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------------------------------