Here is a link to a web page with an image: http://www.fracton.org/fmlposts/astroid_out.html The formula for this fractal is called True_Astroid and is based on the original Astroid_Mset by Paul Carlson. The original draws an "inside out" astroid curve while this one draws it in true form. The orbit trap formula is modified to use the polar form instead of the parametric form. The changes to the formula were suggested by Gerald Dobiasovsky. The parameter file used to make this image is below: Astroid_Out { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=True_Astroid passes=1 float=y center-mag=-1.265578607178311/0.1218562499999997/2\ 22.222225/1/0/0 params=0.01/0.59/8/30/0/0/0/0/0/0 maxiter=500 inside=255 outside=summ colors=000fOz<28>I0Kz0f<28>O08z88<28>O00zW0<28>c40\ zz0<28>aG00zR<28>0C40zz<28>0CCGGz<28>00O000<12>000\ z88 } frm:True_Astroid { ; Based on ; Astroid_Mset copyright (c) Paul W. Carlson, 1997 ; Modified for compatibility with Fractint 20.04 and ; Fracton by Mike Frazier, 2011 ; Additional improvements by Gerald Dobiasovsky ;**************************************************** ; Always use floating point math and outside=summ. ; ; Parameters: ; real(p1) = a factor controlling the width of the curves ; imag(p1) = radius of the astroid ; real(p2) = number of color ranges ; imag(p2) = number of colors in each color range ; ; Note that the equation variable is w, not z. ; Initialize cindex to the index of the background color ; Formula modified to avoid color index 0 which can not ; be used with outside=summ in FractInt v20.04 ;**************************************************** w=0, c=pixel, z=0, cindex=254,; Background color 254 bailout=0, iter=0, range_num=0, i=(0,1), r=imag(p1), ;**************************************************** ; In the accompanying par file, ; we have 8 color ranges with 30 colors in each range ; for a total of 240 colors. The first range starts at ; color 1. Pixels will use color 254 when |w| > 1000. ; Other values can be used here as long as the product ; of num_ranges times colors_in_range is less than 255. ; Color 254 is reserved for the background color and ; color 255 can be used for the inside color. ;**************************************************** num_ranges=real(p2), colors_in_range=imag(p2), ;**************************************************** ; Real(p1) controls the width of the curves. ; These values will usually be in the range 0.001 to 0.1 ;**************************************************** width=real(p1), index_factor=(colors_in_range-1)/width: ;**************************************************** ; The equation being iterated. Almost any equation ; that can be expressed in terms of a complex variable ; and a complex constant will work with this method. ; This example uses the standard Mandelbrot set equation. ;**************************************************** w=w*w+c, ;**************************************************** ; The orbit trap curve. This example uses an "astroid" ; curve (which has absolutely nothing to do with huge ; rocks in outer space). Any two-dimensional curve can ; be used which can be expressed in parametric form in ; terms of the angle from the origin. ;**************************************************** ; ang is really tan(ang) here ang=imag(w)/real(w), astroid=r*sqrt((ang^2+1)/(|ang|^(1/3)+1)^3), ;**************************************************** ; If the orbit point is within some distance of the curve, ; set z to the index into the colormap and set the bailout ; flag. ;**************************************************** distance=abs(|w|-|astroid|), if(distance<width&&iter>1), cindex=index_factor*distance+range_num*colors_in_range+1, bailout=1, endif, ;**************************************************** ; Cycle through the range numbers (0 thru num_ranges - 1) ; With two color ranges, even iterations use color ; range 0, odd iterations use color range 1. ;**************************************************** range_num=range_num+1, if(range_num==num_ranges), range_num=0, endif, ;**************************************************** ; Since we are using outside=summ, we have to subtract ; the number of iterations from z. ;**************************************************** iter=iter+1, z=cindex-iter, ;**************************************************** ; Finally, we test for bailout ;**************************************************** bailout==0&&|w|<1000 } -- Mike Frazier www.fracton.org
A long time ago Jim Muth initiated a discussion in this forum concerning the question... "can Fractals be art". I was always a "con". I believed that very few people could frame and hang a fractal on the living room wall, and keep it there for very long. They rapidly became visually uninteresting. Now, however, I think I'm going to change my mind. Mike Frazier's recent work might do it for me. I'm going to try hanging him! John W. ----- Original Message ----- From: Mike Frazier To: Fractint and General Fractals Discussion Sent: Sunday, February 27, 2011 6:13 PM Subject: [Fractint] Astroid Out Here is a link to a web page with an image: http://www.fracton.org/fmlposts/astroid_out.html The formula for this fractal is called True_Astroid and is based on the original Astroid_Mset by Paul Carlson. The original draws an "inside out" astroid curve while this one draws it in true form. The orbit trap formula is modified to use the polar form instead of the parametric form. The changes to the formula were suggested by Gerald Dobiasovsky. The parameter file used to make this image is below: Astroid_Out { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=True_Astroid passes=1 float=y center-mag=-1.265578607178311/0.1218562499999997/2\ 22.222225/1/0/0 params=0.01/0.59/8/30/0/0/0/0/0/0 maxiter=500 inside=255 outside=summ colors=000fOz<28>I0Kz0f<28>O08z88<28>O00zW0<28>c40\ zz0<28>aG00zR<28>0C40zz<28>0CCGGz<28>00O000<12>000\ z88 } frm:True_Astroid { ; Based on ; Astroid_Mset copyright (c) Paul W. Carlson, 1997 ; Modified for compatibility with Fractint 20.04 and ; Fracton by Mike Frazier, 2011 ; Additional improvements by Gerald Dobiasovsky ;**************************************************** ; Always use floating point math and outside=summ. ; ; Parameters: ; real(p1) = a factor controlling the width of the curves ; imag(p1) = radius of the astroid ; real(p2) = number of color ranges ; imag(p2) = number of colors in each color range ; ; Note that the equation variable is w, not z. ; Initialize cindex to the index of the background color ; Formula modified to avoid color index 0 which can not ; be used with outside=summ in FractInt v20.04 ;**************************************************** w=0, c=pixel, z=0, cindex=254,; Background color 254 bailout=0, iter=0, range_num=0, i=(0,1), r=imag(p1), ;**************************************************** ; In the accompanying par file, ; we have 8 color ranges with 30 colors in each range ; for a total of 240 colors. The first range starts at ; color 1. Pixels will use color 254 when |w| > 1000. ; Other values can be used here as long as the product ; of num_ranges times colors_in_range is less than 255. ; Color 254 is reserved for the background color and ; color 255 can be used for the inside color. ;**************************************************** num_ranges=real(p2), colors_in_range=imag(p2), ;**************************************************** ; Real(p1) controls the width of the curves. ; These values will usually be in the range 0.001 to 0.1 ;**************************************************** width=real(p1), index_factor=(colors_in_range-1)/width: ;**************************************************** ; The equation being iterated. Almost any equation ; that can be expressed in terms of a complex variable ; and a complex constant will work with this method. ; This example uses the standard Mandelbrot set equation. ;**************************************************** w=w*w+c, ;**************************************************** ; The orbit trap curve. This example uses an "astroid" ; curve (which has absolutely nothing to do with huge ; rocks in outer space). Any two-dimensional curve can ; be used which can be expressed in parametric form in ; terms of the angle from the origin. ;**************************************************** ; ang is really tan(ang) here ang=imag(w)/real(w), astroid=r*sqrt((ang^2+1)/(|ang|^(1/3)+1)^3), ;**************************************************** ; If the orbit point is within some distance of the curve, ; set z to the index into the colormap and set the bailout ; flag. ;**************************************************** distance=abs(|w|-|astroid|), if(distance<width&&iter>1), cindex=index_factor*distance+range_num*colors_in_range+1, bailout=1, endif, ;**************************************************** ; Cycle through the range numbers (0 thru num_ranges - 1) ; With two color ranges, even iterations use color ; range 0, odd iterations use color range 1. ;**************************************************** range_num=range_num+1, if(range_num==num_ranges), range_num=0, endif, ;**************************************************** ; Since we are using outside=summ, we have to subtract ; the number of iterations from z. ;**************************************************** iter=iter+1, z=cindex-iter, ;**************************************************** ; Finally, we test for bailout ;**************************************************** bailout==0&&|w|<1000 } -- Mike Frazier www.fracton.org ------------------------------------------------------------------------------ _______________________________________________ Fractint mailing list Fractint@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint
John, I have had two pieces of fractal art on my walls for years. It is without question that fractals "can" be art. Whether any given piece is art to you or anyone else is another question. It's like all forms of art. What is art to you, may not be art to me. Ken... On 2/28/2011 10:24 PM, juanw@shaw.ca wrote:
A long time ago Jim Muth initiated a discussion in this forum concerning the question... "can Fractals be art". I was always a "con". I believed that very few people could frame and hang a fractal on the living room wall, and keep it there for very long. They rapidly became visually uninteresting. Now, however, I think I'm going to change my mind. Mike Frazier's recent work might do it for me. I'm going to try hanging him! John W.
----- Original Message ----- *From:* Mike Frazier <mailto:fractonorg@gmail.com> *To:* Fractint and General Fractals Discussion <mailto:fractint@mailman.xmission.com> *Sent:* Sunday, February 27, 2011 6:13 PM *Subject:* [Fractint] Astroid Out
Here is a link to a web page with an image:
http://www.fracton.org/fmlposts/astroid_out.html
The formula for this fractal is called True_Astroid and is based on the original Astroid_Mset by Paul Carlson. The original draws an "inside out" astroid curve while this one draws it in true form. The orbit trap formula is modified to use the polar form instead of the parametric form. The changes to the formula were suggested by Gerald Dobiasovsky.
The parameter file used to make this image is below:
Astroid_Out { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=True_Astroid passes=1 float=y center-mag=-1.265578607178311/0.1218562499999997/2\ 22.222225/1/0/0 params=0.01/0.59/8/30/0/0/0/0/0/0 maxiter=500 inside=255 outside=summ colors=000fOz<28>I0Kz0f<28>O08z88<28>O00zW0<28>c40\ zz0<28>aG00zR<28>0C40zz<28>0CCGGz<28>00O000<12>000\ z88 }
frm:True_Astroid { ; Based on ; Astroid_Mset copyright (c) Paul W. Carlson, 1997 ; Modified for compatibility with Fractint 20.04 and ; Fracton by Mike Frazier, 2011 ; Additional improvements by Gerald Dobiasovsky ;**************************************************** ; Always use floating point math and outside=summ. ; ; Parameters: ; real(p1) = a factor controlling the width of the curves ; imag(p1) = radius of the astroid ; real(p2) = number of color ranges ; imag(p2) = number of colors in each color range ; ; Note that the equation variable is w, not z. ; Initialize cindex to the index of the background color ; Formula modified to avoid color index 0 which can not ; be used with outside=summ in FractInt v20.04 ;**************************************************** w=0, c=pixel, z=0, cindex=254,; Background color 254 bailout=0, iter=0, range_num=0, i=(0,1), r=imag(p1), ;**************************************************** ; In the accompanying par file, ; we have 8 color ranges with 30 colors in each range ; for a total of 240 colors. The first range starts at ; color 1. Pixels will use color 254 when |w| > 1000. ; Other values can be used here as long as the product ; of num_ranges times colors_in_range is less than 255. ; Color 254 is reserved for the background color and ; color 255 can be used for the inside color. ;**************************************************** num_ranges=real(p2), colors_in_range=imag(p2), ;**************************************************** ; Real(p1) controls the width of the curves. ; These values will usually be in the range 0.001 to 0.1 ;**************************************************** width=real(p1), index_factor=(colors_in_range-1)/width: ;**************************************************** ; The equation being iterated. Almost any equation ; that can be expressed in terms of a complex variable ; and a complex constant will work with this method. ; This example uses the standard Mandelbrot set equation. ;**************************************************** w=w*w+c, ;**************************************************** ; The orbit trap curve. This example uses an "astroid" ; curve (which has absolutely nothing to do with huge ; rocks in outer space). Any two-dimensional curve can ; be used which can be expressed in parametric form in ; terms of the angle from the origin. ;**************************************************** ; ang is really tan(ang) here ang=imag(w)/real(w), astroid=r*sqrt((ang^2+1)/(|ang|^(1/3)+1)^3), ;**************************************************** ; If the orbit point is within some distance of the curve, ; set z to the index into the colormap and set the bailout ; flag. ;**************************************************** distance=abs(|w|-|astroid|), if(distance<width&&iter>1), cindex=index_factor*distance+range_num*colors_in_range+1, bailout=1, endif, ;**************************************************** ; Cycle through the range numbers (0 thru num_ranges - 1) ; With two color ranges, even iterations use color ; range 0, odd iterations use color range 1. ;**************************************************** range_num=range_num+1, if(range_num==num_ranges), range_num=0, endif, ;**************************************************** ; Since we are using outside=summ, we have to subtract ; the number of iterations from z. ;**************************************************** iter=iter+1, z=cindex-iter, ;**************************************************** ; Finally, we test for bailout ;**************************************************** bailout==0&&|w|<1000 }
-- Mike Frazier www.fracton.org <http://www.fracton.org>
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I agree with Ken, Furthermore, art quality depends upon many things, but especially * The tools used * The skill and experience of the artist Janet Parke is a well recognized and published artist, and taught several courses on fractal art for several years. Her basic principles are the same as for anyone in the fine arts, and those taking her courses were given fine art reference materials to study and apply. Good fractal art is not something where you can turn on the computer and play around with formulas and colors. It requires practice, dedication and time. Ron Barnett http://www.hiddendimension.com http://www.hiddendimension.com/Challenges/UF5Challenges.html http://www.hiddendimension.com/Challenges/OneLayer/UFOneLayer.html http://www.hiddendimension.com/GalleryMain/Xenodream_Gallery/Xenodream_Galle... http://www.renderosity.com/mod/gallery/browse.php?username=barnettr Life is about art. Art is about life. ----- Original Message ----- From: "Ken Childress" <kenc@urassociation.com> To: "Fractint and General Fractals Discussion" <fractint@mailman.xmission.com> Sent: Tuesday, March 01, 2011 10:08 AM Subject: Re: [Fractint] Astroid Out
John,
I have had two pieces of fractal art on my walls for years. It is without question that fractals "can" be art. Whether any given piece is art to you or anyone else is another question. It's like all forms of art. What is art to you, may not be art to me.
Ken...
On 2/28/2011 10:24 PM, juanw@shaw.ca wrote:
A long time ago Jim Muth initiated a discussion in this forum concerning the question... "can Fractals be art". I was always a "con". I believed that very few people could frame and hang a fractal on the living room wall, and keep it there for very long. They rapidly became visually uninteresting. Now, however, I think I'm going to change my mind. Mike Frazier's recent work might do it for me. I'm going to try hanging him! John W.
----- Original Message ----- *From:* Mike Frazier <mailto:fractonorg@gmail.com> *To:* Fractint and General Fractals Discussion <mailto:fractint@mailman.xmission.com> *Sent:* Sunday, February 27, 2011 6:13 PM *Subject:* [Fractint] Astroid Out
Here is a link to a web page with an image:
http://www.fracton.org/fmlposts/astroid_out.html
The formula for this fractal is called True_Astroid and is based on the original Astroid_Mset by Paul Carlson. The original draws an "inside out" astroid curve while this one draws it in true form. The orbit trap formula is modified to use the polar form instead of the parametric form. The changes to the formula were suggested by Gerald Dobiasovsky.
The parameter file used to make this image is below:
Astroid_Out { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=True_Astroid passes=1 float=y center-mag=-1.265578607178311/0.1218562499999997/2\ 22.222225/1/0/0 params=0.01/0.59/8/30/0/0/0/0/0/0 maxiter=500 inside=255 outside=summ colors=000fOz<28>I0Kz0f<28>O08z88<28>O00zW0<28>c40\ zz0<28>aG00zR<28>0C40zz<28>0CCGGz<28>00O000<12>000\ z88 }
frm:True_Astroid { ; Based on ; Astroid_Mset copyright (c) Paul W. Carlson, 1997 ; Modified for compatibility with Fractint 20.04 and ; Fracton by Mike Frazier, 2011 ; Additional improvements by Gerald Dobiasovsky ;**************************************************** ; Always use floating point math and outside=summ. ; ; Parameters: ; real(p1) = a factor controlling the width of the curves ; imag(p1) = radius of the astroid ; real(p2) = number of color ranges ; imag(p2) = number of colors in each color range ; ; Note that the equation variable is w, not z. ; Initialize cindex to the index of the background color ; Formula modified to avoid color index 0 which can not ; be used with outside=summ in FractInt v20.04 ;**************************************************** w=0, c=pixel, z=0, cindex=254,; Background color 254 bailout=0, iter=0, range_num=0, i=(0,1), r=imag(p1), ;**************************************************** ; In the accompanying par file, ; we have 8 color ranges with 30 colors in each range ; for a total of 240 colors. The first range starts at ; color 1. Pixels will use color 254 when |w| > 1000. ; Other values can be used here as long as the product ; of num_ranges times colors_in_range is less than 255. ; Color 254 is reserved for the background color and ; color 255 can be used for the inside color. ;**************************************************** num_ranges=real(p2), colors_in_range=imag(p2), ;**************************************************** ; Real(p1) controls the width of the curves. ; These values will usually be in the range 0.001 to 0.1 ;**************************************************** width=real(p1), index_factor=(colors_in_range-1)/width: ;**************************************************** ; The equation being iterated. Almost any equation ; that can be expressed in terms of a complex variable ; and a complex constant will work with this method. ; This example uses the standard Mandelbrot set equation. ;**************************************************** w=w*w+c, ;**************************************************** ; The orbit trap curve. This example uses an "astroid" ; curve (which has absolutely nothing to do with huge ; rocks in outer space). Any two-dimensional curve can ; be used which can be expressed in parametric form in ; terms of the angle from the origin. ;**************************************************** ; ang is really tan(ang) here ang=imag(w)/real(w), astroid=r*sqrt((ang^2+1)/(|ang|^(1/3)+1)^3), ;**************************************************** ; If the orbit point is within some distance of the curve, ; set z to the index into the colormap and set the bailout ; flag. ;**************************************************** distance=abs(|w|-|astroid|), if(distance<width&&iter>1), cindex=index_factor*distance+range_num*colors_in_range+1, bailout=1, endif, ;**************************************************** ; Cycle through the range numbers (0 thru num_ranges - 1) ; With two color ranges, even iterations use color ; range 0, odd iterations use color range 1. ;**************************************************** range_num=range_num+1, if(range_num==num_ranges), range_num=0, endif, ;**************************************************** ; Since we are using outside=summ, we have to subtract ; the number of iterations from z. ;**************************************************** iter=iter+1, z=cindex-iter, ;**************************************************** ; Finally, we test for bailout ;**************************************************** bailout==0&&|w|<1000 }
-- Mike Frazier www.fracton.org <http://www.fracton.org>
------------------------------------------------------------------------
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Mike,
Here is a link to a web page with an image:
[snip] Of course the obvious did escape me: One can use the cartesian form of a curve formula also. As long as there is a function f(z) = 0 for points on the curve, |f(z)| = delta describes a point off the curve (for delta != 0). The Astroid case then becomes ;ang = ... ;astroid = ... distance = abs(abs(real(w))^(2/3) + abs(imag(w))^(2/3) - r^(2/3)) The constant "r^(2/3)" better be moved into the initialisation part, but that's a detail. Another example is below. Regards, Gerald --- 8< ---------------- start of par ---------------------------------------------------------- Deltoid_Example { reset=2004 type=formula formulafile=test.par formulaname=deltoid_mset passes=t center-mag=+0.36285434995112430/+0.66554088657105560/155.059 params=0.002/0.125/8/30 float=y maxiter=500 inside=255 outside=summ colors=000fOz<22>N5TM4RL3Q<3>I0Kz0f<22>W0FV0ET0D<3>O08z88<22>W22V11T11<3\
O00zW0<22>hA0g90f80<3>c40zz0<22>fQ0eO0dM0<3>aG00zR<22>0N90L80J7<3>0C40z\ z<22>0NN0LL0JJ<3>0CCGGz<22>33W33V22T<3>00O000<7>000<4>000z88 }
frm:Deltoid_Mset { ; Asteroid_Basic.par ; Copyright (c) Paul W. Carlson, 1997 ; Modified for compatibility with Fractint 20.04 and ; Fracton by Mike Frazier, 2011 ;**************************************************** ; Always use floating point math and outside=summ. ; ; Parameters: ; real(p1) = a factor controlling the width of the curves ; imag(p1) = radius of the astroid ; real(p2) = number of color ranges ; imag(p2) = number of colors in each color range ; ; Note that the equation variable is w, not z. ; Initialize cindex to the index of the background color ; Formula modified to avoid color index 0 which can not ; be used with outside=summ in FractInt v20.04 ;**************************************************** w=0, c=pixel, z=0, cindex=254,; Background color 254 bailout=0, iter=0, range_num=0, i=(0,1), r=imag(p1), ;**************************************************** ; In the accompanying par file, ; we have 8 color ranges with 30 colors in each range ; for a total of 240 colors. The first range starts at ; color 1. Pixels will use color 254 when |w| > 1000. ; Other values can be used here as long as the product ; of num_ranges times colors_in_range is less than 255. ; Color 254 is reserved for the background color and ; color 255 can be used for the inside color. ;**************************************************** num_ranges=real(p2), colors_in_range=imag(p2), ;**************************************************** ; Real(p1) controls the width of the curves. ; These values will usually be in the range 0.001 to 0.1 ;**************************************************** width=real(p1), index_factor=(colors_in_range-1)/width: ;**************************************************** ; The equation being iterated. Almost any equation ; that can be expressed in terms of a complex variable ; and a complex constant will work with this method. ; This example uses the standard Mandelbrot set equation. ;**************************************************** w=w*w+c, ;**************************************************** ; The orbit trap curve. This example uses an "astroid" ; curve (which has absolutely nothing to do with huge ; rocks in outer space). Any two-dimensional curve can ; be used which can be expressed in parametric form in ; terms of the angle from the origin. ;**************************************************** ;ang=atan(imag(w)/real(w)), ;astroid=r*(cos(ang)^3+i*sin(ang)^3), xx = real(w), yy = imag(w) a = 2*xx + 3*r ;**************************************************** ; If the orbit point is within some distance of the curve, ; set z to the index into the colormap and set the bailout ; flag. Note: the way we use the "distance" here has ; the effect of turning the curves inside-out in the image. ;**************************************************** distance=abs(sqr(|w|+12*r*xx+9*r*r)-4*r*sqr(a)*a) if(distance<width&&iter>1), cindex=index_factor*distance+range_num*colors_in_range+1, bailout=1, endif, ;**************************************************** ; Cycle through the range numbers (0 thru num_ranges - 1) ; With two color ranges, even iterations use color ; range 0, odd iterations use color range 1. ;**************************************************** range_num=range_num+1, if(range_num==num_ranges), range_num=0, endif, ;**************************************************** ; Since we are using outside=summ, we have to subtract ; the number of iterations from z. ;**************************************************** iter=iter+1, z=cindex-iter, ;**************************************************** ; Finally, we test for bailout ;**************************************************** bailout==0&&|w|<1000 } --- 8< ---------------- end of par ----------------------------------------------------------
On Tue, Mar 1, 2011 at 3:35 PM, Gerald K. Dobiasovsky <gerald.dob@aon.at>wrote:
Of course the obvious did escape me: One can use the cartesian form of a curve formula also. As long as there is a function f(z) = 0 for points on the curve, |f(z)| = delta describes a point off the curve (for delta != 0).
Another great tip. Thanks for sharing it. This one looks like it would work for curves with loops. For folks trying this on their own, some of the formula is missing. To get the Deltoid_Example to work, I pasted the xx,yy,a, and distance equations into the formula for Astroid_Mset_v2. -- Mike Frazier www.fracton.org
Mike Frazier wrote:
Another great tip. Thanks for sharing it. This one looks like it would work for curves with loops.
Yes, but that doesn't solve the case of, say, your epicycloids in general. I shudder at the thought of converting the formula (for a fixed number of cusps) to cartesian and/or polar form even with the aid of Mathematica/Maple/Maxima. Another way would be - for each orbit point - to step (with a sufficiently small stepsize) along the curve and record the smallest distance to the orbit point. Although the formula parser has no user loop construct, changing the formula to do both in the main loop can be done (and has been done for other purposes). But think of the slowdown!
For folks trying this on their own, some of the formula is missing. To get the Deltoid_Example to work, I pasted the xx,yy,a, and distance equations into the formula for Astroid_Mset_v2.
Oh? I checked it with DOS Fractint before pasting it into the mail. Any format munging by the mail service, perhaps? Or fracton not liking "passes=t" (I forgot to set this back to "passes=1"). Anyway, sorry for the inconvenience. Regards, Gerald P.S. I had to send this a second time, because xmission refused to accept the first post. Seems Jim Muth is not the only person "spamming" the list.
On Fri, Mar 4, 2011 at 4:41 PM, Gerald K. Dobiasovsky <gerald.dob@aon.at>wrote:
Yes, but that doesn't solve the case of, say, your epicycloids in general. I shudder at the thought of converting the formula (for a fixed number of cusps) to cartesian and/or polar form even with the aid of Mathematica/Maple/Maxima.
The epicycloid formula seems to be fairly close even with driving the parametric form with the angle. I had no luck finding or deriving the other forms. It makes a good curve the way it is even if it isn't exactly correct.
Oh? I checked it with DOS Fractint before pasting it into the mail. Any format munging by the mail service, perhaps? Or fracton not liking "passes=t" (I forgot to set this back to "passes=1"). Anyway, sorry for the inconvenience.
I figured out what happened to the formula. There was a small clickable line in the middle of the formula in my Gmail mail reader that said "Show quoted text". When I clicked that, the missing part of the formula came back. It still didn't run though because the place that said "Show quoted text" changed to "Hide quoted text". Deleting the Hide quoted text from the pasted formula made it work just fine. I don't know if that quoted thing is unique to my mail reader but I have never seen it in formulas before. Fracton ignores the passes= parameter so that is no problem. The Deltoid_Mset formula looks like it will be a good one because of the 3 sided symmetry. The cartesian form method you mentioned worked great. I used it to make a curve with a loop. See my other post for today. Thanks again for the great suggestion. -- Mike Frazier www.fracton.org
Mike Frazier wrote:
I figured out what happened to the formula. There was a small clickable line in the middle of the formula in my Gmail mail reader that said "Show quoted text". When I clicked that, the missing part of the formula came back. It still didn't run though because the place that said "Show quoted text" changed to "Hide quoted text". Deleting the Hide quoted text from the pasted formula made it work just fine. I don't know if that quoted thing is unique to my mail reader but I have never seen it in formulas before.
Perhaps some mail client setting somewhere found something in the formula it thought indicated a bit of quoted text. Some mail clients allow user to change what character is used to indicate a quote (bad idea, the ">" is the standard!), then they think that when they find "their" quote character in some other part of the mail text, it indicates a quote, too. -- David gnome@hawaii.rr.com authenticity, honesty, community
Gerald K. Dobiasovsky wrote:
But think of the slowdown!
If I ever think of the slowdown, then I won't use DosBOX. In jeneral, though, *never* think of the slowdown. I know at least one guy on this list who is all too happy to use iteration counts and escape bounds that only add three percent more image. Computers love it when they are not idle: It distributes heat more evenly.
participants (8)
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david -
David W Riccio -
Gerald K. Dobiasovsky -
Jay Litwyn -
juanw＠shaw.ca -
Ken Childress -
Mike Frazier -
Ron Barnett