November 2012 - Fractint - mailman.xmission.com

FOTD 17-11-12 (A Twist of Reason [?])
by Jim Muth 18 Nov '12

18 Nov '12

FOTD -- November 17, 2012 (Rating ?) Fractal visionaries and enthusiasts: NEW FORMULA ALERT! At least I don't think I've posted it before. Today's image is the first in a series of distorted Mandelbrot sets. The distortion is created by applying the 'exp' function to different initial values of 'C'. Doing this creates the effect of viewing the M-set from the point determined by the value assigned the (p3) parameter. The farther from this point, the features lie, the smaller they appear. In today's image the value is +0.255, which places the viewer deep in East Valley and greatly enlarges the surrounding area. Today's image is its own parent fractal, though due to the nature of the exponential function, there are a multitude of parent fractals. The name "A Twist of Reason" indicates that there is nothing at all unreasonable about the Mandelbrot distortion. The same may not be true of the upcoming images however. The rating of a question mark shows my uncertainty as to the true value of the image. The calculation time of 10 seconds will simply fly by. It will take a bit longer to see the finished image on the web sites, but doing so will be more convenient. Check the finished image at: <http://www.crosscanpuzzles.com/Archives.html> and the hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back inages are at: <http://www.Nahee.com/FOTD/> Total sun and a temperature of 52F 11C made today a day to be remembered here at Fractal Central. The next FOTD will be posted in the proper spacetime. Until whenever and wherever this might be, take care, and have a good time taking it easy. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= A_Twist_of_Reason { ; time=0:00:10.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotFNC function=exp periodicity=6 center-mag=-3.39731/3.1415927/0.2989/1/180 inside=0 params=2/0/0/0/0.255/0 float=y maxiter=1500 colors=000Xd8Xe7Xf7Wg7UhASiDQjFOkIMlKKmNKnPKoSKpUK\ qXKrZLsaNtcPu`PvZRvXTwUVvSXuQZtN`sLbrJdqHfpKhoMjnP\ lmRnlUpkWrjZti`vhcvgevfgughtghshhrhhpihoihmjikjihk\ ifkidlibli`ljZmjXmjVnjTnjRojPokNpkLpkJqkHqkGqkInhJ\ lfLjdMhbOf`PdZRaXS_VTYTVWRWUPYSNZPL`NJaLHcJFdHDeFB\ gGEhHHiIJkJMlKPmLRoMUpNXqOZsPatQduRfwSixTlyUn4AW5G\ Y6M_7R`8Xb9acAgeBlfCrhCwiBtgAqfAoe9lc9ib8ga7d_7aZ6\ _Y6XX5UV4SU4PT3MR3KQ2HP2FOGKQTOSfTUsXWtVUtUTtTSuSR\ uRQuQPvPOvONvNMwMLwLKwKIwJHxIGxHFxGEyFDyECyDBzCAzB\ 9zA8z97wABuBFsBIqCMoDQmDTjEXhF`fFcdGgbHk`HnXEhUBcQ\ 8ZN5UQQVSiVXgQaeLfdHWSBMF5LI7KL9KNBJQDITFIVHHYJG`L\ GbNFePEhREjSIXTMJUP6UOdsLcrIbqFapCap9`o6_n3Zm0Zm2X\ n4Wn6Vn8UnAToCSoERoGQoIPpKOpMNpOMpQLqSKqUJqWIqVLmV\ OjURfUTcUW`TZXTaUTcRUaVV`ZV_aWYeXXhXWlYUoZTsZSvYTr\ YUoYUkXVhXWdXWaXXZWYVWYSWZOV_LV_HV`EV`BQWLMSVINdEJ\ mHKlKLkNMkQNjTOiWPiZQhaRg } frm:MandelbrotFNC {; Jim Muth b=p1, z=p2, c=p3+fn1(pixel): z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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Arrival
by Albrecht 17 Nov '12

17 Nov '12

Hi, this is the (almost) total view of the Fractal-Journey image, therefore the title. Looking closely you will detect a lot of structures and elements not seen before. Another slow one like all border-defined images but available for immediate watching in full HD on Hal?s server. http://www.emarketingiseasy.com/Albrecht/71635XE.GIF Happy zooming! Albrecht -----------------start-par---------------------------- 71635xe { ; Arrival ; time 23.17 1600/1200 ; newt-sec-phoen-bees-mmods ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=cos/exp/exp/sin passes=t center-mag=-0.105102/-0.00180651/0.6699414/1.1324/\ -90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/716\ 35.03564901002/14253.2207090221/151024.0204808192/\ 384.32768524288/384.00482000595/128.3007683001/256\ .3007682001/512.2007681001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=-4 periodicity=0 rseed=-2436 colors=000zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8K\ J8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriA\ tm9vq8xu7zz5zz4zz3<4>zj4zg4zc4<3>zS5zP5zL6zI6zE6wE\ 6tD6<6>vAIv9Kv9M<3>x7Sy7Uy6Wz6Yz5_<3>f5Ma5IW4E<2>_\ 4H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0g\ y0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4K\ W0Qc<3>5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>civf\ lvinvlqvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP\ 8FL8CI<3>SCCXCAaB9<3>uA2zA0xA0<12>SA1QA1NA1<3>D92<\ 6>UXAW`BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi\ _5fc0ce7_jFRoNIzb0zj0000zr0 } 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-----------------------

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Trapped Cosine
by Mike Frazier 17 Nov '12

17 Nov '12

This fractal uses a modified Paul Carlson orbit trap coloring method with the parallel resistor formula. Disconnected minibrots and long arms make it easier to avoid overlap issues I have had with this method in the past. Here is a link to an image: http://dl.dropbox.com/u/33642054/image/trapped_cosine_1200_5.jpg The Fractint compatible PAR file for the image is: Trapped_Cosine { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20121117_1037 passes=1 float=y center-mag=-3.240788740145593/-5.614587198083252e-\ 15/8333333437.5/1/0/0 params=0.03/0.3/8/30/6/0.25/0/0/0/0 maxiter=500 inside=255 outside=summ colors=000fOz<28>I0Kz0f<28>O08z88<28>O00zW0<28>c40\ zz0<28>aG00zR<28>0C40zz<28>0CCGGz<28>00O000<12>000\ z88 } frm:F_20121117_1037 { ; Epicycloid_Mset based on Astroid_Mset ; Astroid_Mset copyright (c) Paul W. Carlson, 1997 ; Epicycloid_Mset by Mike Frazier, 2011 ;**************************************************** ; Always use floating point math and outside=summ. ; ; Parameters: ; real(p1) = a factor controlling the width of the curves ; imag(p1) = radius of the curve ; real(p2) = number of color ranges ; imag(p2) = number of colors in each color range ; real(p3) = number of cusps, even integers ; imag(p3) = cusp amplitude (0 to 1) ; ; Note that the equation variable is w, not z. ; Initialize cindex to the index of the background color ; Formula modified to avoid color index 0 which can not ; be used with outside=summ in FractInt v20.04 ;**************************************************** w=0, c=pixel, c1=pixel+1, c2=pixel-1, z=0, cindex=254,; Background color bailout=0, iter=0, range_num=0, i=(0,1), r=imag(p1), f=real(p3)+1, b=imag(p3), ;**************************************************** ; In the accompanying par file, ; we have 8 color ranges with 30 colors in each range ; for a total of 240 colors. The first range starts at ; color 1. Pixels will use color 254 when |w| > 1000. ; Other values can be used here as long as the product ; of num_ranges times colors_in_range is less than 255. ; Color 254 is reserved for the background color and ; color 255 can be used for the inside color. ;**************************************************** num_ranges=real(p2), colors_in_range=imag(p2), ;**************************************************** ; Real(p1) controls the width of the curves. ; These values will usually be in the range 0.001 to 0.1 ;**************************************************** width=real(p1), index_factor=(colors_in_range-1)/width: ;**************************************************** ; The equation being iterated. Almost any equation ; that can be expressed in terms of a complex variable ; and a complex constant will work with this method. ; This example uses the parallel resistor formula ;**************************************************** ww=w*w, w=1/(1/(-1*ww*(cos(w)-1)+c1)+1/(ww*ww+c2)), ;**************************************************** ; The orbit trap curve is an epicycloid. ; Any two-dimensional curve can ; be used which can be expressed in parametric form in ; terms of the angle from the origin. ;**************************************************** ang=atan(imag(w)/real(w)), astroid=r*(cos(ang)-b*cos(f*ang)+i*(sin(ang)-b*sin(f*ang))), ;**************************************************** ; If the orbit point is within some distance of the curve, ; set cindex to the index into the colormap and set the bailout ; flag. Note: the way we use the "distance" here has ; the effect of turning the curves inside-out in the image. ;**************************************************** distance=abs(|w|-|astroid|), if(distance<width&&iter>1), cindex=index_factor*distance+range_num*colors_in_range+1, bailout=1, endif, ;**************************************************** ; Cycle through the range numbers (0 thru num_ranges - 1) ; With two color ranges, even iterations use color ; range 0, odd iterations use color range 1. ;**************************************************** range_num=range_num+1, if(range_num==num_ranges), range_num=0, endif, ;**************************************************** ; Since we are using outside=summ, we have to subtract ; the number of iterations from z. ;**************************************************** iter=iter+1, z=cindex-iter, ;**************************************************** ; Finally, we test for bailout ;**************************************************** bailout==0&&|w|<1000 } -- Mike Frazier www.fracton.org

1 0

Fractal_Journey
by Albrecht 17 Nov '12

17 Nov '12

Hi, yesterday I posted the "Mystery" which was a zoom into an inside-out conversion of an otherwise normal and pretty fractal. That?s what it is: The outside became the empty circle inside and the inside was converted into the looks and structure of the outer frame. Today I?m presenting the reconversion. As it was a zoom, I had no idea what to expect. Here it is without any editing. Judge yourself. Albrecht --------------------------------start-par------------------------------ 71635XC { ; Fractal_Journey ; Time 46.21 1600/1200 ; Conversion of Mystery Image ; back to regular reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=cos/exp/exp/sin passes=t center-mag=0.0104739/-0.881323/3.318983/0.8831 params=-0.05825983458967864/0.3785210730307932/716\ 35.03564901002/14253.2207090221/151024.0204808192/\ 384.32768524288/384.00482000595/128.3007683001/256\ .3007682001/512.2007681001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=-4 periodicity=0 rseed=-2436 colors=000zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8K\ J8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriA\ tm9vq8xu7zz5zz4zz3<4>zj4zg4zc4<3>zS5zP5zL6zI6zE6wE\ 6tD6<6>vAIv9Kv9M<3>x7Sy7Uy6Wz6Yz5_<3>f5Ma5IW4E<2>_\ 4H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0g\ y0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4K\ W0Qc<3>5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>civf\ lvinvlqvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP\ 8FL8CI<3>SCCXCAaB9<3>uA2zA0xA0<12>SA1QA1NA1<3>D92<\ 6>UXAW`BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi\ _5fc0ce7_jFRoNIzb0zj0000zr0 } 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

Mystery
by Albrecht 16 Nov '12

16 Nov '12

Hi, this is a MOST unsusual image. Got it using border-out values for bailout instead of border-in. The In-version is a pretty multistructural one and then this. Can anybody tell me what happened? Invisible mandels seem to be outside with their heads turned to the inside. Jim, or Paul, if listening, what do you think? Note the FRM version with an improved input section. Albrecht -----------------------start-par------------------ 71635x { ; Mystery ; time 28.57 1600/1200 ; Newt-secant-phoen-bees-mmods reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=cos/exp/exp/sin passes=t center-mag=0.0104739/-0.881323/3.318983/0.8831 params=-0.05825983458967864/0.3785210730307932/716\ 35.03564901002/14253.2207090221/151024.0204808192/\ 384.32768524288/384.00482000595/128.3007681001/256\ .3007682001/512.3007683001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=-4 periodicity=0 rseed=-2436 colors=000zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8K\ J8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriA\ tm9vq8xu7zz5zz4zz3<4>zj4zg4zc4<3>zS5zP5zL6zI6zE6wE\ 6tD6<6>vAIv9Kv9M<3>x7Sy7Uy6Wz6Yz5_<3>f5Ma5IW4E<2>_\ 4H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0g\ y0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4K\ W0Qc<3>5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>civf\ lvinvlqvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP\ 8FL8CI<3>SCCXCAaB9<3>uA2zA0xA0<12>SA1QA1NA1<3>D92<\ 6>UXAW`BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi\ _5fc0ce7_jFRoNIzb0zj0000zr0 } frm:multifractal_10 { ; Albrecht Niekamp Jan2005 ;RP2 Left:5 Dig_Chan: (1)shape (2)outside (3)inside1 (4)inside2 (5)inside3 ; Frm:0_off 1_Sec 2_Mand(2) 3_Bees 4_Jul 5_Mmod 6_phoen 7_newt 8_spid ; Right:2 Dig_MMods_Number of sides 2 Dig_Phoenix 2 Dig_Spider ; 1 Dig_TransReset-Shape: 0_no 1_DblMand 2_Iter-res 3_both +5_warp ; 4 Dig_TransReset-Ch 2-5:0_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: Shape: Warp-factor (fn1 is used) ; Right: 5 Digits_Colour4 6 Digits_Colour5 ;RP4 Left: Outside: 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 }

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FOTD 14-11-12 (Julia Intrusion [7])
by Jim Muth 15 Nov '12

15 Nov '12

FOTD -- November 14, 2012 (Rating 7) Fractal visionaries and enthusiasts: The formula behind today's image takes 0.8 part of Z^(-5.8) and subtracts 0.8 part of Z(-9.9) from it on each iteration before adding (1/C). The resulting parent fractal is little more than a mostly open ellipse with its longer axis in the vertical direction and eight patches of debris arranged in a ring just inside the perimeter of this ellipse. Today's scene is located in the debris along the negative X-axis at the western edge of the open ellipse. The name "Julia Intrusion" refers to the 'almost' Julia set at the center. Such miniature Julia sets in Mandelbrot images indicate that an unseen Mandelbrot set or minibrot lies hidden beneath the surface detail of the image. The shape of the Julia set corresponds to the part of the M-set over which it lies. A bit of the underlying Mandelbrot set shows through the surface Julia set as the bright bluish debris filling the left half of the J-set. The rating of a 7 is based mostly on the coloring, which in turn was created by the outside=tdis option. The calculation time of one minute has been rounded for convenience, but the parameter file will run in about this time on most SOTA (State of the Art) computers. Those with machines that lack art appreciation may view the image on one of the web sites. The image has already been calculated and is posted at: <http://www.crosscanpuzzles.com/Archives.html> with high-definition variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are available at: <http://www.Nahee.com/FOTD/> After a few early morning clouds, the day passed with total sun and a temperature of 46F +8C. The next FOTD will be posted in the near future. Until whenever, take care, and ask questions. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Julia_Intrusion { ; time=0:08:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-0.89492913214/+0.01017421388/579726/1/\ -80/0 params=0.8/-5.8/-0.8/-9.9/0/0/0/0 float=y maxiter=15000 inside=0 outside=tdis periodicity=6 colors=000QfNWcNa`OgYOmVPsSPyQPvONsMMpLLmJKjIJgGHd\ FGaDFZBEWADT8BQ7AN59K48H27E16J58N8ARBBVEDZHFbKGfNI\ jQKnTLoRJpPHpNFqLDrJBrH9sF7tD5tC4oG7jK9eNB`REWVGRY\ IcaKceNchPclRcoTclVciXcfYmnOmnPmnQmnQmnRmnSmoTmoTz\ oUzoVzoWzoWzpXzpYzpZzpZzp_zp`zqazqazqbzqczqdzqdFqe\ FrfErgErgDrhDriCrjCsjBskBslAsmAsm9sn9to8tp8tp7tq7t\ r6ts5ut6ts7tr7sq8sq8sp9roArnAqnBqmBqlCpkDpkDpjEoiE\ ohFnhGngGnfHmeHmeImdJlcJlbKkbKkaLk`Mj`Mj_NiZNiYOiY\ PhXPhWQhVQgVRgUSfTSfSTfSTeRUeQVePVdPWdOWcNXcMYcMYb\ LZbKehJbfK`dKZbKXaKV_KTYKRXKPVLNTLLRLJQLHOLFMLCKKD\ LLDLLDMMDMMDNNDNNDOODOODPPDPPDPQDQQDQRDRRDRSESSEST\ ETTETUEUUEUVEUVEVWEVWEWXEWXEXYEXYEYZEYZEYZFZ_FZ_F_\ `F_`F`aF`aFabFabFbcFbcFbdFcdFceFdeFdfGefGegGfgGfhG\ ghGgiGgiGhjGhjGikGikGjlGjlGkmGkmFmnGlmGlmGkmGkmHkm\ HjmHjmHjmHimIimIilIhlIhlIglJglJglJflJflKflKelKekKe\ kKdkLdkLckLckLckLbkMbkMbk } 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

MFRX194h
by Albrecht 15 Nov '12

15 Nov '12

Hi, I?m presenting this image because it has a story. About 10 years ago, when I did not think about my multifractal project, I was experimenting and testing combinations of formulas. The results later partly went into the project. As I always was in a hurry the image was not finished and the experiments went on. Later, when I looked at it I saw that the Many-mods holes contained small fractal images which you could zoom into. But the data were lost and I couldn?t finish it, but always kept it. Just lately, cleaning up my working folder, I stumbled on some old experimental formulas, tested them and voila! one was the correct one. So here it is. Albrecht ----------------------------------start-par------------------------------- MFRX194h { ; An_early_Wonder ; Time 27.48 1600/1200 ; Multifrac_236 reset=2004 type=formula formulafile=mfr.frm formulaname=multifrac_236 ismand=y function=exp/exp/exp passes=t center-mag=-1.19904e-014/1.59872e-014/0.3704381 params=0.4546494949186682/-0.6008903775139622/384.\ 0001/256.512/2084.0008/768.256/768.1536/2560.1025/\ -4/2 float=y maxiter=2048 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=20009C<19>0bo0cq0es<3>0kz<25>09C08A068<2>02\ 2000211<22>keOmgPoiQqjRslSunT<2>zsX<25>CB7A96875<3\ >000400<23>o00q00s00<3>z00<25>C00A00800<3>000<23>e\ eegggiiijjjlllnnn<2>sss<18>NNNLLLJJJ<3>DDDCCCAAA<3\ >222000022<3>08A } frm:multifrac_236 { ; d=real(p2) fac1=trunc(d) b1=(d-fac1)*10000 ; d=imag(p2) mi1=trunc(d) p6r=trunc((d-out1)*10000) if (mi1<0) mi1=-mi1 endif ; d=real(p3) ba=trunc(d) p6i=trunc((d-ba)*10000) if (ba<0) ba=-ba endif p6=p6r,p6i ; d=imag(p3) fac2=trunc(d) b2=(d-fac2)*10000 ; d=real(p4) mi2=trunc(d) fac3=trunc((d-mi2)*10000) ; d=imag(p4) b3=trunc(d) mi3=trunc((d-b3)*10000) ; d=real(p5) vb=(d<0) If (vb) d=-d endif d1=trunc(d) d=trunc((d-d1)*100) ab1=(d==10)+(d==11) ab=(d==1)+(d==11) ir1=(d1>1000) d1=d1-1000*ir1 wo=(d1>100) d1=d1-100*wo tj=(d1<10) d1=d1-10*(tj==0) v1=(d1==3) v2=(d1==4) d1=(d1==2)+(d1==4) ; d=imag(p5) st=(d<0) if (st) d=-d endif d2=trunc(d) ab2=((d-d2)>0) ir2=(d2>1000) d2=d2-1000*ir2 ni=2*(d2>100) st=st*(ni==0) d2=d2-50*ni mj=(d2<10) d2=d2-10*(mj==0) v3=(d2==3) v4=(d2==4) d2=(d2==2)+(d2==4) d3=(ismand==0) t=0 u=1 bx=ba start=2-st-ni if (ismand) z=0 if (vb) c=0.4*log(sqr(pixel^p6i)) else c=pixel endif else c=p1 z=pixel endif : ba=bx if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) else z2=sin(z)+c sqz2=cos(z2) z=c*(1-sqz2)/(1+sqz2) ba=p6 endif else if (ab) q=sqr(z) z=real(q)+flip(real(z*q))+c else z=z*z+c endif endif bo=|z| If (wo) t=t+1 if ((t<mi1)+(bo>b1)) u=2*(fn1(t/fac1)) if (ismand) z=z*u c=pixel if (vb) c=0.4*log(sqr(pixel^p6i)) endif else z=pixel c=p1*u endif wo=0 if (ir1) t=0 endif endif else if (start) t=t+1 if (start==2) if ((t>mi2)+(bo>b2)) u=2*(fn2(t/fac2)) ab=ab1 if (d1) if (tj) z=pixel endif c=p1*u vb=v2 d3=vb else d3=0 z=z*u c=z if (mj) z=0 endif vb=v1 if (vb) p6=mi2,p6i c=0.4*log(sqr(pixel^p6i)) endif endif start=1 if (ir2) t=0 endif endif else if ((t>mi3)+(bo>b3)) u=2*(fn3(t/fac3)) ab=ab2 if (d2) if (tj) z=pixel endif c=p1*u vb=v4 d3=vb else d3=0 z=z*u c=z if (mj) z=0 endif vb=v3 if (vb) p6=mi3,p6i c=0.4*log(sqr(pixel^p6i)) endif endif start=0 endif endif endif endif bo<=ba } ------------------------------------------------end-------------------------------------------------------

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Alien Toy
by Albrecht 15 Nov '12

15 Nov '12

Hi, I got a present for you - a beautiful alien toy. Have fun playing and exploring! ----------------------start-par--------------------------------------------------------------- 16731x { ; Alien_Toy ; 0.11.71 1600/1200 ; sec-phoen-newt-bees-sec reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=0.0763248/-0.491648/16.48972/1.0471/-54\ .1932378046361691/-6.44479795856680848 params=-0.05825983458967864/0.3785210730307932/167\ 31.32595752213/25234.0311091622/151024.0204808192/\ 384.32768524288/384.00482000595/128.2007683001/256\ .2007683001/384.8007683001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=000000zr0zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>L\ Q8KM8KJ8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>\ qeBriAtm9vq8xu7zz5zz4zz3<4>zj4zg4zc4<3>zS5zP5zL6zI\ 6zE6wE6tD6<6>vAIv9Kv9M<3>x7Sy7Uy6Wz6Yz5_<3>f5Ma5IW\ 4E<2>_4H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>\ y0fz0gy0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAA\ G7FO4KW0Qc<3>5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<\ 3>civflvinvlqvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa\ <3>8JP8FL8CI<3>SCCXCAaB9<3>uA2zA0xA0<12>SA1QA1NA1<\ 3>D92<6>UXAW`BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJo\ SFlWAi_5fc0ce7_jFRoNIzb0zj0 } frm:multifractal_10 { ; Albrecht Niekamp Jan2005 ; ;RealP2 Left: 5 Digits_Channels: (1)shape (2)outside (3)inside1 (4)inside2 (5)inside3 ; Frm: 0_off 1_Secant 2_Mand(2) 3_Bees 4_Jul 5_Mmods 6_Phoen 7_Newt 8_Spid ; Right: 2 Digits_ManyMods_Number of sides 2 Digits_Phoenix 2 Digits_Spider ; 1 Digit_ TransitionReset - Shape: 0_no 1_DbleMand 2_Iter-reset 3_both +5_warp ; 4 Digits_TransitionReset - Ch 2-5: 0_no 1_z-reset 2_Iter-reset 3_both +5_warp ;ImagP2 Left: 5 Digits_Bailout Number for Channels 1 to 5 ; Right: Variables: 4 Digits_Mand/Jul (2 var) 2 Digits_Secant 4 Digits_Bees ;RealP3 Left: 2 Digits_Newtonvariable 4 Digits_Colour1 ; Right: 5 Digits_Colour2 5 Digits_Colour3 ;ImagP3 Left: Shape: Warp-factor (fn1 is used) ; Right: 5 Digits_Colour4 6 Digits_Colour5 ;RealP4 Left: Outside: Warp-factor (fn2 is used) ; Right: Outside: 4 Digits+1fractal digit_Border-out 4 Digits+1 fractaldigit_border-in ;ImagP4 Left: Inside1_Maxiter ; Right: Inside1_Transition: 1_maxiter 2_borderout 3_borderin +5_maxiter+border ; 5 Digits_warp factor (fn2 is used) 4 Digits+1 fractaldigit_border1 ;RealP5 Left: Inside2_Maxiter ; Right: Inside2_Transition: 1_maxiter 2_borderout 3_borderin +5_maxiter+border ; 5 Digits_warp factor (fn3 is used) 4 Digits+1 fractaldigit_border2 ;ImagP5 Left: Inside3_Maxiter ; Right: Inside3_Transition: 1_maxiter 2_borderout 3_borderin +5_maxiter+border ; 5 Digits_Warp factor (fn4 is used) 4 Digits+1 fractaldigit_border3 ; Alternate : Left: 1_Lake effect enabled (Inside3 disabled) ; Right: 2 Digits_Frequency 2 Digits_Waterlevel 2 Digits_Amplitude ;fn(1) shared by many-mods+bees ; 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---------------------------------------

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FOTD 13-11-12 (Ghostly Intruder [6.5])
by Jim Muth 13 Nov '12

13 Nov '12

FOTD -- November 13, 2012 (Rating 6.5) Fractal visionaries and enthusiasts: Today's image in a perturbed Mandelbrot set has a blue wedge intruding into the background. At first, this wedge appears to be totally out of place, with no connection at all to the surface pattern, but if the parameters are changed to 0,0, the connection will become perfectly clear. I named the image "Ghostly Intruder" because of this mysterious brilliant blue wedge, which is actually the ghost of a valley of an everyday Mandelbrot bud. The rating of 6-1/2 indicates that the image, which was done in haste, leaves much to be desired. The calculation time of 15 seconds will pass in a flash, but the web sites are still less of a hassle. View the finished wonder-image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> And check the hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are available at: <http://www.Nahee.com/FOTD/> The overnight rain ended shortly after daybreak, leading to a partly cloudy day with a temperature of 46F +8C. Fractal cat Nicholas is eagerly awaiting the arrival of his new companion in a day or so. The next FOTD, maybe better, maybe worse, will be posted in the appropriate time. Until whenever, take care, and keep your cool. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Ghostly_Intruder { ; time=0:00:15.00 SF5 at 2000MHZ reset=2004 type=mandel center-mag=-0.7070327249/\ -0.2812099475/1318/1/-111.1/0 params=-0.45/0.27 float=y maxiter=32767 bailout=16 inside=0 logmap=17 periodicity=6 colors=00050Y60X70W80V90UA0TB0SC1RD2QE3PF4OG5KH6HI\ 7II8JI8KJ9KJ9LJ9MKANKANKAOLBPLBQLBQLCRMCSMCTMDTNDU\ NDVNEWOEWOEXOFYPFZPFZPG_PG`QGaQHaQHbRHcRIdRIdSIeSJ\ fSJgSJgTIhTIhUIhUHhUHhVHhVHiVGiWGiWGiWFiXFiXFjXFjY\ EjYEjYEjZDjZDkZDk_Dk_Ck`Ck`Ck`ClaBlaBlaBlbAlbAlbAm\ cAmc9mc9md9md8md8ne8ne8ne7nf7nf7ne6sf7ng7jg7fh8ai8\ Yi7Qi8Uh9XgA_fBbeCedEccGbbIaaK``LZ`MY`NX`OV`PW`QWa\ RXaSYaTZaUZaV_aW`aX`aYaaZbbYaaZbaZb`Zc`Zc_Zc__d__d\ Z_dZ_eY_eY`fX`fX`fX`gW`gW`gVahVahUaiUaiUaiTbjTbjSb\ jSbkSbkRclRclQclQcmPcmPcmPdnOdnOdoNdoNdoMepMepMepL\ eqLeqKfrKfrKfrJfsJfsIfsIgtHgtHguHguGmuGmvFmvFmvEmw\ EmwEmxDmxDmxCmyCmyCmyDmxDmwDmwDmvDrzDrzDrzDrzDrzDr\ zErzErzErzErzErzErzErzErzErzErzEzzFzzFzzFzzFzzFzzF\ zzFzzFzzFzzFzzFzzGzzGzzGzzGzzGzzGzzGzzGzzGzzGzzGzz\ HzzHzzHzzHzzHzzHzzHzzHzzHzzHzzHzzHzzHzzGzzGzzFzzFz\ zEzzEzzEzzDzzDzzCzzCzzBzz } END PARAMETER FILE=========================================

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Web Opposition
by Mike Frazier 13 Nov '12

13 Nov '12

This fractal makes a web in a very different way than the Web Rings fractal I posted previously. By pure chance, this fractal has an area with two closely spaced spirals that rotate in opposite directions. The opposite rotation seems to cause arms to connect the two spirals. I zoomed in using mostly trial and error to find this fractal. The last zoom was particularly surprising as it changed the rings into a mesh. The equation is: z = 1 / (1 / ((z ^ 3) * tan(z) + pixel + 1) + 1 / (z ^ 4 + pixel - 1)) Here is a link to an image: http://dl.dropbox.com/u/33642054/image/web_opposition_1200_5.jpg The Fractint compatible PAR file for the image is: Web_Opposition { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20121113_0951 passes=1 float=y center-mag=0.706758545849994/0.2398003577709398/15\ 686274705.88235/1/17/0 params=1/1/4/4/-1/0/1/0/0/0 maxiter=2000 inside=0 logmap=128 periodicity=6 colors=000JqzLqzNqzPrzRrzTszVszXszZtz`tzbuzduzfuzh\ vzjvzlwznwzpwzrxztxzvyzxyzzzzyzzxzzwzzuzztzzszzqzz\ pzzozzmzzlzzkzzizzhzzgzzgzzgzzgyyfyyfxyfxxexxewwew\ wevwdvvduvduucuuctucttbstbssbrsbrsarraqraqq`pq`pq`\ op_op_oo_no_noZmnZmnZlmYlmYlmYklXklXjkXjkXikWijWij\ WhiVhiVgiVghVfhUfgUfgUegTefTdfTdeSdeSceScdSbdRbcRa\ cRacQabQ`bQ`aP_aP_aPZ`PZ`OZ_OY_OY_NXZNXZNWYMWYMWYM\ VXMVXLUWLUWLTWKTVKTVKSUKSUJRUJRTJQTIQSIQSIPSHPRHOR\ HOQHNQGNQGNPGMPFMOFLOFLOELNEKNEKMEJMDJMDILDILCIKCH\ KCHKBGJBGJBFIBFIAFIAEHAEH9DG9DG9CG9CF8CF8BE8BE7AE7\ AD79D69C69C68C68B57B57A56A46A469459358348348337237\ 23622612611511500400401502603713814915A16A17B27C28\ D29E2AF3AG3BH3CH3DI3EJ4EK4FL4GM4HN5HN5IO5JP5KQ5LR6\ LS6MT6NU6OU7OV7PW7QX7RY7SZ8S_8T_8U`8Va9Vb9Wc9Xd9Ye\ 9ZfAZfA_gA`hAaiBajBbkBclBdlBemCenCfoCgpChqDhrDisDj\ sDktDluElvEmwEnxEoyFpzHpz } frm:F_20121113_0951 { ; Similar to the parallel resistance formula a=real(p1),b=real(p2)-1,d=imag(p1),f=imag(p2), z=0,c1=pixel-p3,c2=pixel-p4: z=1/(1/(a*(z^b)*tan(z)+c1)+1/(d*(z^f)+c2)), |z|<100 } -- Mike Frazier www.fracton.org

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