Hi, here are two images I found today. The spiral is the most unusual one Iïve ever seen. Fractal greetings, Al ------------------------------start-frm------------------------------------ FRM:Multifractal_9 { ; Albrecht Niekamp 280803 ;p1 (spider)julia-seed ;real(p2) 5digits : (1)shape (2)outside (3)inside1 (4)inside2 (5)inside3 ; 0_off 1_secant 2_mand 3_bees 4_jul 5_m_mods 6_phoen 7_newt 8_spider ; input2 : 2digits_many-mods 2digits_phoenix 2digits_spider ; 5digits_reset : 0_no 1_z-reset 2_iter-reset 3_both +5_warp ;imag(p2)(-) 5digits_colour(bailout) number ; input2 : 4digits(-)_mand/jul 2digits_secant 4digits_bees ;real(p3) 2digits_newt 4digits_colour1, 5digits_colour2 5digits_colour3 ;imag(p3) shape : factor (fn1), 5digits_colour4 5digits_colour5 ;real(p4) outside: factor (fn2), 4+1digits_bord-out 4digits+fract_bord-in ;imag(p4) inside1: maxit1, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor1 (fn2) 4digits+fract_border1 ;real(p5) inside2: maxit2, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor2 (fn3) 4digits+fract_border2 ;imag(p5) inside3: maxit3, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor3 (fn4) 4digits+fract_border3 ;fn(1) shared by many-mods+bees ; 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 ab=(d==3)+(d==5)+(d==7)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 v1m=(d==6)+(d==7) v1j=d>7 dd1=(d==4)+(d==5)+v1j ab1=(d==3)+(d==5)+(d==7)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 v2m=(d==6)+(d==7) v2j=d>7 dd2=(d==4)+(d==5)+v2j ab2=(d==3)+(d==5)+(d==7)+(d==9) d=trunc(dd/10) ex3=d>1 v3m=(d==6)+(d==7) v3j=d>7 dd3=(d==4)+(d==5)+v3j ab3=(d==3)+(d==5)+(d==7)+(d==9) d=dd-d*10 ex4=d>1 v4m=(d==6)+(d==7) v4j=d>7 dd4=(d==4)+(d==5)+v4j ab4=(d==3)+(d==5)+(d==7)+(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 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=ex0+ex1+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)*10000000000 ba4=trunc(da/100000) ba5=da-ba4*100000 ; 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 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 ; d=imag(p5) mi3=trunc(d) da=(d-mi3)*10000000000 d=trunc(da/1000000000) 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 ; mo=vb>ab mo1=v1m>ab1 mo2=v2m>ab2 mo3=v3m>ab3 mo4=v4m>ab4 ; sc=((ab+vb)==0) sc1=((ab1+v1m)==0) sc2=((ab2+v2m)==0) sc3=((ab3+v3m)==0) sc4=((ab4+v4m)==0) ; px=((ab+vb)==2) px1=((ab1+v1m)==2) px2=((ab2+v2m)==2) px3=((ab3+v3m)==2) px4=((ab4+v4m)==2) ; if (d4) z=0 if (vb) if (mo) c=0.4*log(sqr(pixel^mm)) else c=pixel z=pixel endif else c=pixel z=pixel*sc endif else c=p1 z=pixel 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(pixel^mm)) else c=pixel endif else z=pixel cb=p9*u c=p1*u p=pp*u endif endif tt=tt-1+ex0 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(pixel^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(pixel^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(pixel^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(pixel^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 ;Qusinewton Pusk s Istv n z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+ph-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 Pusk s Istv n 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) z2=z*z ;Mandel Pusk s Istv n z=z2*z2+p6*z2+c-p0 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 } ---------------------------------------start-par------------------------- The_spiral { ; Time 0.32.55.43 ; Albrecht Niekamp Sep,03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_9 function=cos/sin/sin/sin passes=t center-mag=-0.00487064/-0.193521/10.41667/1/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/31687.32595705005/15243.0\ 506030602/52048.0408808896/384.1688690886/384.00782000645/128.1007683333\ 1/256.10076833331/384.10076833331 float=y maxiter=3072 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=2000HM<4>09C08A068<2>022000211<21>icNkeOmfP<3>unTwpVxqWzsX<25>CB7\ A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<23>eeegggiiijjjlll\ nnn<2>sss<25>BBB999777<2>222000022<24>0bo0cq0es<3>0kz<19>0IO } Ornaments { ; in a golden frame ; Albrecht Niekamp Sep,03 ; Time 0.14.13.16 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_9 function=cos/sin/sin/sin passes=t center-mag=-0.6404/-2.22045e-016/0.6666667/1/-90/3.88578058618804789e-01\ 6 params=-0.05825983458967864/0.3785210730307932/31687.32595705005/15243.0\ 506030602/52048.0408808896/384.1688690886/384.00782000645/128.1007683333\ 1/256.10076833331/384.10076833331 float=y maxiter=3072 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=200DDC<3>554443221000<25>0bn0cp0er<3>0ky<25>09B089067<2>021000210\ <21>icMkeNmfO<3>unSwpUxqVzsW<25>CB6A95874653442220000400<23>o00q00s00<3>\ z00<25>C00A00800<3>000<2>554776998BBACCB<16>eedggfiihjjillknnm<2>ssr<23>\ EED } ------------------------------------------end-------------------------------