From: owner-fractint-digest@lists.xmission.com (fractint-digest) To: fractint-digest@lists.xmission.com Subject: fractint-digest V1 #138 Reply-To: fractint-digest Sender: owner-fractint-digest@lists.xmission.com Errors-To: owner-fractint-digest@lists.xmission.com Precedence: bulk fractint-digest Thursday, March 19 1998 Volume 01 : Number 138 ---------------------------------------------------------------------- Date: Wed, 18 Mar 1998 22:57:09 -0700 (MST) From: Kerry Mitchell Subject: Re: (fractint) Sqrt(3) in the Mset I agree with Jay. And if anyone's got 25 Megs to burn up, I've got a 421 frame 320x240 avi that shows the zoom from a magnitude of 1 to 10^12. Kerry - ------------------------------------------------------------------------------- Kerry Mitchell lkmitch@primenet.com - ------------------------------------------------------------------------------- On Wed, 18 Mar 1998, Jay Hill wrote: > > From: Peter Gavin > > the new midget : (-1.75,0) :: (-1.75,0) : the main mset > > Over and over and over again, and I realized that a familiar number was > > coming up, sqrt(3). Atleast I think it was that... I'll have to double > > check. Anyways, the center of each successive zoom approached closer and > > closer to that. > > I get the limit as -1.78644025556369 - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Wed, 18 Mar 1998 22:10:57 -0800 From: "Jay Hill" Subject: Re: (fractint) Sqrt(3) in the Mset Wow Kerry, Talk about quick analysis! Peter posted the question only about 5 hours ago and you have 421 frames already!??!@?! This and a few more like it might make a good CD. I had to change color schemes at least once while I did the zoom. It gets a little messy near the arbitrary precision limit. I might add that we KNOW sqrt(3) is wrong because sqrt(3) > -1.75 = base of period 3 midget which is on the wrong side. The limit is on the '-' side of the midget so we must have limit<-1.75. Jay - ---------- > From: Kerry Mitchell > To: fractint@lists.xmission.com > Subject: Re: (fractint) Sqrt(3) in the Mset > Date: Wednesday, March 18, 1998 9:57 PM > > I agree with Jay. And if anyone's got 25 Megs to burn up, I've got a 421 > frame 320x240 avi that shows the zoom from a magnitude of 1 to 10^12. > > Kerry > > - ------------------------------------------------------------------------------- > Kerry Mitchell > lkmitch@primenet.com > - ------------------------------------------------------------------------------- > > On Wed, 18 Mar 1998, Jay Hill wrote: > > > > From: Peter Gavin > > > > the new midget : (-1.75,0) :: (-1.75,0) : the main mset > > > Over and over and over again, and I realized that a familiar number was > > > coming up, sqrt(3). Atleast I think it was that... I'll have to double > > > check. Anyways, the center of each successive zoom approached closer and > > > closer to that. > > > > I get the limit as -1.78644025556369 > - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Thu, 19 Mar 1998 02:44:35 -0500 (EST) From: ao950@freenet.carleton.ca (Paul Derbyshire) Subject: (fractint) Fractals Just Went Nuclear! Introducing the Nuclear formula. 3 Julia parameters. 3 Critical points. 3 6-dimensional Mandelbrot sets. 9 Mandelbrot slices. 3 Quadcolored Mandelbrot slices using all 3 critical points. Short PAR included, many more parameters to come. And preliminary exploration has turned up structures in the Mandelbrot set (see PAR entry fracmini_zoom2) indicative of Herman rings lurking in the Julia equation... The last image, fracmini_zoom1a, is currently generating in a window in disk video. - ---8<--- Formulas --->8--- Nuclear_Jul { ; p1, p2, p3 parameters. Use float=y. a=p1, c=p2, k=p3, a2=a*a, ac=a*c, r3=sqrt(3), r3a2=r3*a2, a6=3*a2 r3ac=r3*ac, ack=k*ac z=pixel: z2=sqr(z) z3=z*z2 z=(r3a2*z3-a6*z2-r3ac*z-ac)/(r3*z+1)+ack, lastsqr<=1000000 } Nuclear_M_k_0 { ; p1, p2 parameters. Use float=y. k is Mandel parameter, ; critical point 0. a=p1, c=p2, k=pixel, a2=a*a, ac=a*c, r3=sqrt(3), r3a2=r3*a2 a6=3*a2, r3ac=r3*ac, ack=k*ac z=0: z2=sqr(z) z3=z*z2 z=(r3a2*z3-a6*z2-r3ac*z-ac)/(r3*z+1)+ack, lastsqr<=1000000 } Nuclear_M_k_1 { ; p1, p2 parameters. Use float=y. k is Mandel parameter, ; critical point 1. a=p1, c=p2, k=pixel, a2=a*a, ac=a*c, r3=sqrt(3), r3a2=r3*a2 a6=3*a2, r3ac=r3*ac, ack=k*ac z=1: z2=sqr(z) z3=z*z2 z=(r3a2*z3-a6*z2-r3ac*z-ac)/(r3*z+1)+ack, lastsqr<=1000000 } Nuclear_M_k_-1 { ; p1, p2 parameters. Use float=y. k is Mandel parameter, ; critical point -1. a=p1, c=p2, k=pixel, a2=a*a, ac=a*c, r3=sqrt(3), r3a2=r3*a2 a6=3*a2, r3ac=r3*ac, ack=k*ac z=-1: z2=sqr(z) z3=z*z2 z=(r3a2*z3-a6*z2-r3ac*z-ac)/(r3*z+1)+ack, lastsqr<=1000000 } Nuclear_M_c_0 { ; p1, p3 parameters. Use float=y. c is Mandel parameter, ; critical point 0. a=p1, c=pixel, k=p3, a2=a*a, ac=a*c, r3=sqrt(3), r3a2=r3*a2 a6=3*a2, r3ac=r3*ac, ack=k*ac z=0: z2=sqr(z) z3=z*z2 z=(r3a2*z3-a6*z2-r3ac*z-ac)/(r3*z+1)+ack, lastsqr<=1000000 } Nuclear_M_c_1 { ; p1, p3 parameters. Use float=y. c is Mandel parameter, ; critical point 1. a=p1, c=pixel, k=p3, a2=a*a, ac=a*c, r3=sqrt(3), r3a2=r3*a2 a6=3*a2, r3ac=r3*ac, ack=k*ac z=1: z2=sqr(z) z3=z*z2 z=(r3a2*z3-a6*z2-r3ac*z-ac)/(r3*z+1)+ack, lastsqr<=1000000 } Nuclear_M_c_-1 { ; p1, p3 parameters. Use float=y. c is Mandel parameter, ; critical point -1. a=p1, c=pixel, k=p3, a2=a*a, ac=a*c, r3=sqrt(3), r3a2=r3*a2 a6=3*a2, r3ac=r3*ac, ack=k*ac z=-1: z2=sqr(z) z3=z*z2 z=(r3a2*z3-a6*z2-r3ac*z-ac)/(r3*z+1)+ack, lastsqr<=1000000 } Nuclear_M_a_0 { ; p2, p3 parameters. Use float=y. a is Mandel parameter, ; critical point 0. a=pixel, c=p2, k=p3, a2=a*a, ac=a*c, r3=sqrt(3), r3a2=r3*a2 a6=3*a2, r3ac=r3*ac, ack=k*ac z=0: z2=sqr(z) z3=z*z2 z=(r3a2*z3-a6*z2-r3ac*z-ac)/(r3*z+1)+ack, lastsqr<=1000000 } Nuclear_M_a_1 { ; p2, p3 parameters. Use float=y. a is Mandel parameter, ; critical point 1. a=pixel, c=p2, k=p3, a2=a*a, ac=a*c, r3=sqrt(3), r3a2=r3*a2 a6=3*a2, r3ac=r3*ac, ack=k*ac z=1: z2=sqr(z) z3=z*z2 z=(r3a2*z3-a6*z2-r3ac*z-ac)/(r3*z+1)+ack, lastsqr<=1000000 } Nuclear_M_a_-1 { ; p2, p3 parameters. Use float=y. a is Mandel parameter, ; critical point -1. a=pixel, c=p2, k=p3, a2=a*a, ac=a*c, r3=sqrt(3), r3a2=r3*a2 a6=3*a2, r3ac=r3*ac, ack=k*ac z=-1: z2=sqr(z) z3=z*z2 z=(r3a2*z3-a6*z2-r3ac*z-ac)/(r3*z+1)+ack, lastsqr<=1000000 } Nuclear_M_k { ; p1, p2 parameters. k is Mandel parameter. Colored based on all ; 3 critical points. Use outside=real, float=y, periodicity=n, ; maxiter>=256, and logmap=0. ; For logmap effect put real(p3) minimum iteration, ; imag(p3) bigger than 1, e.g. 2. ; Color 0 is for all critical points trapped. ; Colors 1-66, 67-129, 130-192, and 193-255 are separate ranges. ; Use first for outside, second thru fourth for two ; critical points escape, one trapped... a=p1, c=p2, k=pixel, a2=a*a, ac=a*c, r3=sqrt(3), r3a2=r3*a2, a6=3*a2 r3ac=r3*ac, ack=k*ac min=real(p3) p=imag(p3) IF(p==0) p=1 ENDIF z1=0, z2=1, z3=-1 qq=10^-2, iter=0, done=0, z2done=0, m=maxit-1, z1done=0, z3done=0 m2=floor(maxit/2), z1a=z1, z2a=z2, z3a=z3, flag=0, z1d2=0, z2d2=0 z3d2=0, qrl=1.5, q2=0.15 : IF(z3done==0) zz2=sqr(z3) zz3=z3*zz2 z3=(r3a2*zz3-a6*zz2-r3ac*z3-ac)/(r3*z3+1)+ack, IF(lastsqr>10000) z3done=iter z3d2=1 ENDIF ENDIF IF(z2done==0) zz2=sqr(z2) zz3=z2*zz2 z2=(r3a2*zz3-a6*zz2-r3ac*z2-ac)/(r3*z2+1)+ack, IF(lastsqr>10000) z2done=iter z2d2=1 ENDIF ENDIF IF(z1done==0) zz2=sqr(z1) zz3=z1*zz2 z1=(r3a2*zz3-a6*zz2-r3ac*z1-ac)/(r3*z1+1)+ack, IF(lastsqr>10000) z1done=iter z1d2=1 ENDIF ENDIF iter=iter+1 IF(iter>=m2 && iter<(m2+1) && flag=0) z1chek=z1 z2chek=z2 z3chek=z3 flag=1 spd=0 first=0 same12=0 same23=0 same13=0 ELSEIF(flag==1) zz2=sqr(z1a) zz3=z1a*zz2 z1a=(r3a2*zz3-a6*zz2-r3ac*z1a-ac)/(r3*z1a+1)+ack zz2=sqr(z2a) zz3=z2a*zz2 z2a=(r3a2*zz3-a6*zz2-r3ac*z2a-ac)/(r3*z2a+1)+ack zz2=sqr(z3a) zz3=z3a*zz2 z3a=(r3a2*zz3-a6*zz2-r3ac*z3a-ac)/(r3*z3a+1)+ack spd=spd+1 IF(|z1a-z2chek|=qq) first=1 ENDIF ENDIF IF(|z2a-z1chek|=qq) first=2 ENDIF ENDIF IF(|z1a-z3chek|=qq) first=1 ENDIF ENDIF IF(|z3a-z1chek|=qq) first=3 ENDIF ENDIF IF(|z2a-z3chek|=qq) first=2 ENDIF ENDIF IF(|z3a-z2chek|=qq) first=3 ENDIF ENDIF ENDIF IF((z1d2>0 && z2d2>0 && z3d2>0) || iter==m) IF(z1done==0 || z2done==0 || z3done==0) IF(z2done>0 && z3done>0) ddd=z2done IF(z3done>ddd) ddd=z3done ENDIF color=((ddd-min)/(m-min))^(1/p)*63 IF(color>63) color=63 ENDIF IF(color<1) color=1 ENDIF color=color+66 ELSEIF(z1done>0 && z3done>0) ddd=z1done IF(z3done>ddd) ddd=z3done ENDIF color=((ddd-min)/(m-min))^(1/p)*63 IF(color>63) color=63 ENDIF IF(color<1) color=1 ENDIF color=color+129 ELSEIF(z1done>0 && z2done>0) ddd=z1done IF(z2done>ddd) ddd=z2done ENDIF color=((ddd-min)/(m-min))^(1/p)*63 IF(color>63) color=63 ENDIF IF(color<1) color=1 ENDIF color=color+192 ELSEIF(z1done>0) IF(same23!=0 && first!=0) ddd=z1done*(q2*abs(z2d2-z3d2))^qrl color=((ddd-min)/(m-min))^(1/p)*63 ELSE color=((z1done-min)/(m-min))^(1/p)*63 ENDIF IF(color>63) color=63 ENDIF IF(color<1) color=1 ENDIF IF(same23==0) color=color+66 ELSE IF(first==0) color=color+66 ELSEIF(first==2) color=color+129 ELSE color=color+192 ENDIF ENDIF ELSEIF(z2done>0) IF(same13!=0 && first!=0) ddd=z2done*(q2*abs(z1d2-z3d2))^qrl color=((ddd-min)/(m-min))^(1/p)*63 ELSE color=((z2done-min)/(m-min))^(1/p)*63 ENDIF IF(color>63) color=63 ENDIF IF(color<1) color=1 ENDIF IF(same13==0) color=color+129 ELSE IF(first==0) color=color+129 ELSEIF(first==1) color=color+66 ELSE color=color+192 ENDIF ENDIF ELSEIF(z3done>0) IF(same12!=0 && first!=0) ddd=z3done*(q2*abs(z1d2-z2d2))^qrl color=((ddd-min)/(m-min))^(1/p)*63 ELSE color=((z3done-min)/(m-min))^(1/p)*63 ENDIF IF(color>63) color=63 ENDIF IF(color<1) color=1 ENDIF IF(same12==0) color=color+192 ELSE IF(first==0) color=color+192 ELSEIF(first==1) color=color+66 ELSE color=color+129 ENDIF ENDIF ELSEIF(same12==1 && same23==1) ddd=abs(z1d2-z2d2) IF(abs(z1d2-z3d2)66) color=66 ENDIF ELSE color=(ddd/m)^(1/p)*63 IF(color>63) color=63 ENDIF ENDIF IF(color<1) color=1 ENDIF IF(first==1) color=color+66 ELSEIF(first==2) color=color+129 ELSEIF(first==3) color=color+192 ENDIF ELSEIF(same12==1) ddd=abs(z1d2-z2d2) color=(ddd/m)^(1/p)*63 IF(color>63) color=63 ENDIF IF(color<1) color=1 ENDIF IF(first==0) color=color+192 ELSEIF(first==1) color=color+66 ELSE color=color+129 ENDIF ELSEIF(same13==1) ddd=abs(z1d2-z3d2) color=(ddd/m)^(1/p)*63 IF(color>63) color=63 ENDIF IF(color<1) color=1 ENDIF IF(first==0) color=color+129 ELSEIF(first==1) color=color+66 ELSE color=color+192 ENDIF ELSEIF(same23==1) ddd=abs(z2d2-z3d2) color=(ddd/m)^(1/p)*63 IF(color>63) color=63 ENDIF IF(color<1) color=1 ENDIF IF(first==0) color=color+66 ELSEIF(first==2) color=color+129 ELSE color=color+192 ENDIF ELSE color=0 ENDIF ELSE color=((iter-min)/(m-min))^(1/p)*66 IF(color>66) color=66 ENDIF IF(color<1) color=1 ENDIF ENDIF done=1 z=color-iter-7 ENDIF done==0 } Nuclear_M_c { ; p1, p3 parameters. c is Mandel parameter. Colored based on all ; 3 critical points. Use outside=real, float=y, periodicity=n, ; maxiter>=256, and logmap=0. ; For logmap effect put real(p2) minimum iteration, ; imag(p2) bigger than 1, e.g. 2. ; Color 0 is for all critical points trapped. ; Colors 1-66, 67-129, 130-192, and 193-255 are separate ranges. ; Use first for outside, second thru fourth for two ; critical points escape, one trapped... a=p1, c=pixel, k=p3, a2=a*a, ac=a*c, r3=sqrt(3), r3a2=r3*a2, a6=3*a2 r3ac=r3*ac, ack=k*ac min=real(p2) p=imag(p2) IF(p==0) p=1 ENDIF z1=0, z2=1, z3=-1 qq=10^-2, iter=0, done=0, z2done=0, m=maxit-1, z1done=0, z3done=0 m2=floor(maxit/2), z1a=z1, z2a=z2, z3a=z3, flag=0, z1d2=0, z2d2=0, z3d2=0 qrl=1.5, q2=0.15 : IF(z3done==0) zz2=sqr(z3) zz3=z3*zz2 z3=(r3a2*zz3-a6*zz2-r3ac*z3-ac)/(r3*z3+1)+ack, IF(lastsqr>10000) z3done=iter z3d2=1 ENDIF ENDIF IF(z2done==0) zz2=sqr(z2) zz3=z2*zz2 z2=(r3a2*zz3-a6*zz2-r3ac*z2-ac)/(r3*z2+1)+ack, IF(lastsqr>10000) z2done=iter z2d2=1 ENDIF ENDIF IF(z1done==0) zz2=sqr(z1) zz3=z1*zz2 z1=(r3a2*zz3-a6*zz2-r3ac*z1-ac)/(r3*z1+1)+ack, IF(lastsqr>10000) z1done=iter z1d2=1 ENDIF ENDIF iter=iter+1 IF(iter>=m2 && iter<(m2+1) && flag=0) z1chek=z1 z2chek=z2 z3chek=z3 flag=1 spd=0 first=0 same12=0 same23=0 same13=0 ELSEIF(flag==1) zz2=sqr(z1a) zz3=z1a*zz2 z1a=(r3a2*zz3-a6*zz2-r3ac*z1a-ac)/(r3*z1a+1)+ack zz2=sqr(z2a) zz3=z2a*zz2 z2a=(r3a2*zz3-a6*zz2-r3ac*z2a-ac)/(r3*z2a+1)+ack zz2=sqr(z3a) zz3=z3a*zz2 z3a=(r3a2*zz3-a6*zz2-r3ac*z3a-ac)/(r3*z3a+1)+ack spd=spd+1 IF(|z1a-z2chek|=qq) first=1 ENDIF ENDIF IF(|z2a-z1chek|=qq) first=2 ENDIF ENDIF IF(|z1a-z3chek|=qq) first=1 ENDIF ENDIF IF(|z3a-z1chek|=qq) first=3 ENDIF ENDIF IF(|z2a-z3chek|=qq) first=2 ENDIF ENDIF IF(|z3a-z2chek|=qq) first=3 ENDIF ENDIF ENDIF IF((z1d2>0 && z2d2>0 && z3d2>0) || iter==m) IF(z1done==0 || z2done==0 || z3done==0) IF(z2done>0 && z3done>0) ddd=z2done IF(z3done>ddd) ddd=z3done ENDIF color=((ddd-min)/(m-min))^(1/p)*63 IF(color>63) color=63 ENDIF IF(color<1) color=1 ENDIF color=color+66 ELSEIF(z1done>0 && z3done>0) ddd=z1done IF(z3done>ddd) ddd=z3done ENDIF color=((ddd-min)/(m-min))^(1/p)*63 IF(color>63) color=63 ENDIF IF(color<1) color=1 ENDIF color=color+129 ELSEIF(z1done>0 && z2done>0) ddd=z1done IF(z2done>ddd) ddd=z2done ENDIF color=((ddd-min)/(m-min))^(1/p)*63 IF(color>63) color=63 ENDIF IF(color<1) color=1 ENDIF color=color+192 ELSEIF(z1done>0) IF(same23!=0 && first!=0) ddd=z1done*(q2*abs(z2d2-z3d2))^qrl color=((ddd-min)/(m-min))^(1/p)*63 ELSE color=((z1done-min)/(m-min))^(1/p)*63 ENDIF IF(color>63) color=63 ENDIF IF(color<1) color=1 ENDIF IF(same23==0) color=color+66 ELSE IF(first==0) color=color+66 ELSEIF(first==2) color=color+129 ELSE color=color+192 ENDIF ENDIF ELSEIF(z2done>0) IF(same13!=0 && first!=0) ddd=z2done*(q2*abs(z1d2-z3d2))^qrl color=((ddd-min)/(m-min))^(1/p)*63 ELSE color=((z2done-min)/(m-min))^(1/p)*63 ENDIF IF(color>63) color=63 ENDIF IF(color<1) color=1 ENDIF IF(same13==0) color=color+129 ELSE IF(first==0) color=color+129 ELSEIF(first==1) color=color+66 ELSE color=color+192 ENDIF ENDIF ELSEIF(z3done>0) IF(same12!=0 && first!=0) ddd=z3done*(q2*abs(z1d2-z2d2))^qrl color=((ddd-min)/(m-min))^(1/p)*63 ELSE color=((z3done-min)/(m-min))^(1/p)*63 ENDIF IF(color>63) color=63 ENDIF IF(color<1) color=1 ENDIF IF(same12==0) color=color+192 ELSE IF(first==0) color=color+192 ELSEIF(first==1) color=color+66 ELSE color=color+129 ENDIF ENDIF ELSEIF(same12==1 && same23==1) ddd=abs(z1d2-z2d2) IF(abs(z1d2-z3d2)66) color=66 ENDIF ELSE color=(ddd/m)^(1/p)*63 IF(color>63) color=63 ENDIF ENDIF IF(color<1) color=1 ENDIF IF(first==1) color=color+66 ELSEIF(first==2) color=color+129 ELSEIF(first==3) color=color+192 ENDIF ELSEIF(same12==1) ddd=abs(z1d2-z2d2) color=(ddd/m)^(1/p)*63 IF(color>63) color=63 ENDIF IF(color<1) color=1 ENDIF IF(first==0) color=color+192 ELSEIF(first==1) color=color+66 ELSE color=color+129 ENDIF ELSEIF(same13==1) ddd=abs(z1d2-z3d2) color=(ddd/m)^(1/p)*63 IF(color>63) color=63 ENDIF IF(color<1) color=1 ENDIF IF(first==0) color=color+129 ELSEIF(first==1) color=color+66 ELSE color=color+192 ENDIF ELSEIF(same23==1) ddd=abs(z2d2-z3d2) color=(ddd/m)^(1/p)*63 IF(color>63) color=63 ENDIF IF(color<1) color=1 ENDIF IF(first==0) color=color+66 ELSEIF(first==2) color=color+129 ELSE color=color+192 ENDIF ELSE color=0 ENDIF ELSE color=((iter-min)/(m-min))^(1/p)*66 IF(color>66) color=66 ENDIF IF(color<1) color=1 ENDIF ENDIF done=1 z=color-iter-7 ENDIF done==0 } Nuclear_M_a { ; p2, p3 parameters. c is Mandel parameter. Colored based on all ; 3 critical points. Use outside=real, float=y, periodicity=n, ; maxiter>=256, and logmap=0. ; For logmap effect put real(p1) minimum iteration, ; imag(p1) bigger than 1, e.g. 2. ; Color 0 is for all critical points trapped. ; Colors 1-66, 67-129, 130-192, and 193-255 are separate ranges. ; Use first for outside, second thru fourth for two ; critical points escape, one trapped... a=pixel, c=p2, k=p3, a2=a*a, ac=a*c, r3=sqrt(3), r3a2=r3*a2, a6=3*a2 r3ac=r3*ac, ack=k*ac min=real(p1) p=imag(p1) IF(p==0) p=1 ENDIF z1=0, z2=1, z3=-1 qq=10^-2, iter=0, done=0, z2done=0, m=maxit-1, z1done=0, z3done=0 m2=floor(maxit/2), z1a=z1, z2a=z2, z3a=z3, flag=0, z1d2=0, z2d2=0, z3d2=0 qrl=1.5, q2=0.15 : IF(z3done==0) zz2=sqr(z3) zz3=z3*zz2 z3=(r3a2*zz3-a6*zz2-r3ac*z3-ac)/(r3*z3+1)+ack, IF(lastsqr>10000) z3done=iter z3d2=1 ENDIF ENDIF IF(z2done==0) zz2=sqr(z2) zz3=z2*zz2 z2=(r3a2*zz3-a6*zz2-r3ac*z2-ac)/(r3*z2+1)+ack, IF(lastsqr>10000) z2done=iter z2d2=1 ENDIF ENDIF IF(z1done==0) zz2=sqr(z1) zz3=z1*zz2 z1=(r3a2*zz3-a6*zz2-r3ac*z1-ac)/(r3*z1+1)+ack, IF(lastsqr>10000) z1done=iter z1d2=1 ENDIF ENDIF iter=iter+1 IF(iter>=m2 && iter<(m2+1) && flag=0) z1chek=z1 z2chek=z2 z3chek=z3 flag=1 spd=0 first=0 same12=0 same23=0 same13=0 ELSEIF(flag==1) zz2=sqr(z1a) zz3=z1a*zz2 z1a=(r3a2*zz3-a6*zz2-r3ac*z1a-ac)/(r3*z1a+1)+ack zz2=sqr(z2a) zz3=z2a*zz2 z2a=(r3a2*zz3-a6*zz2-r3ac*z2a-ac)/(r3*z2a+1)+ack zz2=sqr(z3a) zz3=z3a*zz2 z3a=(r3a2*zz3-a6*zz2-r3ac*z3a-ac)/(r3*z3a+1)+ack spd=spd+1 IF(|z1a-z2chek|=qq) first=1 ENDIF ENDIF IF(|z2a-z1chek|=qq) first=2 ENDIF ENDIF IF(|z1a-z3chek|=qq) first=1 ENDIF ENDIF IF(|z3a-z1chek|=qq) first=3 ENDIF ENDIF IF(|z2a-z3chek|=qq) first=2 ENDIF ENDIF IF(|z3a-z2chek|=qq) first=3 ENDIF ENDIF ENDIF IF((z1d2>0 && z2d2>0 && z3d2>0) || iter==m) IF(z1done==0 || z2done==0 || z3done==0) IF(z2done>0 && z3done>0) ddd=z2done IF(z3done>ddd) ddd=z3done ENDIF color=((ddd-min)/(m-min))^(1/p)*63 IF(color>63) color=63 ENDIF IF(color<1) color=1 ENDIF color=color+66 ELSEIF(z1done>0 && z3done>0) ddd=z1done IF(z3done>ddd) ddd=z3done ENDIF color=((ddd-min)/(m-min))^(1/p)*63 IF(color>63) color=63 ENDIF IF(color<1) color=1 ENDIF color=color+129 ELSEIF(z1done>0 && z2done>0) ddd=z1done IF(z2done>ddd) ddd=z2done ENDIF color=((ddd-min)/(m-min))^(1/p)*63 IF(color>63) color=63 ENDIF IF(color<1) color=1 ENDIF color=color+192 ELSEIF(z1done>0) IF(same23!=0 && first!=0) ddd=z1done*(q2*abs(z2d2-z3d2))^qrl color=((ddd-min)/(m-min))^(1/p)*63 ELSE color=((z1done-min)/(m-min))^(1/p)*63 ENDIF IF(color>63) color=63 ENDIF IF(color<1) color=1 ENDIF IF(same23==0) color=color+66 ELSE IF(first==0) color=color+66 ELSEIF(first==2) color=color+129 ELSE color=color+192 ENDIF ENDIF ELSEIF(z2done>0) IF(same13!=0 && first!=0) ddd=z2done*(q2*abs(z1d2-z3d2))^qrl color=((ddd-min)/(m-min))^(1/p)*63 ELSE color=((z2done-min)/(m-min))^(1/p)*63 ENDIF IF(color>63) color=63 ENDIF IF(color<1) color=1 ENDIF IF(same13==0) color=color+129 ELSE IF(first==0) color=color+129 ELSEIF(first==1) color=color+66 ELSE color=color+192 ENDIF ENDIF ELSEIF(z3done>0) IF(same12!=0 && first!=0) ddd=z3done*(q2*abs(z1d2-z2d2))^qrl color=((ddd-min)/(m-min))^(1/p)*63 ELSE color=((z3done-min)/(m-min))^(1/p)*63 ENDIF IF(color>63) color=63 ENDIF IF(color<1) color=1 ENDIF IF(same12==0) color=color+192 ELSE IF(first==0) color=color+192 ELSEIF(first==1) color=color+66 ELSE color=color+129 ENDIF ENDIF ELSEIF(same12==1 && same23==1) ddd=abs(z1d2-z2d2) IF(abs(z1d2-z3d2)66) color=66 ENDIF ELSE color=(ddd/m)^(1/p)*63 IF(color>63) color=63 ENDIF ENDIF IF(color<1) color=1 ENDIF IF(first==1) color=color+66 ELSEIF(first==2) color=color+129 ELSEIF(first==3) color=color+192 ENDIF ELSEIF(same12==1) ddd=abs(z1d2-z2d2) color=(ddd/m)^(1/p)*63 IF(color>63) color=63 ENDIF IF(color<1) color=1 ENDIF IF(first==0) color=color+192 ELSEIF(first==1) color=color+66 ELSE color=color+129 ENDIF ELSEIF(same13==1) ddd=abs(z1d2-z3d2) color=(ddd/m)^(1/p)*63 IF(color>63) color=63 ENDIF IF(color<1) color=1 ENDIF IF(first==0) color=color+129 ELSEIF(first==1) color=color+66 ELSE color=color+192 ENDIF ELSEIF(same23==1) ddd=abs(z2d2-z3d2) color=(ddd/m)^(1/p)*63 IF(color>63) color=63 ENDIF IF(color<1) color=1 ENDIF IF(first==0) color=color+66 ELSEIF(first==2) color=color+129 ELSE color=color+192 ENDIF ELSE color=0 ENDIF ELSE color=((iter-min)/(m-min))^(1/p)*66 IF(color>66) color=66 ENDIF IF(color<1) color=1 ENDIF ENDIF done=1 z=color-iter-7 ENDIF done==0 } - --->8--- Parameter sets ---8<--- nukek_col { reset=1960 type=formula formulafile=nuclear.frm formulaname=nuclear_m_k center-mag=0.890013/0.607993/1.355191 params=1/0/1/0/0/1.2 float=y maxiter=257 inside=0 outside=real periodicity=0 colors=000zzz<64>000K0e<61>hlze0K<61>zhqU0U<61>zcz } fractured_minibrot { reset=1960 type=formula formulafile=nuclear.frm formulaname=nuclear_m_k center-mag=-14.5982/-5.6488/0.01620407 params=0.2/0.4/-0.3/0.3/0/1.2 float=y maxiter=257 inside=0 outside=real periodicity=0 colors=000zzz<64>000K0e<61>hlze0K<61>zhqU0U<61>zcz } fracmini_zoom1 { reset=1960 type=formula formulafile=nuclear.frm formulaname=nuclear_m_k passes=t center-mag=7.27982/-0.821195/0.1025574 params=0.2/0.4/-0.3/0.3/0/1.2 float=y maxiter=257 inside=0 outside=real periodicity=0 colors=000zzz<64>000K0e<61>hlze0K<61>zhqU0U<61>zcz } fracmini_zoom2 { reset=1960 type=formula formulafile=nuclear.frm formulaname=nuclear_m_k passes=t center-mag=6.66151/-0.658413/0.2913562 params=0.2/0.4/-0.3/0.3/0/1.2 float=y maxiter=257 inside=0 outside=real periodicity=0 colors=000zzz<64>000K0e<61>hlze0K<61>zhqU0U<61>zcz } fracmini_zoom3 { reset=1960 type=formula formulafile=nuclear.frm formulaname=nuclear_m_k passes=t center-mag=6.69587/-1.21995/1.400751 params=0.2/0.4/-0.3/0.3/0/1.2 float=y maxiter=257 inside=0 outside=real periodicity=0 colors=000zzz<64>000K0e<61>hlze0K<61>zhqU0U<61>zcz } fracmini_zoom4 { reset=1960 type=formula formulafile=nuclear.frm formulaname=nuclear_m_k passes=t center-mag=6.62916/-1.67046/10.29964 params=0.2/0.4/-0.3/0.3/0/1.2 float=y maxiter=257 inside=0 outside=real periodicity=0 colors=000zzz<64>000K0e<61>hlze0K<61>zhqU0U<61>zcz } fracmini_zoom1a { reset=1960 type=formula formulafile=nuclear.frm formulaname=nuclear_m_k passes=t center-mag=7.08534/2.64775/3.387863 params=0.2/0.4/-0.3/0.3/0/1.2 float=y maxiter=257 inside=0 outside=real periodicity=0 colors=000zzz<64>000K0e<61>hlze0K<61>zhqU0U<61>zcz } - ---8<--- End --->8--- - -- .*. Friendship, companionship, love, and having fun are the reasons for -() < life. All else; sex, money, fame, etc.; are just to get/express these. `*' Send any and all mail with attachments to the hotmail address please. Paul Derbyshire ao950@freenet.carleton.ca pgd73@hotmail.com - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Thu, 19 Mar 1998 02:53:19 -0500 (EST) From: ao950@freenet.carleton.ca (Paul Derbyshire) Subject: (fractint) BUG REPORT The formula parser chokes on Nuclear_M_k if disk video 1024x768 or bigger is set, but not with normal video or smaller disk video modes. Suspect a bad interaction between disk video code and formula code, which would have been avoided if Fractint had been written in C++ (shameless C++/objects/encapsulation/information hiding plug here!). When the parser chokes it displays a red error box and emits a buzz, then generates a blank image. The precise error message resembles "Not enough memory for 'formula'", and is useless, since it is clearly wrong. (I have enough memory to run "formula" types; obviously, or I'd not have all these PARs from hring and so forth...) - -- .*. Friendship, companionship, love, and having fun are the reasons for -() < life. All else; sex, money, fame, etc.; are just to get/express these. `*' Send any and all mail with attachments to the hotmail address please. Paul Derbyshire ao950@freenet.carleton.ca pgd73@hotmail.com - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Thu, 19 Mar 1998 03:22:41 -0500 (EST) From: ao950@freenet.carleton.ca (Paul Derbyshire) Subject: Re: (fractint) FRACTINT.ORG >Yipes....I saw my name. What do I have to do?? :) Relax, I was just reminding everyone of the wonderful unlimited-flat-rate internet access you found out there, as a possible host for fractint.org. - -- .*. Friendship, companionship, love, and having fun are the reasons for -() < life. All else; sex, money, fame, etc.; are just to get/express these. `*' Send any and all mail with attachments to the hotmail address please. Paul Derbyshire ao950@freenet.carleton.ca pgd73@hotmail.com - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Thu, 19 Mar 1998 00:29:21 -0800 From: "Jay Hill" Subject: Re: (fractint) BUG REPORT > From: Paul Derbyshire > > The formula parser chokes on Nuclear_M_k if disk video 1024x768 or bigger > is set, but not with normal video or smaller disk video modes. Suspect a [...] > blank image. The precise error message resembles "Not enough memory for > 'formula'", and is useless, since it is clearly wrong. (I have enough Reminds me of release 6 of the IBM/360 operating system years ago. No matter how simple my FORTRAN program was, I even had 3 line subroutine stubs like SUBROUTINE X RETURN END the compiler emitted this message SUGGEST SUBDIVIDING PROGRAM. Care to explain your formula? By the way, Paul, you should get a kick out of the last three issues of Fractal of the Night beginning with http://home.san.rr.com/jayrhill/FotN/FotN61.html Peter Jakubowicz has taken a swing at the quiz questions posed there. He and I are wondering what you will make of them. Jay - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Thu, 19 Mar 1998 04:06:56 -0500 (EST) From: ao950@freenet.carleton.ca (Paul Derbyshire) Subject: Re: (fractint) BUG REPORT >Care to explain your formula? It colors in one of 4 ranges based on what happens to all 3 critical points. All escape -> The largest of the three iteration counts chooses color from range 0. 2 escape, 1 does not -> The largest iteration for the escapees chooses color from range n, n being the critical point that found a finite attractor. So, for example, a mini Mandelbrot for critical point 1 in and near which critical points 2 and 3 escape, will be colored from range 1, the surroundings from range 0, and dendrites in the surroundings caused by critical points 2-3 will be seen intersecting the mini Mandelbrot! The mini's own dendrites will show up outside the baby, where they will overlap other dendrites from 2 and 3. 1 escapes, 2 stay but don't converge -> Escaping picks color range and colors by its iteration. So if two minis intersect, the intersection will "null out" to the third color range, and still the dendrites are visible through it. 1 escapes, 2 stay and hit same attracting cycle or point -> Whichever critical point hit the finite attractor first (determined by rerunning the iterations), the other picks the range, and the specific color by convergence speed. So if you have a minibrot for critical point 2, and in a region inside it critical point 3 converges to its attractor instead of infinity, there will be a blob of color from range 3. It will in fact typically look like a Julia set corresponding roughly to where in the minibrot it is located! Picture a seahorsey connected Julia set embedded in a mini Mandelbrot near its seahorse valley inside the cardioid. None escape: If they all converge to separate attractors, the color is color 0. If two meet the same attractor, the second one to do so picks the range and color. If they all meet the same attractor, the last chooses the index and the color comesfrom range 0. >By the way, Paul, you should get a kick out of the last three issues of >Fractal of the Night beginning with >http://home.san.rr.com/jayrhill/FotN/FotN61.html Gonna browse over there shortly. :-) >Peter Jakubowicz has taken a swing at the quiz questions posed there. >He and I are wondering what you will make of them. OK...will do. Make something of them that is. No guarantees as to what, yet. BTW I came up with the formula quite simply. I wanted a generic rational function with critical points at -1, 0, and 1. So I supposed I had r(z) = p(z)/q(z) and noted the zeros of the derivative would be zeros of p'q-pq', so I set p(z) = az^3+bz^2+cz+d, q(z) = pz^3+qz^2+rz+s, and [p'q-pq'](z) = z^3-z. This led to a collection of nonlinear constraints on the 8 unknowns. I found these virtually intractable and arbitrarily chose p = 0. Eventually I derived all the others in terms of a and c, and so the formula was born, with a and c variable. A square root of 3 popped up, interestingly in light of the earlier discussion of sqrt(3). I added a constant to the formula to generalize it further (constants don't alter the derivative). Since the rational evaluated to -ac at z=0, I chose the constant at the end to be ack, so that k=1 would produce a convenient superattracting fixed point at 0. A quick check with w = 1/z and s(w) = 1/r(1/w) verified that infinity was superattracting. (s had a zero at zero and also had a derivative a multiple of w^3-w, so the critical points z=w=1, z=w=-1 showed up again as a check on my math, and w=0 meaning z=infinity as well.) Have you run the PAR file and/or explored? - -- .*. Friendship, companionship, love, and having fun are the reasons for -() < life. All else; sex, money, fame, etc.; are just to get/express these. `*' Send any and all mail with attachments to the hotmail address please. Paul Derbyshire ao950@freenet.carleton.ca pgd73@hotmail.com - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Thu, 19 Mar 1998 03:56:41 PST From: "Koppens,Ton" Subject: (fractint) Thanks par, volume 1 Having been a lurker now for some months I finally found the time to play around with fractint and to put some things learned from this list into practice. Perhaps I'm a bit too enthusiast but I would like to share the results with you. Consider it as a big thank you to all contributors. I had some trouble copying the whole par into one mailnote, so it comes in 4 volumes. Most of the FRM's come from the orgform collection. Greetings to you all, Ton Koppens ======================================================================== tk-gj-01 { ; CalcTime 0:02:25.07 at1024x768 on a 486DX 100 ; Image Copyright 14 Mar 1998 by Ton Koppens ; e-mail:Ton_Koppens.RXNL@eur.xerox.com reset=1960 type=formula formulafile=_g.frm formulaname=gravijul function=sin/sqr/sinh center-mag=6.783e-005/1.0165e-005/0.6666712 params=1.5468/1.231568/0.89889/0.02546848/1.878989/1.2265 decomp=256 colors=000VZi<6>UhoX8W<42>7MXW8W<30>10EX8X<25>eLvX8W<44>GIfX9W<26>doUV9Y\ <11>4PvX8W<24>XPUXCVXQU<17>WbS<6>z_C<3>k_E } tk-gj-02 { ; CalcTime 0:02:25.07 at1024x768 on a 486DX 100 ; Image Copyright 14 Mar 1998 by Ton Koppens ; e-mail:Ton_Koppens.RXNL@eur.xerox.com reset=1960 type=formula formulafile=_g.frm formulaname=gravijul function=sin/sqr/sinh center-mag=6.783e-005/1.0165e-005/0.6666712 params=1.5468/1.231568/0.89889/0.02546848/1.878989/1.2265 decomp=256 colors=000AP0<28>mZ10N0<57>j7g0N0<62>g`B0N0<66>De10N0Ee1<7>Fg1Gh2Gh2Hh3I\ h4<19>WhO } tk-gj-03 { ; CalcTime 0:00:59.26 at1024x768 on a 486DX 100 ; Image Copyright 14 Mar 1998 by Ton Koppens ; e-mail:Ton_Koppens.RXNL@eur.xerox.com reset=1960 type=formula formulafile=_g.frm formulaname=gravijul function=sin/sqr/sinh center-mag=5.5343e-005/1.055e-005/1.344096 params=1.5468/1.231568/0.89889/0.02546848/1.878989/1.2265 float=y maxiter=483 inside=bof60 decomp=128; colors=@phong1.map colors=000<59>00b00c00d00e01e<29>0ce0ee0ee<30>LzzLzzMzy<60>yzMzzLyyL<29>\ 22d00e00d<30>000 } tk-gj-04 { ; CalcTime 0:00:59.26 at1024x768 on a 486DX 100 ; Image Copyright 14 Mar 1998 by Ton Koppens ; e-mail:Ton_Koppens.RXNL@eur.xerox.com reset=1960 type=formula formulafile=_g.frm formulaname=gravijul function=sin/sqr/sinh center-mag=5.5343e-005/1.055e-005/1.344096 params=1.5468/1.231568/0.89889/0.02546848/1.878989/1.2265 float=y maxiter=483 inside=bof60 decomp=128 colors=000_2P<19>l3Y100<30>ZTP100<46>ojR000<46>eMS010fNT<19>xXdS0A<11>Id\ j<70>f7n } tk-gj-05 { ; CalcTime 0:00:59.26 at1024x768 on a 486DX 100 ; Image Copyright 14 Mar 1998 by Ton Koppens ; e-mail:Ton_Koppens.RXNL@eur.xerox.com reset=1960 type=formula formulafile=_g.frm formulaname=gravijul function=sin/sqr/sinh center-mag=5.5343e-005/1.055e-005/1.344096 params=1.5468/1.231568/0.89889/0.02546848/1.878989/1.2265 float=y maxiter=483 inside=bof60 decomp=128 colors=000MUZ<2>fyKd7_QRb<2>xlYlaMCaU9tJ0dNBJd7Ie2HgDsHNNf<2>lZrORnYYzES\ UD_KCh9GHZIEUAV`5eY0qUCjEJHfOEiTBlJGUNCKS7AKUc<2>_zdKVZPfTEbKCv0TKegLgJI\ V<2>V94FVgFfkGroETW<2>Bv6iYgGBgI2kbZFMNW<2>gY5CXV8iM4vDCOU9TJ6Y8EKcDJcj7\ 4EWfDgiCtmNLX<2>kPCNPh<2>mfyAVS4fFNPcWVdd`eUTcibcylbDpVGLV<2>MR1EOfCSiAX\ mISf<2>SrrRFfb9iGNWIRNKVERKTbKHoL5QP_<2>xcOPZdZnfrW9BIY7GRJKc<2>XHcCNh<2\ >1WxEId<2>ACiCZl9nuWxFg3rRFbbAan4`MLfTNj_PmfRqlRBCTb<2>0vYTYXgkQvzJGHh<2\ >K7zkapGdNHz6GS_<2>LrNbyaeE9QFea9hm3kbASFUc<2>CwaKNeQQhWTkCNg<2>2YtHdRPK\ c<2>sKdHRNJZ5PFXZAPi4HPUb<2>sx_oUNEMaDOZCRWaEOx87BHc7EbKL_<2>_RMKK_PLWVM\ SKgDBSi6`p1iwLSOo7xuVV<2>5l4<3>zSe<2>wlUb`_<3>FB21mm<2>576FM3Qa0fzS<2>hA\ G<3>PPD<2>mHh<2>KJeVZC } tk-gj-06 { ; CalcTime 0:00:57.01 at1024x768 on a 486DX 100 ; Image Copyright 14 Mar 1998 by Ton Koppens ; e-mail:Ton_Koppens.RXNL@eur.xerox.com reset=1960 type=formula formulafile=_g.frm formulaname=gravijul function=sin/sqr/sinh center-mag=0.191675/0.109528/13.33363 params=1.5468/1.231568/0.89889/0.02546848/1.878989/1.2265 float=y maxiter=483 decomp=256 colors=CCCQCM<16>`76FJd<27>hpwMLd<4>z_`EId<58>E7kD6lEId<59>jISFKc<14>WvA\ EId<42>iOOEIdjOO<11>sQJtRItRItRI<2>tRJ } tk-gj-07 { ; CalcTime 0:00:38.72 at1024x768 on a 486DX 100 ; Image Copyright 14 Mar 1998 by Ton Koppens ; e-mail:Ton_Koppens.RXNL@eur.xerox.com reset=1960 type=formula formulafile=_g.frm formulaname=gravijul function=sin/sqr/sinh center-mag=0.191682/0.109528/13.33363 params=1.5468/1.231568/0.89889/0.02546848/1.878989/1.2265 maxiter=147 inside=bof61 decomp=128 colors=000_OG<4>bM4VRa<44>IyXWSa<7>icdVRa<27>sMJVRa<40>UR5TQ4VR`<30>Z_1V\ Ra<9>`PSVR`<19>cP1VRa<44>c_xVRaVSaVTaVR_VTa<6>VYb } tk-gj-08 { ; CalcTime 0:02:04.24 at1024x768 on a 486DX 100 ; Image Copyright 14 Mar 1998 by Ton Koppens ; e-mail:Ton_Koppens.RXNL@eur.xerox.com reset=1960 type=formula formulafile=_g.frm formulaname=gravijul function=cosxx/recip/cosh center-mag=6.783e-005/1.0165e-005/0.6666712 params=1.35465/1.9713/0.546/0.878989/1.78/1.0897 maxiter=483 inside=zmag decomp=256 biomorph=1 colors=000nDh<13>j6yj6zk7y<30>zYpzYpxXo<37>01F<20>BS8f6E<17>416<35>Qba<1\ 5>1MV<44>yU5<29>oEf } tk-gj-09 { ; CalcTime 0:02:21.93 at1024x768 on a 486DX 100 ; Image Copyright 14 Mar 1998 by Ton Koppens ; e-mail:Ton_Koppens.RXNL@eur.xerox.com reset=1960 type=formula formulafile=_g.frm formulaname=gravijul function=cosxx/recip/cosh center-mag=-0.617719/-0.606247/2.380953 params=1.35465/1.9713/0.546/0.878989/1.78/1.0897 maxiter=483 inside=zmag decomp=256 biomorph=1 colors=000nDh<13>j6yj6zk7y<30>zYpzYpxXo<37>01F<20>BS8f6E<17>416<35>Qba<1\ 5>1MV<44>yU5<29>oEf } tk-gj-10 { ; CalcTime 0:02:21.93 at1024x768 on a 486DX 100 ; Image Copyright 14 Mar 1998 by Ton Koppens ; e-mail:Ton_Koppens.RXNL@eur.xerox.com reset=1960 type=formula formulafile=_g.frm formulaname=gravijul function=cosxx/recip/cosh center-mag=-0.617719/-0.606247/2.380953 params=1.35465/1.9713/0.546/0.878989/1.78/1.0897 maxiter=483 inside=zmag decomp=256 biomorph=1 colors=0000fz<45>02z01z01z11y<92>kN2lO1lO1lP1<61>zz0zzQ<45>zzz } tk-gj-11 { ; CalcTime 0:00:39.44 at640x350 on a 486DX 100 ; Image Copyright 14 Mar 1998 by Ton Koppens ; e-mail:Ton_Koppens.RXNL@eur.xerox.com reset=1960 type=formula formulafile=_g.frm formulaname=gravijul function=tan/cotan/exp center-mag=-1.59531/-0.00234222/2.447421/1.0906 params=1.0876/0.945435/1.878/1.1264/0.9878/0.2135 maxiter=483 inside=zmag decomp=256 biomorph=1 colors=000VLPhFBhHFjHDVLRhHDjHFjJFjHHTNRlJDjJHXNRVNRVNTlJFnJFjLHhLJhHDhL\ LjLJlJHZPTlLHfNNnLFnJHlLJpLHpLJhNLjNJnLHjNLnLJlNLlNJpNHnNHlPNlPLpNJnNJnP\ JrNJpPHpPLpPJlRNnPLrNHrPHpRJtPJjJFjHHTNRlJDjJHXNRVNRVNTpTNtRLnTNtRJpTLrT\ LpVPtTJtTNrTJnVPpVNtTLnVNrVLrVPtVLrVNtVJtVNpZPnXPpXNpXPtZNrXNtZPpZRrXPtX\ LnZRrZPpXRnXRtXPpZTtXNrZRrXRtZRp`Vt`Pp`Ttpttrt55793773553973793995773975\ 7559959759B3995BB5775B97BD5BD59B5BB59979F5DD79D7DH59B7BF5BF59H5BB79D7BJ5\ BD9BH79F7BH7BJ59F79H7DD9DF7DH9BH9FF9FJ7BF9BH9DJ7DF9DH9HL7BJ9FJ9DN7BJ9BJB\ FL9DJBDJ9HN9BL9FN9DN9FL9BJBJL9HLBFP9BNBFLBDJBHP9DR9BNBDNBHPBFPBDLBJNBJRB\ DT99RBFLBHT9BX99V9BTBDPBHNDFX9BV99JDJLDJNDJNDHZ99LDHXBBZ9BPDFNDLPDHPDLPD\ JNFJNFLRDJ`BBZBBRDHbBBNHNPFJRFJNHLRFLPFL`DBRHNPHLTFJRHLPHNdBBTFLPJNbDBTH\ NRJPTHLRJNTJPfDBVHLTJNVHNdDBVJPTLPfFDXJNdFDfFBVJNhFDTLR } frm:gravijul {; r^(-2) Mark Christenson 1/25/98 ; defaults: p1 = (1,0) p2 = (0,0) p3 = (4,0) z = pixel: w = fn1(z) z = fn3(p1/fn2(w*w)) + p2 |z| < p3 ;SOURCE: 98msg.frm } frm:ManInTheOzone (XAXIS_NOPARM) { z=p1, x=1: (x<10)*(z=sqr(z)+pixel), (10<=x)*(x<20)*(z=cos(z)+pixel), (20<=x)*(z=sin(z)+pixel), x=x+1, |z|<=4 ;SOURCE: form1.frm } frm:OblManPlusLow {; Jim Muth z=p1+pixel, c=p2+(p3*pixel): z=sqr(z)+c, |z| <=4 ;SOURCE: 97msg.frm } frm:zmincoszb {; David Walter z =c= pixel: z10=z*z+c fz = z - cos(z10); fdashz = 1 + sin(z); z = z - fz/(fdashz + P1); 0.0001 <= |fz| ;SOURCE: sg-bc-bj.frm } frm:IslandOfChaos (XAXIS_NOPARM) { z=p1, x=1: (x<10)*(z=sqr(z)+pixel), (10<=x)*(z=sin(z)/cosxx(z)+pixel), x=x+1, |z|<=4 ;SOURCE: choice.frm } frm:au0 { z=pixel,y=fn1(z-1)^fn1(z),x=(z-1)*fn1(z+1),t=(z/2)*fn1(z-1): z=fn1(fn2(t^y)/fn3(x^t))^fn4(t^z) |z|<4 ;SOURCE: ad1_miss.frm } frm:Olio_3 (XAXIS) { z = pixel, fpix = fn1(pixel) + p1: z = z*z + pixel z = z * fpix z = fn2(1/z) |z| < 4 ;SOURCE: olio.frm } frm:Olio_Srand { z = pixel : z = z + p1 z = z * z + srand(z) |z| < 4 ;SOURCE: olio.frm } frm:BirdOfPrey (XAXIS_NOPARM) { ; Optimized by Sylvie Gallet z = p1 : z = cosxx(sqr(z) + pixel) + pixel |z| <= 4 ;SOURCE: fract196.frm } frm:HorLineia (ORIGIN) {; Tom Schumm ; Attempt to change the shape of the escape boundry z = Pixel, z = Sqr(z): ; Just like a julia z = z + p1 z = Sqr(z) imag(z) <= 4 ; Different escape boundry ;SOURCE: phong2.frm } frm:hypercomplex {; Chuck Ebbert -- must use periodicity=0 ; P1 is (cj,ck), bailout is real(p2) (default 64) z = zi = 0, t = (64 * (real(p2)<=0) + real(p2) * (0