FOTD 07-10-06 (Triternion Travels [Not Rated])
FOTD -- October 07, 2006 (Not Rated) Fractal visionaries and enthusiasts: Today's image makes use of a formula revised by Gilles Nadeau and posted to the Fractint list on Friday. (I have changed the space between Neo and T-set in the formula name to an under- score. A space band in a formula name is not permitted.) The formula is designed to draw the three-dimensional triternion Mandelbrot set. It does this very well. But I notice that the images it draws are the same as those drawn by the type=quat formula in Fractint, which claims to draw slices of a four- dimensional quaternion M-set, but which I have always suspected actually draws slices of a circular three-dimensional object. It is apparent that the three-dimensional object being sliced by both formulas is the figure that is traced out when the M-set is rotated around its X-axis. The value I gave (p1) in today's image is +0.64952, which is the Y-value of the prominent valley of the large north bud of the M-set. And not surprisingly, the valley appears in distorted form in today's image. The large open areas at the top and bottom of the frame are oblique slices of the northern bud itself, or rather of the donut-shaped ring this bud traces out as it rotates around the X-axis. The chaos across the middle of the frame is the fringe of the detail on the main-bay side of the valley, grossly stretched as would be expected when slicing through the edge of a donut. What I would like to see is a way of rotating the slice 90 degrees, so that the circles of revolution are drawn, and also the fascinating ovals that must lie in between. I have no idea of how to do this however. The image is titled "Triternion Travels", which is a fair enough opinion of the scene. Since the image has mathematical value but little artistic worth, I gave it no rating. The render time of 7-1/2 minutes on my 10-year-old machine may be avoided by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the image as it is posted there. A cloudy cool day here at Fractal Central on Friday went un- noticed by the dynamic duo of fractal cats, who still were more interested in playing with each other and waiting for another mouse to come out. They exhausted themselves playing, and showed little disappointment when no mouse appeared. The usual evening treat was fully enjoyed. My day was totally average. Tomorrow will probably be the same. Until then, when the next FOTD will shine forth, take care, and would the true number of dimensions that make up sub-atomic reality please stand up. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Triternion_Travels { ; time=0:07:26.44--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=Neo_T-set center-mag=-0.124889193/0/42.27946/3.2951 params=0.64952/0 float=y maxiter=5000 inside=0 logmap=186 symmetry=xaxis periodicity=10 colors=000kdff_g`ViWQjTJmSKlRLkRMkQNjQNjPOiOPhOQhN\ RgNRgMSfLTeLUeKVdBjCGbRKVdJKuMMsONrQOqSPpUQoXRnZSm\ `TlbVjdWigXhiYgkZfm_eo`dtddqaco_cmYckWciUcgSceQccO\ caMc_KcYIcWGcUEcSCcN5fQAcSFaVK_XPYZTWaYUcbSfgQhlOj\ pMhqPfrSdrVbsX`s_ZtbXueWugUvjSvmQwpOxrMxuKyxJyzHwy\ FuxDsxBqwAow8mv6kv4iu3hu7isBjrFkpJloNmmRnlVokZpibq\ hfrfjsentcrubvx`uuatsasqasoarmaqkapiaqfbpgapgaph`p\ h`pi_oi_ojZojZokYokYnlXnlXnmWnmWnnVqoUnnVknVhnWenW\ cnW`nXYnXVnXSnYQnYNnYKnZHnZ4bsCsWFnZIj`LfbOaeRYgUU\ iXPl_LnbHpeCsh8uk4wn0yh9lcI_ZRNRX4TY8UZBVZEW_IY`LZ\ `O_aS`aVbbYccadcdedghghfdjdbkc_laYm_WnZToXRqWOrUMs\ SKtRHuPFvODwUEjZFZcGNMAELEGKHIKKJJNLJQMITOHWPHZRGa\ SGdUFgVEjXEmYDp_AxfCucDs`EqZGnWHlUIjRJhPPeUVcZ_abe\ _gkYlpWprVsAao8Wg7Q`6KU5EN7LK9RIBYGDcEFjCGpAAsU5ul\ `FLRMJHTI8ZHQaVgdhyfuvXotOirFcp6YmHWkRVh`TfjSdtR`m\ SXfST_TPTTLMUIFUFP`CZfAgm } Neo_T-set { X=real(pixel), Y=imag(pixel), V=real(p1) x1 = y1 = v1 = 0: x2 = x1^2-y1^2-v1^2 + X y2 = 2*x1*y1 + Y v2 = 2*x1*v1 + V x1=x2, y1=y2, v1=v2 z = x1^2+y1^2+v1^2 z < 8 } END PARAMETER FILE=========================================
Hello Jim, Thank you to retort with this message. Your image is interesting. I admire so much the work of Russell Walsmith! I did not add anything to his formula. It is right an example of a method suggested by Ron Barnett to write the quat by using the complex numbers and the functions. I would be grateful to you to say to me if this formula cubic quat is readable by fractint. I use especially software UF. Here the formula. Gilles CubicQ_Msetb {;Quaternion Mandel formula ; Gilles Nadeau, April, 2005 ; z=(0,0) w=(0,0) cz=pixel cw=p1: c=conj(z) d=conj(w) s=sqr(z) t=sqr(w) a=z*s-2*z*d*w-d*c*w b=w*s-d*t+c*w*z+c^2*w z=a+cz w=b+cw (|z|+|w|)<64 } ----- Original Message ----- From: "Jim Muth" <jamth@mindspring.com> To: <fractint@mailman.xmission.com> Cc: <philofractal@lists.fractalus.com> Sent: Friday, October 06, 2006 22:45 Subject: [Fractint] FOTD 07-10-06 (Triternion Travels [Not Rated])
FOTD -- October 07, 2006 (Not Rated)
Fractal visionaries and enthusiasts:
Today's image makes use of a formula revised by Gilles Nadeau and posted to the Fractint list on Friday. (I have changed the space between Neo and T-set in the formula name to an under- score. A space band in a formula name is not permitted.) The formula is designed to draw the three-dimensional triternion Mandelbrot set. It does this very well. But I notice that the images it draws are the same as those drawn by the type=quat formula in Fractint, which claims to draw slices of a four- dimensional quaternion M-set, but which I have always suspected actually draws slices of a circular three-dimensional object.
It is apparent that the three-dimensional object being sliced by both formulas is the figure that is traced out when the M-set is rotated around its X-axis. The value I gave (p1) in today's image is +0.64952, which is the Y-value of the prominent valley of the large north bud of the M-set. And not surprisingly, the valley appears in distorted form in today's image. The large open areas at the top and bottom of the frame are oblique slices of the northern bud itself, or rather of the donut-shaped ring this bud traces out as it rotates around the X-axis. The chaos across the middle of the frame is the fringe of the detail on the main-bay side of the valley, grossly stretched as would be expected when slicing through the edge of a donut.
What I would like to see is a way of rotating the slice 90 degrees, so that the circles of revolution are drawn, and also the fascinating ovals that must lie in between. I have no idea of how to do this however.
The image is titled "Triternion Travels", which is a fair enough opinion of the scene. Since the image has mathematical value but little artistic worth, I gave it no rating. The render time of 7-1/2 minutes on my 10-year-old machine may be avoided by visiting the FOTD web site at:
<http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
and viewing the image as it is posted there.
A cloudy cool day here at Fractal Central on Friday went un- noticed by the dynamic duo of fractal cats, who still were more interested in playing with each other and waiting for another mouse to come out. They exhausted themselves playing, and showed little disappointment when no mouse appeared. The usual evening treat was fully enjoyed.
My day was totally average. Tomorrow will probably be the same. Until then, when the next FOTD will shine forth, take care, and would the true number of dimensions that make up sub-atomic reality please stand up.
Jim Muth jamth@mindspring.com jimmuth@aol.com
START PARAMETER FILE=======================================
Triternion_Travels { ; time=0:07:26.44--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=Neo_T-set center-mag=-0.124889193/0/42.27946/3.2951 params=0.64952/0 float=y maxiter=5000 inside=0 logmap=186 symmetry=xaxis periodicity=10 colors=000kdff_g`ViWQjTJmSKlRLkRMkQNjQNjPOiOPhOQhN\ RgNRgMSfLTeLUeKVdBjCGbRKVdJKuMMsONrQOqSPpUQoXRnZSm\ `TlbVjdWigXhiYgkZfm_eo`dtddqaco_cmYckWciUcgSceQccO\ caMc_KcYIcWGcUEcSCcN5fQAcSFaVK_XPYZTWaYUcbSfgQhlOj\ pMhqPfrSdrVbsX`s_ZtbXueWugUvjSvmQwpOxrMxuKyxJyzHwy\ FuxDsxBqwAow8mv6kv4iu3hu7isBjrFkpJloNmmRnlVokZpibq\ hfrfjsentcrubvx`uuatsasqasoarmaqkapiaqfbpgapgaph`p\ h`pi_oi_ojZojZokYokYnlXnlXnmWnmWnnVqoUnnVknVhnWenW\ cnW`nXYnXVnXSnYQnYNnYKnZHnZ4bsCsWFnZIj`LfbOaeRYgUU\ iXPl_LnbHpeCsh8uk4wn0yh9lcI_ZRNRX4TY8UZBVZEW_IY`LZ\ `O_aS`aVbbYccadcdedghghfdjdbkc_laYm_WnZToXRqWOrUMs\ SKtRHuPFvODwUEjZFZcGNMAELEGKHIKKJJNLJQMITOHWPHZRGa\ SGdUFgVEjXEmYDp_AxfCucDs`EqZGnWHlUIjRJhPPeUVcZ_abe\ _gkYlpWprVsAao8Wg7Q`6KU5EN7LK9RIBYGDcEFjCGpAAsU5ul\ `FLRMJHTI8ZHQaVgdhyfuvXotOirFcp6YmHWkRVh`TfjSdtR`m\ SXfST_TPTTLMUIFUFP`CZfAgm }
Neo_T-set { X=real(pixel), Y=imag(pixel), V=real(p1) x1 = y1 = v1 = 0: x2 = x1^2-y1^2-v1^2 + X y2 = 2*x1*y1 + Y v2 = 2*x1*v1 + V x1=x2, y1=y2, v1=v2 z = x1^2+y1^2+v1^2 z < 8 }
END PARAMETER FILE=========================================
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On Saturday 07 October 2006 10:01, GillesNadeau wrote:
Hello Jim,
Thank you to retort with this message. Your image is interesting. I admire so much the work of Russell Walsmith! I did not add anything to his formula. It is right an example of a method suggested by Ron Barnett to write the quat by using the complex numbers and the functions. I would be grateful to you to say to me if this formula cubic quat is readable by fractint. I use especially software UF. Here the formula.
yes, it works giles, thanks. :) sammi
Hello Sammi, Thank you to say to me that this formula functions well. Here images which I composed with fractint towards the end of the Nineties. I would be grateful to you to say to me if you like them. Gilles http://www.mathsong.com/casaraku/pages/004/20001104.htm http://www.mathsong.com/casaraku/pages/016/20001205.htm http://www.mathsong.com/casaraku/pages/018/20000909.htm http://www.mathsong.com/casaraku/pages/015/20031029.htm ----- Original Message ----- From: "sam ende" <sam@sende.co.uk> To: "Fractint and General Fractals Discussion" <fractint@mailman.xmission.com> Sent: Saturday, October 07, 2006 15:44 Subject: Re: [Fractint] FOTD 07-10-06 (Triternion Travels [Not Rated])
On Saturday 07 October 2006 10:01, GillesNadeau wrote:
Hello Jim,
Thank you to retort with this message. Your image is interesting. I admire so much the work of Russell Walsmith! I did not add anything to his formula. It is right an example of a method suggested by Ron Barnett to write the quat by using the complex numbers and the functions. I would be grateful to you to say to me if this formula cubic quat is readable by fractint. I use especially software UF. Here the formula.
yes, it works giles, thanks. :)
sammi
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On Saturday 07 October 2006 23:27, GillesNadeau wrote: hallo gilles :),
http://www.mathsong.com/casaraku/pages/004/20001104.htm
http://www.mathsong.com/casaraku/pages/016/20001205.htm
i think you have wonderful fractals, i have spent a little time browsing, of the three above i think i like encre brune (dessin) the best but the Phoenix Mandelbrot-zoom is also fascinating, they all are really, i also like the koch challenge ones, and this one i think really beautiful; http://www.mathsong.com/casaraku/pages/014/20010403.htm and this one too, it's got a wonderful atmospheric effect: http://www.mathsong.com/casaraku/pages/014/20010429.htm vision surréaliste i think is fascinating, and this one made me laugh :)Quaternion Julia (bronze). fluide intererstellaire is very interesting, i assume that means fluid universe ?, was you thinking of that particular theory when naming it ? and this one i think is incredibly witty :) http://www.mathsong.com/casaraku/pages/014/20030901.htm i see you've got quite a few galleries and fractals and it will take me some time to look at them all properly, i think they're great, thank you for showing/sharing :) sammi
participants (3)
-
GillesNadeau -
Jim Muth -
sam ende