December 2012 - Fractint - mailman.xmission.com

Fractint version 20.04 patch 12 released
by Jonathan Osuch 25 Feb '15

25 Feb '15

Folks, Fractint version 20.04 patch 12 was released today. The executables can be found at: www.fractint.net or www.fractint.org Here is what's new: Fixed buffer overflow in disk video mode when savename was too long. Jonathan

5 10

Cloud Service
by Albrecht 31 Dec '12

31 Dec '12

Hi, as my web page project has passed away I need a better solution, a free cloud service where I can keep the multifractal images and software available for watching and download even when my computer is offline. Dropbox apparently is no good in that aspect, but there are others. Any help will be appreciated, I need a solution in order to go on- there still is a large amount of new territory to be explored. Thank you! Albrecht

2 1

FOTD 30-12-12 (Spooky Julia Set [7.5])
by Jim Muth 30 Dec '12

30 Dec '12

FOTD -- December 30, 2012 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image is another venture into the apparently boring (-Z)^(2)+C Julibrot. This time it is a Julia set of the tip of the sharp Mandelbrot valley pointing directly west. The image is extremely sensitive to changes in some parameters, especially the real parameters. Some changes create surprising variations; others fail miserably. Change any of them at your own risk, but don't say I failed to warn you if a blank screen appears. The Julia set in today's scene is shaped surprisingly like the Julia set of Seahorse Valley of the Mandelbrot set. This is likely a coincidence, though who am I to try to outguess the numbers? The name "Spooky Julia Set" refers to this strange similarity. The rating of a 7-1/2 includes a half-point bonus for the coloring. The adjacent color bands are in no order, but are scattered wildly all over the palette, making coloring quite difficult. The calculation time of 40 seconds will pass rapidly. Setting the symmetry to xyaxis will cut this time by 2/3, but will distort the images with no symmetry that result from changing the parameters. The image is so fast that it will take more time to go to the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> and view the finished image there. But going to the web site will avoid the problem of setting up and running the included parameter file. Augmented variations in hi-def are online at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images from as long ago as 1997 are posted at: <http://www.Nahee.com/FOTD/> Yesterday's snow ended at nightfall after dropping a fresh 6 inches or 15cm on Fractal Central. Today was cloudy with a few minor flurries blowing in from the lakes. The temperature of 34F +1C was just about normal. Fractal cat Nicholas spent the day chasing his catnip ball and asking for food. My greatest task was clearing the fractal sidewalk; FL kept busy supplying the hot coffee. The next FOTD will be posted in a reasonable time. Until whenever, take care, and I wonder why happiness in life now comes from purchasing the latest trendy gadgets. Maybe when we're pushing buttons, we don't have time to think about the horrors lurking just beneath the surface of our decaying culture. Jim (always the optimist) Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Spooky_Julia_Set { ; time=0:00:40.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=0/0/0.3909394 params=90/0/90/0/-1.889/0/0/0/-2/5 float=y maxiter=5000 inside=0 periodicity=0 colors=0000AmYK9LFANIAPKBRMCTPCVRDXUDZWE`YEb`FdbGf\ eGhgHjjHllInnJpqJrsKtvKvxLwzLluPapTRlXGg`2fb5cc8ac\ A_cDYcGWcIUcLRd00UQNdTLdWJdd5_YHdRTiKdnDptEpsEpsFp\ sFprFprGprGpqGpqHpqHppHppIppIpoJpoJpoJpnKpnKpnKpmL\ pmLpmNqiLpmKopJoszzuzzwzzzzzrzzpzznzzkzzizzgzzezzb\ zz`zzZzzXzzUzzSzzQzzOHELHEJHFHHFFIGBIHDKIFMJH0LU00\ ZEHeOPKYTR_VTbXVdZXg`Zib`kdbnfdphfsjhuljwmkumismhq\ mfomemmdkmbimagm_emZcmYamW_mVYmTWmSSqRVmRXjRZfRacR\ c_ReXR00PjQRlMRoJRqFRsCRv8Rx5Rz2Rx3Sw4Sv5Su6Ss7Sr8\ Sq8Sp9SnASmBSlCSkDSiEShESgFSfGSdHScISbJSaJSYIQVHOR\ GMOFLNENMEOLEPKEQJESIETHDUGDVFDXEDYDDZCD_BCaACb9Cc\ 8Cd7Cf6Cg5Bh4Bi3Bk2Bl1Bm0Bn0Ej0Hf0Kb0QZ00XKKc3TU5T\ W8TXATZDT_FTaITbKTdNTfPTgSTiUTjXTlZTmaTocTqfTrhTti\ TuiTwiTwjTxjVvkXulZtm`sRbrMdqHfpCho7in8ij9hfBhb00K\ DhWEgSFgOHgKIfGJfCKf8Lf5Fk7Ap99lF9iL9fR9cX8_b8Xh8U\ n8Rt8OyBSuEWqHZmKbiMefPib } 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=========================================

1 0

Happy New Year!
by Albrecht 30 Dec '12

30 Dec '12

Hi, as I did this image just for today, I?m posting it, although it?s the last link used. Don?t overdo it! Happy New Year! Albrecht http://www.emarketingiseasy.com/Albrecht/21267.GIF ----------------------------------start-par--------------------------------- 23267 { ; HappyNewYear ; time 1.23.17.36 1600/1200 ; man-bees-man-phoen-newt reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=6.08751/-0.00145029/6.412837/1/90/-1.23373533611470521e-014 params=-0.05825983458967864/0.3785210730307932/21267.64595702002/14235.4\ 911030602/152048.0404808048/384.1604894048/384.00482000595/128.300768100\ 1/256.3007682001/384.2007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000<7>000000000<3>000<7>Q0UU0YX0a_0dc0hf0l<2>p0w<4>_0dX0aU0Y<2>K0\ NH0JG0NE1R<3>7UX6`Z4h_2oa0wc<10>2WI2TG2RE<3>4G54D36F5<16>kkammcpoe<3>zwm\ <3>mhZjdVfaS<3>VMCRI8OE4KA0000<43>000<4>000330<6>220220220<3>110000110<2\ >000KA4<7>gcOjgRmjT<3>zzc<9>UOFRKDOGA<3>A00<9>f0Ci0Dl0F<3>z0K<6>Z0EV0DR0\ C<3>A08004000<17>000 } frm:multifractal_10 { ; Albrecht Niekamp Jan2005 ;RP2 Left: 5 Digits_Channel:1_main 2_outside 3_inside1 4_inside2 5_inside3 ; Frms: 0_off 1_Sec 2_Mand(2) 3_Bees 4_Jul 5_Mmod 6_Phoen 7_Newt 8_Spid ; Right: 2 Digits_MMods_Number of sides 2 Dig_Phoenix 2 Dig_Spider ; 1 Dig_TransReset_main :0_no 1_dblmand 2_Iter-res 3_both +5_warp ; 4 Dig_TransReset_Ch2-5:0_no 1_z-reset 2_Iter-res 3_both +5_warp ;IP2 Left: 5 Digits_Bailout Number for Channels 1 to 5 ; Right: Variab: 4 Digits_Mand/Jul(2 var) 2 Digits_Secant 4 Digits_Bees ;RP3 Left: 2 Digits_Newtonvariable 4 Digits_Colour1 ; Right: 5 Digits_Colour2 5 Digits_Colour3 ;IP3 Left: Main: 5 Digits_Warp-factor (fn1 is used) ; Right: 5 Digits_Colour4 6 Digits_Colour5 ;RP4 Left: Outside: 5 Digits_Warp-factor (fn2 is used) ; Right: Outside: 4 Dig+1 fractaldig_bord-out 4 Dig+1 fractaldig_bord-in ;IP4 Left: Inside1_Maxiter ; Right: Inside1_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn2 used) 4 Dig+1 fractaldig_border1 ;RP5 Left: Inside2_Maxiter ; Right: Inside2_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn3 used) 4 Dig+1 fractaldig_border2 ;IP5 Left: Inside3_Maxiter ; Right: Inside3_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn4 used) 4 Dig+1 fractaldig_border3 ; Altnat: Left: 1_Lake effect enabled (Inside3 disabled) ; Right: 2 Digit_Frequency 2 Digit_Waterlevel 2 Digit_Amplitude ; le=0 z=pixel da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=d3==0 vb=d>5 sc=d==2 mo=d==6 px=d==7 ab=px+(d==3)+(d==5)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 sc1=d==2 mo1=d==6 px1=d==7 v1m=mo1+px1 v1j=d>7 dd1=v1j+(d==4)+(d==5) ab1=px1+(d==3)+(d==5)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 sc2=d==2 mo2=d==6 px2=d==7 v2m=mo2+px2 v2j=d>7 dd2=v2j+(d==4)+(d==5) ab2=px2+(d==3)+(d==5)+(d==9) d=trunc(dd/10) ex3=d>1 sc3=d==2 mo3=d==6 px3=d==7 v3m=mo3+px3 v3j=d>7 dd3=v3j+(d==4)+(d==5) ab3=px3+(d==3)+(d==5)+(d==9) d=dd-d*10 ba=imag(p5) mi3=trunc(ba) dd=(d>1)+(mi3>1) ex4=dd==2 sc4=d==2 mo4=d==6 px4=d==7 v4m=mo4+px4 v4j=d>7 dd4=v4j+(d==4)+(d==5) ab4=px4+(d==3)+(d==5)+(d==9) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 dm=(d==2)+(d==4) ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex1+ex0+ex2+ex3+ex4 ; d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 ; d=imag(p3) sfac=trunc(d) da=(d-sfac)*100000000000 ba4=trunc(da/1000000) ba5=da-ba4*1000000 ; d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) ; d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 dp=p6+p0/100 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=d==3 fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=d==3 fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 ; if (mi3==1) d=(ba-mi3)*1000000 fr=round((trunc(d/10000))*10) ;lake effect by S.Gallet d=d-fr*1000 lv=(trunc(d/100))/100 d=d-lv*10000 am=d/100 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)) da=2*q*t rs=2*bo*(dd+flip(1))*t zz=center+(-q-bo*dd-flip(bo))*t z=z-zz d=imag(conj(da)*z)/imag(conj(da)*rs) le=d<=lv if (le) dd=lv-d z=z+2*dd*(1+am*sin(fr*dd^0.2))*rs endif z=z+zz else da=(ba-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=d==3 fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 endif ; if (vb) if (d3) if (ab) z=z*le+pixel*(le==0) ;Spider c=p1 else z=z*le+pixel*(le==0) c=p1 ;newton endif elseif (ab) c=z ;Phoenix z=z*le+pixel*(le==0) else c=0.4*log(sqr(z^mm)) ;many mods z=0 endif elseif (d3) if (ab) c=p1 ;Julia z=z*le+pixel*(le==0) else ;bees c=p1 z=z*le+pixel*(le==0) endif elseif (ab) c=z ;Mandel z=0 else c=z ;Secant z=z*le+pixel*(le==0) endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(z^mm)) else c=pixel endif else z=z*le+pixel*(le==0) cb=p9*u c=p1*u p=pp*u endif tt=tt-1+ex0 endif elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(z^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Quasinewton Puskas Istvan z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+0.56+ph/100-0.5*zold ;Phoenix Mike Wareman zold=z z=z1 else z2=fn1(z)+c ;Many_mods Linda Allison z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z ;Julia Puskas Istvan z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) if (dm) z=z*z+c+c*c-dp ;Double Mandel else z2=z*z ;Mandel Puskas Istvan z=z2*z2+p6*z2+c-p0 endif else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba } ---------------------------------------------end---------------------

1 0

FOTD 29-12-12 (Faerie Fantasyland [7])
by Jim Muth 29 Dec '12

29 Dec '12

FOTD -- December 29, 2012 (Rating 7) Fractal visionaries and enthusiasts: On its surface, the Z^(-2)+C Mandeloid is not much to look at -- little more than a triangle consisting of flat overlapping disks. The disks can be made larger or smaller by changing the escape radius, but this has little effect on the worth of the fractal. All is not lost however. When the entire Julibrot is sliced in different directions, it shows some aspects that are more interesting. In today's image I have double rotated the slice 66 and 66 degrees toward the Julia orientation, and rendered it with the outside parts set to 'real'. In the image, we see that the flat disks have become organized into more attractive semi- chaotic spirals. (The parent fractal actually has buds, but this is a story for another day.) I named the image "Faerie Fantasyland". The odd spelling is kind of a trendy pseudo-magical way of spelling the word 'fairy', which is used by those who are into new-age stuff. The rating of a 7 includes a full point for the smooth GIF coloring, which I really did put an hour or so of effort into. Without the coloring, the underlying scene would rate only a 6. The image is very fast. It finishes in under one minute on all but the oldest and slowest units. The image may be viewed without the inconvenience of setting up and running the included parameter file. Simply surf over to the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> and view it there. High-definition variations are posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are posted to the venerable FOTD web site at <http://www.Nahee.com/FOTD/> Snow fell all day here at Fractal Central today, while the light winds and relatively mild temperature of 30F -1C actually made the snow enjoyable. At post time about 5 inches or 12cm had piled up, but it was still falling. I'll give a final report in the next FOTD. The fractal cat alternated between stretching out on the radiator and hunching on the shelf in the southwest window, watching the snowflakes drift down. The humans took it as easy as possible, but I am concerned with the sidewalk that will eventually need to be cleared. The next FOTD will be posted when it is ready, most likely in 24 hours. Until whenever, take care, and I see that two people have been pushed in front of subway trains within a month. These trains are dangerous. We must do something about the needless deaths caused by misused subway trains. We must pass tighter train-control laws to keep subway trains from the hands of those who would misuse them. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Faerie_Fantasyland { ; time=0:00:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=+1.49344425/\ +0.22623503/210/1/-90/0 params=66/0/66/0/0/0/0/0/\ -2/0 float=y maxiter=1500 inside=0 outside=real periodicity=6 colors=000CbFCcGDcGEcGEcHFcHGcHGcIHcIIcIIcJJcJKdJK\ eKLfKMgKMhLNiLOjLOkNPlNQmOQmPRmQSnQSnSToUUoWUoYVo_\ WoaWocVoeUogToiSokRomQnoQnqRnsRnuRmvQlwRkwRjvRitRg\ sSfqSdoSbnSalT_jTZiTXgTVeTUdUSbUR`UP_UNYVMWVKVVJTV\ IRVJQWJRXJSYKTZLUZMV_NV`OWaPXaQYbSZcT_dU_dV`eWafXb\ gYchZch_di`ejbfkcgkdhlehmfingjnhkoilpjlqkmrmnrnoso\ ptpquqqurrvsswttxuuxvuvututttstsrtrqtqpsposonsnmsm\ lslksjjriirhhrggrffreerddqccqbbqaaq``q__qYZpXYpWXp\ VWpUVpTUpSToRSoQRoPQoOPoNQrNOoNNmNMkNLiNKgNJeNHbNG\ `NFZNEXNDVNCTNAQN9ON8MN7KN6IN5GN4EM6HL8KKAMJCPJESI\ GUHIXGKZGLaFNdEPfDRiCTkCVnBXqAZs9`v9ax9cu9ds9ep9fn\ 9gk9hi9if9jd9ka9l_9mY9nV9oT9pQ9qO9rL9sJ9tG9uE8u99v\ CAvFBvIBvKCvNDvQDvSEvVFvYFvYHtYIrYJpYKnYMlYNjYOiZP\ g_Re`ScaTabU_cVZdXXeYVeZTf_RfaPfbNgcMgdKhfIhgGhhEi\ hCig9lgBifDfcFc_H`WJYTLVPNSMPPIRMETJBVG7XD4YB5ZC6Z\ C6_D7_D8`D8`E9aEAaEAaFBbF } 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=========================================

1 0

FOTD 28-12-12 (Into the Aether [8])
by Jim Muth 29 Dec '12

29 Dec '12

FOTD -- December 28, 2012 (Rating 8) Fractal visionaries and enthusiasts: Today's parent fractal came from the formula (-Z)^(2.003)+C rather than (+Z)^(2.003)+C. This negative Z parent resembles the more familiar positive Z, though it has no rectangles just east of the main minibrot, and the East Valley has split apart. Today's scene lies along the infinitely divided main stem, just east of a smaller minibrot that lies well east of the large minibrot. The name "Into the Aether" refers to that hypothetical all- pervading stuff that was once assumed to be the medium that transmits electromagnetic radiation. Nowadays we know that abstract waves of probablilty do the vibrating, though it's fun to think that the aether actually exists, interpenetrating the objects around us. (And who knows? Maybe something similar [a neutrino field] actually does interpenetrate our space.) The image rates an 8, which makes it the highest rated FOTD in quite some time. The parameter file finishes in 2 minutes on most SOTA units, which makes it about average. And the web sites are always available to make life easier. Get smart. View the image on the official FOTD web site without the need of calculating it. <http://www.crosscanpuzzles.com/Archives.html> And check the augmented variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are at: <http://www.Nahee.com/FOTD/> Clouds prevailed here at FC today, though the lack of sun and resulting chill was mitigated by the lack of wind and relatively mild temperature of 34F +1C. The fractal cat passed the day in the southwest window, watching the world go by. The fractal humans passed the day closing out the old year and preparing for another year. The next FOTD image will be posted in the proper time. Until whenever, take care, and the first step in solving a problem is to see that everyone agrees on what the problem is. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Into_the_Aether { ; time=0:06:37.05 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot5 center-mag=-1.621649157\ 158942/+0.00000020374490837/6.614526e+010/1/-155/0 params=0/0/0/0/0/0/0/0/2.003/0 float=y maxiter=3200 inside=0 logmap=392 periodicity=6 colors=00030441653865A77C89E9BGADICFKEHMGJOILQKNSM\ PUORWQTYSV`UXcWZfZaiaeldiohmtmqwpuzozzmwwjsthqqfon\ dmjdmhcmfcmdclbXgYQbTJYOCTJ6PFATHEWJL_KQbMUfNZiPcl\ RinSoqUssVwvXzxYnuZlr_jo`hmafjadgbbec`bdZ_eXYeWYeW\ YdWYdWZcVZbVZbVZaVZ`UZ`UZ_UZZUZZTZYTZXTZXTZWRVdSWc\ SWcSWcSWbCWNE`MGdMHiLJnLKrLInOHkQGgTFdVD`YCY_BUaAR\ d9Nf7Ki6Gk5Dn49p36r6Do9KmCRjFYhIdeLkcOr`QxZRtURqPS\ nKSkFShAJPEA6H9AJ9DL8GN8JP7MR7PS6SU6VW6ZY5a_5d`4gb\ 4jdzufnphYsi6ig8_fAQeCGdE6cK9dPCeUFeZIfdKfiNgnQgsT\ hxVhrOelHcfBaeDZdEXcFVbGSaHQ`IO_JLZKJYLHXMEWNCVOAU\ P7TQ5SR3RS1TV3UX5V_6Xa8Yd9ZfB`iDakEbnGdpHesJfuKbjH\ Z_FVPCSEAUDBWDBYCC_CCaCCcBDdBDfBDnAEjAEzAEn9Fp9Fq9\ FpHNoOVaI_PCdC6iL7dT8_`9WiARqBMyCIrQNlbSjaRhcRfcQd\ cQbmPamP_mPYmOWmOUmNSmNRmNcmJozFmzGkzHjzIhzzgzzezz\ czz`zzZzzWzzUzzSzzPzzNzzLzzIzzGzzEzzBzz9zz7zz8zz8z\ z9zzAzzBzzCzzDzzEzzFzzFzz } frm:SliceJulibrot5 {; 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=========================================

1 0

76531Z2 Circles-zoom
by Albrecht 28 Dec '12

28 Dec '12

Hi, as announced yesterday this is a zoom into one of the fractal miniatures building every second circle, a complete and pretty image with unusual structures. You may recall that there were previous postings with similar zooms, but these were not complete images, just the underlying image made visible. I?m going to explore border defined images further but it is not easy because every participating frm reacts differently and the border values must take care of that. But IF you get a usable image it?s always worth the effort. You may try and zoom into any miniatures even the smaller outside circles and you?ll see that every one is different and has it?s own structures. Here?s Hal?s link: http://www.emarketingiseasy.com/Albrecht/76531Z2.GIF Albrecht ---------------------------------start-par-------------------------------- 76531z2 { ; Inside View 2 ; time 0.08.26.25 1600/1200 ; newt-phoen-mmods-bees-sec reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=+0.10593790239912770/+0.00000000000026454/56.75406/1/90/3.885\ 78058618804789e-016 params=-0.05825983458967864/0.3785210730307932/76531.07595702022/14235.4\ 911030602/150512.0404808048/384.3204896048/384.00482000595/128.200000859\ 1/256.2000004001/512.3000008001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000220<4>110110000110<2>000KA4<7>gcOjgRmjT<3>zzc<9>UOFRKDOGA<3>A0\ 0<9>f0Ci0Dl0F<3>z0K<6>Z0EV0DR0C<3>A08004000<26>000<4>000<7>Q0UU0YX0a_0dc\ 0hf0l<2>p0w<4>_0dX0aU0Y<2>K0NH0JG0NE1R<3>7UX6`Z4h_2oa0wc<10>2WI2TG2RE<3>\ 4G54D36F5<16>kkammcpoe<3>zwm<3>mhZjdVfaS<3>VMCRI8OE4KA0000<43>000<4>0003\ 30<5>220 } frm:multifractal_10 { ; Albrecht Niekamp Jan2005 ;RP2 Left: 5 Digits_Channel:1_main 2_outside 3_inside1 4_inside2 5_inside3 ; Frms: 0_off 1_Sec 2_Mand(2) 3_Bees 4_Jul 5_Mmod 6_Phoen 7_Newt 8_Spid ; Right: 2 Digits_MMods_Number of sides 2 Dig_Phoenix 2 Dig_Spider ; 1 Dig_TransReset_main :0_no 1_dblmand 2_Iter-res 3_both +5_warp ; 4 Dig_TransReset_Ch2-5:0_no 1_z-reset 2_Iter-res 3_both +5_warp ;IP2 Left: 5 Digits_Bailout Number for Channels 1 to 5 ; Right: Variab: 4 Digits_Mand/Jul(2 var) 2 Digits_Secant 4 Digits_Bees ;RP3 Left: 2 Digits_Newtonvariable 4 Digits_Colour1 ; Right: 5 Digits_Colour2 5 Digits_Colour3 ;IP3 Left: Main: 5 Digits_Warp-factor (fn1 is used) ; Right: 5 Digits_Colour4 6 Digits_Colour5 ;RP4 Left: Outside: 5 Digits_Warp-factor (fn2 is used) ; Right: Outside: 4 Dig+1 fractaldig_bord-out 4 Dig+1 fractaldig_bord-in ;IP4 Left: Inside1_Maxiter ; Right: Inside1_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn2 used) 4 Dig+1 fractaldig_border1 ;RP5 Left: Inside2_Maxiter ; Right: Inside2_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn3 used) 4 Dig+1 fractaldig_border2 ;IP5 Left: Inside3_Maxiter ; Right: Inside3_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn4 used) 4 Dig+1 fractaldig_border3 ; Altnat: Left: 1_Lake effect enabled (Inside3 disabled) ; Right: 2 Digit_Frequency 2 Digit_Waterlevel 2 Digit_Amplitude ; le=0 z=pixel da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=d3==0 vb=d>5 sc=d==2 mo=d==6 px=d==7 ab=px+(d==3)+(d==5)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 sc1=d==2 mo1=d==6 px1=d==7 v1m=mo1+px1 v1j=d>7 dd1=v1j+(d==4)+(d==5) ab1=px1+(d==3)+(d==5)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 sc2=d==2 mo2=d==6 px2=d==7 v2m=mo2+px2 v2j=d>7 dd2=v2j+(d==4)+(d==5) ab2=px2+(d==3)+(d==5)+(d==9) d=trunc(dd/10) ex3=d>1 sc3=d==2 mo3=d==6 px3=d==7 v3m=mo3+px3 v3j=d>7 dd3=v3j+(d==4)+(d==5) ab3=px3+(d==3)+(d==5)+(d==9) d=dd-d*10 ba=imag(p5) mi3=trunc(ba) dd=(d>1)+(mi3>1) ex4=dd==2 sc4=d==2 mo4=d==6 px4=d==7 v4m=mo4+px4 v4j=d>7 dd4=v4j+(d==4)+(d==5) ab4=px4+(d==3)+(d==5)+(d==9) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 dm=(d==2)+(d==4) ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex1+ex0+ex2+ex3+ex4 ; d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 ; d=imag(p3) sfac=trunc(d) da=(d-sfac)*100000000000 ba4=trunc(da/1000000) ba5=da-ba4*1000000 ; d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) ; d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 dp=p6+p0/100 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=d==3 fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=d==3 fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 ; if (mi3==1) d=(ba-mi3)*1000000 fr=round((trunc(d/10000))*10) ;lake effect by S.Gallet d=d-fr*1000 lv=(trunc(d/100))/100 d=d-lv*10000 am=d/100 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)) da=2*q*t rs=2*bo*(dd+flip(1))*t zz=center+(-q-bo*dd-flip(bo))*t z=z-zz d=imag(conj(da)*z)/imag(conj(da)*rs) le=d<=lv if (le) dd=lv-d z=z+2*dd*(1+am*sin(fr*dd^0.2))*rs endif z=z+zz else da=(ba-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=d==3 fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 endif ; if (vb) if (d3) if (ab) z=z*le+pixel*(le==0) ;Spider c=p1 else z=z*le+pixel*(le==0) c=p1 ;newton endif elseif (ab) c=z ;Phoenix z=z*le+pixel*(le==0) else c=0.4*log(sqr(z^mm)) ;many mods z=0 endif elseif (d3) if (ab) c=p1 ;Julia z=z*le+pixel*(le==0) else ;bees c=p1 z=z*le+pixel*(le==0) endif elseif (ab) c=z ;Mandel z=0 else c=z ;Secant z=z*le+pixel*(le==0) endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(z^mm)) else c=pixel endif else z=z*le+pixel*(le==0) cb=p9*u c=p1*u p=pp*u endif tt=tt-1+ex0 endif elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(z^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Quasinewton Puskas Istvan z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+0.56+ph/100-0.5*zold ;Phoenix Mike Wareman zold=z z=z1 else z2=fn1(z)+c ;Many_mods Linda Allison z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z ;Julia Puskas Istvan z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) if (dm) z=z*z+c+c*c-dp ;Double Mandel else z2=z*z ;Mandel Puskas Istvan z=z2*z2+p6*z2+c-p0 endif else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba } ------------------------------------------end------------------------------

1 0

FOTD 27-12-12 (The End of the End [7])
by Jim Muth 28 Dec '12

28 Dec '12

FOTD -- December 27, 2012 (Rating 7) Fractal visionaries and enthusiasts: After a brief break during which the world did not end, the FOTD has returned with another fractal. Like all other fractals, today's has existed for all eternity but has never been seen by intelligent beings until today. The parent fractal shows what happens when 2 parts of Z^2 are mixed with 2 negative parts of Z^(-0.9) and straight C is added on each iteration. This parent consists of a rather distorted Mandeloid set with a large triangular area of chaos to the northwest and a much smaller Mandeloid set some distance to the southwest. Today's image lies in the triangular area of chaos. The name "The End of the End" points out that the latest end of the world has come and gone, and like all previous ends of the world, it was a total failure. Of course, true believers will claim that some hugely important but invisible thing, such as a 'harmonic convergence', did actually happen, but was not noticed or reported by the mass media, which is controlled by the big greedy corporations for their own benefit. The calculation time of 1-1/3 minutes will pass in less time than it takes for a harmonic convergence to manifest. But the web sites will remove all traces of harmonic convergency. The chore of calculation may be avoided by viewing the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> High definition variations are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images may be accessed at: <http://www.Nahee.com/FOTD/> 1-1/2 inches (4cm) of snow fell on Christmas Eve here at Fractal Central, not quite enough to make an honest white Christmas, but just enough to make the kids happy. The day after Christmas brought 5 inches (12cm) of heavy sleety snow to the area, making more of a nuisance than a post card scene. Today was cloudy with a temperature of freezing. The fractal cat kept busy watching for the occasional passing snowflake, while the humans recovered from the holiday. The next FOTD will be ready by this time tomorrow. Whether it is posted as soon as it is ready remains to be seen. Until whenever, take care, and we should not even think of passing futile laws to solve our current problems such as climate change or easy access to guns. Such laws will do nothing but create more division, more criminals, and increase overall contention. If a solution to our problems is to be successful, it must be accepted and acted upon by everyone from the far right to the far left. If no such solution is possible, then our problems have no solution, and it is time to stop wasting energy, to blame the other guy and prepare for the end. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_End_of_the_End { ; time=0:01:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+0.1098265398921243/-0.2191813687286491\ /2.018e+012/1/-27.5/0 params=-2/-0.9/2/2/-0.6/0/0/0 float=y maxiter=800 inside=0 logmap=96 periodicity=6 mathtolerance=0.05/1 colors=000OKfNHcKFZHCUE9PB6K83F502KD3ZQ3mb4sn4qdAd\ VFVHKTBMO1RGAAAA08A0PQAUhAZqRcwRZtVUpZWkbdgea_`ZSW\ UKSLDND5J02E00AA5XzZznZzjZzeZzbXzdYzf_zhmzjpzlsvzv\ xzzzzzzmYmkUmjQmiMmlOmnQgpSbrUXtWSvYMx_HsWFnTDiQBq\ N9rJ7wG5rS3tY1u_0ta0ni0Yl0Qo0Dw0iXZgYVfYSeYPdYMbZJ\ aZG`ZD_ZAa_Bc_Ce`Df`Eh`FjaGlaHmaHgjVbrhYzuTdqPcnOc\ rRcnUcjXcg_ccbc`emXhmUkmQnmNimMemMamMYmMTmMPmMLmMH\ mMDmMGmOJmPMmQPmRSmTVmUYmV_mWamVbmVcmVdmUfzUgzUhzT\ izTkzTlzSmzSnzSpzRqzRrzRszRpzPnzNlzLizKgzzezzczzbz\ zbzzbzzazzazzazz`zz`zz`zzczzezzhzzjzzlzzozzqzzszzo\ zzlzzizzfzzbzz_zzXzzUzzQzzNzzKzzHzzDzzAzz7zz4zzJzz\ Yzzkzzjzzizzhzzgzzfzzezzdzzczzbzzaqf`rh_rjZslYsnXs\ pWtrVttUuvTuxTuzStvRtrRtoQtkQthPzdPz`OzYOzUNzRNzNM\ zJMzGLzCLz9Oz9Rz9Uz9Xz9_z9bz9ez9hz9kz9gzNdz_`zmYzz\ XzyWzyWzyVzyUzyUzyTzySzxSzxRzxQzxQzxPzxPzxOzwNzvNz\ uMztLzsLzrKzqJzpJzpLznMzm } 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

76531Z Circles
by Albrecht 27 Dec '12

27 Dec '12

Hi, I?m back again amd taking over. First a BIG Thank You! to Hal for his wonderful way of presenting the Multifractal_10 Images. Guess I have to improve to keep his standards. All images presented in the next days are new and created for this purpose. "Circles" shoes the Many Mods formula which is well known to all regular viewers with one big exception: This one uses the Newton Formula for outer structures, I haven?t seen anything like it myself and it forms a beautiful image. The reason is: This image is border defined, Newton is used as main shape. Three freely designed borders are used by Multifractal_10: outside-shape, inside 1 and 2, inside 2 and 3. The sequence of formulas used is: Newton-phoenix-manymods-bees-secant. Another thing is unique: Every second circle consists of fractal miniatures ready to explore!! The next presentation will show one of them. Here?s Hal?s link to the image: http://www.emarketingiseasy.com/Albrecht/76531Z.GIF ; ----------------start par------------------------------------------------- 76531z { ; Circles ; time 0.17.38.19 1600/1200 ; newt-phoen-mmods-bees-sec reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-0.0575112/2.64538e-013/2.735546/1/90/3.88578058618804789e-01\ 6 params=-0.05825983458967864/0.3785210730307932/76531.07595702022/14235.4\ 911030602/150512.0404808048/384.3204896048/384.00482000595/128.200000859\ 1/256.2000004001/512.3000008001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000<3>000000000330<6>220220220<3>110000110<2>000KA4<7>gcOjgRmjT<3\ >zzc<9>UOFRKDOGA<3>A00<9>f0Ci0Dl0F<3>z0K<6>Z0EV0DR0C<3>A08004000<26>000<\ 4>000<7>Q0UU0YX0a_0dc0hf0l<2>p0w<4>_0dX0aU0Y<2>K0NH0JG0NE1R<3>7UX6`Z4h_2\ oa0wc<10>2WI2TG2RE<3>4G54D36F5<16>kkammcpoe<3>zwm<3>mhZjdVfaS<3>VMCRI8OE\ 4KA0000<42>000 } frm:multifractal_10 { ; Albrecht Niekamp Jan2005 ;RP2 Left: 5 Digits_Channel:1_main 2_outside 3_inside1 4_inside2 5_inside3 ; Frms: 0_off 1_Sec 2_Mand(2) 3_Bees 4_Jul 5_Mmod 6_Phoen 7_Newt 8_Spid ; Right: 2 Digits_MMods_Number of sides 2 Dig_Phoenix 2 Dig_Spider ; 1 Dig_TransReset_main :0_no 1_dblmand 2_Iter-res 3_both +5_warp ; 4 Dig_TransReset_Ch2-5:0_no 1_z-reset 2_Iter-res 3_both +5_warp ;IP2 Left: 5 Digits_Bailout Number for Channels 1 to 5 ; Right: Variab: 4 Digits_Mand/Jul(2 var) 2 Digits_Secant 4 Digits_Bees ;RP3 Left: 2 Digits_Newtonvariable 4 Digits_Colour1 ; Right: 5 Digits_Colour2 5 Digits_Colour3 ;IP3 Left: Main: 5 Digits_Warp-factor (fn1 is used) ; Right: 5 Digits_Colour4 6 Digits_Colour5 ;RP4 Left: Outside: 5 Digits_Warp-factor (fn2 is used) ; Right: Outside: 4 Dig+1 fractaldig_bord-out 4 Dig+1 fractaldig_bord-in ;IP4 Left: Inside1_Maxiter ; Right: Inside1_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn2 used) 4 Dig+1 fractaldig_border1 ;RP5 Left: Inside2_Maxiter ; Right: Inside2_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn3 used) 4 Dig+1 fractaldig_border2 ;IP5 Left: Inside3_Maxiter ; Right: Inside3_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn4 used) 4 Dig+1 fractaldig_border3 ; Altnat: Left: 1_Lake effect enabled (Inside3 disabled) ; Right: 2 Digit_Frequency 2 Digit_Waterlevel 2 Digit_Amplitude ; le=0 z=pixel da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=d3==0 vb=d>5 sc=d==2 mo=d==6 px=d==7 ab=px+(d==3)+(d==5)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 sc1=d==2 mo1=d==6 px1=d==7 v1m=mo1+px1 v1j=d>7 dd1=v1j+(d==4)+(d==5) ab1=px1+(d==3)+(d==5)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 sc2=d==2 mo2=d==6 px2=d==7 v2m=mo2+px2 v2j=d>7 dd2=v2j+(d==4)+(d==5) ab2=px2+(d==3)+(d==5)+(d==9) d=trunc(dd/10) ex3=d>1 sc3=d==2 mo3=d==6 px3=d==7 v3m=mo3+px3 v3j=d>7 dd3=v3j+(d==4)+(d==5) ab3=px3+(d==3)+(d==5)+(d==9) d=dd-d*10 ba=imag(p5) mi3=trunc(ba) dd=(d>1)+(mi3>1) ex4=dd==2 sc4=d==2 mo4=d==6 px4=d==7 v4m=mo4+px4 v4j=d>7 dd4=v4j+(d==4)+(d==5) ab4=px4+(d==3)+(d==5)+(d==9) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 dm=(d==2)+(d==4) ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex1+ex0+ex2+ex3+ex4 ; d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 ; d=imag(p3) sfac=trunc(d) da=(d-sfac)*100000000000 ba4=trunc(da/1000000) ba5=da-ba4*1000000 ; d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) ; d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 dp=p6+p0/100 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=d==3 fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=d==3 fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 ; if (mi3==1) d=(ba-mi3)*1000000 fr=round((trunc(d/10000))*10) ;lake effect by S.Gallet d=d-fr*1000 lv=(trunc(d/100))/100 d=d-lv*10000 am=d/100 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)) da=2*q*t rs=2*bo*(dd+flip(1))*t zz=center+(-q-bo*dd-flip(bo))*t z=z-zz d=imag(conj(da)*z)/imag(conj(da)*rs) le=d<=lv if (le) dd=lv-d z=z+2*dd*(1+am*sin(fr*dd^0.2))*rs endif z=z+zz else da=(ba-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=d==3 fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 endif ; if (vb) if (d3) if (ab) z=z*le+pixel*(le==0) ;Spider c=p1 else z=z*le+pixel*(le==0) c=p1 ;newton endif elseif (ab) c=z ;Phoenix z=z*le+pixel*(le==0) else c=0.4*log(sqr(z^mm)) ;many mods z=0 endif elseif (d3) if (ab) c=p1 ;Julia z=z*le+pixel*(le==0) else ;bees c=p1 z=z*le+pixel*(le==0) endif elseif (ab) c=z ;Mandel z=0 else c=z ;Secant z=z*le+pixel*(le==0) endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(z^mm)) else c=pixel endif else z=z*le+pixel*(le==0) cb=p9*u c=p1*u p=pp*u endif tt=tt-1+ex0 endif elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(z^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Quasinewton Puskas Istvan z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+0.56+ph/100-0.5*zold ;Phoenix Mike Wareman zold=z z=z1 else z2=fn1(z)+c ;Many_mods Linda Allison z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z ;Julia Puskas Istvan z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) if (dm) z=z*z+c+c*c-dp ;Double Mandel else z2=z*z ;Mandel Puskas Istvan z=z2*z2+p6*z2+c-p0 endif else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba }

1 0

FOTD 21-12-12 (DOOMSDAY!!!! [No Rating])
by Jim Muth 22 Dec '12

22 Dec '12

FOTD -- December 21, 2012 (No Rating) Fractal visionaries and enthusiasts: It's come! It's the end of the world! This is it! There's no tomorrow! Today is doomsday! Armageddon! The Apocalypse! Nostradamus was right! All this doom rolled into one! . . . . . . etc. . . . Ah nuts! The hour has passed. It was all a media scare tactic. What a disappointment! I have seen nothing happen that could be considered out of the ordinary in even the slightest degree, except that darkness seems to be falling unusually early lately. I believe the precise moment of doom was 11:11am EST, or 16:11pm GMT. But that time has come and gone, and the world is still here. The apocalypse was a flop. The Mayans were wrong. So let's move on to the fractals. In today's image the strange rectangle has totally vanished as predicted. Only a few traces of yellow mark the spot where it was last seen. Actually, the rectangle still exists in its full glory -- elsewhere. It is we who have changed our view of it and moved on. The name explains itself. If I had rated the image, it would have had the lowest rating in FOTD history -- most likely a 2. Luckily, the image is very fast. It finishes in only 30 seconds. The finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> Hi-def variations are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are at: <http://www.Nahee.com/FOTD/> The parameter file for a second image is included with this FOTD. The name "One from Doomsday" shows the spirit of the departed rectangle happily floating through the ethers of whereever good fractals go when they die. Those who do not believe in spirits may bypass this second image. The day began wet and windy, with a temperature of 50F 10C. The rain ended during the morning, but the clouds remained and the temperature dropped fast in the afternoon, reaching freezing by 4pm. A few flurries of snow fell later in the day, though the ground remained only wet. The fractal cat passed the day watching the world go by; the humans spent the day thinking of the holidays. The next FOTD will be posted in around six days, around December 27. There is simply too much to do here at FC to keep the FOTD going uninterrupted through the holidays. Until whenever, take care, and the next doomsday (fiscal cliff) is only ten days off. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= DOOMSDAY!!!! { ; time=0:00:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=+0.001962114\ 25377242/+0.00121653453603809/107.7586/1.3369/0/\ -38.6598082540901018 params=99/98/79/82/-1.7435/\ -0.002/0.000175/0.073883/2.003/0 float=y maxiter=8000 inside=0 logmap=55 periodicity=6 colors=00022M22M22L22L22K22K22J22J12I12I12H12H12G1\ 2G11F11F11E11E11D11D11C41011C11B11B11A11A119019018\ 018007007006006005005004004003003002002001001000Lc\ nKbmKbmKalKalKakJ`kJ`jJ`jJ_iJ_iIZhIZhIZgIYgIYfHYfH\ XeHXeHWeHWdGWdGVcGVcGVbGUbFUaFUaFT`FT`FS_ES_ESZERZ\ ERYERYEQYDQXDPXDPWDPWDOVCOVCOUCNUCNTCMTBMSBMSBLRBL\ RBLQAKQAKPAKPAJPAJO9IO9IN9IN9HM9HM8HL8GL8GK8FK8FJ7\ FJ7EI7EI7EH7DH7DH6CG6CG6CF6BF6BE5BE5AD5AD5AC59C49B\ 48B48A48A479379378368368357257256246245045134134A2\ 3KA3UK2cU2mc1zm1zm0zm0xp7un6sl6qj6nh5zm5zm5zm5zm4z\ m4zm4zm4zm3zm3zm3zm3zm2zm2zm2zm2zm1zm1zm1zm1zm0zm0\ zm0zm3zm2zm2zm2zm2zm2zm2zm2zm2zm2zc2zc2zc2zc2zc2zc\ 2zc2zc2zc2zc2zcbzcdzcfzchzcjzckzcjzcizcizchzchzcgz\ cgzcfzcmzcmzcmzcmzcmzcmzcmzcmzczzczzczzczzczzczzcz\ zUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzU\ zzUzzUzzUzzUzzUzzUzzUzzUz } One_from_Doomsday { ; time=0:01:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=+0.007190875\ 14157552/+0.0019266285650588/3195327/0.5078/55.814\ 0458117172074/54.4657933543971922 params=99/98/79/\ 82/-1.7435/-0.002/0.000175/0.073883/2.003/0 float=y maxiter=1000 inside=0 logmap=130 periodicity=6 colors=00022M22M22L22L22K22K22J22J12I12I12H12H12G1\ 2G11F11F11E11E11D11D11C41011C11B11B11A11A119019018\ 018007007006006005005004004003003002002001001000Lc\ nKbmKbmKalKalKakJ`kJ`jJ`jJ_iJ_iIZhIZhIZgIYgIYfHYfH\ XeHXeHWeHWdGWdGVcGVcGVbGUbFUaFUaFT`FT`FS_ES_ESZERZ\ ERYERYEQYDQXDPXDPWDPWKOVKOVKOUKNUKNTKMTKMSKMSULRUL\ RULQUKQUKPUKPUJPUJOcIOcINcINcHMcHMcHLcGLcGKmFKmFJm\ FJmEImEImEHmDHmDHzCGzCGzCFzBFzBEzBEzADzADzKCzKCzKB\ zKBzKAzKAzK9zK9zU8zU8zU8zU7zU7zU6zU6zU5zc5zc4zc4zc\ 3zc3zc2zc2zc1zm1zm0zm0xp7un6sl6qj6nh5zm5zm5zm5zm4z\ m4zm4zm4zm3zm3zm3zm3zm2zm2zm2zm2zm1zm1zm1zm1zm0zm0\ zm0zm3zm2zm2zm2zm2zm2zm2zm2zm2zm2zc2zc2zc2zc2zc2zc\ 2zc2zc2zc2zc2zcbzcdzcfzchzcjzckzcjzcizcizchzchzcgz\ cgzcfzcmzcmzcmzcmzcmzcmzcmzcmzczzczzczzczzczzczzcz\ zUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzU\ zzUzzUzzUzzUzzUzzUzzUzzUz } 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=========================================

1 0