Newsgroups: sci.fractals Path: unixg.ubc.ca!vanbc.wimsey.com!news.bc.net!sunserver.insinc.net!news.Direct.CA!hookup!news.sprintlink.net!howland.reston.ans.net!swrinde!cs.utexas.edu!news.tamu.edu!news.utdallas.edu!corpgate!brtph500.bnr.ca!bcarh189.bnr.ca!nott!cunews!freenet.carleton.ca!FreeNet.Carleton.CA!ao950 From: ao950@FreeNet.Carleton.CA (Paul Derbyshire) Subject: Re: c-sin-z idea Fractint FRM file Message-ID: Sender: ao950@freenet2.carleton.ca (Paul Derbyshire) Reply-To: ao950@FreeNet.Carleton.CA (Paul Derbyshire) Organization: The National Capital FreeNet Date: Wed, 19 Apr 1995 01:31:22 GMT Lines: 43 I decided to do it myself, creating a julia fractal based on c cos z where c varies with z. It produces fascinating and fantastic results! The two complex number parameters are the start and end c-value; at z=-8+0i c is parameter 1 and at z=8+0i c is parameter 2, varying continuously between. I have included the formula entry below, and a sample par entry. To use the par put the formula entry into a file called coslider.frm. Note that this fractal type is probably best served with floating point. Enjoy! Comment {;This formula by Paul PGD Derbyshire ;ao950@freenet.carleton.ca} Coslider {z=pixel; d=8; b=d*2 s=z+d; n=z-d; c=s*p2/b-n*p1/b: z=c*cos(z), |imag(z)|<127} Comment {;This parameter file by Paul PGD Derbyshire ;ao950@freenet.carleton.ca} fuse_burning { reset type=formula formulafile=\fractint\coslider.frm formulaname=coslider corners=0.0/16.0/6.0/-6.0 params=1/0.4/0/1 float=y inside=0 colors=555000<29>x11z00z10<29>zx0zz0zz1<29>zzxzzzzzz<61>zV1zU0zU0zT0<28>z10z\ 00z00y00<30>c00b11a11`22_22<25>333 } -- Cheers, | "There was a sale. The biggest going-out-of-business sale you ________PGD__| ever saw... But in the end, some of us decided not to buy." ___ ~~~ --Needful Things __| * |_______ ASGND Full Silly and Ysiggian _______________________________ Newsgroups: sci.fractals Path: unixg.ubc.ca!vanbc.wimsey.com!news.bc.net!sunserver.insinc.net!news.Direct.CA!hookup!news.sprintlink.net!howland.reston.ans.net!swrinde!cs.utexas.edu!news.tamu.edu!news.utdallas.edu!corpgate!bcarh189.bnr.ca!nott!cunews!freenet.carleton.ca!FreeNet.Carleton.CA!ao950 From: ao950@FreeNet.Carleton.CA (Paul Derbyshire) Subject: More coslider stuff--generalised to FNslider Message-ID: Sender: ao950@freenet2.carleton.ca (Paul Derbyshire) Reply-To: ao950@FreeNet.Carleton.CA (Paul Derbyshire) Organization: The National Capital FreeNet Date: Wed, 19 Apr 1995 02:23:00 GMT Lines: 38 Yeah, me again :-) I have made a generalised coslider (FNslider) where you select the function from cos, sin, and others. Also, another PAR entry, one I like, for coslider (won't work with FNslider) (for FNslider.frm) Comment {;FRM entry by Paul PGD Derbyshire ;ao950@freenet.carleton.ca} FNslider {z=pixel; d=8; b=d*2 s=z+d; n=z-d; c=s*p2/b-n*p1/b: z=c*fn1(z), |imag(z)|<127} Comment {;PAR entry by Paul PGD Derbyshire ;ao950@freenet.carleton.ca} Spiral_Flip { reset type=formula formulafile=c:\fractint\coslider.frm formulaname=Coslider corners=-8.0/7.999987/5.999982/-6.0 params=-0.01597/0.7115/0.0156/0.7115 float=y maxiter=1000 bailout=127 inside=0 colors=000F0K<59>T0bU0cU0cV1cV2d<60>zzzzzzzzy<60>zz1zz0zy0yx0<58>G2JF0KF0KF0\ KF0K } -- Cheers, | "There was a sale. The biggest going-out-of-business sale you ________PGD__| ever saw... But in the end, some of us decided not to buy." ___ ~~~ --Needful Things __| * |_______ ASGND Full Silly and Ysiggian _______________________________ Newsgroups: sci.fractals Path: unixg.ubc.ca!vanbc.wimsey.com!scipio.cyberstore.ca!math.ohio-state.edu!howland.reston.ans.net!gatech!bloom-beacon.mit.edu!news.tamu.edu!news.utdallas.edu!corpgate!bcarh189.bnr.ca!nott!cunews!freenet.carleton.ca!FreeNet.Carleton.CA!ao950 From: ao950@FreeNet.Carleton.CA (Paul Derbyshire) Subject: WEEEEEird formula CORRECTION Message-ID: Sender: ao950@freenet2.carleton.ca (Paul Derbyshire) Reply-To: ao950@FreeNet.Carleton.CA (Paul Derbyshire) Organization: The National Capital FreeNet Date: Thu, 4 May 1995 06:45:52 GMT Lines: 48 Use this one, not the earlier one. If you don't want to re-download it change "formulaname=PhonyMandel" to "formulaname=PhonyMandelJ" in your copy. The formula file must be named 'pgd.frm' Note: this formula can be slow. If you have fractint 19, use floating point. Comment {;Formulas by: Paul Derbyshire (PGD) ;ao950@freenet.carleton.ca} PhonyMandelJ {z=pixel f=15/8: k=z*z z=(k*k/4-k*z*f/3-k/2+f*z-.25)*p1, |z|<=127} PhonyMandelM {c=pixel f=15/8 z=1: k=z*z z=(k*k/4-k*z*f/3-k/2+f*z-.25)*c, |z|<=127} Comment {;Para,eter file by: Paul Derbyshire (PGD) ;ao950@freenet.carleton.ca} PhonyMandel { ; This Julia set looks like a bunch of Mandelbrots! ; Close examination shows this to be illusion. reset type=formula formulafile=pgd.frm formulaname=PhonyMandelJ corners=-2.158188/2.961973/-1.931917/1.914223 params=1 maxiter=200 inside=0 logmap=yes colors=000<2>00z<2>0zzzzezz0<2>z00e00L00zzLzL0000<2>00z<2>0zzzzezz0<2>z00e00\ L00zzLzL0000<2>00z<2>0zzzzezz0<2>z00e00L00zzLzL0000<2>00z<2>0zzzzezz0<2>z00e\ 00L00zzLzL0000<2>00z<2>0zzzzezz0<2>z00e00L00zzLzL0000<2>00z<2>0zzzzezz0<2>z0\ 0e00L00zzLzL0000<2>00z<2>0zzzzezz0<2>z00e00L00zzLzL0000<2>00z<2>0zzzzezz0<2>\ z00e00L00zzLzL0000<2>00z<2>0zzzzezz0<2>z00e00L00zzLzL0000<2>00z<2>0zzzzezz0<\ 2>z00e00L00zzLzL0000<2>00z<2>0zzzzezz0<2>z00e00L00zzLzL0000<2>00z<2>0zzzzezz\ 0<2>z00e00L00zzLzL0000<2>00z<2>0zzzzezz0 } -- .*. "Clouds are not spheres, mountains are not cones, coastlines are not -() < circles, and bark is not smooth, nor does lightning travel in a `*' straight line." ,------------------------------------------------ -- B. Mandelbrot | Paul Derbyshire (PGD) ao950@freenet.carleton.ca Newsgroups: sci.fractals Path: unixg.ubc.ca!rover.ucs.ualberta.ca!tribune.usask.ca!canopus.cc.umanitoba.ca!newsflash.concordia.ca!news.mcgill.ca!mcrcim.mcgill.edu!bloom-beacon.mit.edu!news.tamu.edu!news.utdallas.edu!corpgate!bcarh189.bnr.ca!nott!cunews!freenet.carleton.ca!FreeNet.Carleton.CA!ao950 From: ao950@FreeNet.Carleton.CA (Paul Derbyshire) Subject: WEEEEEird formula :) Message-ID: Sender: ao950@freenet3.carleton.ca (Paul Derbyshire) Reply-To: ao950@FreeNet.Carleton.CA (Paul Derbyshire) Organization: The National Capital FreeNet Date: Thu, 4 May 1995 03:40:03 GMT Lines: 50 This Julia formula (PhonyMandelJ) with the parameter set to 1 produces ersatz mini Mandelbrots! They are actually illusory. The (true) Mandelbrot formula is printed below with it, and a parameter entry showing the phony Mandelbrots. Comment {;Formulas by: Paul Derbyshire (PGD) ;ao950@freenet.carleton.ca} PhonyMandelJ {z=pixel f=15/8: k=z*z z=(k*k/4-k*z*f/3-k/2+f*z-.25)*p1, |z|<=127} PhonyMandelM {c=pixel f=15/8 z=1: k=z*z z=(k*k/4-k*z*f/3-k/2+f*z-.25)*c, |z|<=127} Comment {;Para,eter file by: Paul Derbyshire (PGD) ;ao950@freenet.carleton.ca} PhonyMandel { ; This Julia set looks like a bunch of Mandelbrots! ; Close examination shows this to be illusion. reset type=formula formulafile=\fractint\pgd.frm formulaname=PhonyMandel corners=-2.158188/2.961973/-1.931917/1.914223 params=1 maxiter=200 inside=0 logmap=yes colors=000<2>00z<2>0zzzzezz0<2>z00e00L00zzLzL0000<2>00z<2>0zzzzezz0<2>z00e00\ L00zzLzL0000<2>00z<2>0zzzzezz0<2>z00e00L00zzLzL0000<2>00z<2>0zzzzezz0<2>z00e\ 00L00zzLzL0000<2>00z<2>0zzzzezz0<2>z00e00L00zzLzL0000<2>00z<2>0zzzzezz0<2>z0\ 0e00L00zzLzL0000<2>00z<2>0zzzzezz0<2>z00e00L00zzLzL0000<2>00z<2>0zzzzezz0<2>\ z00e00L00zzLzL0000<2>00z<2>0zzzzezz0<2>z00e00L00zzLzL0000<2>00z<2>0zzzzezz0<\ 2>z00e00L00zzLzL0000<2>00z<2>0zzzzezz0<2>z00e00L00zzLzL0000<2>00z<2>0zzzzezz\ 0<2>z00e00L00zzLzL0000<2>00z<2>0zzzzezz0 } -- .*. "Clouds are not spheres, mountains are not cones, coastlines are not -() < circles, and bark is not smooth, nor does lightning travel in a `*' straight line." ,------------------------------------------------ -- B. Mandelbrot | Paul Derbyshire (PGD) ao950@freenet.carleton.ca Newsgroups: sci.fractals Path: unixg.ubc.ca!news.bc.net!torn!nott!cunews!freenet.carleton.ca!FreeNet.Carleton.CA!ao950 From: ao950@FreeNet.Carleton.CA (Paul Derbyshire) Subject: Cubebrot 2 Message-ID: Sender: ao950@freenet2.carleton.ca (Paul Derbyshire) Reply-To: ao950@FreeNet.Carleton.CA (Paul Derbyshire) Organization: The National Capital FreeNet Date: Sat, 2 Sep 1995 03:32:41 GMT Lines: 26 Super-weird formula: z -> 1/3 z*z*z + z + c Critical points for mandelbrot sets are +i and -i; they are identical but one is flipped relative to the other. Cubebrot2j {z=pixel: z=z*z*z/3+z+p1, |z|<=25} Cubebrot2m {z=P1: z=z*z*z/3+z+pixel, |z|<=25} Try them out! -- .*. "Clouds are not spheres, mountains are not cones, coastlines are not -() < circles, and bark is not smooth, nor does lightning travel in a `*' straight line." ,------------------------------------------------ -- B. Mandelbrot | Paul Derbyshire (PGD) ao950@freenet.carleton.ca