Hi, a lot of changes and new options this time. 1. All channels now have an own input, which is referred to by name, no shared inputs anymore. This means all formulas can be tested without doing any changes except imag(p2) as explained. Use the second input to alternately use an (almost) basic mandel (channel1) or julia (channel2) instead of the default frms. If you want to test a formula exclusively, just type the number followed by four zeros as first input. 2. Just add 5 to the secondary inputs after the 2digits many_mods input to activate the warp-effect separetely for each channel. This is useful in many instances f.e. to change the looks of the inside/outside images and to preserve the julia settings. Add 5 to the primary inputs to do a reset for each channel. This causes that the in/outside image is adjusted to the screen instead of the surroundings. This also works if the warp-effect is shut off, test it. 3. For simplicity reasons "ismand" is not used anymore, so one more line of the text is displayed and the inputs are not ambivalent anymore. 4. A new mixing formula "Secant" is available as default channel one. Check the first par to see what it looks like. In order to go on with this I need some feedback, so I know what Iïm doing this for. So please post your images and your comments. I regard this as a "living" process on the way to perfection, I still have some ideas and critics should help to improve it. Dont hesitate to play around with multifractal, if youïre interested. Youïll see that itïs fun and quite easy once the basics are understood. An easy tweak is to use other functions, fn1 if bees or many_mods is used, the other ones to affect the warp effects. Cosxx will create weird effects in many cases. Fractal greetings, Al. ----------------------------start-par------------------------------------- Mandelbug { ; Albrecht Niekamp July, 03 ; Outside secant inside newton\bees\julia ; Time 0.18.47.56 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult244.frm formulaname=multifractal_6 function=cos/exp/exp/cos passes=t center-mag=0.420263/4.44089e-016/1.718213/1/-90/3.88578058618804789e-016 params=0.8202154606769005/-0.06207464827417833/11972.3215501/5040.060802\ 1613/4084.02048/384.000004/768.00024/128.00768/384.00768/768.00768000000\ 01 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200000<3>764985BA6DC7FE8<17>niQpjRrlS<3>ysX<25>BB7996775<3>000<24\

n00p00r00<3>y00<25>B00900700<3>000<2>455677899ABBBCC<18>hiijkkkll<3>rss\ <21>HIIFGGEFF<3>677455344122000<25>0bo0cq0es<3>0kz<30>022 }

---------------------------------end--------------------------------------- Gran_canyon { ; inside mandel,mandel,julia ; Albrecht Niekamp July, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult244.frm formulaname=multifractal_6 function=cos/exp/exp/cosxx passes=t center-mag=1.10912/0.314452/26.9208/1/-90/3.88578058618804789e-016 params=0.8202154606769005/-0.06207464827417833/10667.3210111/2543.060802\ 1613/4084.02048/384.0000076/768.00024/128.0076800000001/384.007680000000\ 1/512.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=old periodicity=0 rseed=-2436 colors=200200000<2>455677899ABBBCC<18>hiijkkkll<3>rss<21>HIIFGGEFF<3>677\ 455344122000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000111<24>niQpjRrlS<3>\ ysX<25>BB7996775<3>000<24>n00p00r00<3>y00<29>400 } Gran_canyon_zoom { ; Albrecht Niekamp July, 03 ; Time 0.20.10.67 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult244.frm formulaname=multifractal_6 function=cos/exp/exp/cosxx passes=t center-mag=+1.14003818818291000/+0.35936443447906610/197.9471/1/-90/3.88\ 578058618804789e-016 params=0.8202154606769005/-0.06207464827417833/10667.3210111/2543.060802\ 1613/4084.02048/384.0000076/768.00024/128.0076800000001/384.007680000000\ 1/512.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=old periodicity=0 rseed=-2436 colors=200N00<6>900<3>200000122<5>BCCDEEFGGGHHIJJKLL<13>hiijkkkll<3>rss<\ 21>HIIFGGEFF<3>677455344122000<25>0bo0cq0es<3>0kz<25>09C08A068<2>0220001\ 11<22>jeOlgPniQpjRrlStnT<2>ysX<25>BB7996775<3>000<24>n00p00r00<3>y00<18>\ P00 } Bishops_hat { ; Albrecht Niekamp July, 03 ; Time 0.33.58.01 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult244.frm formulaname=multifractal_6 function=exp/sin/exp/sin passes=t center-mag=0.431817/2.22045e-016/1.34604/1/-90/3.88578058618804789e-016 params=0.8202154606769005/-0.06207464827417833/10112.3210611/2543.060802\ 1613/4084.02048/384.0000076/768.00024/128.0076800000001/512.007680000000\ 1/768.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=6 periodicity=0 rseed=-2436 colors=200700<3>000<5>9AABCCDEEFGGGHH<15>hiijkkkll<3>rss<21>HIIFGGEFF<3>\ 677455344122000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000111<22>jeOlgPniQ\ pjRrlStnT<2>ysX<25>BB7996775<3>000<24>n00p00r00<3>y00<26>900 } Magic_circle_2 { ; Albrecht Niekamp July, 03 ; Time 0.10.55.37 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult244.frm formulaname=multifractal_6 function=cos/exp/exp/exp passes=t center-mag=2.22045e-016/-2.22045e-016/0.8392416/1/90/3.88578058618804789\ e-016 params=0.8202154606769005/-0.06207464827417833/40673.3255005/25040.06080\ 21613/2048.02048/768.0000045/768.00024/128.0076800000001/512.00768000000\ 01/768.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=old periodicity=0 rseed=-2436 colors=200JHA<13>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<7>HF9 } Universal_robot { ; Time 0.34.13.72 ; Albrecht Niekamp July,03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult244.frm formulaname=multifractal_6 function=cos/exp/exp/sin passes=t center-mag=-0.0124931/3.747e-016/11.03753/1/-90/3.88578058618804789e-016 params=0.8202154606769005/-0.06207464827417833/14178.321055/2540.0608021\ 613/4084.02048/384.0000045/768.00024/128.0076800000001/256.0076800000001\ /512.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=200554<2>000<24>n00p00r00<3>y00<25>B00900700<3>000<2>455677899ABB\ BCC<18>hiijkkkll<3>rss<21>HIIFGGEFF<3>677455344122000<25>0bo0cq0es<3>0kz\ <25>09C08A068<2>022000111<22>jeOlgPniQpjRrlStnT<2>ysX<27>775 } Mandelmania_zoom { ; makes the 4th generation mandel visible ; Albrecht Niekamp July,03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult244.frm formulaname=multifractal_6 function=cos/exp/exp/sqr passes=t center-mag=+0.84947498866192170/+0.00000000000000022/895.0965/1/180 params=0.8202154606769005/-0.06207464827417833/10111.3210116/2543.060802\ 1613/4084.03072/384.0000055/768.00024/128.0076800000001/384.007680000000\ 1/512.00746 float=y maxiter=10000 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=200b00<6>p00<3>w00y00w00<24>C00A00800<3>000<2>455677899ABBBCC<18>\ hiijkkkll<3>rss<21>HIIFGGEFF<3>677455344122000<25>0bo0cq0es<3>0kz<25>09C\ 08A068<2>022000111<24>niQpjRrlS<3>ysX<25>BB7996775<3>000<17>`00 } Mandeline { ; most unsual musical instrument ; Albrecht Niekamp July,03 ; Mandelmania deepzoom, takes a while reset=2002 type=formula formulafile=mult244.frm formulaname=multifractal_6 function=cos/exp/exp/sqr passes=t center-mag=+0.84820315604180700/+0.00000000000000022/29638.96/1/-90/3.88\ 578058618804789e-016 params=0.8202154606769005/-0.06207464827417833/10111.3210116/2543.060802\ 1613/4084.03072/384.0000055/768.00024/128.0076800000001/384.007680000000\ 1/512.00746 float=y maxiter=10000 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=200C00<4>200000<2>455677899ABBBCC<18>hiijkkkll<3>rss<21>HIIFGGEFF\ <3>677455344122000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000111<24>niQpjR\ rlS<3>ysX<25>BB7996775<3>000<24>n00p00r00<3>y00<24>E00 } The_big_bed { ; Time 0.29.40.30 ; Albrecht Niekamp July,03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult244.frm formulaname=multifractal_6 function=cos/exp/exp/sin passes=t center-mag=-0.0108791/3.46945e-016/16.7049/1/90/3.88578058618804789e-016 params=0.8202154606769005/-0.06207464827417833/14182.3215551/5040.060802\ 1613/4084.02048/384.0000045/768.00024/128.0076800000001/384.00768/768.00\ 76800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=3 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 }

Mandelmania_2 { ; Time 0.16.49.48 ; Albrecht Niekamp July,03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult244.frm formulaname=multifractal_6 function=cos/exp/exp/sqr passes=t center-mag=0.47425/2.22045e-016/1.249125/1/-90/3.88578058618804789e-016 params=0.8202154606769005/-0.06207464827417833/10111.3210116/2543.060802\ 1613/4084.03072/384.0000055/768.00024/128.0076800000001/384.007680000000\ 1/512.00746 float=y maxiter=4084 inside=maxiter outside=tdis logmap=yes periodicity=0 rseed=-2436 colors=200VVV<7>iiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0cq0es<2>\ 0jy0kz0jy<24>09C08A068<2>022000211<24>oiQqjRslS<3>zsX<25>CB7A96875<3>000\ 400<23>o00q00s00<3>z00<25>C00A00800<3>000<16>UUU } ------------------------------------------start-frm----------------------- FRM:Multifractal_6 { ; Albrecht Niekamp 020703 ;only integers as first input, second input 5 digits to the right ;real(p2) 5digits: shape, outside, in1, in2, in3 ; 0_off 1_secant/mand 2_bees/jul 3_m_mods 4_newt +5_reset (not shape) ; input2 : 2digits_m_mods 5digits_mand/jul use : 0_no 1_yes +5_warp ;imag(p2)(-) 2-4digits : quasinewton input (max 2000) ; 1digit : no m_mods multipl. : 1_out 2_in1 3_in2 4_all ; 1digit : iter-reset 1_out 2_in1 3_in2 4_all ; input2 : 4digits(-)_mand 2digits_secant 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) ;fn(1) is shared by bees and many_mods ; da=real(p2) dd=trunc(da) da=round((da-dd)*10000000)+11111 d=trunc(dd/10000) t=d>5 dd=dd-d*10000 d=d-5*t d3=(d==2)+(d==4) d4=(d3==0) vb=(d==3)+(d==4) 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) ; mm=trunc(da/100000) da=da-mm*100000 d=trunc(da/10000) ex0=d>5 ab=(d==2)+(d==7) da=da-d*10000 d=trunc(da/1000) w1=d>5 ab1=(d==2)+(d==7) da=da-d*1000 d=trunc(da/100) w2=d>5 ab2=(d==2)+(d==7) da=da-d*100 d=trunc(da/10) w3=d>5 ab3=(d==2)+(d==7) da=da-d*10 w4=da>5 ab4=(da==2)+(da==7) tt=ex0+ex1+ex2+ex3+ex4 ; 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 (d4) z=0 if (vb) c=0.4*log(sqr(pixel^mm)) else c=pixel z=pixel*(ab==0) endif else if (bg) c=p9 else c=p1 endif z=pixel endif t=0 u=d3 bo=z p=pp z0=p7 : If (tt) t=t+1 if ((ex0) && bo>b0) u=2*(fn1(t/sfac)) if (d4) 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) if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif 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=pixel*(ab==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) if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif 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=pixel*(ab==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) if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif 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=pixel*(ab==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) if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif 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=pixel*(ab==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) ;quasinewton Pusk s Istv n z1=z^p-1 z2=p*z*z z=z-z1/z2 else z2=fn1(z)+c ;many_mods Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z2=z*z ;mandel Pusk s Istv n z=z2*z2+p6*z2+c-p0 elseif (d3) z1=fn1(z)-c ;bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) else z3=z ;secant unknown 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 }