Hi, Now a Newton formula is included. This was not easy as all newton types have a different bailout and generally they dont like to be mixed. The one I finally found is again by Pusk s Istv n, the third one I use in the multifractal series. A big Thank you! just in case heïs listening. The images really are unique for me and I guess for all of you. Fractals are fun! Al. ------------------------------start-par------------------------------------- Newtonflowers { ; Time 0.11.02.46 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult243.frm formulaname=multifractal_5 ismand=y function=cos/exp/exp/sin passes=t center-mag=1.17906/-0.00478368/1.573582/1/-90/3.88578058618804789e-016 params=-0.1156346324045534/-0.5338602862636189/12482.00001/130000.321314\ 0212/2048.02048/384.000008/384.00024/128.0076800000001/512.0076800000001\ /768.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200F00<4>500400200000<2>455677899ABBBCC<18>hiijkkkll<3>rss<21>HII\ FGGEFF<3>677455344122000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000111<22>\ jeOlgPniQpjRrlStnT<2>ysX<25>BB7996775<3>000<24>n00p00r00<3>y00<22>H00 } Magic_circle { ; Time 0.25.12.59 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult243.frm formulaname=multifractal_5 ismand=y function=cos/exp/exp/sin passes=t center-mag=1.17906/-0.00478368/1.573582/1/-90/3.88578058618804789e-016 params=-0.1156346324045534/-0.5338602862636189/14282.3200001/130040.1314\ 021203/2048.02048/384.000002/384.00024/128.0076800000001/512.00768000000\ 01/768.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200332<21>jeOlgPniQpjRrlStnT<2>ysX<25>BB7996775<3>000<24>n00p00r0\ 0<3>y00<25>B00900700<3>000<2>455677899ABBBCC<18>hiijkkkll<3>rss<21>HIIFG\ GEFF<3>677455344122000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000111 } Newtmand { ; Time 0.32.45.46 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult243.frm formulaname=multifractal_5 ismand=y function=cos/exp/exp/sin passes=t center-mag=1.1197/-0.00478368/1.573582/1/-90/-1.23373533611470521e-014 params=-0.1156346324045534/-0.5338602862636189/14282.3200001/2540.131402\ 0602/2048.02048/384.0000045/384.00024/128.0076800000001/512.007680000000\ 1/768.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=2000Wd<14>09C08A068<2>022000111<22>jeOlgPniQpjRrlStnT<2>ysX<25>BB\ 7996775<3>000<24>n00p00r00<3>y00<25>B00900700<3>000<2>455677899ABBBCC<18\
hiijkkkll<3>rss<21>HIIFGGEFF<3>677455344122000<25>0bo0cq0es<3>0kz<9>0Xf }
Mixdown2 { ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult243.frm formulaname=multifractal_5 ismand=y function=exp/exp/exp/sin passes=t center-mag=1.1197/-0.00478368/1.573582/1/-90/-1.23373533611470521e-014 params=-0.1156346324045534/-0.5338602862636189/14237.3200001/72500.13140\ 216052/2048.02048/384.0000049/768.00024/128.0076800000001/768.0076800000\ 001/1024.00768 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200000<2>455677899ABBBCC<18>hiijkkkll<3>rss<21>HIIFGGEFF<3>677455\ 344122000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000111<22>jeOlgPniQpjRrlS\ tnT<2>ysX<25>BB7996775<3>000<24>n00p00r00<3>y00<30>200 } Mixdown3 { ; Time 0.38.29.40 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult243.frm formulaname=multifractal_5 ismand=y function=cos/exp/exp/sin passes=t center-mag=1.1197/-0.00478368/1.573582/1/-90/-1.23373533611470521e-014 params=-0.1156346324045534/-0.5338602862636189/14237.3200001/53000.13140\ 21613/2048.02048/384.0000049/768.00024/128.0076800000001/768.00768000000\ 01/1024.00768 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=000<3>000000000<9>X0a_0dc0h<3>p0w<4>_0dX0aU0Y<2>K0NH0JG0NE1R<3>7U\ X6`Z4h_2oa0wc<11>2TG2RE3OC<3>4D3<17>kkammcpoe<3>zwm<6>cYO`UKYQG<3>KA0000\ <43>000<4>000330<11>110110110<3>000KA4<7>gcOjgRmjT<3>zzc<9>UOFRKDOGA<3>A\ 00<9>f0Ci0Dl0F<3>z0K<6>Z0EV0DR0C<3>A08004000<25>000 } Newton_frame { ; Time 0.17.06.50 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult243.frm formulaname=multifractal_5 ismand=y function=cos/exp/exp/sin passes=t center-mag=-0.507813/-0.00478368/0.9488575/1.0685/180 params=-0.1156346324045534/-0.5338602862636189/14287.3210001/53000.13140\ 61613/2048.02048/384.0000049/768.00024/128.0076800000001/768.00768000000\ 01/1024.00768 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200000<2>455677899ABBBCC<18>hiijkkkll<3>rss<21>HIIFGGEFF<3>677455\ 344122000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000111<22>jeOlgPniQpjRrlS\ tnT<2>ysX<25>BB7996775<3>000<24>n00p00r00<3>y00<30>200 } Only_one { ; can be the winner ; Time 0.17.15.61 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult243.frm formulaname=multifractal_5 ismand=y function=cos/exp/exp/sin passes=t center-mag=-0.302531/-0.00478368/0.842554/1.0685/180 params=-0.1156346324045534/-0.5338602862636189/19287.3210001/53000.13140\ 81613/2048.02048/384.0000135/768.00056/128.0076800000001/768.00768000000\ 01/1024.00768 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=000<2>110110000KA4<7>gcOjgRmjT<3>zzc<9>UOFRKDOGA<3>A00<9>f0Ci0Dl0\ F<3>z0K<6>Z0EV0DR0C<3>A08004000<26>000<4>000<9>X0a_0dc0h<3>p0w<4>_0dX0aU\ 0Y<2>K0NH0JG0NE1R<3>7UX6`Z4h_2oa0wc<11>2TG2RE3OC<3>4D3<17>kkammcpoe<3>zw\ m<6>cYO`UKYQG<3>KA0000<43>000<4>000330<12>110 } -------------------------start-frm------------------------------------------ FRM:Multifractal_5 { ; Albrecht Niekamp 230603 ;only integers as first input, second input 5 digits to the right ;real(p2) 5digits: shape, outside, in1, in2, in3 ; 0_off 1_mand 2_jul/bees 3_many_mods 4_newtjul +5_reset digit1: +5_warp ; input2 : 2digits_many_mods 5digits_frm2 use : 0_no 1_yes ;imag(p2)(-) 2-4digits : quasinewton input (max 2000) ; 1digit : many_mods multipl. off 1_out 2_in1 3_in2 4_all ; 1digit : iter-reset 1_out 2_in1 3_in2 4_all ; input2 : 4digits(-)_frm1 2digits_frm2 4digits_bees ;real(p3) many_mods bailout, bailout ;imag(p3) shape : factor (fn1), outside : border-in ;real(p4) outside : factor (fn2), border-out ;imag(p4) inside1 : maxiter1, factor1 (fn2) ;real(p5) inside2 : maxiter2, factor2 (fn3) ;imag(p5) inside3 : maxiter3, factor3 (fn4) ; da=real(p2) dd=trunc(da) da=round((da-dd)*10000000)+11111 d=trunc(dd/10000) ex0=d>5 d=d-5*ex0 vb=(d==3)+(d==4) dd=dd-d*10000 d=trunc(dd/1000) ex1=d>0 dd=dd-d*1000 rs1=d>5 d=d-5*rs1 v1m=(d==3) v1j=(d==4) dd1=(d==2)+(d==4) d=trunc(dd/100) ex2=d>0 dd=dd-d*100 rs2=d>5 d=d-5*rs2 v2m=(d==3) v2j=(d==4) dd2=(d==2)+(d==4) d=trunc(dd/10) ex3=d>0 dd=dd-d*10 rs3=d>5 d=d-5*rs3 v3m=(d==3) v3j=(d==4) dd3=(d==2)+(d==4) ex4=dd>0 rs4=dd>5 dd=dd-rs4*5 v4m=(dd==3) v4j=(dd==4) dd4=(dd==2)+(dd==4) tt=ex0+ex1+ex2+ex3+ex4 ; mm=trunc(da/100000) da=da-mm*100000 d=trunc(da/10000) ab=(d==2) da=da-d*10000 d=trunc(da/1000) ab1=(d==2) da=da-d*1000 d=trunc(da/100) ab2=(d==2) da=da-d*100 d=trunc(da/10) ab3=(d==2) da=da-d*10 ab4=(da==2) ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) d=round((d-dd)*10000000000) pp=trunc(dd/100)/10 dd=dd-1000*pp da=trunc(dd/10) so1=((da==1)+(da==4)==0) so2=((da==2)+(da==4)==0) so3=((da==3)+(da==4)==0) dd=dd-10*da ir1=(dd==1)+(dd==4) ir2=(dd==2)+(dd==4) ir3=(dd==3)+(dd==4) ; 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 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=real(p3) mb=trunc(d) ba=(d-mb)*100000 ; d=imag(p3) sfac=trunc(d) b1=(d-sfac)*100000 b0=b1/2 ; d=real(p4) ofac=trunc(d) b2=(d-ofac)*100000 ; d=imag(p4) mi1=trunc(d) fac1=(d-mi1)*100000 ; d=real(p5) mi2=trunc(d) fac2=(d-mi2)*100000 ; d=imag(p5) mi3=trunc(d) fac3=(d-mi3)*100000 ; bg=((ab+vb)==0) bg1=((ab1+v1j)==0) bg2=((ab2+v2j)==0) bg3=((ab3+v3j)==0) bg4=((ab4+v4j)==0) ; if (ismand) z=0 if (vb) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else if (bg) c=p9 else c=p1 endif z=pixel endif t=0 d3=(ismand==0) u=d3 bo=z p=pp : If (tt) t=t+1 if ((ex0) && bo>b0) u=2*(fn1(t/sfac)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) ba=mb else c=pixel endif else z=pixel if (bg) c=p9*u else c=p1*u p=pp+u endif endif ex0=0 tt=tt-1 elseif ((ex1) && bo>b1 && bo<b2) u=2*(fn2(t/ofac)) rs=rs1 ab=ab1 if (dd1) if (rs) z=pixel endif vb=v1j d3=1 if (bg1) c=p9*u else c=p1*u p=pp+u endif else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1m if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir1) t=0 endif ex1=0 tt=tt-1 elseif ((ex2) && t>mi1) u=2*(fn2(t/fac1)) rs=rs2 ab=ab2 if (dd2) if (rs) z=pixel endif vb=v2j if (bg2) c=p9*u else c=p1*u p=pp+u endif d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v2m if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir2) t=0 endif ex2=0 tt=tt-1 elseif ((ex3) && t>mi2) u=2*(fn3(t/fac2)) ab=ab3 rs=rs3 if (dd3) if (rs) z=pixel endif vb=v3j if (bg3) c=p9*u else c=p1*u p=pp+u endif d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3m if (vb) if (so3) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir3) t=0 endif ex3=0 tt=tt-1 elseif ((ex4) && t>mi3) u=2*(fn4(t/fac3)) ab=ab4 rs=rs4 if (dd4) if (rs) z=pixel endif vb=v4j if (bg4) c=p9*u else c=p1*u p=pp+u endif d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v4m if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif ex4=0 tt=tt-1 endif endif if (vb) if (d3) n=z^p-1 d=p*z*z z=z-n/d else z2=fn1(z)+c ;Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z=z*z+c+c*c-p7 ;Pusk s Istv n elseif (d3) z1=fn1(z)-c ;Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p0 endif bo=|z| bo<=ba } ----------------------------------end-------------------------------------