Hi all, somme pars with kleinian-formulas. Enjoy --Jo Weber-- http://www.joweber.de jo_kl_02 { ; June 02, 2002 0:00:53.77 ; Pentium 900 Mhz by Jochen Weber ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=formulas.frm formulaname=mod5klein_group passes=1 center-mag=0.794169/-1.15521/2.593386/1/115.000000039194887/-1.455482248\ 89102684e-007 params=1/1.25/1.5/2.25/0.25/0.5/1/0 float=y maxiter=15000 inside=bof60 outside=atan periodicity=0 colors=000fH0<3>sM0wO0zP0<8>PA0L80H70<3>000<3>B94EB5HD6JF7MH8<2>RMBSNBTN\ CUOCVOCVPC<3>SNBRMBPKAOJ9<3>EB5C94973<2>000<4>0KU0NZ0Qc0Uh0Wl0Zp0`s0bu0c\ x0dy0ez<3>0cx0bu0`s0Zp0Wl0Uh<3>0FN0BH07B046000<3>B94EB5HD6JF7MH8<2>RMBSN\ BTNCUOCVOCVPC<3>SNBRMBPKAOJ9<3>EB5B84863642321611<3>U55Z66c77h88l99pAAsB\ BuBBxBByCCzCC<3>xBBuBBsBBpAA<3>Z66U55O44<3>000<3>9J4BN5DR6<3>KdAMgBNiBNj\ BOlCOlCPmCOlCOlCNjBNiB<2>Ja9HZ8FV7<3>6D3492241000<3>99OBBUDDZFFcHHhJJlKK\ pMMsNNuNNxOOyOOzPPzOOyOOyNNxNNuMMsKKp<3>DDZBBU99O<3>000<3>OJ4UN5ZR6cV7hZ\ 8la9pdAsgBuiBxjBylCzlCzmCzlCylCxjBuiBsgBpdA<3>ZR6UN5OJ4<3>000620C40<7>bF\ 0 } jo_kl_06 { ; June 02, 2002 0:00:32.30 ; Pentium 900 Mhz by Jochen Weber ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=formulas.frm formulaname=mod5klein_group passes=1 center-mag=0.540167/1.42224/2.655525/1/-135.000000055134819/4.3111121429\ 6842071e-008 params=1.25/2/1.5/2.25/0.25/0.5/1/0 float=y maxiter=15000 inside=bof60 outside=atan periodicity=0 colors=000<3>000000UUU___oie<6>eSQdQOcNM<3>YDDWBAV88T55<9>kA9mB9oBA<2>uD\ BwECwGC<10>yf4yi3yk2ym1<3>zz0<4>ye1ya1yY1<3>xH2<9>N61J51F41<3>000<4>000<\ 2>000<3>D08H0AJ09<3>T05V04Y03<2>d00<20>K5GJ6HI6H<2>F7JD8KA9J<2>0BG<28>1R\ c1Sc1Sd1Te1Ue<6>7Xf8Xf9Ye<41>nsbotbptb<2>svbtwbuwd<2>zzm<3>ojjlfiibhfZgc\ Uf<3>OIQKFMGCH<3>000000zaF000 } jo_kl_10 { ; June 02, 2002 0:01:37.99 ; Pentium 900 Mhz by Jochen Weber ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=formulas.frm formulaname=mod5klein_group passes=1 center-mag=-0.52781230222012580/+1.43454734330997400/971.0747/1/37.50000\ 00000024016/-5.55922669009945025e-012 params=25/1/3.5/2/5/5/5/0 float=y maxiter=1000 proximity=2 outside=fmod periodicity=0 cyclerange=0/255 colors=000SPV<13>E__D``Ca`<2>9da8da9b_<18>CFGCEFCCD<2>C8AD79D79<55>lZ8m_\ 8n`7<18>pc6pd6pd6<4>oc6oc6oc6nb6nb6nb6<79>NCAMBAMBA<3>K9BGAB<23>po3rq2ss\ 2<3>zz0TOV } jo_kl_13 { ; June 02, 2002 0:00:50.37 ; Pentium 900 Mhz by Jochen Weber ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=formulas.frm formulaname=mod5klein_group passes=1 center-mag=-1.95883/2.28763/20.11368/0.8969/49.0566696128656687/2.050903\ 62691718253 params=5/2.5/3.5/2/5/5/5/0 float=y maxiter=1000 inside=0 proximity=2.1 outside=fmod periodicity=0 cyclerange=0/255 colors=000FF0<55>vv0vv0ww0<2>zz0zz0yy0<55>KK0JJ0II0<3>FF000F<57>00v00v00\ w<2>00z00z00y<55>00K00J00I<3>00FFF0 } jo_kl_15 { ; June 02, 2002 0:01:45.36 ; Pentium 900 Mhz by Jochen Weber ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=formulas.frm formulaname=mod5klein_group passes=1 center-mag=-83.7064/-101.095/0.08510823/1/-90/-1.23373533611470521e-014 params=2.9/0.58/1.5/1/0/1.51/0.85/0 float=y maxiter=1023 proximity=3.45 outside=fmod periodicity=0 colors=000qsw<15>WgnUfnTfm<3>NbkMajKajJ`iH_h<2>LaiNbjPcjRdkSel<8>gnqiorj\ pr<3>rtutuvuvvwww<8>WZgTWeQUc<3>DIWAFUCHV<17>eglgimhjn<3>pqrrststuuvv<5>\ kloijnghmffldek<2>``hZ_gXYfVWdUUc<6>IIWGGVEFU<3>77Q55P44O22N00L<5>99RBBS\ DDTFFUGGV<6>SSaUUbWWcYYdZZe``g<6>llonnpppq<2>uutwwvwwt<17>ysUysSysR<2>ys\ MzrKypK<8>saHr_HqYH<2>oTGnRFlQE<7>QB6OA5L84<3>A00<4>F00<3>K00<3>TC0<8>lc\ `ngepji<3>zwz<5>rtx } jo_kl_17 { ; June 02, 2002 0:00:12.03 ; Pentium 900 Mhz by Jochen Weber ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=formulas.frm formulaname=inv4klein_group passes=1 center-mag=0.253411/-0.0274059/0.381288 params=2/4/0/0.54 float=y maxiter=1000 inside=0 proximity=6 outside=fmod periodicity=0 cyclerange=0/255 colors=000d_h<93>WL5WL5WL4<2>VK3VK3VL4<88>swhtwhtxi<3>uyjuyjtxj<55>bhg } frm:Mod5Klein_Group {;Modification of "4Klein_Group" by Morgan L. Owens ;Circle 1 and 2 touch, 3 and 4 each touch 1 and 2. ;Parameters of circle 5 are not restricted. Circle has "inverted" function. ;periodicity=no ;------------------------------------ ;p1r: radius 1 ;p1i: radius 2 ;p2r: radius 3 ;p2i: radius 4 ;p3r: Center of circle 5 x-coordinate ;p3i: Center of circle 5 y-coordinate ;p4r: radius 5 ;------------------------------------ r1 = real(p1) r2 = imag(p1) r3 = real(p2) r4 = imag(p2) r5 = real(p4) ;c1 = -r1 ;c2 = r2 c3 = ((r1-r2)*r3+flip(sqrt((r1+r2+r3)*r1*r2*r3)*2))/(r1+r2) c4 = ((r1-r2)*r4-flip(sqrt((r1+r2+r4)*r1*r2*r4)*2))/(r1+r2) rr1 = sqr(r1) rr2 = sqr(r2) rr3 = sqr(r3) rr4 = sqr(r4) rr5 = sqr(r5) z = pixel: inside = 0 IF (|z+r1| < rr1) z = r1*conj(r1/(z+r1)) - r1 inside = 1 ELSEIF (|z-r2| < rr2) z = r2*conj(r2/(z-r2)) + r2 inside = 1 ELSEIF (|z-c3| < rr3) z = r3*conj(r3/(z-c3)) + c3 inside = 1 ELSEIF (|z-c4| < rr4) z = r4*conj(r4/(z-c4)) + c4 inside = 1 ELSEIF (|z-p3| > rr5) z = r5*conj(r5/(z-p3)) + p3 inside = 1 ENDIF inside } frm:Inv4Klein_Group {;Modification of "3Klein_Group" by Morgan L. Owens ;Circle 4 has "inverted" function. ;periodicity=no ;( Circles all touching: r123 = sqrt(3)/2 ; r4 = sqrt(3)/2 + 1 ; c4 = 0 ) ;------------------------------------ ;p1r: radii 1 to 3 ;p1i: radius 4 ;p2r: Center of circle 4 x-coordinate ;p2i: Center of circle 4 y-coordinate ;------------------------------------ ; ang = 2*pi/3 c1 = 1 c2 = exp((0,1)*ang) c3 = exp((0,2)*ang) r123 = real(p1) r4 = imag(p1) rr123 = sqr(r123) rr4 = sqr(r4) z = pixel: inside = 0 IF (|z-c1| < rr123) z = r123*conj(r123/(z-c1)) + c1 inside = 1 ELSEIF (|z-c2| < rr123) z = r123*conj(r123/(z-c2)) + c2 inside = 1 ELSEIF (|z-c3| < rr123) z = r123*conj(r123/(z-c3)) + c3 inside = 1 ELSEIF (|z-p2| > rr4) z = r4*conj(r4/(z-p2)) + p2 inside = 1 ENDIF inside }