http://maxitersfractalfollies.blogspot.com fract112.gif { ; pseudo-brot ; blank ; calctime 0:01:33.82 ; created Apr 29, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_m.frm formulaname=mand2_step center-mag=-0.520651/2.22045e-016/0.8130081 params=0/0/0/0 float=y maxiter=1500 inside=0 periodicity=0 colors=w0dv0bt0ar0_q0Zo0Xm0Wl0Uj0Ti0Rg0Qe0Pd0Nb0M`0K_0JY0HX0GV0ET0DS0BQ0\ AO08P08Q08R08S18U18V18W18X28Y28_28`28a38b38d38e38f48g48h48j48k58l58m58o5\ 8p68q68r68s68u78v78w78x78z88z98zA8zB8zC8zD8zE8yF8yG7yH7yI7yJ7yK7xL7xM7xN\ 7xO6xP6xQ6wR6wS6wT6wU6wV6wW5vX5vY5vZ5v_5v`5va5ub5uc4ud4ue4uf4ug4th4ti4tj\ 4tk3tl3tm3sn3so3sp3sq3sr3rs2qs2os3ns3mr4lr4kr5jr5hr6gr6fr6er7dr7cq8aq8`q\ 9_q9ZqAYqAXqBVqBUpCTpCSpDRpDQpDOpENpEMpFLpFKoGJoGHoHGoHFoIEoIDoJCoJAnK8q\ L5tN3wP0zR0wQ0sO0pN0lL0hJ0eI0aG0YE0VD0RB0N90K80G60C40H90MF0RL0WR0`X0eb0j\ h0on0tt0zz0xx0vv0st0qr0no0lm0jk0gi0ef0bd0`b0Y`0WY0UW0RU0PS0MP0KN0HL0FJ1C\ G2CL4DP5DU7DZ8EbAEgBElDFpEFuGGzGGxFFvEEtDDrCCpBBnBBlAAj99h88f77d66b66`55\ Z44X33V22T11R00O53SA6XG9aLCfQFkWIp`LufOzfNyfMweLveKtdJsdIqdHpcGncFmbEkbD\ jaChaBgaAe`9d`8b_7a_6__5ZZ4XZ3WY2UY1TX0Rc0Vk0Zr0bz0fy0e } frm:mand2_step { ;warps the Mandelbrot-set from p1 to a value increasing ;each time with p2 ;it's like the stuff in EXPLOD.FRM ;default for p1: 0.01 s=p2,s=s+(s==0)*0.01 p=p1 z=c=pixel: z=z*z+c-p p=p+s |z|<4 ;SOURCE: specials.frm } Roger Alexander _________________________________________________________________ Got a phone? Get Hotmail & Messenger for mobile! http://go.microsoft.com/?linkid=9724464

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FOTD 01-05-10 (Lilacs in Bloom [9.25])
by Jim Muth 30 Apr '10

30 Apr '10

FOTD -- May 01, 2010 (Rating 9.25) Fractal visionaries and enthusiasts: NEW FORMULA ALERT! Today's formula, FinDivBrot-2, is a new one. Actually, it's nothing more than a slight simplification of the FinalDivideBrot formula that eliminates some redundant minus signs and the awkward 0.00000...1 that was added to the imag(p1) parameter in the FinalDivideBrot, but had become extra baggage carried over from even earlier versions. The speed increase is insignificant if it exists at all, but the new formula certainly does look more compact and pleasing on the screen. The FinalDivideBrot formula is compatible with the new FinDivBrot-2 formula if the sign of the imag(p1) parameter is changed. There is no error in the rating of a 9.25 that I gave today's image. If I had actually created the colors from scratch, I might have rated it a 9.75 or even an exalted 10. As it is, with the program-created colors, the image is still, IMO, one of the best in FOTD history, and well worth its rating. The name "Lilacs in Bloom" refers to the colors of the lilacs blooming beside the front door of FC at this time of year. The parent fractal is strange indeed. It is little more than a circle with only hints of a fractal nature on its west side. In fact, if imag(p1) is reduced any significant amount at all, the entire parent disappears, leaving only a blank screen consisting of inside stuff. The ghost of the parent does still exist in this blank screen however, and can be made visible by rendering the scene with the inside set to an active inside fill, as I do with the 'evaporated' images, but in this case, the ghost image holds nothing worthwhile. The calculation time of 1-1/2 minutes is just about the FOTD normal. The finished image is available on the FOTD web site at: <http://www.Nahee.com/FOTD/> The high temperature of 82F 28C and the hot sun here at Fractal Central on Friday got no response at all from the fractal cats. As long the inside conditions are within their comfort range, they couldn't care less about the outside conditions. But except for those doing heavy work in the sun, Friday was near perfect. My day was within reason, which is reasonable enough. The next FOTD is due in 24 hours. As experience shows however, the Sat- urday images are frequently delayed by an unexpected antiquing trip. Until whenever, take care, and enjoy all FOTD fractals, even the handicapped ones. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Lilacs_in_Bloom { ; time=0:01:33.79-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip float=y center-mag=-0.108015555288/+0.541125139154/2916769\ /1/15/0 params=1/0.97/1500/0 maxiter=1500 inside=0 outside=tdis periodicity=6 colors=000HHyDMyARy7WyIRfSMPRSVRY`RbfQhlQnrQswWtha\ uUfvGbnE_fCXZAUS8YcK`nWfqMlsCqu2pqApnHokOohVoeanbh\ n_onXvo_ppbjqddrgZsjTtlNuoHuqCnoIhnObmUXl_RkeLjjNg\ iOdhQagRZfWV`_SVcPPhMJz00pG8_QpcVigZbkbWngQrkJvoCy\ s6rS7l08RNF6hMEiIMiFUiC`j9hj6pj3wj0k8FfBAaE5aNWaWv\ VPhOIVHCHGHVFLhCSaAZV7eP5lI2sB0k57cAEUFGCFRLIXRHbY\ FhcEnjCtpBncGhUKcLP000YMYgQbnVlsZtybzzhzgHWeHYdHYc\ HZbH_`Ha_HbZHd_HfYKTXNLWQDVSAVXEV`IUdLUiPcmSmqWzsZ\ zvUzzQzzRV2YR3XO3XL3WI4WF4VC4VABP8IJ7PEbnJRj_GgpRb\ aaYOkUAXNUJGmIUfIf`LdXObTR`PU_LXYH_WDbU9eT60cm2eo3\ gq4is5ku6mw7nyIkqShibealbUecWZcXXOZ_TYaYXcdTdjQeqM\ fwJimOkdSnVXpM`rDdpC_oCVmBQlBMjBHiACgA7fA3XDFNGRDI\ aELXENTEPOFRKFTFFVBFX7DTECPLALS9cz8Ez6cz56z4cz99zD\ czIJzMczRUzVcz_chchf`eaZcYXaUV_QSXMQVIOTEMRALOCLLE\ LIGKFIKCKK9MR7GY5Bd36j11fRv_YqUcmOjiIpeCvaAbQ8KEAI\ KCGQEFWGDaIBgKAmM8sO7yKCy } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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FOTD 30-04-10 (On the Eastern Front [6])
by Jim Muth 29 Apr '10

29 Apr '10

FOTD -- April 30, 2010 (Rating 6) Fractal visionaries and enthusiasts: Today's image is another scene on the southeast shore line of the main bay of the Mandelbrot set, near East Valley. To view it, either run the included parameter file and see the image in an astonishing 14 seconds, or switch to arbitrary precision math and wait about two hours. The difference in the final image is barely noticeable. There is not much to be said about the image, which lies in a second-order spiral in the chaos on the side of a period-10 bud. This bud lies at the point where the associated radicals just begin to take on an elephant-like appearance. I rendered the image with an artificially large negative logmap to create the flat solid black outer parts. The solid black inner area was created by the coloring. I named the image "On the Eastern Front" because the scene lies in one of the easternmost parts of the M-set. I rated it at a 6 because the M-set is such an overworked fractal. Those without 14 seconds to spare may see the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> A near ideal spring day prevailed here at Fractal Central on Thursday, with cloudless skies, and a temperature of 70F 21C. Only a rather strong wind kept it from being absolutely ideal. The fractal cats enjoyed the outdoor conditions from indoors, where they got into a heated tussle behind the books on the hall shelves and knocked several books onto the floor. Like the weather, my day was fair enough. The next FOTD will be posted in 24 hours. It will be the first FOTD of a new month, so maybe I'll decide on a single theme for the entire month. I have not yet decided. Until next time, take care, and would those disappointed with world events please line up on the right. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= OnTheEasternFront { ; time=0:00:14.05-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=+0.3317\ 756417482987/-0.05802874132832721/7.106239e+013/1/\ 34/0 params=0/0 float=y maxiter=4000 inside=0 logmap=-1686 sound=off mathtolerance=0.05/1 colors=000000FdzDfzBiz9kz7mzGezOZzXRzdKzq7zlDzhJzd\ Pz_VzW_zSezNkzJqzFvzIrzKozNkzPhzSdzUazWZzZVz`SzcOz\ eLzgIzbGzZFzUEzQDzMCzHBzDAz89z48z07z49z8BzCCzGEzKG\ zOHzSJzWLz_MzcOzzQTzRUzTVzVWzVUzWXzWZzWazWczWfzXhh\ XkfXmdXpcTwbXrbzmbzibzdbz_zzbzzWzzPzzIzz6zzBXzF_Nz\ aNzdMzzLzzKzzKzzJzzIzrHzkHzcHz00000000000L00000000\ 00000000000000000000000000000000000000000000000000\ 00000zmzzmizmzzm_zmzzmRzmzzzGzzzzzKzzzzzzzzzzzzzzz\ zzzzzzemzimzmmzqmzxmzumzsmzpmznmzkmzimzfmUdmTamS_m\ QXmPVmOTmNTmNTmNTmNQmJOmELmAMm6Jm6Hm6Fc6CZ6AV68R6P\ SEeTMtgwu`hvUUDI0`L8JqncaXwNFpPGiRHbSIWUJPWKEU1FV6\ GWBHWGIXKJXPKYU8iTEcWKYY7lvGnKK8QNIVQS_Q4bRDcSLcT`\ cUhcXLJV`UzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzBzzEzzHz\ zTzzPzzMzzJzzGzzDzz0zz5zzAzzFzzJzzOzzTzzXzzWzzWzzV\ zzVzzUzzUzzhzzczzZzzUzz_zzXczVezSgzQizNkzLmzIozEnz\ GmzIlzKTzaRzaOz`Mz_Kz_IzZ } END PARAMETER FILE=========================================

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Green Tendrils?
by Roger Alexander 28 Apr '10

28 Apr '10

Lotsa arms for everybody... For express delivery go to http://maxitersfractalfollies.blogspot.com fract110.gif { ; Like arms-or tentacles-or tendrils ; blank ; calctime 0:06:08.67 ; created Apr 28, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=*.frm formulaname=quadrosinq passes=1 center-mag=0/0/0.6666667 params=-0.7349162266914884/0.7073885311441389 float=y maxiter=1500 inside=0 colors=0Uz0200300400500700800900A00B00D00E00F00G00H00J00K00L00M00N00P00Q\ 00R00S00T00V00W00X00Y00Z00`00a00b00c00d00f00g00h00i00k00k01k02k03l04l05l\ 05m06m07m08n09n0An0Bo0Bo0Co0Dp0Ep0Fp0Gp0Hq0Hq0Iq0Jr0Kr0Lr0Ms0Ns0Ns0Ot0Pt\ 0Qt0Ru0Su0Tu0Tu0Uv0Vv0Wv0Xw0Yw0Zw0Zx0_x0`x0ay0by0cy0dz1dz1ez1ez1fz2fz2gz\ 2gz2hz3hz3iz3iz3jz4jz4kz4kz4lz5mz5mz5nz5nz6oz6oz6pz6pz7qz7qz7rz7rz8sz8sz\ 8tz8uz9uz9uz9tz9tz9tz9sz9sz8sz8rz8rz8rz8qz8qz7qz7pz7pz7oz7oz7oz6nz6nz6nz\ 6mz6mz6mz5lz5lz5lz5kz5kz5kz4jz4jz4iz4iz4iz4hz3hz3hz3gz3gz3gz3fz2fz2fz2ez\ 2ez2dz1dz1cz1bz1ay1`y1_y1_x1Zx1Yx1Xw1Ww1Vw1Uv1Uv1Tv1Su1Ru1Qu1Pt1Ot1Ot1Nt\ 1Ms1Ls1Ks1Jr1Ir1Ir1Hq1Gq1Fq1Ep1Dp1Cp1Co1Bo1Ao19n18n17n16m06l06k06j06i06h\ 06g06f05e05d05c05b05a05`05_05Z04Y04X04W04V04U04T04S04R03P03O03N03M03L03K\ 03J03I02H02G02F02E02D02C02B02A0190180170160150140130010 } frm:quadrosinq {; bs and rjr ; As posted in Fractal-Art, 4/28/97 z=sqr(pixel)/cabs(pixel): z=p1*sin(z) |z| <= 100 ;SOURCE: 97msg.frm } Roger Alexander _________________________________________________________________ Videos that have everyone talking! Now also in HD! http://go.microsoft.com/?linkid=9724465

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FOTD 29-04-10 (East-Valley Study [8])
by Jim Muth 28 Apr '10

28 Apr '10

FOTD -- April 29, 2010 (Rating 8) Fractal visionaries and enthusiasts: With nothing better at hand on Wednesday, I returned to the warhorse (but not stale) Mandelbrot set and checked the south- east shore of the main bay, where I found today's scene in an infinitesimal spiral in a tiny spiral in a small spiral. I named the image "East-Valley Study" even though its location is not quite far enough around to actually lie in East Valley. As expressed in the name, today's image is basically a study in getting smooth coloring with only a measly 256 colors to work with. I think I did rather well, and gave myself a whole point bonus, which adds up to a rating of an 8. The magnitude of the image is well into the range of arbitrary precision math. This makes the image a rather slow one, taking a little over 11 minutes to calculate. As always however, the already-calculated image is posted on the FOTD web site at: <http://www.Nahee.com/FOTD/> where it may be seen instantly and enjoyed at leisure. Conditions remained rather brisk for the season here at Fractal Central on Wednesday, but the sun was strong and the temperature reached a rather pleasant 59F 15C. It was not quite good enough for the fractal cats, who gathered on their window shelf and wondered why the sun, which was so strong outside, was not reach- ing the shelf. When I explained that the angle of the sun was too high, they gave me a puzzled look and went to sleep. My day was satisfactory if not over-productive. The next FOTD will be posted in 24 hours. Until then, take care, and dream onward. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= East-Valley_Study { ; time=0:11:09.54-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=0.36215\ 085944136195661173707/-0.0769690896257914660701519\ 7/3.231519e+021/1/37.5/0 params=0/0 float=y maxiter=3200 inside=0 logmap=565 periodicity=6 colors=000OKzPKzQKzRKySKxTKwUKvVKuWLtXMsXNrXOqWPpX\ PoVRkVShTTgSUfRUeRUdQUcQUaQTdPTfPSgPShPRiORjOQlOQn\ OQpTPqTPmUPiUOeVNaVMYWLWXKU_JUcHUfEUiCUm4UoAUpGUrL\ UsRRtXOv_LwbIxeFzhCzk9zm7zoAzqCzsEzuHzwJzzLzz_zzzz\ zz3Cj2Uo1ct0my3zz3zz3fv3`r3WmRQhPRcNSZMTUKUPJVK`RS\ UKRNERG8R23UA2RI2OQ1LX1Id0Fl0Cs09l6BeCCeF8_HDUIHOJ\ LJLPDMT7NX2O`9PXGPUNPQUQN`QJgQGsN4nQDiSLdVUZTb`Xab\ _`cc_efZfjYhmXipWegQa_LYSGUJBQB6N31Q85TD9WIDZMHaRL\ dWPg`TidWfeSdfPbgL`jIZmEXpBVs5Vr8VoBVmDVjGXgHZdI`a\ JbZKdWKfTKfQIbMG_IGXEHUBHQ8HN4IK1IH0IKGRNFPQEOTDDV\ D0YC2`C3cB5mF6rK8vP9zUAc8Ff7Jd6Ob5Sh1``4WU7SNANFDJ\ 8Gc3HC1IAefMbgT_h_XifUjmSktRnhQpXPsLOuAPsFPqKPoPPn\ UQjYQg`RcdR`gRXkSUnSQrSNuUStWXtXatZet`jtaotcttdxt`\ ynXzhTzbPzXLzRFzLKzDPzFUzHZzJczEhzKmzNrzPvzRzzTzzZ\ zzVzzRzzNzz5zz1zz7zzDzzJzzOzzNzzNzzFzzNzzVzzazzZzz\ WzzUzzRzzOzzMzzRzzWzz`zze } END PARAMETER FILE=========================================

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Metallics
by Roger Alexander 28 Apr '10

28 Apr '10

Today's fractal combines the characteristics of the man made mechanical -rigid simplicity- and the complexity of life. The basic design is simple enough a spiral but iteration has produced detail upon detail. Like a convenient minimart the fractal is ready made at http://maxitersfractalfollies.blogspot.com fract089.gif { ; more metallics ; blank ; calctime 0:01:18.92 ; created Apr 26, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_l.frm formulaname=La03-03 center-mag=0.488153/0.905017/27.8856 params=1.093234046449171/-0.5292519913327434/-1.250099185155797/-0.77816\ 09546189764 float=y maxiter=1500 inside=0 outside=atan colors=zzzzzzzzzzzzzzzyyyyyyyyyyyyxxxxxxxxxxxxwwwwwwwwwwwwvvvvvvvvvvvvuu\ uuuuuuuuuuttttttttttttssssssssssssrrrrrrrrrrrrqqqqqqqqqqqqppppppppppppoo\ oooooooooonnnnnnnnnnnnmmmmmmmmmmmmllllllllllllkkkkkkkkkkkkjjjjjjjjjjjjii\ iiiiiiiiiihhhhhhhhhhhhggggggggggggffffffffffffeeeeeeeeeeeeeeeddddddddddd\ dccccccccccccbbbbbbbbbbbbaaaaaaaaaaaa````````````____________ZZZZZZZZZZZ\ ZYYYYYYYYYYYYXXXXXXXXXXXXWWWWWWWWWWWWVVVVVVVVVVVVUUUUUUUUUUUUTTTTTTTTTTT\ TSSSSSSSSSSSSRRRRRRRRRRRRQQQQQQQQQQQQPPPPPPPPPPPPOOOOOOOOOOOONNNNNNNNNNN\ NMMMMMMMMMMMMLLLLLLLLLLLLLLLKKKKKKKKKKKKJJJJJJJJJJJJIIIIIIIIIIIIHHHHHHHH\ HHHHGGGGGGGGGGGGFFFFFFFFFFFFEEEEEEEEEEEEDDDDDDDDDDDDCCCCCCCCCCCCBBBBBBBB\ BBBBAAAAAAAAAAAA99999999999988888888888877777777777766666666666655555555\ 5555444444444444333333333333222222222222111111111111000 } frm:La03-03 {; V.1.1 - earlier versions may be discarded ; Copyright (c)1998,1999 Morgan L. Owens ; = ((a+5-z)La(2)-(a+2)La(1))/3 a=p2, d=(a+3)/2, c=d*(a+2), b=c*(a+1)/3 const=p1, z=pixel: z=z*(z*(d-z/6)-c)+b+const |z|<100 ;SOURCE: chby3.frm } Roger Alexander _________________________________________________________________ Hotmail & Messenger are available on your phone. Try now. http://go.microsoft.com/?linkid=9724461

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FOTD 28-04-10 (Cubic Anticipation [6])
by Jim Muth 27 Apr '10

27 Apr '10

FOTD -- April 28, 2010 (Rating 6) Fractal visionaries and enthusiasts: Today's image, which shows a cubic minibrot, is interesting, which means I see nothing unusually good in it, yet I want to say something. I could rate it no higher than a 6 because all day Tuesday I had a case of 'fractalist's block'. This strange ailment is much the same as writer's block, where no matter how hard the writer tries, the inspired words simply will not come. With a fractal artist, the inspired images will not come. I worked on the coloring for a full 20 minutes, which is a long time by FOTD standards, and ended up with a color palette no better than the one I started with. In the end, I returned to the original colors and did a bit of tweaking. The parent fractal is a standard Mandelbrot set caught in the act of morphing into a cubic Mandeloid, and doing it without the discontinuities that usually plague the fractals with in-between exponents. Today's image is located on the negative X-axis deep in a valley that splits the cubic bud at that location into two halves The name "Cubic Anticipation" implies great things to come. Un- fortunately, the result falls short of the anticipation. The calculation time of 3-1/4 minutes is a little more than the image is worth, but the result, if not awe-inspiring, will at least be 'interesting'. The interesting image may be found in finished form on the FOTD web site at: <http://www.Nahee.com/FOTD/> The sky was partly cloudy here at Fractal Central on Tuesday, but the brisk north wind and temperature of 50F 10C made it feel like anything but the end of April. The fractal cats must have agreed. They spent a good part of the day climbing all over the book shelves in the hallway. Nicholas was a little too athletic when he squeezed behind a row of books and knocked them onto the floor, sending me running to see what had happened. For FL and me the day was averagely normal. The next FOTD, maybe average, maybe not, will be posted in 24 hours. Until then, take care, and I have no qualms about admitting when the Fractal of the Day falls short, as it does today. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Cubic_Anticipation { ; time=0:03:13.73-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinalDivideBrot function=recip passes=1 center-mag=-1.7542946013084/+0.0002529651317445\ /6.3388e+009/1/20/0 params=3/1/0/0 float=y inside=0 maxiter=2400 logmap=338 symmetry=none periodicity=6 colors=000ME1LF2LF3KF4KF5JF6JG7IG8IG9HGAHGBGHCGHDG\ HEFHFFHHEIJEILDINDIPCIRCJTBJVBJXAJZAJZAJZBLZCMZDNZ\ STIRQGQNDOKBNH8zeczdczbczacz_czZczXczWczUczTczRczQ\ czOUzNUzMUzPUzRUzUUzWUzYUz`UubUseUpdWpaYp__pYapWcq\ ocqobroaro`so_soZtoYtoXtrWuuVuwUvzTwzSxzRyzQzzPzzQ\ zzRzzSzzTzzUzzVzzWvzXrv_mrbhmehhhickj_nkWqlStmQwjO\ shMoeKkcNgaQcZT_XWWVZSSaOQdKOgGMdHKaIIZIGWJESJCOKB\ KJ9GJ7CD58830210000040670EA4KE3NH3QK2TO2WR1ZU1aT7e\ SDkRIpTKvVLzXMzZOw`PwbQxdRxfTxhUyjVykWyLmvQkwUjwYi\ wagwefwjexncxrbxvaxz`xuZvqYumWtiVreUqaSpYRoUQmQOlM\ NkIMjPJgVGdaDagAZn7Wt4Tz1Qw8NuELsKJqQHoWFmbCkhAin8\ gt6zzmcv8zsCapG`mKZiNYfRXcVW`ZVYaXZZYZW_ZUzzzbZPcZ\ MeZJfZHhZziZzdUz`PzXzzTWzQZzTXzWVzZTzaRzdPzgNziLzj\ OzjRzjz8jzAjzBjzCjzDjzFjzGjzHjzzjzzjzzjzzhzzfzzdzz\ PzzRzzSzzUzzVzzUzzUzzUzzTzzTzzTzzTzzWzzYzz`zzbzzez\ zgzzjzzlzzlzzlzzlzzlzzlzz } frm:FinalDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1)+0.00000000000000000001: z=(-b)*(z*z*fn1(z^(a)+b))-c |z| < esc } END PARAMETER FILE=========================================

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Minibrots everywhere-green ones this time
by Roger Alexander 26 Apr '10

26 Apr '10

The minibrot- not merely iconic but iconically iconic. They're everywhere like hidden taxes in a modern economy. Instead of cheerful coloring scheme I aimed for something rather dark and murky. Think of a poster for a low budget horror flick. Go to http://maxitersfractalfollies.blogspot.com for the finished product. fract095.gif { ; minibrots minibrots ; blank ; calctime 0:05:34.56 ; created Apr 26, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=fractint.frm formulaname=Cubic corners=0.10027279866/0.10039868877/0.666547846179/0.666642263759 params=0/0 float=y maxiter=1200 bailout=1023 inside=0 logmap=51 colors=0_F0200300400500700800900A00B00D00E00F00G00H00J00K00L00M00N00P00Q\ 00R00S00T00V00W00X00Y00Z00`00a00b00c00d00f00g00h00i00k00k01k02k03l04l05l\ 05m06m07m08n09n0An0Bo0Bo0Co0Dp0Ep0Fp0Gp0Hq0Hq0Iq0Jr0Kr0Lr0Ms0Ns0Ns0Ot0Pt\ 0Qt0Ru0Su0Tu0Tu0Uv0Vv0Wv0Xw0Yw0Zw0Zx0_x0`x0ay0by0cy0dz1dz1ez1ez1fz2fz2gz\ 2gz2hz3hz3iz3iz3jz4jz4kz4kz4lz5mz5mz5nz5nz6oz6oz6pz6pz7qz7qz7rz7rz8sz8sz\ 8tz8uz9uz9uz9tz9tz9tz9sz9sz8sz8rz8rz8rz8qz8qz7qz7pz7pz7oz7oz7oz6nz6nz6nz\ 6mz6mz6mz5lz5lz5lz5kz5kz5kz4jz4jz4iz4iz4iz4hz3hz3hz3gz3gz3gz3fz2fz2fz2ez\ 2ez2dz1dz1cz1bz1ay1`y1_y1_x1Zx1Yx1Xw1Ww1Vw1Uv1Uv1Tv1Su1Ru1Qu1Pt1Ot1Ot1Nt\ 1Ms1Ls1Ks1Jr1Ir1Ir1Hq1Gq1Fq1Ep1Dp1Cp1Co1Bo1Ao19n18n17n16m06l06k06j06i06h\ 06g06f05e05d05c05b05a05`05_05Z04Y04X04W04V04U04T04S04R03P03O03N03M03L03K\ 03J03I02H02G02F02E02D02C02B02A0190180170160150140130010 } frm:Cubic (XYAXIS) {; Lee Skinner p = pixel, test = p1 + 3 t3 = 3*p, t2 = p*p a = (t2 + 1)/t3, b = 2*a*a*a + (t2 - 2)/t3 aa3 = a*a*3, z = 0 - a : z = z*z*z - aa3*z + b |z| < test } Roger Alexander _________________________________________________________________ Reinvent how you stay in touch with the new Windows Live Messenger. http://go.microsoft.com/?linkid=9706116

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FOTD 27-04-10 (A Hazy Serenity [7.5])
by Jim Muth 26 Apr '10

26 Apr '10

FOTD -- April 27, 2010 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image is one of the bluest of all time. Since blue is a serene color and I seem to see a bit of haziness surrounding the brilliant center of the image, I named it "A Hazy Serenity". The parent fractal was created when I subtracted Z^(1.7) from Z^(0.3) and added straight C. This parent appears as a distorted Mandelbrot set rotated 180 degrees. It has no main spike pointing east but this lack is made up for by an unexpected area of chaos where its East Valley should be, which is on the west side of its main bay. Today's scene is located in a patch of this chaos on the southwest shore line of the main bay. The minibrot at the center is not rotated to the 'normal' orientation, with East Valley on the right side, as are most of the minibrots in the FOTD's. I got lazy. But the minibrot is so tiny that its wrong orientation is hardly noticeable. In addition, the minibrot is somewhat beyond full resolution. The rating of a 7-1/2 includes a 1/2 point bonus for the coloring, which I worked on for almost 30 minutes. The calculation time of just under 3 minutes is a cheap price to pay for the image. The trip to the FOTD web site at: <http://www.Nahee.com/FOTD/> to see the image already completed, costs even less, Heavy clouds, occasional rain and a temperature of only 54F 12C made Monday an unpleasant day here at Fractal Central. The fractal cats were too busy getting into indside trouble to notice the outside conditions. Cassie somehow wrapped herself in a blanket and was unable to get the blanket untangled when she wanted to get out. If we had not heard her calling for help, she might have been stuck there for hours. For me the day was average, and what could make a duller story than that. For FL the day was busy, but I gave moral support. The next FOTD will appear in 24 hours, almost by magic. Until then, take care, and look onward toward the vastnesses of the world of fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Hazy_Serenity { ; time=0:02:56.79-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.5865278768076774/-0.4425192247142974\ /3e+012/1/-152.5/0 params=1/0.3/-1/1.7/0/0/0/0 float=y maxiter=1000 inside=0 logmap=226 periodicity=6 mathtolerance=0.05/1 colors=000I4MI5PJ6SJ7VJ8YJ8`J9cJAgJBjJBmJCqJDtJDwD\ 1xH7yKHzNMzQQzTVzW_zZezajzdpzguzKblLZmMWnNTnOQoPNo\ QKpRHpSEqSBqPGlMKgJObGSYKWTU_OccJmgEzn9zzzzzzzzzzz\ zXmUVzUUkVTzVRjVQzWPiWNzXMgXLzXPhUSzRVjOYzM`kJczGf\ mDimBj`LzOVzHOzAHz4Bz7CzACzCCzFCzHDzKDzMDzPDvREsUE\ sWEsZEs`EocFkeFggFdiG`kGXnGUpHQrHMtHJvHKuzLtzzsKMr\ zNqzzpMzzzzzzzzzzzPzzQzzzzzzzzzzzzzzzzzzzzzWuGVtLU\ sQTrUSqZRpcQohPnmOmrOlvRjlThbVgUYeK_cAab1Za4W`6T`9\ Q_BN_EKZGHZJEYLBYO8XQ6XS5WQ5WO5VN5VL5UK5UI5TH5TF5S\ E5SC5SBBVFGYIL`LQcPVfS_iVdkYemVfnSfpPgqMhsJhtGWrSJ\ qbPr`UrZZrXcsVhsTmsRSSI709GB8PK7XT6zzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzUczTczSczQczPczOc\ zNczLczKczJczIczGczFczEczDczEczFzzGzzGzzHzzIzzJzzJ\ zzNzzOzzOzzPzzPzzQzzQzzRzzRzzSzzSzzSzzTzzUzzUzzLzz\ DzzjzzgzzezzczzazzBzzCzzDzzDzzEzzEzzEzzEzzFzzFzzFz\ zFzzGzzGzzGzzGzzHzzHzzHzz } 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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Wallpaper and Bugs
by Roger Alexander 26 Apr '10

26 Apr '10

Arggh! More problems. Looks like another broken link this time for my Apr.24 post. Fixed it but who do I blame? Blogspot, Flickr or maybe.....myself. Signed out of Blogger composer,cleared my browser cache and double checked. Its gotta work! Now for some fractal wallpaper-how's that for a segue? Ready made at http://maxitersfractalfollies.blogspot.com The tippity top secret code follows. apr25_10.gif { ; wallpaper ; blank ; calctime 0:00:46.96 ; created Apr 25, 2010 ; Fractint Version 2004 Patchlevel 9 reset=1950 type=formula formulafile=frac_ml.frm formulaname=gallet-6-04 function=tan/cos/asinh passes=1 center-mag=43.8581/5.77127/0.05568668/1/-37.5/3.88578058618804789e-016 params=120/200/0.5/0/4/2 float=y maxiter=255 inside=0 outside=atan decomp=256 periodicity=0 cyclerange=0/255 colors=2I04H05F06E07D09C0AA0B90C80E70F50G40H30I20K00M00P00S00U00X00_00b0\ 0d00g00j00l00o00r00u00w00z00w00u00r00p00m00j00h00e00b00`00Y00W00T00Q00N0\ 0K00J01I02H04F05E06D07C09A0A90B80C70E50F40G30H20I00K00M00P00S00U00X00_00\ b00d00g00j00l00o00r00u00w00z00w00u00r00o00m00j00g00e00b00_00Y00V00S00Q00\ N00K01J02I04H05F06E07D09C0AA0B90C80E70F50G40H30I20K00M00P00S00U00X00_00b\ 00d00g00j00l00o00r00u00w00z00w00u00r00o00m00j00g00e00b00_00Y00V00S00Q00N\ 00K01J02I04H05F06E07D09C0AA0B90C80E70F50G40H30I20K00M00P00R00U00X00_00a0\ 0d00g00j00l00o00r00u00w00z00v04r08n0Cj0Gf0Kb0O_0SW0VS0ZO0bK0fG0jC0n80r40\ v20x00z00w00t00q00o00l00i00f00c00`00Y00W00T00Q00N00K01J02I04H05F06E07D09\ C0AA0B90C80E70F50G40H30I20K00M00P00S00U00X00_00b00d00g00j00l00o00r00u00w\ 00z00w00u00r00o00m00j00g00e00b00_00Y00V00S00Q00N00K01J0 } frm:Gallet-6-04 {; Sylvie Gallet [101324,3444], 1996 z = pixel, x = real(z), y = imag(z) : x1 = x - p1*fn1(y + fn2(p2*x) * fn3(p3*y)) y1 = y - p1*fn1(x + fn2(p2*y) * fn3(p3*x)) x = x1, y = y1 z = x + flip(y) |z| <= 32 ;SOURCE: gallet-6.frm } Roger Alexander _________________________________________________________________ Hotmail & Messenger. Get them on your phone now. http://go.microsoft.com/?linkid=9724463

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Another fmod spiral
by Roger Alexander 26 Apr '10

26 Apr '10

Todays post is another outside=fmod spiral. Yup it's a modest gray spiral but I like it. Speaking of spirals thanks to Lee H. Skinner for pointing out the link for the thumbnail for Apr.22's Bubble Spiral was broken and wouldn't download. It's those details. URL for today's finished product-http://maxitersfractalfollies.blogspot.com Coming up next --info!!! fract069.gif { ; sort of spiralish ; blank ; calctime 0:09:20.40 ; created Apr 23, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_g.frm formulaname=GenInvMand_rjr function=atanh/atan/one/log center-mag=1.597/1.11185/13.33333 params=-0.9226050599688711/-0.3284096804712058/-0.3594775231177709/-0.38\ 85921811578723 float=y maxiter=1500 inside=0 proximity=0.8 outside=fmod colors=000000111222333333444555666777777888999AAAAAABBBCCCDDDDDDEEEFFFGG\ GHHHHHHIIIJJJJJJKKKLLLMMMMMMNNNOOOPPPPPPQQQRRRRRRSSSTTTUUUUUUVVVWWWWWWXX\ XYYYYYYZZZ______``````aaabbbbbbcccddddddeeeeeeffffffggghhhhhhiiiiiijjjjj\ jkkkkkkllllllmmmmmmnnnnnnoooooopppppppppqqqqqqrrrrrrrrrssssssssstttttttt\ tuuuuuuuuuvvvvvvvvvwwwwwwwwwwwwxxxxxxxxxxxxxxxyyyyyyyyyyyyyyyyyyyyyzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzyy\ yyyyyyyyyyyyyyyyyyyxxxxxxxxxxxxxxxwwwwwwwwwwwwvvvvvvvvvuuuuuuuuutttttttt\ tsssssssssrrrrrrrrrqqqqqqpppppppppoooooonnnnnnmmmmmmllllllkkkkkkjjjjjjii\ iiiihhhhhhgggffffffeeeeeeddddddcccbbbbbbaaa``````______ZZZYYYYYYXXXWWWWW\ WVVVUUUUUUTTTSSSRRRRRRQQQPPPPPPOOONNNMMMMMMLLLKKKJJJJJJIIIHHHHHHGGGFFFEE\ EDDDDDDCCCBBBAAAAAA999888777777666555444333333222111000 } frm:GenInvMand_rjr { ; Jm Collard-Richard and rjr 2k03 c=z=1/pixel+p1: z=fn1(z)*fn2(z+p2)+fn3(fn4(c)) |z|<=4 ;SOURCE: fractint.frm } _________________________________________________________________ Videos that have everyone talking! Now also in HD! http://go.microsoft.com/?linkid=9724465

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FOTD 26-04-10 (The Fortunate Four [6])
by Jim Muth 25 Apr '10

25 Apr '10

FOTD -- April 26, 2010 (Rating 6) Fractal visionaries and enthusiasts: Today's image is named "The Fortunate Four". No one is more puzzled about this name than myself. The rating of merely a 6 indicates that I consider the image to be a come-down from the past several days. Perhaps the most striking thing about the image is the obvious black square surrounding the central minibrot. This square is almost entirely due to the coloring. The parent fractal is some kind of weird mixture of Z^(-20) and Z^2, which on the surface resembles an unexceptional Mandelbrot set. This M-set is unusual however because it is surrounded by blobs arranged into rings, which are loaded with minibrots. Today's image is located in one of these blobs, rather deep in East Valley. The calculation time of 3 minutes seems about right to me. I leave it to the individual fractalist to decide whether the result is worth the effort. The finished image may be seen at leisure on the FOTD web site at: <http://www.Nahee.com/FOTD/> The rain ended by 9am here at Fractal Central on Sunday, but the clouds hung tough through the rest of the day, while the tempera- ture of 54F 12C made it feel like November. The fractal cats slept through most of it until a brief but noisy thunder-shower moved in at 6pm. When Nicholas heard the crashing and booming, he decided the bathroom closet would be the safest place, while Cassie ducked behind the couch for the duration. Otherwise, the day was spent recovering from Saturday's not- entirely-surprise antiquing expedition. Actually, I'm kind of getting to enjoy these Saturday trips around the Central Pennsyl- vania countryside, which is pleasantly rural. The next FOTD will be posted in 24 hours. Until then, take care, and if one actually sees a ghost, would it then be more rational for that person to believe in the reality of ghosts, or to go rational and assume their mind is playing tricks? Tricks of the mind are real enough, but in reality, what are tricks of the mind made of? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Fortunate_Four { ; time=0:03:09.07-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinalDivideBrot function=recip passes=1 center-mag=+0.2517290144756433/+0.0000000033082999\ /5.1796e+012/1/111/0 params=-20/100000000000.0/0/0 float=y maxiter=1500 inside=0 logmap=270 periodicity=6 mathtolerance=0.05/1 colors=000X6oXCyTKuPXrLjn1`J5fR9lYDrdnW`Sl4PoFMrQJ\ u`LMnuet`noMLZKVbJdeInhlL4XdQZE_UQbQ`eLlhSNZO_cKkg\ CxIFwXermXtlPvkbi_VncOsgWg4RmJMrYXCkRSkMgkrocerfTu\ ir0chFe_UgQhiffFUoWLBrJ_niqW_saQufTm2NrP4gj8kkBokE\ skQjQNnWLq`Jtf6C_C_eJeHInXDtyFXcD_rFen80BBFLDUUFhb\ nX0sZyfgtUooblInkQjwXqedHSkHfkrvwewsTwo7SFzIF1ce5h\ g9mhDrjhUdZcgQmitDg``irNZtp1fsHUuXi8XBlTDoYErbGugz\ GMcaZD2gQf_gcl32l7HkAVkEik4k4B4LoMucZqSkng6x`KtUXq\ NjnAcxm92lA1cBUWCvVDjUE_TFPSGE_QDgZDaXBXW9SU7NT5O_\ EOfNOmWOsdIFKHUUHhbzzGzpOzhWNbcddtZiqTnoNsmDR2E_EF\ gPGo`VbKQiULzbmKgbYiSjjVnhRqiOsjKuk48A9QNDf_S5Zyze\ jOgWei5A3BZQyadXGydDbZPeT`gNliHuDHvVCJSFcazzqMGHKR\ PJaXIldjh5blGWpROta3UB7aLAhUEpbwoVlq_ascRugdjMXoVP\ scvyAhxNVw_oYycftSoo7DHC`XzZapOPgXVZe`Qnf`PNl3OaMW\ RdcaHaWSdRbfMmiz8ycYr9uCDvUcynJaaEMJFWRGdYHndrEPeU\ XThdei5ZmGTpRNtaTeVdXsXep } frm:FinalDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1)+0.00000000000000000001: z=(-b)*(z*z*fn1(z^(a)+b))-c |z| < esc } END PARAMETER FILE=========================================

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FOTD 25-04-10 (Things so Deep [7])
by Jim Muth 25 Apr '10

25 Apr '10

FOTD -- April 25, 2010 (Rating 7) Fractal visionaries and enthusiasts: Today's image is a fractal object, a fractal thing if you will, located in a valley in the parent fractal that results when 2.8 parts of Z^(1.5) are subtracted from 2.8 parts of Z^(2.5) and (1/C) is added. I named the image "Things so Deep" because it lies rather deep in its parent valley, and while studying it, I had the distinct impression that I was looking at an actual object. The parent fractal was turned inside out by calculating it with (1/C) instead of straight C, and then turned rightside out again by increasing real(p1) and real(p2) to 2.8. It is a fractal with four large lobes, facing the four directions. Today's image lies deep in the valley separating the north lobe from the east lobe. The rating of a 7 indicates that in my opinion, which is the opinion that counts when the FOTD's are rated, the image is somewhat but not all that far above average. I tried to make the coloring as smooth as possible, but there are not enough bands in the image to make the borders totally invisible. The image is slower than I would have preferred. 14-1/3 minutes is slow by any standard. Relief is at hand however on the FOTD web site, where the finished image is posted for satisfaction fast enough even for those with the shortest attention spans. The web site may be accessed at: <http://www.Nahee.com/FOTD/> A sunny morning here at Fractal Central on Saturday was followed by a cloudy afternoon and a rainy evening. The temperature reached its high of 63F 17C around noon and dropped to 55F 13C by evening. Needless to say, the fractal cats were most conten- ted in the morning, when the sun streamed in the windows on the east side of F.C. My day, as well as FL's day, was good enough. The next FOTD will be posted in around 13 hours. Until then, take care, and be a big-time thinker, whatever one of them is. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Things_so_Deep { ; time=0:14:21.98-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip center-mag=+1.991386892236/+0.360569839963/9.68377\ 4e+007/1/-70/0 params=2.8/2.5/-2.8/1.5/0/0/0/0 float=y maxiter=175000 inside=0 periodicity=6 colors=000ybzy_zyYzyVzyTzyRzyOzyMzyJzyHzyEzyCzy9zy\ 7zy4zy2zy0zv1zt1xq2uo2sm3pj3nh4kf4ic5fa5e_6dX6bV7a\ S7_Q8YO8VL9UJ9UHAUEAUCBUABU8AU79U68U57W46Y35_25`46\ a57b77c88d98eB9fC9gDAiFAjGBlHBnJCpKCrLDtNDvOExPEyM\ FnNGcOGTRNSURSXTS_VSaWRcYRe_RgaRicRkeQmgQoiQqkQsmP\ uoPwqPzrPzqNxpLvoOumOskOqiOogNmeNkcNiaNg_NgYNgWMfU\ MeSMdQMcOMbMMbKLaIL`GL_ELZCLZALX8OW7QU7TT9VRCXQE_O\ GaNIcLLfKNhIPkHRmFUoEWrCYtB_vDZtEYrFXpGWnHVlIVjKUh\ LTfMSdNRbOQ`PQ_RVYSZXUbWVfUXiTYhSZgRZgRZhR_iT_jW_k\ Z_la`md`ng`oj`pmaqparsarvarzbrzbrzbrzbrz`pzZnzXmzW\ kzUizShvRfrPemNchMacK`ZIZUHXPFWKDUFCTEDUDDVDEWDEXD\ EYDFZDF_DF`DGaDGbDGcDHdDHeDHfDIgDIhDIiDuA9tCCtDFsF\ HsGKrHNrJPqKSqLVpNXpO_pPboRdoSgnTjnVlmWomXrlZtl_wl\ `yj_vh_tgZreZodZmbYk`Yi_YfYXdXXbVW`UWYSWWQVUPVSNVP\ MUNKULJUJKUJLTJLSIMRIMQINPHNOHONHOMGPLGMIIPLGROEUQ\ DWTBZVA`Y8fZ1d_4b_7ygnydo } 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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A bug with bugs
by Roger Alexander 25 Apr '10

25 Apr '10

Sort of looks like a bug with bugs. Remembering Jonathan Swift: "So nat'ralists observe, a flea Hath smaller fleas that on him prey, And these have smaller fleas that bite 'em, And so proceed ad infinitum." Where would I be without Wikipedia? As usual go to http ://maxitersfractalfollies.blogspot.com for the finished product. Data for ya!!!! fract068.gif { ; bugs on a bug ; blank ; calctime 0:00:33.34 ; created Apr 23, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_g.frm formulaname=gloob function=cotanh/sqr center-mag=0.793378/-0.453938/4.069552 params=-0.02923673207800529/-0.2841273232215339 float=y maxiter=1500 inside=0 proximity=1 outside=fmod colors=zzzzzzzzzzzzzzzyyyyyyyyyyyyxxxxxxxxxxxxwwwwwwwwwwwwvvvvvvvvvvvvuu\ uuuuuuuuuuttttttttttttssssssssssssrrrrrrrrrrrrqqqqqqqqqqqqppppppppppppoo\ oooooooooonnnnnnnnnnnnmmmmmmmmmmmmllllllllllllkkkkkkkkkkkkjjjjjjjjjjjjii\ iiiiiiiiiihhhhhhhhhhhhggggggggggggffffffffffffeeeeeeeeeeeeeeeddddddddddd\ dccccccccccccbbbbbbbbbbbbaaaaaaaaaaaa````````````____________ZZZZZZZZZZZ\ ZYYYYYYYYYYYYXXXXXXXXXXXXWWWWWWWWWWWWVVVVVVVVVVVVUUUUUUUUUUUUTTTTTTTTTTT\ TSSSSSSSSSSSSRRRRRRRRRRRRQQQQQQQQQQQQPPPPPPPPPPPPOOOOOOOOOOOONNNNNNNNNNN\ NMMMMMMMMMMMMLLLLLLLLLLLLLLLKKKKKKKKKKKKJJJJJJJJJJJJIIIIIIIIIIIIHHHHHHHH\ HHHHGGGGGGGGGGGGFFFFFFFFFFFFEEEEEEEEEEEEDDDDDDDDDDDDCCCCCCCCCCCCBBBBBBBB\ BBBBAAAAAAAAAAAA99999999999988888888888877777777777766666666666655555555\ 5555444444444444333333333333222222222222111111111111000 } gloob{; Roger z = Pixel: z = (fn1(z^4)) * (fn2(z^4)+p1) ;SOURCE: roger4.frm } _________________________________________________________________ Hotmail & Messenger are available on your phone. Try now. http://go.microsoft.com/?linkid=9724461

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FOTD 24-04-10 (Infernal Eruption [8])
by Jim Muth 23 Apr '10

23 Apr '10

FOTD -- April 24, 2010 (Rating 8) Fractal visionaries and enthusiasts: Today's image is an imaginary scene near the edge of a huge volcanic eruption on an alien planet. The generating formula, 'escher julia' is one of the lesser-used ones hard-coded into the Fractint program. In fact, I think this is the first time I have used it as the source of an FOTD image. The formula generates pseudospherical fractals from Julia sets of the Mandelbrot set, in which the Julia elements are repeated ever smaller as the edge of the circle is approached. Today's scene, based on an East Valley Julia set, is located at center- bottom of the parent circle, where the Julia sets are divided quite small. Of course, as in all fractals, there is no limit to how much smaller and more numerous the Julia sets become. The rating of an 8 includes one full point for the effort I put into the coloring. The name "Infernal Eruption" needs no explanation. The calculation time of 1-1/4 minutes will bring palpitations to the heart of the true fractal fanatic. Another way to have a leaping heart is to visit the FOTD web site at: <http://www.Nahee.com/FOTD/> and view the finished image there. Another totally perfect April day came and went here at Fractal Central on Friday, with clear sunny skies and a temperature of 66F 19C. But the weather experts tell us that Friday was the last perfect day we will see for quite some time. This worried the fractal cats not one bit. My day was average; FL's day was the same. The next FOTD will be posted in 24 hours. Until then, take care, and why, in our mind's eye, can we so easily remove all objects from the universe and imagine a vast emptiness, and yet be unable to remove the empty three-dimensional space? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Infernal_Eruption { ; time=0:01:14.85-SF5 on P4-2000 reset=2004 type=escher_julia passes=1 center-mag=-0.00000000497631643/-0.999999989886774\ 70/5.064638e+007 params=0.27/0.0059 maxiter=1500 float=y inside=0 outside=summ periodicity=6 colors=000HNU2E091BA7HBDNCITDOZcEF_HJWJNSLQONUKPXG\ R`qsO0SR7TYq8pjCmCWSATOPNKPNJPMJPLJPKIPJIPIIEIIcYQ\ XWXOPQLMKzmEtr8lqCzpFXoJPnMHnPXTLl7HfBL`FPVITPMXCV\ e1fd2ec3ec4eb5eb6da7da8d`9d`Ad`Bc_Cc_DcZEcZFbYGbYH\ bXIbXzBqwDouFnrGmpIlmJkkLjTNPMJMFFJ8BG27E4BG6EI8HK\ 9KM0JMDRQEUSONPNZbI_WsO0zgFzfHzX0zeLzeNzc0zcRzmTzh\ 0zD5zF7zm0zIAzJBzr0zzEzzGzzHzzJzzKzzzzzNzzPzzQJYSJ\ ZTJ`VJaWC`jDaiDahEagEafFaeFadFadFbcFcbFdbFeaFf`Feb\ EddEbfDaiD`kCZmCYoBWrGYqL`pQcoVfn_hmdklinknqinnfnj\ cnf`obYoZVoVRoROpNLpJIpFFqBBjAAb99V78N67F46OPQYijY\ ijYijXiiXiiWihWihVigVigUifUifTieRhePfdNddLbcJacH_b\ FYaDWaBV`9T`7R_5PZ7Q_AS`DUaGWbIYcL_dO`eRbfTdgWfhZh\ iajjdlkdkjcjichgbgfbeeadcabb`aa``__ZZ_YYZWWZVVYTTY\ TUYTWXTXXTZWT_WTaVUbVUdUUeUUgTUhTUjSVlSRkSNiTJgTFe\ UBcVEaWH_XKYZNW_QU`TSbWQ_XRWYSTZUP`VMaXIbYFdZBe`8f\ a4hc5hc6hb7haAb7CbEFbKHbR } END PARAMETER FILE=========================================

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Re: [Fractint] sucker.par Distorting a fractal with harmony.
by Jay Litwyn 23 Apr '10

23 Apr '10

comment { I decided to see what a tune does to a more noisy fractal (one with high frequency, fine textures in it), namely "Club_Lambda", z=z^2 -conj(z) +c, as I posted about four years ago. The tune makes the usual snohman's torso bigger, fills in some of limbs, and fills a head in, especially a neck. The most interesting things are that no textures are in it, only spines, and shape of inner set *reverts to the m-set*, rather than a triangle in Club_Lambda. The outside=atan view of FlauBug is just as noisy as Club_Lambda, though. I would think that my tune is putting order into chaos were it not for that inverse tangent view. http://ecn.ab.ca/~brewhaha/img/FlauBug.jpg HSL combo. I put new parameters and formula into an old file. The tune is the same. The name and formula has been changed to protect the lawyers :-) begin fractint formulafile=crown.par parmfile=crown.par} Club_Lambda { ; Formula with texture. ; CC-BY BrewJay's Babble Bin z=fn1(pixel), c=fn2(pixel), t=|P1|: z = z*z -conj(z) +c ;c = c/2 +z, |z| <= t } FlauBug { ;Same synthesizer input as sucker.par ; CC-BY http://ecn.ab.ca/~brewhaha/ z=fn1(pixel), c=fn2(pixel), iter=0: iter=iter+1 if (iter>= 1 ) && (iter<= 1 ) z=z*z/ 9 -conj(z)/ 22 +c endif if (iter>= 2 ) && (iter<= 4 ) z=z*z/ 11 -conj(z)/ 16 +c endif if (iter>= 5 ) && (iter<= 6 ) z=z*z/ 14 -conj(z)/ 11 +c endif if (iter>= 7 ) && (iter<= 10 ) z=z*z/ 12 -conj(z)/ 16 +c endif if (iter>= 11 ) && (iter<= 12 ) z=z*z/ 11 -conj(z)/ 28 +c endif if (iter>= 13 ) && (iter<= 14 ) z=z*z/ 9 -conj(z)/ 22 +c endif if (iter>= 15 ) && (iter<= 16 ) z=z*z/ 7 -conj(z)/ 14 +c endif if (iter>= 17 ) && (iter<= 20 ) z=z*z/ 9 -conj(z)/ 18 +c endif if (iter>= 21 ) && (iter<= 24 ) z=z*z/ 10 -conj(z)/ 20 +c endif if (iter>= 25 ) && (iter<= 26 ) z=z*z/ 14 -conj(z)/ 22 +c endif if (iter>= 27 ) && (iter<= 29 ) z=z*z/ 10 -conj(z)/ 15 +c endif if (iter>= 30 ) && (iter<= 32 ) z=z*z/ 11 -conj(z)/ 18 +c endif if (iter>= 33 ) && (iter<= 33 ) z=z*z/ 14 -conj(z)/ 22 +c endif if (iter>= 34 ) && (iter<= 35 ) z=z*z/ 11 -conj(z)/ 11 +c endif if (iter> 35 ) iter=0 endif |z| <= real(P1)} FlauBugLumo { ; 51.41/megapixel at 866Mhz ; CC-BY-NC Bohgosity BumaskiL ; Fractint Version 2004 Patchlevel 4 ; Fractint saved name without case. reset=2004 type=formula formulafile=crown.par formulaname=flaubug function=zero/ident passes=b center-mag=-7.99646/7.77156e-016/1.262778/4.3849 params=3072/0 float=y maxiter=255 inside=255 outside=atan invert=0.755748621589819/-7.83908667367891/0 symmetry=xaxis periodicity=0 colors=(a)altern.map } FlauBugChromo { ; 43.99s/megapixel at 866Mhz ; Map is a loud emphasis on complements. ; CC-BY-NC Jay Litwyn. ; Fractint Version 2004 Patchlevel 4 reset=2004 type=formula formulafile=crown.par formulaname=flaubug function=zero/ident passes=b center-mag=-7.99646/7.77156e-016/1.262778/4.3849 params=3072/0 float=y maxiter=255 inside=255 invert=0.755748621589819/-7.83908667367891/0 symmetry=xaxis periodicity=0 colors=0000z0z0z0z9z0p0zIz0e0zRz0W0z_z0L0zhz0B0zqz000zzz700szzF00kzzN0\ 0czzV00Wzzb00Ozzj00Gzzr008zzz000zsz070zkz0F0zcz0N0zWz0V0zOz0b0zGz0j0z8\ z0r0z0z0z0z0z7z0s0zFz0k0zNz0c0zVz0W0zbz0O0zjz0G0zrz080zzz000szz700kzzF\ 00czzN00WzzV00Ozzb00Gzzj008zzr000zzz070zsz0F0zkz0N0zcz0V0zWz0b0zOz0j0z\ Gz0r0z8z0z0z0z0z0s0z7z0k0zFz0c0zNz0W0zVz0O0zbz0G0zjz080zrz000zzz700szz\ F00kzzN00czzV00Wzzb00Ozzj00Gzzr008zzz000zsz070zkz0F0zcz0N0zWz0V0zOz0b0\ zGz0j0z8z0r0z0z0z0z0z7z0s0zFz0k0zNz0c0zVz0W0zbz0O0zjz0G0zrz080zzz000sz\ z700kzzF00czzN00WzzV00Ozzb00Gzzj008zzr000zzz070zsz0F0zkz0N0zcz0V0zWz0b\ 0zOz0j0zGz0r0z8z0z0z0z0z0s0z7z0k0zFz0c0zNz0W0zVz0O0zbz0G0zjz080zrz000z\ zz700szzF00kzzN00czzV00Wzzb00Ozzj00Gzzr008zzz000zsz070zkz0F0zcz0N0zWz0\ V0zOz0b0zGz0j0z8z0r0z0z0z0z0z7z0s0zFz0k0zNz0c0zVz0W0zbz0O0zjz0G0zrz080\ zz000 } Crown_ClubsH { ; 16.59s/megapixel at 866Mhz. ; CC-BY-SA, as given to wikipedia ; Fractint Version 2004 Patchlevel 4 ; Demonstrates texture. reset=2004 type=formula formulafile=crown.par formulaname=club_lambda function=zero/ident passes=t center-mag=-0.848329/0/0.7526244/1.2756 params=4/0 float=y maxiter=255 inside=0 outside=imag invert=0.5/-0.25/0 symmetry=xaxis periodicity=0 colors=(a)rainboh.map } Crown_ClubsL { ; 17.02s/megapixel at 866Mhz. ; CC-BY-NC Jay Litwyn ; Fractint Version 2004 Patchlevel 4 ; Once selected for card suits. reset=2004 type=formula formulafile=crown.par formulaname=club_lambda function=zero/ident passes=t center-mag=-0.848329/0/0.7526244/1.2756 params=4/0 float=y maxiter=255 inside=0 outside=atan invert=0.5/-0.25/0 symmetry=xaxis periodicity=0 colors=(a)altern.map } FlauBugDefault { ; 11.43s/megapixel at 866Mhz ; CC-BY Jay Litwyn ; Fractint Version 2004 Patchlevel 4 ; Fractint saved name with case. reset=2004 type=formula formulafile=crown.par formulaname=FlauBug function=zero/ident passes=b center-mag=-6.30788/5.32907e-015/0.08020317/1.1807 params=3072/0 float=y maxiter=255 inside=254 symmetry=xaxis periodicity=0 colors=(a)defaultw.map }

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Bubble Spiral
by Roger Alexander 23 Apr '10

23 Apr '10

Yup it's a spiral of bubbles with more outside=fmod hijinx. Go to http://maxitersfractalfollies.blogspot.com for the finished product. Top secret info follows. fract056.gif { ; fmod bubble spiral ; blank ; calctime 0:10:53.88 ; created Apr 22, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_k.frm formulaname=kfact2_jul function=flip center-mag=+0.45156445556946170/-0.13973288814691200/266.6667 params=-0.3343913083285012/-0.2642597735526597/0.1786858729819636/-0.845\ 3321939756462 float=y maxiter=1500 inside=0 proximity=0.1 outside=fmod colors=wwwvvvvvvvvvvvvvvvvvvvvvvvvvvvuuuuuuuuuuuuuuuuuuuuutttttttttttttt\ tttttttssssssssssssssssssrrrrrrrrrrrrrrrqqqqqqqqqqqqqqqqqqpppppppppppppp\ pooooooooooooooonnnnnnnnnnnnnnnmmmmmmmmmmmmmmmlllllllllllllllkkkkkkkkkkk\ kkkkjjjjjjjjjjjjiiiiiiiiiiiiiiihhhhhhhhhhhhgggggggggggggggffffffffffffee\ eeeeeeeeeedddddddddddddddccccccccccccbbbbbbbbbbbbaaaaaaaaaaaa```````````\ `_______________ZZZZZZZZZZZZYYYYYYYYYYYYXXXXXXXXXXXXWWWWWWWWWWWWVVVVVVVV\ VUUUUUUUUUUUUTTTTTTTTTTTTSSSSSSSSSSSSRRRRRRRRRRRRQQQQQQQQQQQQPPPPPPPPPPP\ POOOOOOOOONNNNNNNNNNNNMMMMMMMMMMMMLLLLLLLLLKKKKKKKKKKKKJJJJJJJJJJJJIIIII\ IIIIHHHHHHHHHHHHGGGGGGGGGGGGFFFFFFFFFEEEEEEEEEEEEDDDDDDDDDCCCCCCCCCCCCBB\ BBBBBBBBBBAAAAAAAAA99999999999988888888877777777777766666666655555555544\ 4444444444333333333222222222222111111111000000000000000 } frm:kfact2_jul {; formula file for patchwork z=pixel, c=p1, kfac=real(p2), dt=imag(p2)*pi, t=0, k=kfac: r=cos(t), kr=k*r, z=fn1(z*kr)/kr z=sqr(z)+c, t=t+dt, k=k*kfac |z| < 4 ;SOURCE: 97msg.frm } _________________________________________________________________ Got a phone? Get Hotmail & Messenger for mobile! http://go.microsoft.com/?linkid=9724464

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FOTD 23-04-10 (The Eastern Horizon [8])
by Jim Muth 22 Apr '10

22 Apr '10

FOTD -- April 23, 2010 (Rating 8) Fractal visionaries and enthusiasts: Today's image earns an 8 because of its unusually brilliant colors. Take away the colors and it's just another fractal with an "East Valley" appearance. The parent fractal is an error. Instead of resetting the function to 'reciprocal' I let it stay at 'cosine' and came up with what might be the start of an entirely new family of fractals. (I would never have made the error if the program would accept the entry 'recip' written directly in the iterated section instead of a more awkward 'fn1', which refers back to the initialization section.) The resulting parent fractal appears as a rough Mandelbrot-set shape rotated 180 degrees, with all kinds of extra stuff stretched along the positive X-axis. Today's scene is located very near the X-axis, just east of the easternmost block of 'stuff'. The magnitude is once again quite large, which makes the mathtolerance entry necessary. The name "The Eastern Horizon" is something that popped to mind when I tried to think of a name. The calculation time of 4 minutes is satisfactory for an image that rates an 8. Also satisfactory is the trip to view the completely calculated image on the FOTD web site at: <http://www.Nahee.com/FOTD/> Despite ominous clouds at times, Thursday proved to be quite a pleasant day here at Fractal Central, with a temperature of 70F 21C and ample sun between the billowing cumulus clouds. The fractal cats ignored the outside weather and enjoyed the inside conditions, which included a treat of tuna and cheddar, and a romp up and down the hallway. My day was good enough, but could have been better if I had not volunteered to satisfy an irate customer who claimed we had not followed her instructions. The next FOTD will be posted in 24 hours. Until then, take care, and if you want it done right, do it yourself. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_EasternHorizon { ; time=0:04:03.07-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinalDivideBrot function=cos float=y center-mag=+1.771974192428845/+0.0000000994273418/\ 2.61846e+012/1/-76.8/0 params=0/1/0/0 periodicity=6 maxiter=2750 inside=0 logmap=400 mathtolerance=0/1 colors=000O6KPAIQEJRGHSHNTKSUNZUReUWlQcschzckzgrzo\ vzzzzzzzzzzEmzHczJUzMKzOAzQ4zWOhafh`bf_ZeZVdYScXOb\ dKafG`iD_mKWrUSzbPzhCzn0zmAzcKmUUcScUQ7KVFE_NBdU8i\ a5mhGjcQgZ_dUaaVbZVcWWeTWfQXgOXbTTYXPU`LPdHKhDGl9B\ p57t1Dh2IY3OM4TB5Y06QEPIRgBcyAfzAiz9lz9oz9qzIgjQaW\ ZWGfQ1PZ38g5BcAD`FGYKIVPKSTRmHemStmbqi`nf_kbYi_XfW\ VtPknMujRqfVnc_j_cgXhcTl`QpYBnUBoWBoYIpUOqQUrNRmPO\ mRMmTQKRTKQzhOzlNzpLztKzwJifVjRehU`fWXdYTb`O`bK_dG\ X`IUXKSTMPQOMMQKISHEUFBVJKZMUaPcdSmgWzjZzmazpdzsiz\ smzsqzs8mwBcpEUiHSbKYWNcPQhJPeLPbNO`POYQOVSNTUNQWN\ OXTVSZaNdhJzoEzwmzdSqOiuKNyH1W_92qG4rc6sc8tcAumCvm\ EwmGxmMpzRimWaK`VMe0NgYOh0PjfQklRfbWbT`j`YqhVxpSok\ Wgg_ZccR_fPZvU_zZUzcUzhUzcdzrhzvmzzrzzvzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzezzfzzgzzhzzizzkzzmzzoz\ znzzkzzhzzezzbzz_zzXzzUzz } frm:FinalDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1)+0.00000000000000000001: z=(-b)*(z*z*fn1(z^(a)+b))-c |z| < esc } END PARAMETER FILE=========================================

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sucker.par Distorting a fractal with harmony.
by Jay Litwyn 22 Apr '10

22 Apr '10

"fractint formulafile=sucker.par" is how I've been running it. http://ecn.ab.ca/~brewhaha/img/Sucker.jpg I used "Inversion" and "Distance" parameters with an HSL combination. I hav no clue what that frm: prefix is supposed to do, so I am not using it here. I put some code into my synthesizer to write numbers into the formula included here. Sucker { ;Formula output from a synthesizer at ; http://groups.google.com/group/rec.music.makers.synth/msg/5c4b7ef1274cb806?… ; CC-BY BrewJay's Babble Bin z=fn1(pixel), c=fn2(pixel), iter=0: iter=iter+1 if (iter>= 1 ) && (iter<= 1 ) z=z*z/( 9 , 22 ) +c endif if (iter>= 2 ) && (iter<= 4 ) z=z*z/( 11 , 16 ) +c endif if (iter>= 5 ) && (iter<= 6 ) z=z*z/( 14 , 11 ) +c endif if (iter>= 7 ) && (iter<= 10 ) z=z*z/( 12 , 16 ) +c endif if (iter>= 11 ) && (iter<= 12 ) z=z*z/( 11 , 28 ) +c endif if (iter>= 13 ) && (iter<= 14 ) z=z*z/( 9 , 22 ) +c endif if (iter>= 15 ) && (iter<= 16 ) z=z*z/( 7 , 14 ) +c endif if (iter>= 17 ) && (iter<= 20 ) z=z*z/( 9 , 18 ) +c endif if (iter>= 21 ) && (iter<= 24 ) z=z*z/( 10 , 20 ) +c endif if (iter>= 25 ) && (iter<= 26 ) z=z*z/( 14 , 22 ) +c endif if (iter>= 27 ) && (iter<= 29 ) z=z*z/( 10 , 15 ) +c endif if (iter>= 30 ) && (iter<= 32 ) z=z*z/( 11 , 18 ) +c endif if (iter>= 33 ) && (iter<= 33 ) z=z*z/( 14 , 22 ) +c endif if (iter>= 34 ) && (iter<= 35 ) z=z*z/( 11 , 11 ) +c endif if (iter> 35 ) iter=0 endif |z| <= real(P1)} Default { ; Basically a distortion of the m-set. CC-BY-NC ; http://ecn.ab.ca/~brewhaha/ ; Fractint Version 2004 Patchlevel 4 reset=2004 type=formula formulafile=sucker.par formulaname=Sucker function=zero/ident center-mag=0/-12.02/0.03333333 params=3072/0 float=y maxiter=255 inside=0 symmetry=none periodicity=0} Inversion { ; 51.08s/megapixel@866Mhz CC-BY-NC ; http://ecn.ab.ca/~brewhaha/ ; Fractint Version 2004 Patchlevel 4 reset=2004 type=formula formulafile=sucker.par formulaname=sucker function=zero/ident center-mag=-1.9074/-3.1791/2.332101/1.4248 params=3072/0 float=y maxiter=255 inside=0 outside=atan invert=4.49797449255688/-1.90237816270341/-3.20530796661091 symmetry=none periodicity=0 colors=(a)altern.map } LastEscape { ; 51.52s/megapixel@866Mhz CC-BY-NC ; http://ecn.ab.ca/~brewhaha/ ; I did not use this one in a JPEG. ; Fractint Version 2004 Patchlevel 4 reset=2004 type=formula formulafile=sucker.par formulaname=sucker function=zero/ident center-mag=-1.9074/-3.1791/2.332101/1.4248 params=3072/0 float=y maxiter=255 inside=0 proximity=1000 outside=fmod invert=4.49797449255688/-1.90237816270341/-3.20530796661091 symmetry=none periodicity=0 colors=(a)rainboh.map } Distance { ; negative of rainboh.map CC-BY-NC ; http://ecn.ab.ca/~brewhaha/ ; 52.62s/megapixel@866Mhz ; I will get a more accurate rainboh out of PSP ; with a grayscale pasted into an HSL separation. ; Fractint Version 2004 Patchlevel 4 reset=2004 type=formula formulafile=sucker.par formulaname=sucker function=zero/ident center-mag=-1.9074/-3.1791/2.332101/1.4248 params=3072/0 float=y maxiter=255 inside=0 outside=tdis invert=4.49797449255688/-1.90237816270341/-3.20530796661091 symmetry=none periodicity=0 colors=zzz0uz0sz0oz<3>0gz0ez0dz0cz<3>0Xz0Wz0Uz<7>0Kz0Jz0Hz<8>07z06z05z\ <3>01z11z21z<12>E0zF0zG0z<5>O0zP0zQ0z<4>Y0zZ0z_0za0zc0zd0ze0zh0zi0zl0z\ m0zo0z<2>z0zz0wz0sz0oz0mz0i<3>z0cz0bz0az0_z0Z<4>z0Rz0Qz0O<16>z06z05z04\ z03z02<4>z41z40z50<9>zG0zH0zI0<4>zP0zQ0zR0<2>zW0zY0zZ0z_0z`0<3>zg0zi0z\ j0zm0zo0<2>zz0wz0sz0oz0<10>Yz0Wz0Uz0<4>Oz0Nz0Mz0<3>Hz0Fz0Ez0<7>6z05z04\ z03z02z0<14>0zD0zE0zF<6>0zP0zQ0zR0zS0zU<2>0zY0zZ0z`0zb<3>0zi0zj0zm<3>0\ zv }

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Fmod Coloring
by Roger Alexander 22 Apr '10

22 Apr '10

In addition to outside=atan and decomposition, tdis and outside=fmod can be used to provide smooth coloring. In today's post the fmod value was 0.1 instead of the default 0.01. With tdis high bailout values often provide the desired effect. Some formulas have the bailout as a user selectable parameter and I have rewritten some formulas to do this. Anyway on with the show. apr_21.gif { ; high fmod ; blank ; calctime 0:09:09.36 ; created Apr 21, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_o.frm formulaname=Olio_Magnet function=cotan center-mag=-0.09106382978723393/-0.42499582637729420/5333.333 params=0/0 float=y maxiter=2600 inside=0 proximity=0.1 outside=fmod colors=000000111222333333444555666777777888999AAAAAABBBCCCDDDDDDEEEFFFGG\ GHHHHHHIIIJJJJJJKKKLLLMMMMMMNNNOOOPPPPPPQQQRRRRRRSSSTTTUUUUUUVVVWWWWWWXX\ XYYYYYYZZZ______``````aaabbbbbbcccddddddeeeeeeffffffggghhhhhhiiiiiijjjjj\ jkkkkkkllllllmmmmmmnnnnnnoooooopppppppppqqqqqqrrrrrrrrrssssssssstttttttt\ tuuuuuuuuuvvvvvvvvvwwwwwwwwwwwwxxxxxxxxxxxxxxxyyyyyyyyyyyyyyyyyyyyyzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzyy\ yyyyyyyyyyyyyyyyyyyxxxxxxxxxxxxxxxwwwwwwwwwwwwvvvvvvvvvuuuuuuuuutttttttt\ tsssssssssrrrrrrrrrqqqqqqpppppppppoooooonnnnnnmmmmmmllllllkkkkkkjjjjjjii\ iiiihhhhhhgggffffffeeeeeeddddddcccbbbbbbaaa``````______ZZZYYYYYYXXXWWWWW\ WVVVUUUUUUTTTSSSRRRRRRQQQPPPPPPOOONNNMMMMMMLLLKKKJJJJJJIIIHHHHHHGGGFFFEE\ EDDDDDDCCCBBBAAAAAA999888777777666555444333333222111000 } Olio_Magnet (XAXIS) { z = pixel : z = z + p1 + 0.5 z = z * fn1(pixel) z = sqr(1/z) |z| < 4 ;SOURCE: olio.frm Go to http://maxitersfractalfollies.blogspot.com for the finished fractal _________________________________________________________________ Live connected. Get Hotmail & Messenger on your phone. http://go.microsoft.com/?linkid=9724462

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FOTD 22-04-10 (Steppes of the East [6.5])
by Jim Muth 21 Apr '10

21 Apr '10

FOTD -- April 22, 2010 (Rating 6.5) Fractal visionaries and enthusiasts: Today's iterated expression subtracts 1/4 part of (1/Z) from 3/4 part of Z^3 then adds straight C. The parent fractal consists of a group of large irregular but connected bays with some areas critical and some not. Like so many fractals produced by the MandAutoCritInZ formula, this fractal is impossible to adequate- ly describe in words. In this type of fractal, an orbit check is often the best way to see what kind of minibrots will be found in a given region. Today's scene lies on the shore line of a bay sprouting eastward from what appears to be the East Valley of a kind of Mandelbrot main cardoid. In the closest part of this bay the periodicity is 3; in the middle it is chaotic, while in the farthest part it is 8. Today's scene is located near the point where the periodi- city shifts from 3 to chaos. The greenish parts of the image consist of 'inside' stuff made visible by the 'fmod' inside fill. The mathtolerance entry was needed because the extreme magnitude of the image could cause the scene to calculate at a lesser magnitude, producing a wrong image. The terraced appearance was achieved by setting the 'outside' to 'tdis'. The rating of 6-1/2 shows my indecision. If I had worked a bit harder on the coloring, I might have been able to raise the rating to at least a 7. The name "Steppes of the East" invokes feelings of the Gobi desert, though I can see no logical connection between that part of the world and today's fractal. The calculation time of just under 2 minutes is not too slow. Neither is the trip to see the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> A near-perfect day prevailed here at Fractal Central on Wednes- day. The hazy sunshine, gentle winds and temperature of 68F 20C made it feel almost like a day in June. But June turned to April at 6pm, when a gusty shower moved in from the west and the temperature dropped to 55F 13C. The fractal cats found a bit of excitement when Nicholas caught sight of a crow hopping around in the yard and Cassie came running to see what Nico was chattering at. The rest of the time the duo spent sleeping, chasing one another up and down the hallway and asking for food. The next FOTD, maybe better or maybe not, will be posted in 24 hours. Until then, take care, and be a fool. Being a fool is more fun. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Steppes_of_theEast { ; time=0:01:57.76-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+0.9225736401877659/-0.1695063536240019\ /1.96e+013/1/-152.5/0 params=0.75/3/-0.25/-1.0/0/0\ /0/0 float=y maxiter=1500 inside=fmod outside=tdis proximity=0.5 periodicity=6 mathtolerance=0.05/1 colors=000MW_SSXYOVcKSiGQoDOW65bPyfMxjKxnHxrFxvDxv\ Ptv`qvlmvxjisiYniMiiAeiEhaHjVKmONoHQqAVjF_cKcYOhRT\ mKYqEav7fx1jr2di2ZZ3TY3NS4UR4SKAPKFOK0KK08JU7MZ6zz\ DzmMzmVzmczPzzmzzVzzmIzWzzmzpWzpXzzXzqXzkTzfPz`LzW\ IkQEkLAjG7jTMbVJYWHTYFPZDK`BFa9Bc76d52`tURYbHCkCI_\ 8OP4UE0Z36_2C`2H`1Na1Sa0Yb0bb0v`8uc6tf4si2rk0ta7uS\ DvIKw8QURzUUzUXzU_zUbzUezUhzUkzUnzUqzUtzUwzUzzOKQQ\ KQSKQUKPWKPYKP_KPaKScKUeMXfOZgQahTclVfpYht_kwamnej\ eigYme_nc`nabn_cnYenXfnVgnTioRjoPloOmoMooKpoIqoHpX\ XpFknMcmTXl_PjfIimAht3iq4in4il5ji5jg5jd6ZHLZMPZSUZ\ XYYbaYhfYmjYsnYxrLeNOcLRbJU`IX_GZYFaXDdVBgUAjS8lR7\ jP9hNBgLCeKEdIGbGHaFJ_DKYBMXAOV8PU6RS5TR3UP1WO0XR2\ WU4WX5W_7Wb9VeAVhCV30g93cE5`K7YP9VUBS_DPdFMiHJmLGp\ ODsSAvV7kS7aQ7SN7IL78J79I6AH6BH5BG5CF4DF4DE3EE3FD2\ FC2GC1HB1HB1IE4IH7IKAINDIQGITJIWMIYOGTOEOOzzOKzGzz\ 8NgCz_GzzJz_OKWiF_fAcdG_a } 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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Subject No Subject (fractal noise) and the Droste Effect
by Roger Alexander 21 Apr '10

21 Apr '10

JackOfTradeZ noted he couldn't do anything with my post Apr. 18. Good thing too. It was meant to illustrate one aspect of chaotic systems-regular inputs can produce highly irregular outputs. I chose it because it superficially is apparent noise. Zooming in repeatedly produces noisy images each unconnected to the last without apparent repetition or structure. Let's all salute the flexibility of self-referential iteration! This post's fractal is an example of the Droste effect (named after a Dutch cocoa manufacture) whose design of their tins and boxes had progressively smaller copies of the labels placed recursively on itself. Go to http://en.wikipedia.org/wiki/Droste_effect for an example. Two sizes of the finished product are at http://maxitersfractalfollies.blogspot.com 800x600 and 3200x2400. Zoom in on the big one to verify the recursive nature of the fractal. fract045.gif { ; Droste effect ; blank ; calctime 0:03:36.30 ; created Apr 20, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=esc-ifs.frm formulaname=Diamont center-mag=-4.44089e-016/4.30211e-016/15.50142 params=2/0 float=y maxiter=1200 inside=0 proximity=1 outside=fmod colors=000000111222333333444555666777777888999AAAAAABBBCCCDDDDDDEEEFFFGG\ GHHHHHHIIIJJJJJJKKKLLLMMMMMMNNNOOOPPPPPPQQQRRRRRRSSSTTTUUUUUUVVVWWWWWWXX\ XYYYYYYZZZ______``````aaabbbbbbcccddddddeeeeeeffffffggghhhhhhiiiiiijjjjj\ jkkkkkkllllllmmmmmmnnnnnnoooooopppppppppqqqqqqrrrrrrrrrssssssssstttttttt\ tuuuuuuuuuvvvvvvvvvwwwwwwwwwwwwxxxxxxxxxxxxxxxyyyyyyyyyyyyyyyyyyyyyzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzyyyyyyyyyyyyyyyxxxxxxxxxxx\ xxxxwwwwwwwwwwwwwwwwwwvvvvvvvvvvvvvvvuuuuuuuuuuuuuuutttsstsssrrsrrrqqrpp\ qppqoopoopnnommommnllnllmkkmkkljjliikiikhhjhhiggiffhffheegeegddfccfccebb\ ebbdaadaac``c__b__bZZaZZaYY`XX`XX_WW_WWZVVZUUYUUXTTXTTWSSWSSVRRVQQUQQUPP\ TPPTOOSNNSNNRMMRMMQLLQKKPKKPJJOJJOIINIINHHMGGMGGLFFKFFKEEJDDJDDICCICCHBB\ HAAGAAG99F99F88E88E77D66D66C55C55B44B33A33A229229118007 } Diamont {; Use p1=2 to get the image z=pixel, j=(0, -1), k=(-1, 0), l=(0, 1), m=(1, 0): x=real(z) y=imag(z) y1=(y>.5) x1=(x>.5) y2=(y<-.5) x2=(x<-.5) z1=(y1==0 && x1==0) a=y1*j b=x1*(y1==0)*k c=z1*y2*l d=(z1>0 && y2==0)*x2*m p=a+b+c+d z=p1*z+p |z|<=100 ;SOURCE: esc-ifs.frm } _________________________________________________________________ Hotmail & Messenger are available on your phone. Try now. http://go.microsoft.com/?linkid=9724461

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FOTD 21-04-10 (Fractalized Ash [?])
by Jim Muth 20 Apr '10

20 Apr '10

FOTD -- April 21, 2010 (Rating ?) Fractal visionaries and enthusiasts: I might have been thinking of the current volcano excitement when I named today's image "Fractalized Ash". The image pictures a foreground haze through which a nearly-obscured quadratic minibrot can vaguely be made out. My first impression is that the starting point of 0,0 is not a critical point of this formula, but I have never been able to actually track down one of these background minibrots by changing the starting point. Doing so merely makes all traces of the obscured minibrot vanish from sight. The parent fractal appears as a slightly distorted and not quite critical Mandelbrot set with a tiny bit of chaotic debris at the center of the main bay. Today's scene is located in this debris. Curiously enough, other smaller minibrots are scattered all through the debris filling the image, and surprisingly, these minibrots are variations of the cubic. I rated the entire scene at a question mark. Almost all of the value is in the mathematical aspect; very little value is in the artistic. The calculation time of 5-1/3 minutes might be more than the image is worth, but it is still interesting to watch the scene unfold as the hidden minibrot gradually appears. If appearing minibrots are not all that exciting, any remaining curiosity may be quickly satisfied by visiting the FOTD web site at: <http://www.Nahee.com/FOTD/> and viewing the finished image there. Tuesday brought a repeat of Monday's weather to Fractal Central here in Central Pennsylvania. The sun was bright, the tempera- ture reached 66F 19C, and the fractal cats were as happy as cats can be, though I'm not quite sure how happy that might be. My day was average, which might or might not be boring. The next FOTD will be posted in 24 hours. It's sure to be a good one. Until then, take care, and if Santa Claus exists only in the mind, what then is Santa made of? (If anyone says thought, I will simply ask what is thought made of.) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fractalized_Ash { ; time=0:05:22.41-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinalDivideBrot function=recip passes=1 center-mag=-0.1736589885/+0.0014729311/81042.99/1/\ 2.5/0 params=3/-10/1000/0 float=y maxiter=15000 inside=0 logmap=42 periodicity=6 colors=000zYAvYArYBmYBhYBcYBZYBUYBPYBKYBFYBAYB6YC6\ YC6YC6YC6YC6YC6YC6YC7YC7YC7YD7YD7YD7YD7YD7YD7YD8YD\ 8YD8YD8YE8YE8YE8YE8YE8YE8YE9YE9YE9YE9YF9YF9YF9YF9Y\ F9YF9YFAYFAYFAYFAYGAYGAYGAYGAYGAYGBYGBYGBYGBYGBYHB\ YHBYHBYHBYHBYHCYHCYHCYHCYHCYHCXICXICXICXIDXIDXIDXI\ DXIDXIDXIDXJDXJDXJDXJEXJEXJEXJEXJEXJEXJEXKEXKEXKFX\ KFXKFXKFXKFXKFXKFXKFXLFXLFXLGXLGXLGXLGXLGXLGXLGXLG\ XMGXMGXMHXMHXMHXMHXMHXMHXMHXMHXNHXNIXNIXNIXNIXNIXN\ IXNIXNIXNIXOIXOJXOJXOJXOJXOJXOJXOJXOJXOJXPKXPKXPKX\ PKXPKXPKXPKXPKXPKXPKXQLXQLXQLXQLXQLXQLXQLXQLXQLXQN\ ULMVNMWOLXQLXRKYSKZUJZVJ_WI`YI`ZHa_HbaGbbGccFdeFef\ EegEfiDgjDgzChzCizBizBjzAkz9jzAkzAkzAkzAkzAkzAkzAk\ zAkzAkzAkzAkzAkzAkzAlzAlzAlzAlzAzzAzzAzzAzzAzzAzzA\ zzAzzAzzBzzBzzBzzBzzBzzBzzBzzBzzBzzBzzBzzBzzBzz4zz\ 4zz3zz3zz3zz3zz3zz2zz3zz3zz3zz3zz3zz3zz3zz3zz3zz4z\ z4zz4zz4zz4zz4zz4zz4zz4zz } frm:FinalDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1)+0.00000000000000000001: z=(-b)*(z*z*fn1(z^(a)+b))-c |z| < esc } END PARAMETER FILE=========================================

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Mr. Fatso Brot
by Roger Alexander 20 Apr '10

20 Apr '10

Argggghh! My last post didn't have a subject line and that messes things up a bit. Proof read everything,checked my spelling, checked my url, checked email formatting, it still got thru. I proof read as badly as a drunken leprechaun with myopia. Leprechaun? Yes everone knows leprechauns can't read English. Last week I posted a mutant big headed minibrot. Now it's an obese waddler of a minibrot. Indeed I call him Mr. Fatso Brot. Go to http://maxitersfractalfollies.blogspot.com to see the finished product. fract042.gif { ; Mr. Fatsobrot ; blank ; calctime 0:00:50.22 ; created Apr 19, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_t.frm formulaname=tangent_rjr function=sinh center-mag=-0.1602/-0.0628247/0.8503401 params=0/0/0/0 float=y maxiter=1500 inside=0 colors=00000000100300400600800900B00C00E00G00H00J00K00M00O00P00R00T00U00\ W00X00Z00`00a00c00d00f00h00i00k00m01m03m04n06n07o09o0Ao0Cp0Ep0Fq0Hq0Iq0K\ r0Lr0Ns0Ps0Qs0St0Tt0Vu0Wu0Yu0Zv0`v0bw0cw0ew0fx0hx0iy0ky0mz1mz3mz5nz7nz9o\ zBozDozFpzHpzJqzLqzNqzPrzRrzTszVszXszZtz`tzbuzduzfuzhvzjvzlwznwzpwzrxztx\ zvyzxyzzzzyzzxzzwzzuzztzzszzqzzpzzozzmzzlzzkzzizzhzzgzzezzdzzczzbzz`zz_z\ zZzzXzzWzzVzzTzzSzzRzzPzzOzzNzzLzzKzzJzzIzzGzzFzzEzzCzzBzzAzz8zz7zz6zz4z\ z3zz2zz0zz0yz0xz0wz0uz0tz0sz0qz0pz0oz0mz0lz0kz0iz0hz0gz0ez0dz0cz0bz0`z0_\ z0Zz0Xz0Wz0Vz0Tz0Sz0Rz0Pz0Oz0Nz0Lz0Kz0Jz0Iz0Gz0Fz0Ez0Cz0Bz0Az08z07z06z04\ z03z02z00z00y00x00w00v00u00t00s00r00q00p00o00n00m00l00k00j00i00h00g00f00\ e00d00c00b00a00`00_00Z00Y00X00W00V00U00T00S00R00Q00P00O00N00M00L00K00J00\ I00H00G00F00E00D00C00B00A009008007006005004003002000000 } tangent_rjr {; Scientific American puzzle. z=pixel c=pixel: z=z*fn1(z)+c+p1 |z| <=4+p2 ;SOURCE: crocker.frm } _________________________________________________________________ Got a phone? Get Hotmail & Messenger for mobile! http://go.microsoft.com/?linkid=9724464

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Re: [Fractint] (no subject) (Roger Alexander)
by JackOfTradeZ＠comcast.net 19 Apr '10

19 Apr '10

. fract031.gif WTF ?!? I can't do anything with it. Zooming in loox exactly the same (hey - ain't that a REAL fractal??), 3D and RDS give nothing. However, zoom OUT a bit and you are floating in the asteroid belt with collision imminent! It does sound cool when run thru AudioPaint though ...... .

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FOTD 20-04-10 (Eight Times Around [7])
by Jim Muth 19 Apr '10

19 Apr '10

FOTD -- April 20, 2010 (Rating 7) Fractal visionaries and enthusiasts: Today's image is named "Eight Times Around" I gave it this name because the elements surrounding the central minibrot are indeed arranged in the expected grouping of multiples of 2, which after all is not so surprising. I rated the image at a 7, which is somewhat above average, though not exceptionally so. The parent fractal can be described as vaguely resembling a classic Mandelbrot set, even though it has no East Valley and no negative spike. It does have lots of chaos on its eastern side however, and today's image is located in this chaos. The image is notable for the chaos in the background. Actually however, this chaos is not total. When it is enlarged, some degree of order does appear in certain places. The calculation time of 1-1/2 minutes is appropriately brief. Equally brief is the trip to the FOTD web site at: <http://www.Nahee.com/FOTD/> where the completed image is or soon will be posted. Except for a slight chill in the air, Monday was a near perfect day here at Fractal Central. The Kodachrome blue of the sky was emphasized by a scattering of puffy white decorator clouds of the cumulus variety, while the temperature hovered around 64F 18C and the fractal cats sat on their shelf, wishing they could go out. My day, as well as FL's day was slightly slow, though still busy enough to keep boredom at bay. And at lunch, I wisely avoided getting drawn into another philosophical discussion about a ques- tion that cannot possibly be answered. The next FOTD will be posted in a brief 24 hours. Until then, take care, and what kind of good luck has fate sent your way today? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Eight_Times_Around { ; time=0:01:29.80-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinalDivideBrot function=recip passes=1 center-mag=+0.8072128463303313/+0.0009535175175191\ /1.919037e+008/1/-69/0 params=1.2/1.1/100/0 float=y maxiter=1600 inside=0 logmap=82 periodicity=6 colors=000GAcB8g7AjBJlEPnIXpLfrOptazz_uzYnzWhtUboS\ YjQTeOP`MNYKNWKLUKJSKHQKFOKDMKDKKDKFDKJDKNDKRDKVDK\ ZDKbDLfDHjDEzzzzzBzwAzp9zfEzXJvTOuOStNStNStMSsMSsL\ SsLSsLSoKTkKUgJVcJW_IXWIYSHZPH_MZjP`gRbdTcbWe_YfY_\ zVazTYhPVzLSfIPeEMzAJc7Gb3Dz0IY7NpDSQzXMzaIzfEzjBz\ aJzUQzMXzEczDWzCPzBIzBBzBCzBCzBDzBDzBDzRWzU_zXbzZf\ zaizdmzfpzitzkwzlszmoznkzogzsJzpczq_zhQzjRzkSzlTzm\ UzoVzpWzqXzrOzrRzrTzrVzCyzJtzPpzVlz`hzfdzl`zgnzjiz\ mezp`zpYzqXzqXzqXzrXzrXzrXzNMzSOzXQz`RzeTziUznWzmP\ znRzoTzpUzqWzBCzIFzOIzULz`OzfRzlUz_SzfUzlWzalzdizg\ fzjdzmazpZzj5zmFzpOzfFzhIziKzkMzlOznRzoTzqVzDDzOIz\ YNzhSzHzzJGzPJzVMz`PzfSzlVzoTzDUzRVzdWzgczibzjazl`\ zm_znZzpYzqXzLIzXNzgSzIGzQKzXNzdRzkUz2lzegzjczn_zA\ EzGHzMJzRMzXOzbQzgTzmVzkCzmIzoNzqSz4xzFrzPlzZgzhaz\ M8zXHzgPzR5z`FziOzbRzeSzgTziUzlVznWzpXzTZz_YzeYzlX\ zBAzXMzzEzvOz07zJGzPDzKBz } frm:FinalDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1)+0.00000000000000000001: z=(-b)*(z*z*fn1(z^(a)+b))-c |z| < esc } END PARAMETER FILE=========================================

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FOTD 19-04-10 (Things and Things [6])
by Jim Muth 18 Apr '10

18 Apr '10

FOTD -- April 19, 2010 (Rating 6) Fractal visionaries and enthusiasts: Today's image came about when I entered whimsically chosen values into the MandAutoCritInZ formula If something looks wrong with the image, it's no illusion. Some- thing actually is wrong with it. The image does not exist. It has been evaporated and a ghostly pseudo-image substituted in its place. The entire scene consists of trapped 'inside' points made visible by the active 'bof61' inside fill, which I think colors the points according to the number of the iteration that brings the points closest to the origin of the parent. I don't know how close the closest point in today's image comes to the 0,0 origin point of the parent, but the real value of the scene's location is around -962, with an imaginary value around 25. By defining another point as the origin of the parent, I could probably get a totally different image, but this is some- thing I'll try on another day. As is apparent from the coordinates, the parent fractal is grossly enlarged. With its bays, buds and chaos, it vaguely resembles a Mandelbrot set, but there the resemblance ends. Today's parent fractal is near 1000 times the size of the classic M-set, and the amount of chaotic debris around it is vastly increased. Today's scene is located in the debris on the western extremity of the parent. The image shows a curious pattern, which for a change, is in no way associated with a minibrot. The coloring is entirely created by the bof61 inside fill. The other non-flat inside fills make other images of this same scene, though none equal the image created by the bof61 fill. I rated the image at a 6 because I feel it falls short of the past few days' FOTD images. The name "Things and Things" is a spoof on the name of one of those trendy but nearly useless 'gift' shops that just opened in town. The calculation time of under 5 minutes will bring some relief to the yearning fractal heart. Even more relief may be found on the FOTD web site at: <http://www.Nahee.com/FOTD/> where the finished image is or soon will be posted. Sunday was hardly spring-like here at Fractal Central. The heavy clouds, brisk winds and temperature of 50F 10C made it feel more like November than April. The fractal cats were slightly chilly in the morning, but started chasing one another up and down the long hallway around lunch time, and then seemed content for the rest of the day. Meanwhile, my day was average. The next FOTD will be posted in 24 hours. Until then, take care, and if God is imaginary, then he must exist as a model in the minds of those who believe. The question is 'how real are things that exist as models in the mind'. Quantum physicists tell us that our concept of atoms is basically a mental model, and I see no one questioning the existence of atoms. (Hmmm, do I see a spate of philosophizing about God starting to build?) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Things_and_Things { ; time=0:04:53.72-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=t center-mag=-961.6751970513/+25.4920570168/62563/1/\ -5/0 params=-1.75/-1.01/-0.175/-11.1/0/1e+100/0/0 float=y maxiter=1600 inside=bof61 periodicity=6 colors=0008Xm9WmA`mAasBdzCguCnzDjzEtzEnzFxzGyzGzzM\ zzRLOW3GT6IR8KPBLNDNLGPJIQGLSENUCQVASX8VZ6X_9_bCbe\ FdhHgkKinNlqPntMlqKjnIhkGfhEdeCbbA`_8ZX6XU8US9SQBP\ OCNMELLNFUHGHIDFKBEL9CN6AO48P27IIDCYJ6mO9jMCgKEeIH\ bGK`EMYDPVBST9UQ7XO5_L3aJ2dH8gGEjEKmDQpCWlFYiIZfK`\ cNa`QcXSdUVfRXgO_iLbjHdlEgmBjo8lp5or2qs4no6ll7ii9g\ fBdcCb`E_YjeWjcXj`YjYYjWZjT_jR_jO`jMajJajGbjEcjBcj\ 9dj6ej4el8emCenGeoKepOeqSerVetZeubevfewjexneyrezue\ xqbvm_tjXsfUqbRo_OmWLlSIjPFhLCfH9eE6bC9ZACW8ES6HP4\ KL2NI1PN3XS4dX5la6tdFpfOmhXjjeflncnw`jsagpacma`jaX\ gaUdaTebSebRebQecPecOecMhYNecNchOanO_sOYxcccLWvKVu\ JUuITtHSs8ZzGRsVGtOJlHLdANXMSOXWGUXJSYLQYNNZPLZRJ_\ TRF_H_VaCq7tRp7aqB`rF_sJZsMZtQYuUXuXXCcdBbcBacB_cA\ ZbAYb9Xa9Wa9Ua8T`8S`7R_7Q_7P_7QY7RX7SW7TV7UU7VT7WS\ 7XR7YQ7ZP7_O7`M7aL7bK7cJ7dI7eH7fG7gF7hE7iD7jCCiDGh\ EKhFOgGTfHXfI`eJddKUKUlYF } 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 subject)
by Roger Alexander 18 Apr '10

18 Apr '10

Todays fractal is not pretty,it's a graphic demonstration of chaos.It looks like a picture of true noise. It has no discernible structure or patten. It is the characteristic of the ziggidy-zaggidy sensitivity of chaotic processes to initial conditions taken to the extreme. The algorithm that produces the convuluted outline of the mandelbrot set, so serpentine that an object with finite area has an infinitely long boundary,is outdone by this process which apparently produces pure randomness. Go to http://maxitersfractalfollies.blogspot.com to see it already made. Roger Alexander fract031.gif { ; White noise! ; Now this is chaos. ; calctime 0:44:24.72 ; created Apr 17, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_num.frm formulaname=9jRoger function=cotanh/cos center-mag=0.0481928/1.38778e-016/7.304324 params=0.7061983092745751/-0.5189672536393323/-0.7412030396435438/1.4590\ 5941953795 float=y maxiter=1500 inside=0 periodicity=0 colors=00000000000000011111111111122222222222233333333333344444444444455\ 5555555555666666666666777777777777888888888888999999999999AAAAAAAAAAAABB\ BBBBBBBBBBCCCCCCCCCCCCDDDDDDDDDDDDEEEEEEEEEEEEFFFFFFFFFFFFGGGGGGGGGGGGHH\ HHHHHHHHHHIIIIIIIIIIIIJJJJJJJJJJJJKKKKKKKKKKKKLLLLLLLLLLLLLLLMMMMMMMMMMM\ MNNNNNNNNNNNNOOOOOOOOOOOOPPPPPPPPPPPPQQQQQQQQQQQQRRRRRRRRRRRRSSSSSSSSSSS\ STTTTTTTTTTTTUUUUUUUUUUUUVVVVVVVVVVVVWWWWWWWWWWWWXXXXXXXXXXXXYYYYYYYYYYY\ YZZZZZZZZZZZZ____________````````````aaaaaaaaaaaabbbbbbbbbbbbccccccccccc\ cddddddddddddeeeeeeeeeeeeeeeffffffffffffgggggggggggghhhhhhhhhhhhiiiiiiii\ iiiijjjjjjjjjjjjkkkkkkkkkkkkllllllllllllmmmmmmmmmmmmnnnnnnnnnnnnoooooooo\ ooooppppppppppppqqqqqqqqqqqqrrrrrrrrrrrrssssssssssssttttttttttttuuuuuuuu\ uuuuvvvvvvvvvvvvwwwwwwwwwwwwxxxxxxxxxxxxyyyyyyyyyyyyzzz } 9jRoger { z=pixel: z=(p2*fn2(z)+z)*z/(fn1(z)+p1)*p2, |z|<=4 ;SOURCE: my_frms.frm } _________________________________________________________________ Hotmail & Messenger. Get them on your phone now. http://go.microsoft.com/?linkid=9724463

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FOTD 18-04-10 (Green Conflagration [8])
by Jim Muth 18 Apr '10

18 Apr '10

FOTD -- April 18, 2010 (Rating 8) Fractal visionaries and enthusiasts: Due to an unsurprising antiquing expedition, today's image is a little late, but it rates another eight, and as long as I can keep these eights coming, the results will be worth the effort. The parent fractal of today's image begins in its East Valley area as a Mandelbrot set. But as we advance westward, things start getting progressively more wrong. To begin, the main bud is far too large. In fact, it's larger than the main bay itself. And the second bud is no longer a single bud. It has split into two parts. Finally, to make things even worse, instead of a single straight negative spike, we have two curved filaments, one shooting out, curving toward the north-northwest, the other toward the south-southwest. Today's image lies on the west side of the northern branch of the valley separating the oversized main bud from the split second bud. The overall pattern resembles the stuff found in Scepter Valley, but nothing like those open, chaos-filled holes can be found in the true Scepter Valley. The rating of an 8 reflects my opinion of the image. The name "Green Conflagration" refers to the strong emerald green areas surrounding the beige central pattern. The calculation time of under 7 minutes might be considered slow by the more impatient fractalists. The way to avoid this minor delay is to surf out to the FOTD web site at: <http://www.Nahee.com/FOTD/> and view the finished image there. Saturday turned most un-springlike here at Fractal Central, with heavy clouds hanging overhead all day, occasional sprinkles of rain, a biting northwest wind and a temperature of 48F +9C. The fractal cats slept through it. My day was busy but otherwise not too bad. The next FOTD will be posted in 12 hours. That's not a promise, but far more likely than not. Until next FOTD, take care, and would the real truth please stand up. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= GreenConflagration { ; time=0:06:56.01-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinalDivideBrot function=recip passes=1 center-mag=-4.426676332106418/+0.483618434342954/\ 709845.2/1/-37.5/0 params=0.8/2/84/0 float=y maxiter=7500 inside=0 logmap=244 periodicity=6 colors=000KGAKHAKIAKJAKKAKLAKNAKPAMUAOZAQcASh9Um6Z\ r3cv0hz5mzArzFvzKzzPzzUzzZzzczzhzzmzzrzzvzzzEMIEQC\ FTEFVGGYHG_JGbLHdMHgOIiPIlRInTJqUJsWJuXKsTKrPKqMKp\ IKnEKmBKl7Kk4Ji5Ig5He5Gc5Fa5E_5DY5CW5BU5EUAHUEKUIN\ UNPURSUVVU_YUc_UgbUleUphUtjUxiWwiYvh_uhathcsgerggq\ fipfkoflnhioifokcpl`pmYqoVqpSrqPrsMstJsuGtwDtxAuy8\ usJknUaoVdpWgpXiqYlqZnp_lp`koajobiochndgnefmfemgdm\ hclibljakk`kl_klZjjYihXhgXgeWgdVfbVeaUd_TcZTcXSbWR\ aUR`TQ_RP_QPVUSRYVM`XId_Dhb9kd8ig7gi6el5cn4aq3_s2Y\ u4Xs6Wq8VpAUnBUlDTkFSiHRgIRfHUaGXYFZTzaPzcLzbKzaKz\ `Kz_KzZKzYKzXKzWKzVKzUKzTKzSKzRKzTIzVzzXzzZzz`zzbz\ zdzzfzzhzzjzzlzznzzozzqzztzzwzzzzzzBzzCzzDzzEzzFzz\ GzzHzzIzzzzzzzzzzzzzzzzzzzzzzzzzzdzzgzzjzzmzzozzgz\ z`zzR8zH9z7Gz5Nz4Uz3`z2fz1_zdgzeozfnz_mzTlzMkzFjz8\ fzBbzEZzHVzKRzNNzPJzSFzVBzY7z`4zb5zb5zc6zc7zd7zd8z\ e8ze9zdAzcBzbCzaDz`Ez_EzZ } frm:FinalDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1)+0.00000000000000000001: z=(-b)*(z*z*fn1(z^(a)+b))-c |z| < esc } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD for 4/17/10
by Brian Prentice 17 Apr '10

17 Apr '10

Very beautiful fractal Jim, but believing in 256 colors is like believing in an imaginary friend called God. Brian Prentice

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Metallic Spiral
by Roger Alexander 16 Apr '10

16 Apr '10

No chaos in this spiral! Today's fractal is an example of a repetitive regimented self-similarity. Note that banding was caused by a high outside=fmod proximity value-0.5. To see it pre-rendered go to http://maxitersfractalfollies.blogspot.com And now for the numbers. fract027.gif { ; metallic spiral ; blank ; calctime 0:11:37.21 ; created Apr 16, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_k.frm formulaname=kg2204 function=cosh/tanh center-mag=0.28035/-1.17195/13.33333 params=-0.6006347849971008/-0.3339030121768853/0.5191503646961882/0.1598\ 254341257973 float=y maxiter=1500 inside=0 proximity=0.5 outside=fmod colors=000111333444666777999AAACCCDDDFFFHHHIIIJJJLLLMMMOOOPPPRRRSSSUUUVV\ VWWWYYYZZZ___```bbbcccdddeeefffhhhiiijjjkkklllmmmnnnoooppppppqqqrrrsssss\ stttuuuuuuvvvwwwwwwxxxxxxxxxyyyyyyyyyzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzyyyyyyyyyxxxxxxxxxwwwwwwvvvuuuuuutttssssssrrrqqqppppppooonnnmmmlllkk\ kjjjiiihhhfffeeedddcccbbb```___ZZZYYYWWWVVVUUUSSSRRRPPPOOOMMMLLLJJJIIIHH\ HFFFDDDCCCAAA999777666444333111000111333444666777999AAACCCDDDFFFHHHIIIJJ\ JLLLMMMOOOPPPRRRSSSUUUVVVWWWYYYZZZ___```bbbcccdddeeefffhhhiiijjjkkklllmm\ mnnnoooppppppqqqrrrsssssstttuuuuuuvvvwwwwwwxxxxxxxxxyyyyyyyyyzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzyyyyyyyyyxxxxxxxxxwwwwwwvvvuuuuuutttssssssrr\ rqqqppppppooonnnmmmlllkkkjjjiiihhhfffeeedddcccbbb```___ZZZYYYWWWVVVUUUSS\ SRRRPPPOOOMMMLLLJJJIIIHHHFFFDDDCCCAAA999777666444333111 } frm:kg2204 { z=pixel^p1: z=fn1(z)/p1 ^ fn2(z)^p2 + c |z| <= p2 ;SOURCE: kg22.frm } -Max Iter _________________________________________________________________ Hotmail & Messenger are available on your phone. Try now. http://go.microsoft.com/?linkid=9724461

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FOTD 17-04-10 (Deep in the Grove [8])
by Jim Muth 16 Apr '10

16 Apr '10

FOTD -- April 17, 2010 (Rating 8) Fractal visionaries and enthusiasts: Today's image will get little description. It needs to be seen to be appreciated fully. The parent fractal is little more than a Mandeloid shaped like a letter V turned on its left side. A rudimentary East Valley lies at the apex of the parent, with today's image located a short distance east of this tiny valley. I rated the image at an 8, one full point of which is due to my coloring efforts. I worked on the colors for almost an hour before I somehow managed to virtually eliminate all traces of the color-band boundaries. It is possible to make 256 colors look like 16-million, but it takes some doing and not all fractals can be colored this smoothly. (I wonder whether the same degree of smoothness will appear on differently adjusted monitors.) The name "Deep in the Grove" was the first thing that came to mind when I saw the finished product. If it ever meant any- thing, the meaning is now totally forgotten. The calculation time of 5-3/4 minutes is about what the image is worth. The trip to the FOTD web site at: <http://www.Nahee.com/FOTD/> will be quicker, but the fun of watching the image come to life will be lost. Friday was very pleasant here at Fractal Central, with partly cloudy skies and a temperature of 79F 26C. It stayed pleasant until 6pm, when a thunder-shower moved in from the west and spoiled the evening. The fractal cats were unconcerned through all of it. They have no interest in the sun when it's warm, and the thunder was not too loud. My day was average, which is all one could hope for. If no big antiquing expedition comes up on Saturday, the next FOTD will be posted in 24 hours. Until next time, whenever that may be, take care, speak loudly and carry a small stick. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Deep_in_the_Grove { ; time=0:05:45.00-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinalDivideBrot function=recip center-mag=+0.9954559592171935/+0.0689868608057073\ /1355256/1/16/0 params=1/1/1000/0 float=y maxiter=3200 inside=0 logmap=800 periodicity=no colors=000AAzAAyAAyAAxAAyAAx9Ax9Az8Aw8By7Cx7Dv6Ev5\ Fu5Gv4Ht4It3Js3Ks2Ir2Kp2Ko2Ko1Kn2Kn2Km2Kl3Kk3Kj3Ki\ 4Kh4Jg4If5He5Gd5Fc5Eb6Da6C`6B_7AZ79Y78X87W86V85U84\ T77S7AR7DR6FR6IR6LR5NR5QR5TS4VS4YS4`S3bS3eS3hS3jS6\ fWMgaJhfGikDjpAltCnqDloFimGfkIdiJagLZeMWcOTaPR_ROY\ SLWUIUWGSZFP`FNcDKeDIgCGjCDlBBoB8qA6rA4oD5mG6jJ6hL\ 7eO7dR8bU8aW9_Z9ZaAYcA_aEa`Ib_LcZPcYScaWce_cicdmgd\ pj3sM6hV9YcBNlFOiIPfMPcPQ`TRYWRV_SSbTPfTMiUJlUHhQH\ dMHaIHYFHUBHR7HN3HPPHUUEccCrmczzcrmcgc7LK8NN8PQ9RS\ 9TV9VYAQFgyO2ZhLSTO3jw8anDUfIMYJKrKIjLHcMFXthQk`Qb\ TQULQP_UQipPaiOUbNMWzeblWYZNU`ywXmnTafPQYoGugFm`Fe\ TEYoz3XaFLr3_sR3w_r9liBfaC`UYielZzjaUDV4U09Q7DMDII\ Ki8mYUaWU1Tc8RuE8zRDzQIpQeclZcdcazmczmSzmcztczmczm\ hzzmKzmozmbzrizvvzzmzzezzYzz`zzXzzTzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzQzzQzzQzzQzzQzzQzzGzzKzzNzzzzzpzz\ gzzZzzgzzazzWzzTzzxzzozzt } frm:FinalDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1)+0.00000000000000000001: z=(-b)*(z*z*fn1(z^(a)+b))-c |z| < esc } END PARAMETER FILE=========================================

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Artificial and Natural
by Roger Alexander 15 Apr '10

15 Apr '10

Again two examples of the chaotic algorithm. The first parallels the iconic regularity of the artificial. The second is almost reminscent of the decay of a rusting surface. To see them precaculated go to http://maxitersfractalfollies.blogspot.com fract024.gif { ; almost thread like ; blank ; calctime 1:01:49.76 ; created Apr 15, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=manfn+zsqrd function=sin center-mag=-0.36468255615460130/+0.67351854481612020/42582.25/1/45/3.885\ 78058618804789e-016 params=-0.4700766014587848/-0.1722769859920041 initorbit=0.2/0.1 float=y maxiter=1500 inside=0 logmap=157 colors=atubuvcwwdxxfzzfzzeyydyydxxcwxbvwavwauv`tv_tuZsuYrtYqtXqsWpsVorVo\ rUnqTmpSlpRloRkoQjnPjnOimOhmNglMglLfkLekKejJdjIciHbhHbhGagF`gE`fE_fDZeCY\ eBYdAXdAWc9Wc8Vb7Ub7Ta6Ta5S`4R_3Q_2PZ2PZ1OY0NX1NX2OY3PY4QZ5R_6R_7S`8Ta9U\ aAVbCWcDXcEYdFZeG_eH_fI`gJagKbhLciMdiNejOfkPgkQhlRhmSimTjnUkoVloXmpYnqZo\ q_pr`qsaqsbrtcsudtueuvfvwgwxhxxiyykzzjyyixyhwxgwxfvweuvdtvcsubrtart`qs_p\ sZorYnqXmqWmpVloUkoTjnSinRhmQhlPglOfkNekMdjLciKciJbhIagH`gG_fFZfEZeDYdCX\ dBWcAVb9Ub8Ua7Ta6S`5R`4R_3QZ2PZ1OY0NX1NX2OY3PY4QZ5R_6S`7T`8Ua9VbAWcBXcCY\ dDZeE_fF`fGagHbhJciKdiLejMfkNglOhlPimQjnRkoSloTmpUnqVorWprXqsYrtZsu_tu`u\ vavwbwxcxxbwxavw`uvZtuYrtXqtWpsUorTnqSmpRkoPjnOimNhmMglKfkJdjIciHbhFagE`\ fD_fCYeAXd9Wc8Vb7Ta5S`4R_3QZ2PY0NX1OX2PY3QZ4RZ6S_7T`8Ua9VbAXbBYcDZdE_eF`\ fGafHbgIchKdiLejMfjNgkOhlPimRjnSlnTmoUnpVoqWprYqrZrs_st } fract026.gif { ;rust,decay ; blank ; calctime 1:22:50.31 ; created Apr 15, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=fotdv1.frm formulaname=ObliqueManPlus center-mag=-0.95057196187760430/+0.51508616539401110/73035.15 params=0/0/1/1/1/1 float=y maxiter=1500 inside=0 colors=000000000000000000000000000000000100100200400500700900B00D00G00I0\ 0L00O10Q10T10W10Z10a10e10h20k20o20r20v20y20z30z50z60z80z90zB0zC0zE0zF0zH\ 0zI0zK0zL0zN0zO0zQ0zR0zT0zU0zW0zX0zZ0z_0za0zb0zd0ze0zg0zh0zj0zk0zm0zn0zp\ 0zq0zs0zt0zv0zw0zy0zz1zz3zz4zz6zz7zz7zy7zx7zx7zw7zv7zv7zu7yt7ys7ys7yr7yq\ 6yq6yp6yo6yo6xn6xm6xl6xl6xk6xj6xj6xi5xh5wh5wg5wf5we5we5wd5wc5wc5vb5va5va\ 5v`4v_4vZ4vZ4vY4vX4uX4uW4uV4uV4uU4uT4uS3uS3uR3tQ3tQ3tP3tO3tO3tN3tM3tL3sL\ 3sK3sJ2sJ2sI2sH2sH2sG2sF2rE2rE2rD2rC2rC2rB1rA1rA1r91q81q71q71q61q51q51q4\ 1q31p20p20o20n20m20m20l20k20j20j20i20h20g20g20f20e20d20d20c20b20a20a20`2\ 0_20Z20Z20Y20X20W20W20V20U20T20T20S20R20Q20Q20P20O20N20N20M20L20K20K20J2\ 0I20H20H20G20F20E20E20E20D20D20C20C20C20B20B20A20A20A2092092092082082072\ 0720720620620520520520420420420320320220220220120120010 } frm:ObliqueManPlus {;Jim Muth z=(p1+pixel), c=p2+(p3*pixel): z=sqr(z)+c, |z| <=100 } _________________________________________________________________ Videos that have everyone talking! Now also in HD! http://go.microsoft.com/?linkid=9724465

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FOTD 16-04-10 (In a Lost Valley [8])
by Jim Muth 15 Apr '10

15 Apr '10

FOTD -- April 16, 2010 (Rating 8) Fractal visionaries and enthusiasts: I gave today's image a rating of 8, which might be a bit liberal. I chose the rating because I kind of enjoy the coloring, and I did most of it myself with only minor help from the program. And then I named the image "In a Lost Valley". The reason for the name will be obvious once the exact location of today's image is seen in its parent fractal. This parent fractal came about when I entered some whimsical values into the MandAutoCritInZ formula. It is little more than scattered bits and pieces of assorted Mandeloid stuff surrounded by disconnected tiny Mandelbrot sets. Today's image is located in the west branch of the valley separating the two largest bays. Since the valley is not really a true one, but a random point of connection between two independent but overlapping Mandeloids, one might consider the valley to be 'lost', which explains the name. The calculation time of 4-1/4 minutes is fair enough for today's image. I leave it to the intrepid fractalist to decide whether the finished image is worth the effort. The way to avoid all this concern about value is by zooming out to the FOTD web site at: <http://www.Nahee.com/FOTD/> and viewing the already-calculated image posted there. A really great day passed unappreciated here at Fractal Central on Thursday, as the sun shone brilliantly and the temperature reached 75F 24C. I was busy working most of the time, while the fractal cats were busy keeping watch on the stray cats that for some reason were quite numerous in the back yard. FL spent most of the time thinking about this year's fractal garden. If all goes well, and I can see no reason why it should not, the next FOTD will be posted in 24 hours. Until then, take care, and perhaps God is what remains when everything vanishes and then even the empty space vanishes. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= In_a_Lost_Valley { ; time=0:04:14.45-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident float=y center-mag=+1.25998949311965/-0.9848802720117678/\ 112937.2/1/120/0 params=0.35/-2.2/-0.35/2.2/0/0/0/0 maxiter=2500 inside=0 logmap=284 periodicity=6 colors=000AJVALWANYAP_9Rb9Te9Vh9Xk8_n8aqBctFhwKmzP\ rzUvzZzzczzhzzmzzrzzvzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzze8Sg9Qi9Ok9Mm9Ko9Iq9GcjUkSMs9FpHMmPTkWZhcefrlfj\ kfckfWkfPkfHkfAkf3kXOeIijNh_RhQVgFZg5Ui7Pk9LlBGnDB\ pFYr``q_cpYeoXhnWjnVgmTelSckQ`jPZiNXhMUgKSfJQeINdG\ LcFJbDGaCE`AC_9A_8MW7XT7_Q6aN6dL6fI5hG5kD5mA4p84r5\ 4t34k74cA4VD4NG4th7ogCkfHgeMceRZdWVc`RbeNbijhmfgha\ gdXg`TfWOfSJfOCcLFfKIhJKjJNlIQnISpHVrHYtG_vGbxFdzF\ fwEguDhrCipBjmBkkAlh9mf8mc3nd8ndCndGndLndPodTodYod\ aodeodgodinejmeklekkelkeljfmifnhfngfogfo7TQHRMQPIZ\ NFgLBpJ8mK9kK9hK9fK9dL9aL9_LAXLAVMATMAQMAOMANN7MMA\ LMCKMEJMHIMJHLLGLOFLQELSDLVCKXBKZAKa9Kc9KeBLbCM`DN\ YEOWFPTGQRHQOIRMJSJKTHLUEMVCMT5NVANWENXJNZNN_SLbYN\ `WOZVPXUQVTRTSOSOSRRVRUZRXaQZeQahQckQelOglOilPklQm\ lRolSqlTslUtlVulWvlYwl_xlaymczmczmczmczmczmczmczmc\ zmczmczmczmczmczmczmczmcz } 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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Contrasts-fire and leaves
by Roger Alexander 15 Apr '10

15 Apr '10

Apocalyptic horizon and leaves swaying in the breeze. I know my contrasts! Already made at http://maxitersfractalfollies.blogspot.com fract143.gif { ;Blast furnace horizon ; blank ; calctime ; created Apr 15, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=*.frm formulaname=pixey02 center-mag=-0.31208420982973470/+0.01301901745773627/233.4021/1/47.49999\ 99999993818/4.9655418665750517e-013 params=0.5359965819269387/-0.5064546647541734 float=y maxiter=1500 logmap=28 cyclerange=0/255 colors=000000000000000000000000000000000100100200400500700900B00D00G00I0\ 0L00O10Q10T10W10Z10a10e10h20k20o20r20v20y20z30z50z60z80z90zB0zC0zE0zF0zH\ 0zI0zK0zL0zN0zO0zQ0zR0zT0zU0zW0zX0zZ0z_0za0zb0zd0ze0zg0zh0zj0zk0zm0zn0zp\ 0zq0zs0zt0zv0zw0zy0zz1zz3zz4zz6zz7zz7zy7zx7zx7zw7zv7zv7zu7yt7ys7ys7yr7yq\ 6yq6yp6yo6yo6xn6xm6xl6xl6xk6xj6xj6xi5xh5wh5wg5wf5we5we5wd5wc5wc5vb5va5va\ 5v`4v_4vZ4vZ4vY4vX4uX4uW4uV4uV4uU4uT4uS3uS3uR3tQ3tQ3tP3tO3tO3tN3tM3tL3sL\ 3sK3sJ2sJ2sI2sH2sH2sG2sF2rE2rE2rD2rC2rC2rB1rA1rA1r91q81q71q71q61q51q51q4\ 1q31p20p20o20n20m20m20l20k20j20j20i20h20g20g20f20e20d20d20c20b20a20a20`2\ 0_20Z20Z20Y20X20W20W20V20U20T20T20S20R20Q20Q20P20O20N20N20M20L20K20K20J2\ 0I20H20H20G20F20E20E20E20D20D20C20C20C20B20B20A20A20A2092092092082082072\ 0720720620620520520520420420420320320220220220120120010 } frm:pixey02 {;Veggies z = pixel + p1, c = pixel: temp = z z = z*z + pixel + c pixel = temp z <= 4 ;SOURCE: jo_weber.frm } fract150.gif { ; blank ; blank ; calctime 0:08:38.67 ; created Apr 15, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=*.frm formulaname=penta_rjr function=sinh passes=1 center-mag=+0.48697144909233390/+0.71414316995856990/154.3672/1/30.00000\ 00000006537/-5.21221954485895367e-013 params=0.314859462263863/0.618640705587939 float=y maxiter=3200 fillcolor=44 periodicity=0 cyclerange=0/255 colors=0100200300400500700800900A00B00D00E00F00G00H00J00K00L00M00N00P00Q\ 00R00S00T00V00W00X00Y00Z00`00a00b00c00d00f00g00h00i00k00k01k02k03l04l05l\ 05m06m07m08n09n0An0Bo0Bo0Co0Dp0Ep0Fp0Gp0Hq0Hq0Iq0Jr0Kr0Lr0Ms0Ns0Ns0Ot0Pt\ 0Qt0Ru0Su0Tu0Tu0Uv0Vv0Wv0Xw0Yw0Zw0Zx0_x0`x0ay0by0cy0dz1dz1ez1ez1fz2fz2gz\ 2gz2hz3hz3iz3iz3jz4jz4kz4kz4lz5mz5mz5nz5nz6oz6oz6pz6pz7qz7qz7rz7rz8sz8sz\ 8tz8uz9uz9uz9tz9tz9tz9sz9sz8sz8rz8rz8rz8qz8qz7qz7pz7pz7oz7oz7oz6nz6nz6nz\ 6mz6mz6mz5lz5lz5lz5kz5kz5kz4jz4jz4iz4iz4iz4hz3hz3hz3gz3gz3gz3fz2fz2fz2ez\ 2ez2dz1dz1cz1bz1ay1`y1_y1_x1Zx1Yx1Xw1Ww1Vw1Uv1Uv1Tv1Su1Ru1Qu1Pt1Ot1Ot1Nt\ 1Ms1Ls1Ks1Jr1Ir1Ir1Hq1Gq1Fq1Ep1Dp1Cp1Co1Bo1Ao19n18n17n16m06l06k06j06i06h\ 06g06f05e05d05c05b05a05`05_05Z04Y04X04W04V04U04T04S04R03P03O03N03M03L03K\ 03J03I02H02G02F02E02D02C02B02A0190180170160150140130010 } frm:penta_rjr {original penta frm by Noel Griffin ;modded by Roger y2k03 ;use periodicity=no for best results z = pixel, zp =p1: temp = z z = z*z - zp zp = fn1(temp) |zp| <= 4 ;SOURCE: noel.frm } _________________________________________________________________ Live connected. Get Hotmail & Messenger on your phone. http://go.microsoft.com/?linkid=9724462

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FOTD 15-04-10 (Bubbles from the Past [8])
by Jim Muth 14 Apr '10

14 Apr '10

FOTD -- April 15, 2010 (Rating 8) Fractal visionaries and enthusiasts: Today's image is a slight revision of an image that first appeared in April, 1997, the first month of the FOTD. When I started the FOTD on the Fractal Art list, I expected to post maybe 5 or 10 images, showing that complicated formulas are not necessary for interesting fractals. Since then I have posted over 4500 fractal images, and the supply of new images is in no danger of running dry. I think today's image is the only one I have created with the formula named 'bubbles'. The formula resembles one of my MandNewt series however, so I might have simply used the same formula under a different name. Curiously, the formula has no variable parameters. Most of the interest, which is in the bubbles, was created by rendering the image with the inside set to bof60. When the dust settled, I gave the result a rating of an 8, despite the fact that it is not entirely new. The name "Bubbles from the Past" needs no explanation. The calculation time of 1-2/3 minutes will seem like 30 seconds once the bubbles start popping into view. Or, to escape the popping, the finished image is instantly available on the FOTD web site at: <http://www.Nahee.com/FOTD/> Wednesday began with fog here at Fractal Central, but a strong sun cleared away the fog by 10am, leading to a sunny day with a temperature of 66F 19C, all of which kept the fractal cats happy. My day, as well as FL's day, was happy also. The work was light and the fractal, despite its venerable age, turned out pretty good. The next FOTD, perhaps another blast from the past, will be posted in 24 hours. Until then, take care, and dream fractal dreams. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= BubblesFromThePast { ; time=0:01:40.72-SF5 on P4-2000 reset=1950 type=formula formulafile=basicer.frm formulaname=bubbles float=y center-mag=+0.26701697\ /+0.92776452/101.211/1/50/0 float=y maxiter=250 passes=1 inside=bof60 logmap=yes periodicity=0 colors=000zzzzskzl`zdUs_HpUOnPMmJLkHKjFIhDHgBGe9Fd\ 7Db5Ca3BZ4CW5CU5DR6DO6EJ7KJ7RUUtUUtUUoUUoqaapaaoba\ obanbambalcakcajcajcaidahdaafZUhVNjSFlO8nL8nN8nQ8n\ S8nZ8nc8nh8nm8mr8pv8sz8vz8tz8qz8pw8lsGhoO`iXXcdcXl\ mRzzLrmNpcQnUSkKViLXgN_ePacQdaSf_UiYWkVYnTZpR`sPbu\ U_nZWgbT_gPTlMMjPMhSMfVMdYLb`L`cL_fLYhLWkLUnLSqKQt\ KOwKMzKKxLJuMHsMGqNEnOClPBjP9hQ7eR6cS4aS3ZT1XU4ZS6\ `R9bPBdOEfMGhKJkJLmHOoFQqETsCVuBYw9_y8`t9ap9bl9chA\ ddAe`AfXAgTAhPAiLBjHBkDBk9BnKJqVRtdYrdVpeSnePlfMkf\ JifFggCeg9ch6ah3`h0Zj3Yl6Xm9VoBUpETrHSsKQuMPvP7hh6\ ce5Zb4U_3PX2KU1FR3WP5mMt8jbFeLN_LUaL_bLfdLleLsgMzi\ KveIraFnXDjTAfP8bK5ZG9aICcLGfNMTRSEVY0ZZ1Z`2Ya4Yb5\ Yd6Xe7Xa8VY9TUAQRCONDMJEKFFHBGFDJDENCGQAIT8JW6L_5M\ b3Oe1Ri9TmGWqOYuV`ybXuaUp_QlZMhYIcWF_VBVT7RS7SO6TK\ 6UH5VD5W9Cz5gOjjadhKolUnocmsmleLpeWqdfrdqsiAhn9`_J\ nUSkN`iHiffPrgctirwb9o_8n } frm:bubbles {; Jim Muth z=c=pixel: a=sqr(z)+(c-1)*z-c b=3*sqr(z)+c-1 z=z-2*a/b, .000000000000000000000000000001 <= |a| } END PARAMETER FILE=========================================

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FOTD 14-04-10 (A Plethora of Ohs [8])
by Jim Muth 14 Apr '10

14 Apr '10

FOTD -- April 14, 2010 (Rating 8) Fractal visionaries and enthusiasts: I put near an hour of effort into trying to make something of yesterday's image, and I achieved nothing. In today's case, a single strike of the <enter> key told the program to supply the coloring. Fractint did an admirable job. All I had to do was a bit of tweaking. The parent fractal, and of course the image itself, came about when I combined 7 negative parts of Z^(-1.1) with one negative part of Z^(-6.2) and added (1/C) on each iteration. This parent is a tremendously over-sized thing. Only a tiny part of it fits on the default opening screen, which has a magnitude of 0.67. Today's image is located inside a huge terminal ring far to the south-southwest of the opening screen. The rating of an 8 means I consider the image good enough to be worth 8 points. The name "A Plethora of Ohs" does not imply gasps of surprise at the sight of the finished image. It refers to the countless bright O-shaped circles scattered throughout the scene. (Actually a plethora means too much of a good thing.) The calculation time of 1-3/4 minutes is brief enough to bring impatience to no one but the most impatient. Total satisfaction for even these few may be found on the FOTD web site at: <http://www.Nahee.com/FOTD/> where the image is or soon will be posted for instant and total satisfaction. Lots of clouds were overhead here at Fractal Central on Tuesday, though the expected rain slipped by to the south. The tempera- ture of 55F 13C was a bit too chilly for the fractal cats, who actually never worry about outdoor conditions, because they never have the chance to venture outside in the first place. My day was moderately busy; Wednesday should be the same. The next FOTD will be posted in 24 hours. Until then, take care, and I have thousands of photographs of fractals, but I have yet to see a single real fractal being photographed. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Plethora_of_Ohs { ; time=0:01:44.04-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-132.269361791939/-60.73661716766502/\ 1.53313e+009/1/-86/0 params=-7/-1.1/-1/-6.2/0/0/0/0 float=y maxiter=1000 inside=0 logmap=63 periodicity=0 mathtolerance=0.05/1 colors=000AAAAABMAAAACLAAAAELAAAAGKAAFAIKBAFCLJDAH\ EOJFAJGPIHOIHUIIZIIUHIUHIUHIUHIUGIUGIUGIUGIUFIUFJU\ FJGzJcmJGAJFzJczJEzJEzJcwJDzJzCKmCKCCKCCKBBKBBKBBK\ AzcAzcAzc9zc9zz9zzzzzzzzAzzAzzAzzAzzAzzAzzAzzBzzBz\ zczzBzzczzBzzczzBzzczzBzzczzCzzczzCzzczzCzzczzCzzz\ zjCzzzziDzzzzhEzzzzgFzzzzfGzzzzeHzzzzdIzzzzcJzbKzz\ KzaLzzLzaLzzMz`MzzNz_NzzOzZOzzPzzPzXQzzQzWRzzRzzSz\ zSzzTzzTzzUzzUzzUzzVzzVzzWzzWzzXzzXzzazzYzzYzzZzzZ\ zz_zz_zz`zz`zzazzazzHzzLzzOzzSzzVzzZzzDzzEzzFzzFzz\ GzzHzzHzzIzzJzzJzzKzzLzzLzzMzzMzzNzzOzzOzzPzzQzzQz\ zRzzSzzSzzTzzUzzUzzVzzVzzWzzXzzXzzYzzZzzZzz_zz`zz`\ zzazzbzzazzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ 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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Infinite Loop Web Cast at ever smaller scales
by Paul N. Lee 14 Apr '10

14 Apr '10

Someone was doing a web cast, using a camera, a computer, and the application running live at the time. They decided to see what happens when one points the camera at the monitor during the live web cast: http://www.noob.us/humor/live-webcast-fail/ I saw some indication that this was originally from: http://www.4playerpodcast.com/ And I found another version of the same on YouTube: http://www.youtube.com/v/et_MmlTxMXA Sincerely, P.N.L. -------------------------------------- http://www.Nahee.com/PNL/Fractals.html http://www.Nahee.com/Fractals/

3 3

Tdis Coloring
by Roger Alexander 14 Apr '10

14 Apr '10

The scaly (layered?) appearance of todays fractals is the result of the outside=tdis combined with high bailout values. According to the Fractint manual tdis "colors the pixels according to the total distance traveled by the orbit." In these two formulas the bailout value can be directly inputed. Other formulas can be rewritten to allow the user to select the bailout values. The value of bailout that produces a desired effect varies with the formula and determined by experiment ( also known as taking a blind guess). This method does't work all time but often enough to give it a try. And as a no strings attached bonus is an Apr.11 gif resized then resampled. fract018.gif { ; leafy scales ; blank ; calctime 0:06:37.18 ; created Apr 13, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_m.frm formulaname=magnet_spirals1 center-mag=1.32164/-0.780518/13.84275/1/144.999999999999972/7.6716411001\ 5983169e-014 params=-0.1222876674703207/0.8740195928830836/700/700 float=y maxiter=1500 inside=0 outside=tdis colors=0000z00z00y00y00y00y00x00x00x00x00w00w00w00w00v00v00v00v00u00u00u\ 00u00t00t00t00t00s00s00s00s00r00r00r00r00q00q00q00q00p00p00p00p00o00o00o\ 00o00n00n00n00n00m00m00m00m00l00l00l00l00k00k00k00k00j00j00j00j00i00i00i\ 00i00h00h00h00h00g00g00g00g00f00f00f00f00e00e00e00e00d00d00d00d00c00c00c\ 00c00b00b00b00b00a00a00a00a00`00`00`00`00_00_00_00_00Z00Z00Z00Z00Y00Y00Y\ 00Y00X00X00X00X00W00W00W00W00V00V00V00V00U00U00U00U00T00T00T00T00S00S00S\ 00S00R00R00R00R00Q00Q00Q00Q00P00P00P00P00O00O00O00O00N00N00N00N00M00M00M\ 00M00L00L00L00L00K00K00K00K00J00J00J00J00I00I00I00I00H00H00H00H00G00G00G\ 00G00F00F00F00F00E00E00E00E00D00D00D00D00C00C00C00C00B00B00B00B00A00A00A\ 00A009009009009008008008008007007007007006006006006005005005005004004004\ 0040030030030030020020020020010010010010000000000000000 } frm:magnet_spirals1 (XAXIS_NOIMAG) { ;needs floating point! ;p2 is the bailout (default=100) b=p2,b=b+(b==0)*100 z=c=pixel: z=( (z*z+(c)) / (2*z+(c-2)) )^2-p1 |z|<b ;SOURCE: magnet.frm } fract019.gif { ; scales ; blank ; calctime 0:06:18.38 ; created Apr 13, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_m.frm formulaname=magnet_spirals2 center-mag=-1.54459830788485500/-1.42141153923205300/201.4615 params=0.7143467513046663/-0.793206579790643/650/650 float=y maxiter=1500 inside=0 outside=tdis colors=0ZzzzWzzWzyVzyVzxUyxUywTywSyvSxvRxuRxuQxtQwtPwsOwsOwrNvrNvqMvqLvp\ LvpKuoKuoJunJunItmHtmHtlGtlGskFskEsjEsjDriDriCrhCrhBrgAqgAqf9qf9qe8pe7pd\ 7pd6pc6oc5ob5ob4oa3na3n`2n`2n_1mZ0lY0lY0lY0lY0kX0kX0kX0kX0jW0jW0jW0jW0iV\ 0iV0iV0iV0hU0hU0hU0hU0gT0gT0gT0gT0fS0fS0fS0fS0eR0eR0eR0eR0dQ0dQ0dQ0dQ0cP\ 0cP0cP0cP0bO0bO0bO0bO0aN0aN0aN0aN0`M0`M0`M0`M0_L0_L0_L0_L0ZK0ZK0ZK0ZK0YJ\ 0YJ0YJ0YJ0XI0XI0XI0XI0WH0WH0WH0WH0VG0VG0VG0VG0UF0UF0UF0UF0TE0TE0TE0TE0SD\ 0SD0SD0SD0RC0RC0RC0RC0QB0QB0QB0QB0PA0PA0PA0PA0O90O90O90O90N80N80N80N80M7\ 0M70M70M70L60L60L60L60K50K50K50K50J40J40J40J40I30I30I30I30H20H20H20H20G1\ 0G10G10G10F00F00F00F00E00E00E00E00D00D00D00D00C00C00C00C00B00B00B00B00A0\ 0A00A00A0090090090090080080080080070070070070060060060060050050050050040\ 0400400400300300300300200200200200100100100100000000000 } frm:magnet_spirals2 (XAXIS_NOIMAG) { ;needs floating point! ;p2 is the bailout (default=1000) b=p2,b=b+(b==0)*1000 z=c=pixel: z=( (z*z+(c-1)) / (c*z+(c-2)) )^2-p1 |z|<b ;SOURCE: magnet.frm } To see the fractals already generated go to http://maxitersfractalfollies.blogspot.com _________________________________________________________________ Hotmail & Messenger. Get them on your phone now. http://go.microsoft.com/?linkid=9724463

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FOTD 13-04-10 (Filamentary Network [5])
by Jim Muth 13 Apr '10

13 Apr '10

FOTD -- April 13, 2010 (Rating 5) Fractal visionaries and enthusiasts: There is no FOTD for April 12. This is because the antiquing bug struck on Sunday, and we spent the day browsing an antique emporium in Hanover, PA, the city where they make potato chips. FL found a water color of a stork nesting on a chimney top, with a cathedral tower in the background. She insisted that we must have the picture. (Actually it's not a bad picture.) Today's image however is totally middling. It takes too long to finish, and when it is finished, it doesn't quite appear to have its act together. I wasted nearly one hour on the coloring and ended up with an image that rates an everyday-average 5. The name "Filamentary Network" is a description of the image. The zig-zaggy effect throughout the scene is a bit unusual, though not enough to raise the rating above average. The parent fractal is a Mandelbrot set with its main spike starting to split apart. Today's image is located in the area between the two large bifurcated minibrots. The wait of 12 minutes while the parameter file runs may be avoided by visiting the FOTD web site at: <http://www.Nahee.com/FOTD/> Sunday and Monday brought partly cloudy skies and a temperature of 64F 18C to Fractal Central. The fractal cats, who wish they could go outside and play like all the other cats, accepted the conditions. For me, Sunday was spent in the antique emporium, which is not too bad a way to spend a day, while Monday was an average workday. The next FOTD will be posted in 24 hours. Until then, take care, and if, as some claim, mankind needs a spiritual solution to its problems and spirits are ghosts, which sensible people know are not real, where do we find the spirit that will rescue us from our problems? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= FilamentaryNetwork { ; time=0:12:02.59-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinalDivideBrot function=recip passes=1 center-mag=-1.933488464180608/+0.00000478103645664\ /4.287836e+009/1/-21/0 params=0.5/20/0/0 float=y maxiter=10000 inside=255 logmap=764 periodicity=6 colors=000zvMgrLgsLhsKhsJisJitIjtIjtHkuIjtHisHhrHg\ qHgpGcpzcozcnzcmzclzckzckzcjzcizchzcgzcgzchzcizcjz\ ckzcuccuccuccuccuccuccuccuccuccuccuccuccuccuccuccu\ c4m44m45m45m46m46m47m47m57m58m58m59m59m5Am5Am5Bm5B\ h5Bh6Cg6Ch6Df6Dh6Ef6Eh6Fe6Fh6Fd7Gh7Gc7Hh7Hb7Ih7Ic7\ Jc7Jc7Jc8Kc8Kc8Lc8Lc8Mc8Mc8Nc8Nc8Oc7Nc8Nc8Nc8Nc8Nc\ 8Nc8Nc8Nc8Nc9Nc9Nc9Nc9Nc9Nc9Nc9Nc9Nc9NcANcANVANWAN\ WANWANWANWANWBNWBNXBNXBNXBNXBNXBNXBNXBNYCNUChUWhUW\ gUVgUVgUVfUUfUUfUUeUTeUTeUTdUSdUSdUScURcURcURdUQcU\ QdUQdUPdUPdUPeUOdUOeUOeUNeUNdUNdUMcUMbTMaSLaRL_QL_\ PKZOKYNKXMJWLJUKJTJISIIRHIQGHQFHQEHPDGPCGPBGOAFO9F\ O8FN7EN6EN5EO5BN4DN4EM4FM4HM4IL4JL4KL4MK4NK4OK4QJ3\ RJ3SJ3TI3VI3WI3XH3ZH3_H3`G3aG3cG3dF2eF2gF2hE2iE2jE\ 2lD2mD2nD2pC2qC2rC2sB3rB4rB5rBUzBUzBUzBUzBUzBUzBUz\ AUzAUzAUzAUzAUzAUzAUzAUzAUzAUz9Uz9Uz9Uz9Uz9Uz9Uz9U\ z9Uz9Uz9Uz8Uz8Uz8Uz8Uzzzz } frm:FinalDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1)+0.00000000000000000001: z=(-b)*(z*z*fn1(z^(a)+b))-c |z| < esc } END PARAMETER FILE=========================================

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