M5KLN02 { ; . t= 0:02:22.43 ; Copyright Sylvie Gallet, May 26, 2002 ; <sylvie_gallet@compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=klein.frm formulaname=mod5klein_group passes=1 center-mag=-7.3926/-0.316566/0.1738033/1/-52.500000000000014\ 2/-1.23373533611470521e-014 params=2/0.6/1.5/0.5/0/1.5/1/1 float=y maxiter=1023 proximity=3.45 outside=fmod periodicity=0 sound=off colors=000<182>000000000000000<10>0A00B00C00D00E0<3>3H04I06J\ 1<20>ejMgkNimO<3>orSpsTrtU<5>svdswftwg<2>txmuyouyqvzs000<2>0\ 00 } M5KLN03 { ; . t= 0:05:24.23 ; Copyright Sylvie Gallet, May 26, 2002 ; <sylvie_gallet@compuserve.com> ; t=calc time using a PII 300 at 1600 x 1200 reset=2002 type=formula formulafile=klein.frm formulaname=mod5klein_group passes=1 center-mag=-31.7027/62.311/0.01391957/1/-30.0000000000000533\ /-2.50563458870090017e-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 sound=off colors=000<181>000000000000000<10>0900A00B00C00D0<3>2G03H04I\ 0<21>ejMgkNimO<3>orSpsTrtU<5>svdswftwg<2>txmuyouyqvzs000<2>0\ 00 } ----------------------------------------------- E-mail: Sylvie_Gallet@CompuServe.com Web site: http://www.fractalus.com/sylvie/homepage.htm -----------------------------------------------
Hello Sylvie, That's the first time I've seen images by you *and* knowing beforehand the formulas they are based on (therefore probably having formed a kind of preconception what kind of pictures I could expect). Needless to say your images were a 100 percent surprise. Many thanks, Gerald P.S.: If it's of any use, the formulas now have another parameter to separate the circles on the x-axis, if need be (a small portion of added flexibility). ------------------------ Pars ahead --------------------------- Alt3Klein_Group {;Modification of "3Klein_Group" by Morgan L. Owens ;Centers of circles 1 and 2 are situated on the x-axis, ;both circles with distance d to the y-axis. ;Circle 3 touches both 1 and 2. ;periodicity=no ;-------------- ;p1r: radius 1 ;p1i: radius 2 ;p2r: radius 3 ;p2i: distance d ( <= radius 3 ) ;----------------------------------------------- r1 = real(p1) r2 = imag(p1) r3 = real(p2) c1 = r1 + imag(p2) ;wrong sign will be compensated for in the loop c2 = r2 + imag(p2) c3 = r3 - imag(p2) c3 = ((c1-c2)*c3+flip(sqrt((c1+c2+c3)*c1*c2*c3)*2))/(c1+c2) rr1 = sqr(r1) rr2 = sqr(r2) rr3 = sqr(r3) z = pixel: inside = 0 IF (|z+c1| < rr1) z = r1*conj(r1/(z+c1)) - c1 inside = 1 ELSEIF (|z-c2| < rr2) z = r2*conj(r2/(z-c2)) + c2 inside = 1 ELSEIF (|z-c3| < rr3) z = r3*conj(r3/(z-c3)) + c3 inside = 1 ENDIF inside } Alt4Klein_Group {;Modification of "4Klein_Group" by Morgan L. Owens ;Centers of circles 1 and 2 are situated on the x-axis, ;both circles with distance d to the y-axis. ;Circles 3 and 4 both touch 1 and 2. ;periodicity=no ;-------------- ;p1r: radius 1 ;p1i: radius 2 ;p2r: radius 3 ;p2i: radius 4 ;p3r: distance d ( <= radius 3, <= radius 4 ) ;------------------------------------------------------------ r1 = real(p1) r2 = imag(p1) r3 = real(p2) r4 = imag(p2) c1 = r1 + real(p3) ;wrong sign will be compensated for in the loop c2 = r2 + real(p3) c3 = r3 - real(p3) c4 = r4 - real(p3) c3 = ((c1-c2)*c3+flip(sqrt((c1+c2+c3)*c1*c2*c3)*2))/(c1+c2) c4 = ((c1-c2)*c4-flip(sqrt((c1+c2+c4)*c1*c2*c4)*2))/(c1+c2) rr1 = sqr(r1) rr2 = sqr(r2) rr3 = sqr(r3) rr4 = sqr(r4) z = pixel: inside = 0 IF (|z+c1| < rr1) z = r1*conj(r1/(z+c1)) - c1 inside = 1 ELSEIF (|z-c2| < rr2) z = r2*conj(r2/(z-c2)) + c2 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 ENDIF inside } Mod4Klein_Group {;Modification of "3Klein_Group" by Morgan L. Owens ;Centers of circles 1 and 2 are situated on the x-axis, ;both circles with distance d to the y-axis. ;Circle 3 touches both 1 and 2. ;Parameters of circle 4 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 4 x-coordinate ;p3i: Center of circle 4 y-coordinate ;p4r: distance d ( <= radius 3 ) ;------------------------------------ r1 = real(p1) r2 = imag(p1) r3 = real(p2) r4 = imag(p2) c1 = r1 + real(p4) ;wrong sign will be compensated for in the loop c2 = r2 + real(p4) c3 = r3 - real(p4) c3 = ((c1-c2)*c3+flip(sqrt((c1+c2+c3)*c1*c2*c3)*2))/(c1+c2) rr1 = sqr(r1) rr2 = sqr(r2) rr3 = sqr(r3) rr4 = sqr(r4) z = pixel: inside = 0 IF (|z+c1| < rr1) z = r1*conj(r1/(z+c1)) - c1 inside = 1 ELSEIF (|z-c2| < rr2) z = r2*conj(r2/(z-c2)) + c2 inside = 1 ELSEIF (|z-c3| < rr3) z = r3*conj(r3/(z-c3)) + c3 inside = 1 ELSEIF (|z-p3| > rr4) z = r4*conj(r4/(z-p3)) + p3 inside = 1 ENDIF inside } Mod5Klein_Group {;Modification of "4Klein_Group" by Morgan L. Owens ;Centers of circles 1 and 2 are situated on the x-axis, ;both circles with distance d to the y-axis. ;Circles 3 and 4 both 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 ;p4i: distance d ( <= radius 3, <= radius 4 ) ;-------------------------------------------- r1 = real(p1) r2 = imag(p1) r3 = real(p2) r4 = imag(p2) r5 = real(p4) c1 = r1 + imag(p4) ;wrong sign will be compensated for in the loop c2 = r2 + imag(p4) c3 = r3 - imag(p4) c4 = r4 - imag(p4) c3 = ((c1-c2)*c3+flip(sqrt((c1+c2+c3)*c1*c2*c3)*2))/(c1+c2) c4 = ((c1-c2)*c4-flip(sqrt((c1+c2+c4)*c1*c2*c4)*2))/(c1+c2) rr1 = sqr(r1) rr2 = sqr(r2) rr3 = sqr(r3) rr4 = sqr(r4) rr5 = sqr(r5) z = pixel: inside = 0 IF (|z+c1| < rr1) z = r1*conj(r1/(z+c1)) - c1 inside = 1 ELSEIF (|z-c2| < rr2) z = r2*conj(r2/(z-c2)) + c2 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 } ------------------------- Pars end ----------------------------
participants (2)
-
Gerald K. Dobiasovsky -
Sylvie Gallet