Nice! Looks like a psychedelic tumbleweed. Bill Jemison Audio Fractals <https://sites.google.com/site/audiofractals/home> On Sat, Mar 3, 2018 at 1:47 PM, Albrecht Niekamp <multifrac@t-online.de> wrote:
One of the images created with 5 instances of the mandelbrot. The warp effect is applied to the basic shape using the acos function. ; https://1drv.ms/u/s!AmWYApv7ZBFGgaBnhy67QbIFil28tA ; A new version of the MFR_14_2 frm is in use - completely compatible, so just exchange it. It eliminates (hopefully) the problem that Fractint applies values to the last unused digits of a basic variable,(max 16 digits) that can cause unwanted variations to the image. Jonathan, maybe you can tell me if the "remedy", multiplying all 16 and then truncating the unused digits is effectful. Thank you ! A new version of the Input_Table optimized for better readability is in the forum folder - here is that link again: ; https://1drv.ms/f/s!AmWYApv7ZBFGgZ87Fm8AyoAc6Und5g ; Albrecht ------------------------------start par-------------------- 22222x21 { ; Complexity_Overload ; Maximum Zoom ; Basic shape warped - acos function ; Time 0.49.55.25 Reso 1280/1024 reset=2004 type=formula formulafile=mfr14.frm formulaname=mfr_14_2 function=acos/exp/exp/sin passes=t center-mag=-1.61826643194085700/-0.11540554091937760/1.183463e+012/1/-12\ 2.503778262566783/0.00443860223400030507 params=-0.05825983458967864/0.3785210730307932/22222.64595711338/11111.4\ 911030602/152048.0404808048/1071.1604894048/384.0003500001/256.100768300\ 1/512.1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter periodicity=0 rseed=-2436 sound=off colors=0006F5<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>Z0EV0DR0C<3>A08004000<26>000<4>000<7>Q0UU0YX0a_0\ dc0hf0l<2>p0w<4>_0dX0aU0Y<2>K0NH0JG0NE1R<3>7UX6`Z4h_2oa0wc<10>2WI2TG2RE<\ 4>4D3 } frm:mfr_14_2 {; Albrecht Niekamp Mar02,2018 lambda1/ precision update ;P1 : Julia-Manowar-(Lambda)-(Magnet)-(Phoenix) seed ;RP2 Left: 5 Digit_Channels: (1)shape (2)out (3)ins_1 (4)ins_2 (5)ins_3 ; Frm: 0_off 1_Secant 2_Mand(2) 3_Bees 4_Jul/Manowar 5_Mmods ; 6_Phoenix 7_Newton 8_Lambda/Magnet ; Right: 2 Digit_ManyMods_Number of sides 2 Digit_Phoen 2 Digit_Lambd ; 1 Digit_TransReset-Shape: 0_no 1_DblMan 2_Iter 3_both +5_nowarp ; 4 Digit_TransReset-Ch 2-5: 0_no 1_z 2_Iter 3_both +5_warp ;IP2 Left: 5 Digit_Bailout Number for Channels 1 to 5 ; Right: Variables: 4 Digit_Mand/Jul (2var) 2 Digit_Secant 4 Digit_Bees ;RP3 Left: 2 Digit_Newtonvariable 4 Digits_bailout1 ; Right: 4 Digit_bailout2 4 Digit_bailout3 1 Digit_Magnet ;IP3 Left: 4 Digit_Shape: Warp-factor (fn1 or fn4 is used) ; Right: 4 Dig_bailout4 4 Dig_bailout5 1 Dig_mow=2 1 Dig_mag=2 1 Dig_fns ;RP4 Left: 4 Digit_Outside: Warp-factor (fn2 used) ; Right: Outside: 4 Digit+fractdig_Border-out 4 Digit+fractdig_border-in ;IP4 Left: Inside1_Maxiter ; Right: Inside1_Transit: 1_maxit 2_borderout 3_borderin +5_maxit+bord ; 5 Digit_warp factor (fn2 used) 4 Digit+fractaldigit_border1 ;RP5 Left: Inside2_Maxiter ; Right: Inside2_Transit: 1_maxit 2_borderout 3_borderin +5_maxit+bord ; 5 Digit_warp factor (fn3 used) 4 Digit+fractaldigit_border2 ;IP5 Left: Inside3_Maxiter ; Right: Inside3_Transit: 1_maxit 2_borderout 3_borderin +5_maxit+bord ; 5 Digits_Warp factor (fn4 used) 4 Digit+fractaldigit_border3 ;Function: fn4_Manymods, fn3_Bees, fn2+fn3+fn4(virtual P1)_Lambda(fn) z=pixel da=real(p2) dd=trunc(da) tt=dd>0 da=(da-dd)*1000000000000 da=trunc((da/10)+11111) dd=trunc(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 ex0=(d>1) sc=d==2 mo=d==6 po=d==7 ab=po+(d==3)+(d==5)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=(d>1) sc1=d==2 mo1=d==6 po1=d==7 lx1=d==5 v1m=mo1+po1 v1j=d>7 dd1=v1j+(d==4)+(d==5) ab1=po1+(d==3)+(d==5)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=(d>1) sc2=d==2 mo2=d==6 po2=d==7 lx2=d==5 v2m=mo2+po2 v2j=d>7 dd2=v2j+(d==4)+(d==5) ab2=po2+(d==3)+(d==5)+(d==9) d=trunc(dd/10) dd=dd-d*10 ex3=(d>1) sc3=d==2 mo3=d==6 po3=d==7 lx3=d==5 v3m=mo3+po3 v3j=d>7 dd3=v3j+(d==4)+(d==5) ab3=po3+(d==3)+(d==5)+(d==9) d=dd ex4=(d>1) sc4=d==2 mo4=d==6 po4=d==7 lx4=d==5 v4m=mo4+po4 v4j=d>7 dd4=v4j+(d==4)+(d==5) ab4=po4+(d==3)+(d==5)+(d==9) tt=ex1+ex0+ex2+ex3+ex4 ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000) da=da-ph*10000000 px=trunc(da/100000) da=da-px*100000 d=trunc(da/10000) da=da-d*10000 wx=(d>4) d=d-5*wx dm=(d==2)+(d==4) ir0=(d==3)+(d==4) d=trunc(da/1000) da=da-d*1000 w1=d>4 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) da=da-d*100 w2=d>4 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) da=da-d*10 w3=d>4 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) w4=da>4 da=da-5*w4 rs4=(da==2)+(da==3)+(da==4) if (ph==0) ph=p1 else ph=ph/10 endif w0=(wx==0) ; d=real(p3) dd=trunc(d) da=(d-dd)*100000000000 da=trunc(da/10) pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/1000000) da=da-1000000*ba2 ba3=trunc(da/100) da=da-100*ba3-4 mg=da/10 if (mg<1) mg=real(p1) endif ; d=imag(p3) dd=trunc(d) da=(d-dd)*1000000000000 da=trunc(da/10) sfac=dd/1000000+(dd==0) ba4=trunc(da/10000000) da=da-ba4*10000000 ba5=trunc(da/1000) da=da-ba5*1000 d=trunc(da/100) mow=(d==2)+(d==3) mv=(d==3)+(da==4) da=da-d*100 d=trunc(da/10) mag=d==2 d=trunc(da-d*10) fdm=(d==4)+(d==7) fdb=(d==3)+(d==7) If (1<px) d=(trunc(px/10))/9 if (fdm) da=fn4(px-100*d) else da=exp(px-100*d) endif d=px/(73.37) px=d+sqr(-da) else px=p1 endif ; d=real(p4) dd=trunc(d) da=(d-dd)*1000000000000 da=trunc(da/100) ofac=dd/1000000+(dd==0) bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 ; d=imag(p2) dd=trunc(d) da=(d-dd)*1000000000000 da=trunc(da/100) 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=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 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)*1000000000000 da=trunc(da/10) d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=d==3 dd=trunc(da/100000) da=da-dd*100000 fac1=dd/1000000+(dd==0) bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*1000000000000 da=trunc(da/10) d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=d==3 dd=trunc(da/100000) da=da-dd*100000 fac2=dd/1000000+(dd==0) bo2=(da/100000)/10 ; d=imag(p5) mi3=trunc(d) da=(d-mi3)*1000000000000 da=trunc(da/10) d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=(d==3) dd=trunc(da/100000) da=da-dd*100000 fac3=dd/1000000+(dd==0) bo3=(da/100000)/10 ; if (vb) if (d3) if (ab) if (mag) c=z z=pixel mg=mg+(mg==0)*3 ;magnet x=mg else z=pixel ;lambdafn x=((1,0.4)*(|px|<=0)+px) m=(64*(real(bb0)<=0)+real(bb0)*(0<bb0)) endif else c=z z=pixel ;newton endif elseif (ab) c=z ;Phoenix z=pixel else c=0.4*log(sqr(z^mm)) z=0 ;many mods endif elseif (d3) if (ab) if (mv) ;manowar+Julia bb0=(4*(real(p1)<=0)+real(p1)*(0<p1) ) if (lx1) bb1=bb0 elseif (lx2) bb2=bb0 elseif (lx3) bb3=bb0 elseif (lx4) bb4=bb0 endif endif c=p1 z=pixel else ;bees c=p1 z=pixel endif elseif (ab) c=z ;Mandel z=0 else c=z ;Secant z=pixel endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt>0) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u0=fn1(t*sfac) if (w0) u=u0 else u=1.0 endif ex0=0 if (ir0) t=0 endif if (d3) z=pixel cb=p9*u x=x*u p=pp*u else z=z*u if (mo) c=0.4*log(sqr(z^mm)) else c=pixel endif tt=tt-1+ex0 endif endif elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=fn2(t*ofac) else u=1.0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u x=x*u p=pp*u else z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+po1) 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=fn2(t*fac1) else u=1.0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u x=x*u p=pp*u else cb=p9 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+po2) 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=fn3(t*fac2) else u=1.0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u x=x*u p=pp*u else cb=p9 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+po3) 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=fn4(t*fac3) else u=1.0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u x=x*u p=pp*u else cb=p9 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+po4) 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) if (mag) ;magnet z=((z^x+c-1)/(2*z+c-2))^(x-1) else if (fdb) z=exp(z)*fn3(x) else z=exp(z)*sin(x) ;Lambdafn endif (abs(imag(z))<=x) && (abs(real(z))<=m) endif else z1=z^p-1 ;newton z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+0.56+ph/100-0.5*zold zold=z ;Phoenix z=z1 else if (fdm) Z2=fn4(z)+c else z2=sin(z)+c ;Many_mods endif z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) if (mow) z1=z ;manowar oldz=z z=sqr(oldz)+z1+c z1=oldz else ;Julia z2=z*z z=z2*z2+p6*z2+c-p0 endif else if (fdb) z1=fn3(z)-cb else z1=sin(z)-cb ;Bees endif 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 z=z2*z2+p6*z2+c-p0 endif else z3=z ;Secant 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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