November 2005 - Fractint - mailman.xmission.com

Re: Gilles Nadeau
by JackOfTradeZ 09 Nov '05

09 Nov '05

Gilles Nadeau, Those are nice, I say NICE images! Good work !! I have been checking out the BuddaBrots for some time; Melinda Green has a nice web site on them. But I am unable so far to decipher the rendering method and figure out how to animate (zoom) them. She says it can't be done. I say NEVER SAY NEVER ! JoTz

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FOTD 08-11-05 (Marigold [6])
by Jim Muth 08 Nov '05

08 Nov '05

FOTD -- November 08, 2005 (Rating 6) Fractal visionaries and enthusiasts: When 0.00006 part of Z^100 is added to 0.6 part of Z^2, C is added to the sum, and then the entire thing is reiterated 1,000 or so times, the result is a lopsided oval-shaped open area with an area of chaos on its western end. This chaotic area, which contains strangely shaped midgets and buds that are more reason- ably shaped, holds most of the interest in the parent fractal. Today's scene lies near the tip of the main filament extending from the most prominent bud. While searching for a name, I glanced out the window and noticed a marigold plant totally covered with late-blooming flowers. The name seemed to fit the feeling of the image, so that is what I named today's FOTD. The rating of a 6 is a little above average. I put too little effort into the coloring to rate the image higher. What we have is a tweaked random palette created by striking the 'enter' key. In this particular case, it works fairly well. The render time of 8-1/2 minutes might be considered a bit slow by those with other things to do. To speed things up, the finished image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> It turned cloudy and chilly before noon here at Fractal Central on Monday. The temperature of 63F 22C held the cats' outdoor time to under an hour, but they made the most of the 50 minutes when they ganged up on an oversized black cat that intruded in the yard and put it to flight. When they came inside soon after, I rewarded them for their bravery with an extra serving of tuna. My day was about as close to average as days can come. Today is starting sunny, but it is chilly again. I don't know how the cats will feel about this, but my day promises to be moderately busy. The next FOTD will appear 24 hours from now. Until then, take care, and see through the mysteries. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Marigold { ; time=0:08:39.43--SF6 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident center-mag=-1.47764158015673700/-0.107961447762803\ 10/1.881266e+011/1/35/-0.0319109923078635185 params=0.6/2/0.00006/100/0/0 float=y maxiter=1600 inside=0 periodicity=10 colors=000SvwRtuQrsPpqOnoNlmMjkLhiKfgJdeIcdHbcGabF\ `aE_`DZ_CZZBZYAcz7CC6AA588DJzCHuBFmAEe9CZ8AR79J67C\ nWjgSd`OZVKTOHNIDHB9BykEvhDsfDqdCnbCk`ChZBdXBbVAZT\ AXRAUO9QM9OK8LI8IG8FE7CC7AA6786dRj`PfYNbVLZRJWOHSL\ FOIDKEBHB9D879k`zjJzhIzfHydHvbGt`Gq_FoYFkWEiUDfSDc\ QC`PCYNBWLBSJAQH9NF9KE8IC8FA7D87A668upyqmunjrkgngd\ kdagaZdYW`VTYSQUONRLKNIHKEEGBBD8896O`5KU5GO5DI59CT\ izQizO_zLRzJOsHLiEI_CFQ9CG79BEe8Db7C`7CZ7BX7BU7AS7\ AQ79O78L68J67H67F66C66A6586wzEryDntCjoCfkBafAYaAUY\ 9QT9LO8frYgr_grahrcisfishjsjktlktnltqmusmuunuwnuyo\ twptupssqsqrrorrmsqktqitpgupeupdqoenofjofgogcog`oh\ YohUoiRojNojKokGokDolAolVnBXpFYqI_rL`sPbtScuVevZfw\ agxdexccxbaua`s_YnXVjUSeSPaPMXMJSJGOHDJEAFB7A8`_fZ\ YdYXbWV`VX_T_YSbWQeVPhTNkRMnQLqOJtMIwLGzJFzHDzGCzE\ AzC9zB7z96z7`zOZzNXzMWzLUzKTzJRzIQzIOzHNzGLzFKzEIz\ DHzCFzCEzBCzAJzeIzcHzaHzZ } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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Fractal web site
by David Dollevoet 08 Nov '05

08 Nov '05

Greetings, My fractal web page is updated for 2005-11. http://www.djd-fractal.com David Dollevoet

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Re: [Fractint] FOTD 07-11-05 (Fork in the Road [5])
by Jim Muth 07 Nov '05

07 Nov '05

FOTD -- November 07, 2005 (Rating 5) Fractal visionaries and enthusiasts: This repost corrects the wrong title in the previous post. Today's image came about when I combined generous portions of Z^3 and Z^5, and added the usual 'C' to produce the parent fractal. I searched one of the less likely valleys of this parent and found a tiny point, which when blown up proved to be an entire fractal universe. Deep in this new universe I found the scene that appears as today's FOTD. It took a few minutes of contemplation before I noticed the fork- like features and decided to name the image "Fork in the Road". Since I put so little effort into the coloring, I could rate the image at only an average 5. I leave it to the individual fractal fan to decide whether it is worth the effort to devote over 13 minutes to rendering an average fractal. Those who decide it is not worth the effort may see the image by downloading it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The rain held off until after dark here at Fractal Central on Sunday, while the ample sun and temperature of 77F 25C made outdoor conditions just what the fractal cats wanted. They spent the entire afternoon in the holly patch, doing little of importance. As for me, I did little of importance also. But today will be quite a bit busier. The next glorious FOTD will appear in 24 hours. Until then, take care, and things may not be as they seem. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fork_in_the_Road { ; time=0:13:44.26--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.23837854398835790/-1.499916180033593\ 00/5.081655e+011/1/-47.5/-0.0031 params=1/3/0.6/5/\ 0/0 float=y maxiter=1500 inside=0 periodicity=10 colors=000pRoqQlqPjqPhqOeqNcqNaqMZqLXqLVqKTrJQrJOr\ IMrHJrHHrGFrFCrFArE8rE6sG7sI8tJ9tL9uMAuOBvPCvRCvSD\ wUEwWExXFxZGy_HyaHzbIzdJzeJycPxaUx`_wZdvXjvWorTpoQ\ plOpiLpfIpbGq_DqXAqU8qR5qO3qN6nN9lNCjNFhNIfNLdMOaM\ R_MUYMXWM_UMaSKcSJdSHfSGgSFhSDjSCkSBlS9nS8oS7pS5rS\ 4sS3tS6qU8nWBkXDiZGf_IcaKabNZdPWeSUgURhXOjZMk`JmcG\ neEphBqj8sl6th9teCtbFt_HtXKtUNtRPtONnMLiJJcHKZIHYJ\ HXKHWKGWLGVMGUNFTNFTOFSPERQEQQEQRDPSDOTDNTmNUmMVmL\ VmLTmOSmQQmTPmVNmYMm_KmbJmdHmfGmiEmkDmnBmpAms8mu7m\ w7mw7mx7mx7mxEmwKmwRmwXmwcmwimwgmufmtemsdmrcmqbmpa\ mo`mnZmmYmlXmkWmjVmiUmhTmgSmfRmeQmcQabQYaQU`PPZPLY\ PHXPDWQCYQC_QB`QBbQAcQAeQAgQ9hQ9jQ8kQ8mQ7nQ7pQ7rQ6\ sQ6uQ5vQ5xP6zQ5yR5xS5xT5wU4wU4vV4vW4uX4uY3tZ3tZ3s_\ 3s`2ra2rb2qc2qc2pd1pe1of1og1ng1ne4ic7da9_`CVZFQXHL\ VKGUMBUKEUIGUGJUFLUDNUBQU9SU8UU6XU4ZV0aU3`U6`T9_TB\ _TEZgXfiWgjVikUjmTknSmoRn } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 07-11-05 (Web Works [5])
by Jim Muth 07 Nov '05

07 Nov '05

FOTD -- November 07, 2005 (Rating 5) Fractal visionaries and enthusiasts: Today's image came about when I combined generous portions of Z^3 and Z^5, and added the usual 'C' to produce the parent fractal. I searched one of the less likely valleys of this parent and found a tiny point, which when blown up proved to be an entire fractal universe. Deep in this new universe I found the scene that appears as today's FOTD. It took a few minutes of contemplation before I noticed the fork- like features and decided to name the image "Fork in the Road". Since I put so little effort into the coloring, I could rate the image at only an average 5. I leave it to the individual fractal fan to decide whether it is worth the effort to devote over 13 minutes to rendering an average fractal. Those who decide it is not worth the effort may see the image by downloading it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The rain held off until after dark here at Fractal Central on Sunday, while the ample sun and temperature of 77F 25C made outdoor conditions just what the fractal cats wanted. They spent the entire afternoon in the holly patch, doing little of importance. As for me, I did little of importance also. But today will be quite a bit busier. The next glorious FOTD will appear in 24 hours. Until then, take care, and things may not be as they seem. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fork_in_the_Road { ; time=0:13:44.26--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.23837854398835790/-1.499916180033593\ 00/5.081655e+011/1/-47.5/-0.0031 params=1/3/0.6/5/\ 0/0 float=y maxiter=1500 inside=0 periodicity=10 colors=000pRoqQlqPjqPhqOeqNcqNaqMZqLXqLVqKTrJQrJOr\ IMrHJrHHrGFrFCrFArE8rE6sG7sI8tJ9tL9uMAuOBvPCvRCvSD\ wUEwWExXFxZGy_HyaHzbIzdJzeJycPxaUx`_wZdvXjvWorTpoQ\ plOpiLpfIpbGq_DqXAqU8qR5qO3qN6nN9lNCjNFhNIfNLdMOaM\ R_MUYMXWM_UMaSKcSJdSHfSGgSFhSDjSCkSBlS9nS8oS7pS5rS\ 4sS3tS6qU8nWBkXDiZGf_IcaKabNZdPWeSUgURhXOjZMk`JmcG\ neEphBqj8sl6th9teCtbFt_HtXKtUNtRPtONnMLiJJcHKZIHYJ\ HXKHWKGWLGVMGUNFTNFTOFSPERQEQQEQRDPSDOTDNTmNUmMVmL\ VmLTmOSmQQmTPmVNmYMm_KmbJmdHmfGmiEmkDmnBmpAms8mu7m\ w7mw7mx7mx7mxEmwKmwRmwXmwcmwimwgmufmtemsdmrcmqbmpa\ mo`mnZmmYmlXmkWmjVmiUmhTmgSmfRmeQmcQabQYaQU`PPZPLY\ PHXPDWQCYQC_QB`QBbQAcQAeQAgQ9hQ9jQ8kQ8mQ7nQ7pQ7rQ6\ sQ6uQ5vQ5xP6zQ5yR5xS5xT5wU4wU4vV4vW4uX4uY3tZ3tZ3s_\ 3s`2ra2rb2qc2qc2pd1pe1of1og1ng1ne4ic7da9_`CVZFQXHL\ VKGUMBUKEUIGUGJUFLUDNUBQU9SU8UU6XU4ZV0aU3`U6`T9_TB\ _TEZgXfiWgjVikUjmTknSmoRn } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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Paul N Lee's FOTD web site
by Barry Smith 07 Nov '05

07 Nov '05

On Friday and again yesterday (Sunday) - Australian Eastern DaylightbSaving Time I was told that th main index page for Jim Muth's FOTD could not be found , but I could get the page above it (~Paul N. Lee). I never had this problem before._ _ <http://home.att.net/%7EPaul.N.Lee/FotD/FotD.html> -------------------- Barry W Smith P O Box 442, Jamison Centre ACT 2614, Australia Tel. (Home & answering machine) (02) 6251 2119 International +61 2 6251 2119 e-mail: bsmith(a)cyberone.com.au

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FOTD 06-10-05 (Web Works [6])
by Jim Muth 06 Nov '05

06 Nov '05

FOTD -- November 06, 2005 (Rating 6) Fractal visionaries and enthusiasts: Today's fractal discussion is brief because most of my energy went into writing the philosophical part of the philofractal version. The parent fractal of today's image came about when I combined the Mandelbrot set with 0.006 parts of Z^(-2). The result is a vague outline of the M-set filled with debris. Today's scene lies in what once was East Valley of the large midget at -1.75 on the X-axis. I have no idea why I named the image "Web Works". Most likely the filaments reminded me of a spider's web. The rating of a 6 means I consider the image a bit better than usual. The render time of 7-1/2 minutes means it will be slightly more efficient to download the finished image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> At this point the philosophy appears in the philofractal version of this discussion. On a more earthly note, yes the fractal cats are real. They most definitely are not a fictional invention of my imagination. I have every intention of taking their pictures and having them posted on the FOTD web site. It certainly will be done before I move from Baltimore. The problem is that my old film camera no longer works and I have no other reason to go out shopping and comparing new-fangled digital cameras before purchasing one. I used to do much photographic work, and I want a camera that will take top-quality photographs. With warm sun and a temperature of 75F 24C, Saturday was like a return to summer here at Fractal Central. The fractal cats made the most of things by passing the entire afternoon lurking in the holly patch. My day was busier than usual, but not excessively so. Today is starting even warmer but with more clouds. If the rain holds off, it will be another good day. The next FOTD will appear in 24 hours. Until then, take care, and must all design be intelligent. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Web_Works { ; time=0:07:33.90--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-1.46543675784757600/+0.000001599029672\ 24/4.670224e+009/1/-82.5/0.00135869043112195331 params=0.006/-2/1/2/0/0 float=y maxiter=1250 inside=0 logmap=155 periodicity=10 colors=0000Vz0Tz0Rz0Pz1Oy2My3Kx4Iv55t59q6El6Jf7Oa8\ TX8YR9bMAhGDhIGgLJgNMfQPfTSeVVeYYd`Zad_Zh`VlbVfzi`\ zgVzeOvaIuZCtW5rS6rO7rK8rD9r7Bi8B`AASB9JD8AE70G60E\ 80BB19E16H14K21NB2PL4RV6Ud8WnAZgK``VbUedMpfPodSnbV\ j`YhZ`ZXcYVcZTccQbiNbnKcsHmvEwzBzuGmoLdiQedVfZ_hTd\ VSaHQZ0Mh3Mh6MgAMfDMeHMdKMcONbRMYUKTXIO_GJbEEeC9hA\ 4gD8fHCeKGdOKcSP`gMXwIXqSWkaWekVZvU`pSbiQdbPfWNhPL\ jIJlBZWQnFdkHagKYcNV_QReYQkfOqnMxwKiaBVG2XH7ZJD`LJ\ cNPeOUgQ_iSelUkaO7lV4wa1wa7xaDxaJyaPyaVza`idWSgRAj\ LJqG_qOppXkmYfj_`gaWcbQ`dLYfFUhGSeIQaJOYLMUMKROINP\ GJREFTJJVPOYUT__Xbdadjfgpkepjcpi`pgZpfWpdUpcRpaSp`\ Tp_UpZWpXXpWYpVZpU`qSxJgaaiEtkUieiY_zMUnRKbXAQb0JQ\ EBDTHIUOOWUTX`ZZfd_miasobzudqjhghmZmrPrwGvyJzyNzyR\ zxVzxYzxazwezwizvizkjz`jzQkzEXzNHzXOzXVzWazVhzUozT\ vzSmzOdzJWzELzY9zr9zo9zl9zi9zf9zc9z`9zXCzUGzQKzMOz\ IRzFVzBZz7bz3ez7hzBlzGozK } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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Triternions Ikenaga and Lambda
by gilles nadeau 06 Nov '05

06 Nov '05

Hello all, I am new on this list but I use Fractint since 1994. I have difficulty in include/understand English and I use a translator. I would like to propose two new models of "Triternion". T_Ikenaga and T_Lambda. The formulas triternion are mysterious. I read that those would be 6-d. I am not a mathematician and I does not know exactly what that means. Here two formulas. Gilles Nadeau T_Ikenaga-XZ {; 6-dimensional M-Set ; based on formulae by Russell Walsmith ; Gilles Nadeau, March, 2005 ; x=y=t=u=v=w=0 cx=real(pixel) cy=real(p1) ct=imag(pixel) cu=imag(p1) cv=real(p2) cw=imag(p2) : tx= x^3+t^3+v^3-3*(x*y^2+t*u^2+v*w^2)+6*(x*t*v-x*u*w-y*u*v-y*t*w) ty=-y^3-u^3-w^3+3*(y*x^2+u*t^2+w*v^2)+6*(y*v*t-y*w*u+x*w*t+x*v*u) tt= 3*(t*x^2-t*y^2+v*t^2-v*u^2+x*v^2-x*w^2)-6*(t*u*w+x*y*u+y*v*w) tu= 3*(u*x^2-u*y^2+w*t^2-w*u^2+y*v^2-y*w^2)+6*(x*v*w+x*y*t+t*u*v) tv= 3*(v*x^2-v*y^2+x*t^2-x*u^2+t*v^2-t*w^2)-6*(u*v*w+x*y*w+y*t*u) tw= 3*(w*x^2-w*y^2+y*t^2-y*u^2+u*v^2-u*w^2)+6*(t*v*w+x*y*v+x*t*u) dx=cx*x-cy*y+cv*t-cw*u+ct*v-cu*w dy=cy*x+cx*y+cw*t+cv*u+cu*v+ct*w dt=ct*x-cu*y+cx*t-cy*u+cv*v-cw*w du=cu*x+ct*y+cy*t+cx*u+cw*v+cv*w dv=cv*x-cw*y+ct*t-cu*u+cx*v-cy*w dw=cw*x+cv*y+cu*t+ct*u+cy*v+cx*w x=tx+dx-x-cx y=ty+dy-y-cy t=tt+dt-t-ct u=tu+du-u-cu v=tv+dv-v-cv w=tw+dw-w-cw z=x+flip(t) z2=y+flip(u) z3=v+flip(w) |z|+|z2|+|z3|<=64 } T_Lambda-XZ {; 6-dimensional M-Set ; based on formulae by Russell Walsmith ; Gilles Nadeau, March, 2005 ; x=0.5 y=t=u=v=w=0 cx=real(pixel) cy=real(p1) ct=imag(pixel) cu=imag(p1) cv=real(p2) cw=imag(p2) : tx=x*x-y*y+v*t-w*u+t*v-u*w ty=y*x+x*y+w*t+v*u+u*v+t*w tt=t*x-u*y+x*t-y*u+v*v-w*w tu=u*x+t*y+y*t+x*u+w*v+v*w tv=v*x-w*y+t*t-u*u+x*v-y*w tw=w*x+v*y+u*t+t*u+y*v+x*w dx=x-tx dy=y-ty dt=t-tt du=u-tu dv=v-tv dw=w-tw x=cx*dx-cy*dy+cv*dt-cw*du+ct*dv-cu*dw y=cy*dx+cx*dy+cw*dt+cv*du+cu*dv+ct*dw t=ct*dx-cu*dy+cx*dt-cy*du+cv*dv-cw*dw u=cu*dx+ct*dy+cy*dt+cx*du+cw*dv+cv*dw v=cv*dx-cw*dy+ct*dt-cu*du+cx*dv-cy*dw w=cw*dx+cv*dy+cu*dt+ct*du+cy*dv+cx*dw z=x+flip(t) z2=y+flip(u) z3=v+flip(w) |z|+|z2|+|z3|<=128 }

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FOTD 05-10-05 (Julia Variation-9 [5])
by Jim Muth 05 Nov '05

05 Nov '05

FOTD -- November 05, 2004 (Rating 5) Fractal visionaries and enthusiasts: A rather busy day on Friday left little time for fractaling, but I did manage to find one image that I consider worthwhile. That image appears as today's FOTD. To create the image, I returned to the JuliaBC formula. The Julia set I found is related to the Z^(1.5)+C Mandeloid as it appears 23 levels up the logarithmic spiral. The 'Seahorse Valley' effect indicates that the Julia set corresponds to a prominent valley area of the Mandeloid. I studied the image for several minutes before coming to the conclusion that it is just another Julia set. I named it "Julia Variation-9" as a continuation of the previous series, and rated it at a 5. The 1-1/2 minute render time is fast enough that little time will have been wasted if the image disappoints its viewers. The easiest way of all to view the image is to down- load it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where, if all goes well, it will be found posted. Well, I have hinted as much in past discussions, but now it is certain. Within a few months, how many I am not sure, (8 is a good guess), Fractal Central and its associated graphic design business will be moving from Baltimore, its present location, to a new location in central Pennsylvania. More details will be known as the time grows closer. Hopefully, the move will be accomplished with as few interruptions in the FOTD as possible. But until we are settled in the new F.C., things will be a bit hectic and the FOTD schedule might become a bit irregular. The fractal cats might or might not move with us to the new Fractal Central. Moving would be hard on them. They are 15 years old and quite settled in their present location. Since my sister will be moving into the old F.C. when fractal lady and I move out, we very possibly may leave Thomas and Tippy to finish their lives in the only home they have ever known. But this means we will find two new fractal cats to occupy the new Fractal Central, so stay tuned for further cat developments. Partly cloudy skies, gentle winds and a high temperature of 68F 20C here at Fractal Central on Friday proved satisfactory for the fractal cats, who were in the yard from noon until 5pm, doing little but sleeping. For me things were a little busier than expected, but by the end of the day everything that needed to be done was out of the way. Today is starting the same, which will likely lead to the same results. The next FOTD will appear in 24 hours. Until then, take care, and keep looking up. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Julia_Variation-9 { ; time=0:01:33.32--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=JuliaBC center-mag=0.237872/-0.157428/\ 0.9363296 params=1.5/0/23/0/0.75/-0.083/0/0 float=y maxiter=1250 inside=0 logmap=yes periodicity=10 colors=0000KK0LK0MK0NK0OK0PK0QK5RKASKFTKKUKPVKUWJZ\ XIcYHjZGs_GriIvsKtqJroIpmHokGmiFkhEifDhdCfbBd`AbZ9\ aY8UY7MY7FY67Y60Y62W74V76U78T8AS8CR8EQ9GP9IO9KNAMM\ AOLAQKBSJBTIBWLAYN9_P8aR7cT6eW5gY4i_3ka2mc1oe0pc5q\ bAqaFr_KsZPsYUtWZuVcuUhvSmwRrwQwvPwuPwtPwtPwsPwrPw\ qPwqPwjMrdJmZHhYGeXGbWF`VFYVEVUETTDQSDNRCLRCIQBFPB\ DOAANA7NA5P97R98S89U8AV7BX7CZ6D_9FaCGbFHdIIfLJgOKi\ RLjUMkXRl_Wlb_medmhhnkmnnqoqvotzUwv9zs8yq8xo8wm7vk\ 7ui7tg6se6rd6qb5p`5oZ5nX4mV4lT4lS7kT9jTBiUDhUGgVIf\ VKeWMdWPcXRbXTaYVaY`VbfOflHjrAnx4rr5ol5mg5ja5hW5eR\ 5cL5`F5ZA5XH6WN6VT6UZ6Td6Sj6RhAQfEQdIQbMQ`PQZTQYXQ\ W`QUdQSgQQkQOoQMsQLvQFmUAdY5Wa0Od7QZESULUPSVKZXFeZ\ Ak_5hY9fWDdUGaTK_ROYPRVNVTMZRKaOIeMGiKFlJEjIDiHDgG\ CfFCeEBcDAbDA`C9_B9ZA8X97W87U76T76SF8ZMAeLBdKCdJCc\ IDcHEbGEbFFaEFaDG`CH`BH_AI_9JZ8IZ7HY7GYAFXDEWGDWJC\ VMBVPAUS9TU8TH7ZF6YD5XB4W } frm:JuliaBC { ; Formula by Andrew Coppin e=p1, p=real(p2)+PI, q=2*PI*floor(p/(2*PI)), r=real(p2)-q, C=p3, Z=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|< p4+100 } END PARAMETER FILE=========================================

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Re: [Fractint] Re: quaternion product correction
by Russell Walsmith 05 Nov '05

05 Nov '05

Gerald, An amazing image... Hell of a job! It'll probably take me a while to fathom the mechanisms you employ in your formula to accomplish this. Could you say a few words about the theory involved? It's been about three years since we began to explore the 'T-set' idea on this list, and it comes to a fascinating fruition in Fractint at last. Ever since Paul Bourke's POVray renditions, I've had some variants on this 3-D M-set in mind, and I've included a par file of the complementary 'C-set' below. Some 2-D renderings of this object are facilitated by a simple toggle in certain M-set formulas. E.g., MsetCset1 {;toggle fn1 between 'ident' and 'conj' z=0, c=(pixel): z=fn1(z^2+c) z < 4 } MsetCset2 {;toggle p1 between '1' and '-1' x=real(pixel),y=imag(pixel) x1=y1=0: a=x1^2-y1^2 b=p1*(2*x1*y1) x1=a+x,y1=b+y z=x1^2+y1^2 z < 4 } To get this effect in the 'T-set_in_3d' formula, I changed the line 'x1 = a + cx, y1 = b + cy, z1 = c + cz' to read 'x1 = c + cx, y1 = b + cy, z1 = a + cz'. Any two-element transposition of a b c gives the same effect, just different orientations. Thanks again for your innovations. Ciao, Russell ---------------------------- Parameters below ------------------------------ C-set_in_3d {;Greyscale depth image ; reset=2004 type=formula formulafile=test.frm formulaname=3d_C-set passes=g center-mag=-0.68046/-0.24858/0.9363296 params=0/0/-0.75/0.75/0/0/0/4/150/253 float=y maxiter=2000000000 outside=summ periodicity=0 colors=000zzzyzzzyzzyyyyyxyyyxzyxxxxxwxxxwyxwwwwwvwwwvxwvvvvvuvvvuwvuuuu\ utuuutvutttttstttsutsssssrsssrtsrrrrrqrrrqsrqqqqqpqqqprqpppppopppoqpoooo\ onooonponnnnnmnnnmonmmmmmlmmmlnmlllllklllkmlkkkkkjkkkjlkjjjjjijjjikjiiii\ ihiiihjihhhhhghhhgihgggggfgggfhgfffffefffegfeeeeedeeedfedddddcdddcedcccc\ cbcccbdcbbbbbabbbacbaaaaa`aaa`ba`````_```_a`_____Z___Z`_ZZZZZYZZZY_ZYYYY\ YXYYYXZYXXXXXWXXXWYXWWWWWVWWWVXWVVVVVUVVVUWVUUUUUTUUUTVUTTTTTSTTTSUTSSSS\ SRSSSRTSRRRRRQRRRQSRQQQQQPQQQPRQPPPPPOPPPOQPOOOOONOOONPONNNNNMNNNMONMMMM\ MLMMMLNMLLLLLKLLLKMLKKKKKJKKKJLKJJJJJIJJJIKJIIIIIHIIIHJIHHHHHGHHHGIHGGGG\ GFGGGFHGFFFFFEFFFEGFEEEEEDEEEDFEDDDDDCDDDCEDCCCCCBCCCBDCBBBBBABBBACBAAAA\ A9AAA9BA9999989998A98888878887987777767776876666656665765555545554654444\ 4344435433333233324322222122213211111011102100000000PPP } frm:3d_C-set {;periodicity=no, outside=summ ;maxit > p5real*(p5imag+1) ;-------------------------------------------- ;p1real: Rotation about x-axis (1st rotation) ;p1imag: Rotation about y-axis (2nd rotation) ;p2real: Far clipping plane ;p2imag: Near clipping plane ;p3real: x1(0) ;p3imag: y1(0) ;p4real: z1(0) ;p4imag: Bailout ;p5real: Maxiter per slice ;p5imag: Number of slices - 1 ;-------------------------------------------- ; bailout = imag(p4), tiefnum = imag(p5) delta = (real(p2)-imag(p2))/tiefnum tmp = pi/180 rotXax = exp(flip(real(p1)*tmp)), rotYax = exp(flip(imag(p1)*tmp)) ; HPixXY = rotYax VPixZ = real(rotXax) VPixXY = flip(conj(rotYax)) NXY = VPixZ*VPixXY NZ = imag(conj(rotXax)) VPixXY = -NZ*VPixXY ; tmp = NXY*imag(p2) + HPixXY*real(pixel) + VPixXY*imag(pixel) cx = cx0 = real(tmp), cy = cy0 = imag(tmp) cz = cz0 = NZ*imag(p2) + VPixZ*imag(pixel) ;HPixZ -> 0 tmp = NXY*delta, dcx = real(tmp), dcy = imag(tmp) dcz = NZ*delta x1 = real(p3) y1 = imag(p3) z1 = real(p4) j = m = i = 0: a = sqr(x1) + 2*y1*z1 b = sqr(z1) + 2*x1*y1 c = sqr(y1) + 2*x1*z1 x1 = c + cx, y1 = b + cy, z1 = a + cz IF (bailout >= (sqr(x1)+sqr(y1)+sqr(z1))) i = i + 1 ELSE i = 0 m = m + 1 cx = cx0 = cx0 + dcx cy = cy0 = cy0 + dcy cz = cz0 = cz0 + dcz x1 = real(p3), y1 = imag(p3), z1 = real(p4) ENDIF z = m - j j = j + 1 tiefnum >= m && p5 >= i } ---------------------------- End of parameters ----------------------------- ----- Original Message ----- From: "Gerald K. Dobiasovsky" <gerald.dob(a)aon.at> To: "Fractint and General Fractals Discussion" <fractint(a)mailman.xmission.com> Subject: [Fractint] Re: quaternion product correction Date: Thu, 3 Nov 2005 02:45:56 +0100 > > > [Russell Walsmith, regarding Triternions and the rendereing thereof] > > Paul Bourke's rendering seems to use some density cloud function (probably > the number of iterations accumulated while stepping along the > line-of-sight for each pixel), so the object's outside is structured > as well. > > All I can offer for the moment is a greyscale depth rendering similar to > Fractint's Julibrot type (that is, the object is solid and the surrounding > space is transparent). > > You can achieve a kind of outside density rendering by switching from > outside=summ to outside=iter, but the colors will wrap around many times, > which really doesn't look good. > > Gerald > > ---------------------------- Parameters below ------------------------------ > > T-set_in_3d {;Greyscale depth image > ; > reset=2004 type=formula formulafile=test.frm > formulaname=Rot3d_T-set passes=g > center-mag=-0.68046/-0.24858/0.9363296 > params=0/0/-0.75/0.75/0/0/0/4/150/253 float=y maxiter=2000000000 > outside=summ periodicity=0 > colors=000zzzyzzzyzzyyyyyxyyyxzyxxxxxwxxxwyxwwwwwvwwwvxwvvvvvuvvvuwvuuuu\ > utuuutvutttttstttsutsssssrsssrtsrrrrrqrrrqsrqqqqqpqqqprqpppppopppoqpoooo\ > onooonponnnnnmnnnmonmmmmmlmmmlnmlllllklllkmlkkkkkjkkkjlkjjjjjijjjikjiiii\ > ihiiihjihhhhhghhhgihgggggfgggfhgfffffefffegfeeeeedeeedfedddddcdddcedcccc\ > cbcccbdcbbbbbabbbacbaaaaa`aaa`ba`````_```_a`_____Z___Z`_ZZZZZYZZZY_ZYYYY\ > YXYYYXZYXXXXXWXXXWYXWWWWWVWWWVXWVVVVVUVVVUWVUUUUUTUUUTVUTTTTTSTTTSUTSSSS\ > SRSSSRTSRRRRRQRRRQSRQQQQQPQQQPRQPPPPPOPPPOQPOOOOONOOONPONNNNNMNNNMONMMMM\ > MLMMMLNMLLLLLKLLLKMLKKKKKJKKKJLKJJJJJIJJJIKJIIIIIHIIIHJIHHHHHGHHHGIHGGGG\ > GFGGGFHGFFFFFEFFFEGFEEEEEDEEEDFEDDDDDCDDDCEDCCCCCBCCCBDCBBBBBABBBACBAAAA\ > A9AAA9BA9999989998A98888878887987777767776876666656665765555545554654444\ > 4344435433333233324322222122213211111011102100000000PPP > } > > frm:Rot3d_T-set {;periodicity=no, outside=summ > ;maxit > p5real*(p5imag+1) > ;-------------------------------------------- > ;p1real: Rotation about x-axis (1st rotation) > ;p1imag: Rotation about y-axis (2nd rotation) > ;p2real: Far clipping plane > ;p2imag: Near clipping plane > ;p3real: x1(0) > ;p3imag: y1(0) > ;p4real: z1(0) > ;p4imag: Bailout > ;p5real: Maxiter per slice > ;p5imag: Number of slices - 1 > ;-------------------------------------------- > ; > bailout = imag(p4), tiefnum = imag(p5) > delta = (real(p2)-imag(p2))/tiefnum > tmp = pi/180 > rotXax = exp(flip(real(p1)*tmp)), rotYax = exp(flip(imag(p1)*tmp)) > ; > HPixXY = rotYax > VPixZ = real(rotXax) > VPixXY = flip(conj(rotYax)) > NXY = VPixZ*VPixXY > NZ = imag(conj(rotXax)) > VPixXY = -NZ*VPixXY > ; > tmp = NXY*imag(p2) + HPixXY*real(pixel) + VPixXY*imag(pixel) > cx = cx0 = real(tmp), cy = cy0 = imag(tmp) > cz = cz0 = NZ*imag(p2) + VPixZ*imag(pixel) ;HPixZ -> 0 > tmp = NXY*delta, dcx = real(tmp), dcy = imag(tmp) > dcz = NZ*delta > x1 = real(p3) > y1 = imag(p3) > z1 = real(p4) > j = m = i = 0: > a = sqr(x1) + 2*y1*z1 > b = sqr(z1) + 2*x1*y1 > c = sqr(y1) + 2*x1*z1 > x1 = a + cx, y1 = b + cy, z1 = c + cz > IF (bailout >= (sqr(x1)+sqr(y1)+sqr(z1))) > i = i + 1 > ELSE > i = 0 > m = m + 1 > cx = cx0 = cx0 + dcx > cy = cy0 = cy0 + dcy > cz = cz0 = cz0 + dcz > x1 = real(p3), y1 = imag(p3), z1 = real(p4) > ENDIF > z = m - j > j = j + 1 > tiefnum >= m && p5 >= i > } > > ---------------------------- End of parameters ----------------------------- > > > _______________________________________________ > Fractint mailing list > Fractint(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint

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