June 2011 - Fractint - mailman.xmission.com

FOTD 24-06-11 (Everyday Mandelbrot [6])
by Jim Muth 24 Jun '11

24 Jun '11

FOTD -- June 24, 2011 (Rating 6) Fractal visionaries and enthusiasts: The FOTD image for today lies on a filament moderately deep in the northeast period-5 radical of the classic Mandelbrot set. It is an everyday scene in the set, which is why I named it "Everyday Mandelbrot". The rating of a 6 is modest, and in fact it could even be excessive for such an everyday scene. I did put some extra effort into the coloring, though not enough to add the usual half-point reward to the rating. The top feature of the image is its lightning-fast calculation time of 1+ second. This incredible speed is a result of the super-fast type=mandel algorithm, with the exact time probably being determined mostly by factors other than pure processor speed. There is not much more to be said about today's FOTD except to remind those who do not run parameter files that the finished image is available at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition version is at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> Thursday began with a light shower here at Fractal Central. The rain ended by 10am but the clouds and humidity hung on for the rest of the day. The fractal cats languished in the temperature of 86F 30C, but found enough energy to ask for food. The humans had another typically uneventful day. The next FOTD image will be posted in 24 hours. Until then, take care, and never forget that the golden rule works both ways. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= EverydayMandelbrot { ; time=0:00:01.21-SF5 on P4-2000 reset=2004 type=mandel center-mag=+0.4465882667194\ 553/+0.3715210822167352/3.768528e+010/1/-175/0 params=0/0 float=y maxiter=3200 inside=0 logmap=224 periodicity=6 mathtolerance=0.05/1 colors=000HAKIAKJAKKAKLAKMAKNAKOAKPAKQAKRAKSAKTAKU\ AKVAKWAKXAKYALZAM_AN`AOaBPbCQcDRdESeFTfGUfHVeIWdJX\ cKYUPSKKNABH000BE68FFAIGCLHEOIFRJHVKJZLLbMNfNRjOWn\ PaoQdsRhvSmxTmzUmvXhrZcm`ZhbVcdS_fRWhQSjPOlOKnNGpM\ CrM9tPCnSEiVIcYLZaOTeSOiVIkXDhUFeRHbOJZLLXINVGPSER\ QCTOAVM8XK6ZO4`U2bc3Zm4Vz5Rz6Nz7Jz8GiMSX_cLlnLdpKa\ nJ_mIYkHWjGTiFRgFPfENeDLcCIbBGaAE_9CZ9AY8CX8EW8GV8\ HU7JT7LS7NR7OQ6QP6SO6UN6VNE_KMcIThF`lDbpBcnDdmFelH\ fkJgjLhiNigOjfQkeSldUmcWnbYoaZpb`qbbrccwcewdgwdhwe\ jvelvfmvfovfpuenteltejsehsdfrddqdbqd`pcZpcXocVocTl\ eRjfQhhOeiNckMalKZnJXoHVqGSrFPtDSuCUvBWwFYwI_wLawO\ cwRewUgwXiw`kwcmwfnwiowlpwoqwrrw`svJtuOutSvsWwr`wq\ dwphwogwnfwmewldwkcwjbwiawhawg`wc_wb_waZw`Zw`Ww`Tw\ `Qw`Nw`Lw`Iw`Fw`Cw`9w`7xa9yaAzaBzaCzbDzbEzbFzbGzcH\ zcIzcJzcKz`LzZMzWNzUOzSPzWDzZ1zX3zV4zT5zS6zQ7zO8zN\ 9zLAzJBzICzHFzTLzYNzbPzfR } END PARAMETER FILE=========================================

1 0

Re: [Fractint] minibrotz
by JackOfTradeZ＠comcast.net 23 Jun '11

23 Jun '11

. "Is it possible to determine from looking at the image where the minibrots are located?" I dont know if there is a rigorous scientific method, but after staring at these things for years you tend to get an "intuitive feel" for it. .

3 3

Multifractal_10 (Necklace)
by Albrecht Niekamp 23 Jun '11

23 Jun '11

Hi, a new image today, created with only 3 of possible 5 formulas. Multifractal_10 is already available. Note: Dont shut off, generation is visible after some minutes! Albrecht --------------------------------start par----------------- 20705a { ; Necklace ; Time 39.15.00 ; Mandel-newton-mmods ; Image-frm-colours Albrecht Niekamp ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr.frm formulaname=multifractal_10 function=cos/exp/exp/sin passes=t center-mag=-0.413195/0.0032193/8.572457/1.1324/-90/-1.23\ 373533611470521e-014 params=-0.05825983458967864/0.3785210730307932/20705.035\ 64960102/25234.2207090221/151024.0204808192/384.32768524\ 288/384.00482000595/128.1007683001/256.1007683001/256.20\ 07683001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=00040C<3>50G50H00E<2>A8TEHaIQj3Yqbe_FYI0L0<3>yrB<\ 3>yB3z00t60<3>UY0Nd0Gk0<2>ns1zz0<3>zI4z66w67<3>h3Fe2Ha1J\ Y0L<3>t8qzAzuAv<3>ZEdTE`OFX<2>6IJ<3>YcMdiMknNrtOzzP<3>`_\ QVTQOMRIFRB8S<3>8Yk7dp6ku5rz<6>7_g7Xd7Ub<3>9IR<10>7fA7i8\ 6k7<3>5u0<3>5c05Z05U0<3>5B0<3>UY0`b0fh0<2>zz0<9>jU1iR2gO\ 2<3>`A3<16>q8Ar8As8At8Bu8Bw7Cw8Cv8Dv9E<7>xA_xBayBd<2>zCm\ zCmzCmzzzYXc<3>JhnFkqBnt7qw<15>KGaLE`MBZ<3>Q1T<4>bGZdK_g\ N`<3>r_f<3>ggPeiKbkF<2>Uq1Xq2_q4<8>40B40B }

2 1

FOTD 23-06-11 (Crack in Ringworld [8])
by Jim Muth 22 Jun '11

22 Jun '11

FOTD -- June 23, 2011 (Rating 8) Fractal visionaries and enthusiasts: When I wrote the description of the 'On the Wrong Track' image of June 21, I assumed that when the sequence of elements switches to order-7, the series increases in powers of 7. But when I checked, I found that the series actually grows by doubling the 7 elements, making a 7,14,28... sequence. My hasty error, which was first noticed by Hal, is made obviously clear in today's image, where the continued doubling of 7 is quite apparent. The scene is the area immediately surrounding the central minibrot of the June 21 image. I have intensified the colors to bring out the background pattern, where smaller order-7 minibrots fill the scene to infinity. Unfortunately, the magnitude of the image is at the limit of resolution, and these smaller minibrots are mostly beyond reach. The rating of an 8 includes a generous full-point reward for my coloring work, which I admit did make use of another program, but also manages to bring out some otherwise almost invisible inner detail and fills the screen with rarely seen shades of intense blue. The name "Crack in Ringworld" gives recognition to one of my favorite sci-fi series. It also refers to the crack in the expected smooth 'powers of two' sequence. The calculation time of just under 5 minutes is a bit on the slow side. Boredom may be held at bay however by viewing the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> and by viewing it in high-definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> A typical summertime day passed uneventfully here at Fractal Central on Wednesday. The temperature of 88F 31C was a little too warm for total comfort, while the clouds were a little too prevalent for sun lovers. The forecast of numerous showers proved to be a scare tactic, as not a single drop of rain fell. The fractal cats alternated between taking it easy and chasing each other up and down the hallway. The humans had a typical uneventful day. The next FOTD will be posted in 24 hours. Until then, take care, and Atheism is doomed to forever remain an unconfirmed philosophy. (Just like Theism?) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Crack_in_Ringworld { ; time=0:04:54.05-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-0.1962128361703373/+0.6526484177635142\ /6.174367e+012/1/-51/0 params=7/1e+017/0/0 float=y maxiter=7200 inside=0 logmap=415 periodicity=6 mathtolerance=0.05/1 colors=000zz05Nb5Nb5Ne5Ne5Ng5Ng5Ng5Nj5Nj5Nl5Nl5Nl5\ No5No5jo5jqzzzzzzzzzzzzzzyzzxvzwpzvhzubztPzsKzoFzj\ GzeSxGNuEIsCGoCCg99`75X73S50N30I30E109005001000000\ 00000000000000000000000000100300500710910C10E30G30\ I50I50L50N70N70P90P90SC0VC0VC0XE0XE0ZG0`G0`G0bI0eI\ 0eL0gL0gL0jN0lN0lP0oP0oP0sS0sV0uX0uZ1x`3x`5zb7ze9z\ gCzjGzjLzlPzoXzq`zsezsjzuoxxsuzxszzqzzqzzqzzqzzqzz\ qzslzjgz`bzPZzGVz7Sz0Nz0Iz0Ez09z09z07z07z0Xz0hz0Xz\ 0hz0Xz0hz0Xz0hz0Xz0hz0Xz0hz0Xz0hz0Xz0hz0Xz0hz0Xz0h\ z0Xz0hz0Xz0hz0Xz0oz0Xz0hz0Xz0hz0Qz0Qz01k01k01a00z0\ 0k00a00k00k00a00a00z00k10a10k10a10a10X10k10k10a10k\ 10i10f10d10d10b10`10Y10T10W10T10T10e10b10`10`10Z10\ X10X10V10S10S10P10P10N10N10L10LN0zN0GN0zN0Ej0zj0Cj\ 0zz09z0zz07zjzz05z0zzj3z0zzj1z0zzj0z0zzj5z0zz0Izjz\ z0Xz0zzjjz0zz0uz0zzjxz0zzjxz0xzjxz0xzjxz0xzjxz0zzj\ zz0zzjzz0zzjzz0zzjzzS`zjb } 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

Lee Skinner MFR zooms
by Albrecht Niekamp 22 Jun '11

22 Jun '11

Hi, I love this one because it keeps you watching. Albrecht -------------------------start par------------------------- Jrula2 { ; Jrula2 ; structures+overlays+partial symmetry ; frm+image Albrecht Niekamp ; source+colours Lee Skinner ; time 11.29.00 ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr.frm formulaname=multifractal ismand=n function=exp/exp/exp passes=t center-mag=+1.09441249371272300/+0.21759644730115380/76.\ 36852/1/-102.499999999999915/-3.17669501814776822e-013 params=-0.1740997192297128/-0.2996141087069308/384.00004\ /256.1106/2048.00016/768.00009/768.01536/256.01025/28424\ .5/12 float=y maxiter=2048 inside=maxiter outside=tdis logmap=10 symmetry=none periodicity=0 rseed=-2436 cyclerange=2/255 colors=000000t2tv2u<3>c5eZ6`U6X<2>F9LAAG7FO4KW0Qc<3>5Xc6\ Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>civflvinvlqvotvsww<2>\ zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI<4>XCAaB9fB7<3>zA\ 0<13>SA1QA1NA1<3>D92<6>UXAW`BYcC<3>hrI<3>UnXRm_NlcJkgFfp\ Aaz<3>PJoSFlWAi_5fc0ce7_jFRoNIzb0<2>zz1zzC<2>zzz<3>jqdfo\ _blU<3>Mb8<3>LQ8KM8KJ8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBi\ ODjQF<3>qeBriAtm9vq8xu7zz5zz4zz3<8>zY4zV5zS5<3>zE6wE6tD6\ <10>w8Px8Rx7S<3>z5_<3>f5Ma5IW4E<2>_4H<3>P3DN2CK2A<3>805G\ 0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0gy0h<5>s1or2qs2r } ----------------------------start frm---------------------- Frm:multifractal { ; Albrecht Niekamp 24.3.03 ; d=real(p2) fac1=trunc(d) b1=(d-fac1)*100000 ; d=imag(p2) da=d<0 if (da) d=-d endif mi1=trunc(d) d=round((d-mi1)*10000) p6=trunc(d/100)/10 d=d-1000*p6 if (da) p6=-p6 endif p7=d/10 ; d=real(p3) ba=trunc(d) mm=round((d-ba)*100000) ; d=imag(p3) fac2=trunc(d) b2=(d-fac2)*100000 ; d=real(p4) mi2=trunc(d) fac3=round((d-mi2)*100000) ; d=imag(p4) b3=trunc(d) mi3=round((d-b3)*100000) ; da=real(p5) t=da<0 if (t) da=-da endif start=2-t dd=trunc(da) da=round((da-dd)*100) if (dd<5) start=0 vb=(dd==3)+(dd==4) else d=trunc(dd/10000) vb=(d==3)+(d==4) dd=dd-d*10000 d=trunc(dd/1000) or1=d>5 d=d-5*or1 vv1=(d==3) vv2=(d==4) dd1=(d==2)+(d==4) dd=dd-d*1000 d=trunc(dd/100) or2=d>5 d=d-5*or2 vv3=(d==3) vv4=(d==4) dd2=(d==2)+(d==4) dd=dd-d*100 d=trunc(dd/10) inr1=d>5 d=d-5*inr1 v1=(d==3) v2=(d==4) d1=(d==2)+(d==4) dd=dd-10*d d=trunc(dd) inr2=d>5 d=d-5*inr2 v3=(d==3) v4=(d==4) d2=(d==2)+(d==4) endif ; d=trunc(da/10) da=da-10*d ab=d>=5 d=d-5*ab bb1=(d==1) bb2=(d==2) dd=da>=5 da=da-5*dd ab=ab+dd ab1=(da==1) ab2=(da==2) ; d=imag(p5) dd=trunc(d) d=round((d-dd)*1000000) le=d>10000 da=trunc(dd/10) so1=((da==1)+(da==3)==0) so2=((da==2)+(da==3)==0) dd=dd-10*da wo=dd>=5 dd=dd-5*wo ir1=(dd==1)+(dd==3) ir2=(dd==2)+(dd==3) if (le) freq=round((trunc(d/10000))*10) ;frequency_lake effect d=d-freq*1000 level=(trunc(d/100))/100 ;water level d=d-level*10000 ampl=d/100 ;amplitude of the wave u=real(rotskew*pi/180) t=exp(-flip(u)) bo=1/real(magxmag) q=bo/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) d3=2*q*t rs=2*bo*(dd+flip(1))*t z2=center+(-q-bo*dd-flip(bo))*t z=pixel-z2 d=imag(conj(d3)*z)/imag(conj(d3)*rs) if (d<=level) da=level-d z=z+2*da*(1+ampl*sin(freq*da^0.2))*rs endif z=z+z2 endif if (ismand) if (vb) c=0.4*log(sqr(pixel^mm)) z=z*le else c=z*le+pixel*(le==0) z=0 endif else c=p1 z=z*le+pixel*(le==0) endif t=0 d3=(ismand==0) u=d3 : if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) else z2=fn1(z)+c ;Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z=z*z+c+c*c-p7 ;Pusk s Istv n elseif (d3) z2=z*z z=z2*z2+(p6+u)*z2+c else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p1 endif bo=|z| If (wo) t=t+1 if ((t<mi1)+(bo>b1)) u=2*(fn1(t/fac1)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) else c=z*le+pixel*(le==0) endif else z=z*le+pixel*(le==0) c=p1*u endif wo=0 if (ir1) t=0 endif endif elseif (start) t=t+1 if (start==2) if (bo>b2) u=2*(fn2(t/fac2)) rs=or1 ab=bb1 if (dd1) if (rs) z=pixel endif c=p1*u vb=vv2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=1 endif elseif (t>mi2) u=2*(fn2(t/fac2)) rs=inr1 ab=ab1 if (d1) if (rs) z=pixel endif c=p1*u vb=v2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=1 if (ir2) t=0 endif endif elseif (bo>b3) u=2*(fn3(t/fac3)) ab=bb2 rs=or2 if (dd2) if (rs) z=pixel endif c=p1*u vb=vv4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=0 endif elseif (t>mi3) u=2*(fn3(t/fac3)) ab=ab2 rs=inr2 if (d2) if (rs) z=pixel endif c=p1*u vb=v4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=0 endif endif bo<=ba }

2 1

FOTD 22-06-11 (In-Depth Examination [7.5])
by Jim Muth 22 Jun '11

22 Jun '11

FOTD -- June 22, 2011 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image is a scene lying very deep in the north shore line of the main bay of the Mandelbrot set, just west of the large northern bud. Yes, I realize that it is a spiral, and I'm not supposed to like spirals, but the image is worth at least one quick glance. The name "In-Depth Examination" refers to the image's magnitude of 6*(10^28). That same magnitude makes the image a slow one however, so don't expect instant gratification if you decide to run the parameter file. I could rate the image no higher than a 7-1/2, since it lies in the Mandelbrot set, the most over-explored of all fractals. The rating of a 7-1/2 includes 1/2 point for my coloring effort. Perhaps I should have rewarded myself only 1/4 point. On second glance the coloring appears to be not all that great. To avoid spending the better part of an hour running the included parameter file, check the finished image posted on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The image is posted in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> Heat, haze and humidity made Tuesday rather stifling here at Fractal Central. When the temperature reached a high of 88F 31C the fractal cats shifted into summer mode and stretched out on the cool tile floor. The humans took things pretty much in stride. The next FOTD will be posted in 24 hours. Until then, take care, and may the guardians of the universe rush to your aid whenever you need it. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= InDepthExamination { ; time=0:50:47.98-SF5 on P4-2000 reset=2004 type=mandel center-mag=-0.1956331366108\ 86566268009760456792/0.653501797677887321513464499\ 778281/6.236299e+028/1/77.5/0 params=0/0 float=y maxiter=12500 inside=0 logmap=3025 periodicity=6 colors=0002273374475676887A99CAAEBBHCDLDEOEFRFHVGI\ YHJ`ILdJMgKNjLNhMNgMNfNNeNNcONbONaPN`PNZQNYQNXRNWR\ NUSNUSOWTPYTQ_SRaRScQTeQUfLVgHWhJXiLYkNZlP_nR`oS`p\ U`oW`mY`k_`ia`gb_edadjcdmeamgZmiXmkUmlSmmPmnMmnKmo\ HmpFmqCmq9mr7ms4ms2mr4mq6mp8moAmnCmmEmlFmfGi`GeVGb\ PGZJHVDHS7HO2HL7GMBGMFGNKGNOGNSFOWFO`FOdFPhFPlFPmH\ UmIZmKcmLhmNmmOqnSpoVppZpqaprdpshptkpunpvrpwupwxpt\ uqqsqopqlnrjkrgiregrbds_bsY_sVYtTVqQTnOUkYVhZVe_Wb\ _T_XQXVNUTKRQHONEMKCLF9KE7KO5KZ4KhzcfncugEtaJtXOzm\ csMYmHb`CQK7KP8Sc8`i8_o8WzUSvJXn8Vh8Tb8RY8UU8XTEQT\ JUTOYTTXTYRTgLcpFms9zzCmmEccGUXIKTKAPM7LO4IQKDKT3H\ ZAEZHBZO8ZV5ZamVemSimOmmLqmHumEwmAkW6Z28QG9HUA8g8A\ h7Ci6Ej4Gk3Il2Kl9MmGOmNQmTSm_UmzWmzYmz_mzc9zfDziGz\ lJzoMzqPzmEzmCzmAzm9zm7zm6zm4mz3mz4mz4mz5mz5mzAmzF\ mzKmzzmzzmzzmzzmzzmzzmzzmzzEzzEzzEzzFzzFzzFzzOzzSz\ zVzzYzz`zzPzzOzzOzzNzzNzz } END PARAMETER FILE=========================================

1 0

Lee Skinner MFR Images
by Albrecht Niekamp 21 Jun '11

21 Jun '11

Hi, this is the second zoom into one of Lee´s images - and....judge yourself! Albrecht ------------------------------start par-------------------- galla2 { ; galla2 ; time 19.07.00 - be amazed! ; frm+zoom albrecht niekamp ; source+colours lee skinner ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr.frm formulaname=multifractal_1 ismand=y function=exp/exp/exp/exp passes=t center-mag=+1.02131581270836200/+0.00006507034526879/217\ .751/1/-90/-1.23373533611470521e-014 params=-0.1738944669942329/-0.3000579851680044/384.00004\ /2048.1133/768.00008/768.00128/1024.00256/1536.01024/189\ 22.01/0.32 float=y maxiter=2048 inside=maxiter outside=tdis logmap=yes symmetry=none periodicity=0 rseed=-2436 cyclerange=2/255 colors=000000uxxwyyzzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP8FL8\ CI<4>XCAaB9fB7<3>zA0<13>SA1QA1NA1<3>D92<6>UXAW`BYcC<3>hr\ I<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi_5fc0ce7_jFRoNIzb0<2>z\ z1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8KJ8<2>I88H44G00<3>\ TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriAtm9vq8xu7zz5zz4zz3<8>zY\ 4zV5zS5<3>zE6wE6tD6<10>w8Px8Rx7S<3>z5_<3>f5Ma5IW4E<2>_4H\ <3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0gy0h<3>u1\ mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4KW0Qc<3>5Xc6Zc7\ `c7aa7c_7eY<3>FcgHciJbl<3>S_v<5>invlqvotvsww } -------------------------------start frm------------------- Frm:multifractal_1 { ; Albrecht Niekamp 270503 ; d=real(p2) fac1=trunc(d) b1=(d-fac1)*100000 ; d=imag(p2) da=d<0 if (da) d=-d endif ba=trunc(d) d=round((d-ba)*10000) p6=trunc(d/100)/10 d=d-1000*p6 if (da) p6=-p6 endif p7=d/10 ; d=real(p3) mi2=trunc(d) b2=(d-mi2)*100000 ; d=imag(p3) fac2=trunc(d) ob2=(d-fac2)*100000 ; d=real(p4) mi3=trunc(d) b3=(d-mi3)*100000 ; d=imag(p4) fac3=trunc(d) ob3=(d-fac3)*100000 ; da=real(p5) t=da<0 if (t) da=-da endif start=2-t dd=trunc(da) da=round((da-dd)*100) if (dd<5) start=0 vb=(dd==3)+(dd==4) else d=trunc(dd/10000) vb=(d==3)+(d==4) dd=dd-d*10000 d=trunc(dd/1000) dd=dd-d*1000 or1=d>5 d=d-5*or1 vv1=(d==3) vv2=(d==4) dd1=(d==2)+(d==4) d=trunc(dd/100) dd=dd-d*100 or2=d>5 d=d-5*or2 vv3=(d==3) vv4=(d==4) dd2=(d==2)+(d==4) d=trunc(dd/10) dd=dd-d*10 inr1=d>5 d=d-5*inr1 v1=(d==3) v2=(d==4) d1=(d==2)+(d==4) inr2=dd>5 dd=dd-inr2*5 v3=(dd==3) v4=(dd==4) d2=(dd==2)+(dd==4) endif ; d=trunc(da/10) da=da-10*d ab=d>=5 d=d-5*ab bb1=(d==1) bb2=(d==2) ab1=(da==1) ab2=(da==2) ; d=imag(p5) dd=trunc(d) mm=round((d-dd)*100) da=trunc(dd/10) so1=((da==1)+(da==3)==0) so2=((da==2)+(da==3)==0) dd=dd-10*da wo=dd>=5 dd=dd-5*wo ir1=(dd==1)+(dd==3) ir2=(dd==2)+(dd==3) ; if (ismand) z=0 if (vb) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else c=p1 z=pixel endif t=0 d3=(ismand==0) u=d3 : if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) else z2=fn4(z)+c ;Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z=z*z+c+c*c-p7 ;Pusk s Istv n elseif (d3) z2=z*z z=z2*z2+(p6+u)*z2+c else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p1 endif bo=|z| If (wo) t=t+1 if (bo>b1) u=2*(fn1(t/fac1)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else z=pixel c=p1*u endif wo=0 if (ir1) t=0 endif endif elseif (start) t=t+1 if (start==2) if (bo>b2&&bo<ob2) u=2*(fn2(t/fac2)) rs=or1 ab=bb1 if (dd1) if (rs) z=pixel endif c=p1*u vb=vv2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=1 endif elseif (t>mi2) u=2*(fn2(t/fac2)) rs=inr1 ab=ab1 if (d1) if (rs) z=pixel endif c=p1*u vb=v2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=1 if (ir2) t=0 endif endif elseif (bo>b3&&bo<ob3) u=2*(fn3(t/fac3)) ab=bb2 rs=or2 if (dd2) if (rs) z=pixel endif c=p1*u vb=vv4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=0 endif elseif (t>mi3) u=2*(fn3(t/fac3)) ab=ab2 rs=inr2 if (d2) if (rs) z=pixel endif c=p1*u vb=v4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=0 endif endif bo<=ba }

2 1

FOTD 21-06-11 (On the Wrong Track [8])
by Jim Muth 21 Jun '11

21 Jun '11

FOTD -- June 21, 2011 (Rating 8) Fractal visionaries and enthusiasts: Today's image is definitely on the wrong track. It lies in the western branch of North Valley of its parent fractal, which on the surface is an un-notable Mandelbrot set. When we start at the surface of this parent, all is as it should be, with the spirals like seahorse tails that would be expected in this area. But by the time we reach the depth of the first minibrot, we find that something has gone wrong. The minibrot has become a disorganized mess rather than the well-defined quadratic midget that would be expected. The inside of this fractal mess is filled with piles of debris however, and in this debris some strange things are happening. Checking one of these debris piles, we find it is an area of anti-bifurcation filled with more seahorse tails. Today's scene lies in one of these tails. Around its edges, today's image presents no problems. It consists of everyday quadratic stuff with the expected 4,8,16... series of elements. But about halfway in, things go terribly awry, and the sequence resets itself to the order-7 series of 7,49,343... When we reach the central minibrot the surprises continue. Instead of a quadratic minibrot we find a full-blown order-7 one, with 6 lobes, surrounded by an area holding a legion of smaller similar minibrots. The reason for all this craziness is known only by the gods of numbers, and they are not revealing their secrets. As for myself, I see simply another fractal surprise in a world where there are so many surprises that the surprises are in danger of losing their ability to surprise. The rating of an 8 includes a half point or so of optimism. The name "On the Wrong Track" describes the 'wrong' minibrots cluttering the center of the image. The calculation time is an eminently reasonable 2-4/5 minutes. The finished image is posted for maximum convenience on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> It is posted in high-definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original classic FOTD site may be accessed at: <http://www.Nahee.com/FOTD/> Monday brought too many clouds for perfection, but it remained dry, and the temperature of 82F 28C was near perfect. The fractal cats had a reasonably peaceful day, though at one point I heard Cassie cussing at Nicholas. The humans had an equally peaceful, but dull day. The next FOTD will be posted in 24 hours. Until then, take care, and if we didn't have all those fantastic wireless internet devices, how would we communicate? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= On_the_Wrong_Track { ; time=0:02:49.16-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-0.1962128361703378/+0.6526484177635086\ /8.891464e+011/1/-7.5/0 params=7/1e+017/0/0 float=y maxiter=3600 inside=0 logmap=339 periodicity=6 mathtolerance=0.05/1 colors=000qBkqElqHmqKnqNoqQpqTqrWrrZsratrdurgvrjwr\ lxrlxpktmhqjdng`keXhbTd_PaYLZVHWTETUDOVCKWCGXBCYA8\ ZC4`D6aG8cH9dKBfMCgOEhQGjSHkVJmXKnZMo_NkZQhWTeTVaR\ YZO_WMbTJePHgMEjJClG9oC7r94t62w30y25t29p2Dl2Ih2Mc2\ Q_2UW1ZS1cO1gJ1lF1pB1s71t3BsFLoRVlbdhnmeyjfveksapp\ dpogpnkolnokonjpllpjmognoeonbqn`smYumWwkXxiXygXzfX\ zdXzbXzaXz`Wz_VzZUzYTzXSzWRzVQzUQzTPzSOzRNzQMzPLzO\ KzNKzMIzMHzMGzMFzMEzMDwMCtMBqL9nL8kL7hL6eL5bL4_L3X\ L2UK3RJ3OI3LH3IG3FF4EE4CD4BC4AC49G6CJ7EN8GQ9IUAKXB\ M`CPcDRgETjFVnGXqHZlQ_hY_de``j`Xl_UnYRmWPjTMfRKcPH\ _MFXKCTHAPF7KD5GA2B80761982BA3DB4FD5HF6JG7KI8LK9ML\ ANNBOOAQQ9RR9SS8TT8UU7VV7WW6XX6YYKZZK__U``Uaacbbcc\ cmecmgcziczkbzmazo`zq_zsZzuYzwXzx_zgWzSTzNUzIVzDWz\ 8Xz9YQAZSB_UC_VD`XEaZFa`GbbHccIdeJdgKeiLfjLfhMggNg\ fOgePhdQhcRhbSiaTi`Ui_VjZWjYXjXYkWZkV_kWaiWchWegXg\ fXheXjcYlbYnaYp`Yq_p5idVj } 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

Bristling Energy
by Mike Frazier 20 Jun '11

20 Jun '11

I was doing some deep zoom exploring in the Mandelbrot set and stumbled across an area that had a minibrot with straight meandering arms and electric looking tendrils. Out of curiosity, I zoomed into some of the deeper minibrots near the original minibrot and compared the image to the original. Is it possible to determine from looking at the image where the minibrots are located? Is there any way to know how each minibrot will differ from the original? Here is a link to a web page with the original image and links to more pages of what I found: http://www.fracton.org/fmlposts/bristling_energy_p1.html The parameter file used to make the original image is below: Bristling_Energy { ; Exported from Fracton. ; time = 32.2 sec at 640 x 480 with no aa ; on a Mac Pro 2 x 2.8 GHZ Quad-Core Xeon reset=2004 type=mandel passes=1 float=y center-mag=-0.126245138931413858672422416646502888\ 500881791e1/0.408335817765869292403054362598174616\ 49786835564/2.22222225e+31/1/0/0 params=0/0/0/0/0/0/0/0/0/0 maxiter=4000 inside=1 logmap=1034 proximity=0 colors=80G80G80G80G80H80H80I81I71I71J71J72J72J72K6\ 2K63K63L63L63L63M54M54M54M54N55N55N45O45O46O46P46P\ 46P37P37Q37Q37Q37R38R28R28S28S29S29S29T19T1AT1AU1A\ U0BV1CV2DW4EW5FX6GX7HY9IYAJZBKZCL_EM_FN`GO`HPaJQaK\ SbLTbNUcOVcPWdQXdSYeTZeU_fV`fXagYbgZch_dhaeibfibfi\ cgjdhkfikgjlhkljlmkmmlnnnpnoqoprorspqropqnopmnnllm\ kkljjkiiighhffgeefdddcccbaba`a`__ZZZYYYXWXWVVVUUUT\ TTRRRSSSUUUVVVXXXYYY___aaabbbdddeeeggghhhjjjkkkmmm\ oooppprrrsssuuuvvvxxxzzzzzyzzxzzwzyuzxsywryvpyunxt\ lxskxsiwrgwqewpdvobvn`vmZulYukWukUujStiRthPtgNsfLs\ eKsdIrcGrcErbDqaBq`9q_7pZ6pY4pX2oW0oW0nV0nU0mU0lT0\ lS0kS0jR0jQ0iQ0iP0hO1gN1gN1fM1eL1eL1dK1dJ1cJ1bI1bH\ 1aH1`G2`F2_E2ZE2ZD2YC2YC2XB2WA2WA2V92U83U73T73T63S\ 53R53R43Q33P33P23O13N04N04M05M05L05L06L06K06K07J07\ J07I08I08I08H09H09G09G0AF0AF0AF0BE0BE0BD0CD0CC0DC0\ DB0DB0EB0EA0EA0F90F90F80G } -- Mike Frazier www.fracton.org

1 0

Lee Skinner MFR Images
by Albrecht Niekamp 20 Jun '11

20 Jun '11

Hi, after some weeks on the mail I finally received Lee´s Multifractal DVD and it´s definetely worth waiting for. All images were created using the preliminary stages of my multifractal formula as it developed in 2003. The smaller part are zooms into images I posted that year but using Lee´s colours. The bigger part he created zooming out into total view and then zooming in again. I will post some own zooms mostly using Lee´s colours and some own new images. The images are posted together with the frm used; as it is not compatible with the final stage it should be used only for calculation of that image and therefore has no input possibilities. Only images created using multifractal_10 are compatible with the frm you have downloaded, there were no changes in the code. Albrecht ---------------------Start par---------------------------- Ascp14a1 { ; Ascp014a1 ; colours and image ; by Lee Skinner ; zoom and frm ; Albrecht Niekamp ; Time 21.03.00 ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr.frm formulaname=multifractal ismand=y function=exp/sin/exp passes=t center-mag=-1.36397552835101600/-0.74493857542845080/916\ 23.65/1/130.000000000123777/4.68308725132260406e-011 params=-0.1740997192297128/-0.2996141087069308/384.00004\ /256.1106/4096.00016/768.00009/768.01536/128.01025/28984\ .5/0 float=y maxiter=2048 inside=maxiter outside=tdis logmap=10 symmetry=none periodicity=0 rseed=-2436 cyclerange=2/255 colors=000000Aaz<3>PJoSFlWAi_5fc0ce7_jFRoNIzb0<2>zz1zzC<\ 2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8KJ8<2>I88H44G00<3>TA5WD6\ ZF7aI8eLAhMBiODjQF<3>qeBriAtm9vq8xu7zz5zz4zz3<8>zY4zV5zS\ 5<3>zE6wE6tD6<10>w8Px8Rx7S<3>z5_<3>f5Ma5IW4E<2>_4H<3>P3D\ N2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0gy0h<3>u1mt1ns1\ or2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4KW0Qc<3>5Xc6Zc7`c7aa7\ c_7eY<3>FcgHciJbl<3>S_v<3>civflvinvlqvotvsww<2>zzz<3>rwz\ ovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI<4>XCAaB9fB7<3>zA0<13>SA1Q\ A1NA1<3>D92<6>UXAW`BYcC<3>hrI<6>JkgFfp } --------------------start frm------------------------------ Frm:multifractal { ; Albrecht Niekamp 24.3.03 ; d=real(p2) fac1=trunc(d) b1=(d-fac1)*100000 ; d=imag(p2) da=d<0 if (da) d=-d endif mi1=trunc(d) d=round((d-mi1)*10000) p6=trunc(d/100)/10 d=d-1000*p6 if (da) p6=-p6 endif p7=d/10 ; d=real(p3) ba=trunc(d) mm=round((d-ba)*100000) ; d=imag(p3) fac2=trunc(d) b2=(d-fac2)*100000 ; d=real(p4) mi2=trunc(d) fac3=round((d-mi2)*100000) ; d=imag(p4) b3=trunc(d) mi3=round((d-b3)*100000) ; da=real(p5) t=da<0 if (t) da=-da endif start=2-t dd=trunc(da) da=round((da-dd)*100) if (dd<5) start=0 vb=(dd==3)+(dd==4) else d=trunc(dd/10000) vb=(d==3)+(d==4) dd=dd-d*10000 d=trunc(dd/1000) or1=d>5 d=d-5*or1 vv1=(d==3) vv2=(d==4) dd1=(d==2)+(d==4) dd=dd-d*1000 d=trunc(dd/100) or2=d>5 d=d-5*or2 vv3=(d==3) vv4=(d==4) dd2=(d==2)+(d==4) dd=dd-d*100 d=trunc(dd/10) inr1=d>5 d=d-5*inr1 v1=(d==3) v2=(d==4) d1=(d==2)+(d==4) dd=dd-10*d d=trunc(dd) inr2=d>5 d=d-5*inr2 v3=(d==3) v4=(d==4) d2=(d==2)+(d==4) endif ; d=trunc(da/10) da=da-10*d ab=d>=5 d=d-5*ab bb1=(d==1) bb2=(d==2) dd=da>=5 da=da-5*dd ab=ab+dd ab1=(da==1) ab2=(da==2) ; d=imag(p5) dd=trunc(d) d=round((d-dd)*1000000) le=d>10000 da=trunc(dd/10) so1=((da==1)+(da==3)==0) so2=((da==2)+(da==3)==0) dd=dd-10*da wo=dd>=5 dd=dd-5*wo ir1=(dd==1)+(dd==3) ir2=(dd==2)+(dd==3) if (le) freq=round((trunc(d/10000))*10) ;frequency_lake effect d=d-freq*1000 level=(trunc(d/100))/100 ;water level d=d-level*10000 ampl=d/100 ;amplitude of the wave u=real(rotskew*pi/180) t=exp(-flip(u)) bo=1/real(magxmag) q=bo/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) d3=2*q*t rs=2*bo*(dd+flip(1))*t z2=center+(-q-bo*dd-flip(bo))*t z=pixel-z2 d=imag(conj(d3)*z)/imag(conj(d3)*rs) if (d<=level) da=level-d z=z+2*da*(1+ampl*sin(freq*da^0.2))*rs endif z=z+z2 endif if (ismand) if (vb) c=0.4*log(sqr(pixel^mm)) z=z*le else c=z*le+pixel*(le==0) z=0 endif else c=p1 z=z*le+pixel*(le==0) endif t=0 d3=(ismand==0) u=d3 : if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) else z2=fn1(z)+c ;Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z=z*z+c+c*c-p7 ;Pusk s Istv n elseif (d3) z2=z*z z=z2*z2+(p6+u)*z2+c else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p1 endif bo=|z| If (wo) t=t+1 if ((t<mi1)+(bo>b1)) u=2*(fn1(t/fac1)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) else c=z*le+pixel*(le==0) endif else z=z*le+pixel*(le==0) c=p1*u endif wo=0 if (ir1) t=0 endif endif elseif (start) t=t+1 if (start==2) if (bo>b2) u=2*(fn2(t/fac2)) rs=or1 ab=bb1 if (dd1) if (rs) z=pixel endif c=p1*u vb=vv2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=1 endif elseif (t>mi2) u=2*(fn2(t/fac2)) rs=inr1 ab=ab1 if (d1) if (rs) z=pixel endif c=p1*u vb=v2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=1 if (ir2) t=0 endif endif elseif (bo>b3) u=2*(fn3(t/fac3)) ab=bb2 rs=or2 if (dd2) if (rs) z=pixel endif c=p1*u vb=vv4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=0 endif elseif (t>mi3) u=2*(fn3(t/fac3)) ab=ab2 rs=inr2 if (d2) if (rs) z=pixel endif c=p1*u vb=v4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=0 endif endif bo<=ba }

2 1