This fractal mixes two copies of z * z * cos(z) * sin(z) at slightly different locations. The area around the fractal has lots of short arms interconnecting the features. If you zoom in more on the main feature on the right it looks like a castle with six towers. The zoomed in images need arbitrary precision math but the first image works fine with double precison. Here is a link to an image: http://dl.dropboxusercontent.com/u/33642054/image/pr_3cossin-3cossin_BC_1200... A deep zoom into the feature on the left using arbitrary precision math and a different color palette: http://dl.dropboxusercontent.com/u/33642054/image/pr_3cossin-3cossin_CD_640_... A zoom into the castle feature on the right using arbitrary precision math and a different color palette: http://dl.dropboxusercontent.com/u/33642054/image/pr_3cossin-3cossin_DD_640_... The FractInt compatible PAR file for the first image is: Shortarm_Castle { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20160221_1004 passes=1 float=y center-mag=-0.6417820664871355/0/9172173044.248877\ /1/0/0 params=1/1/0/0/-1/0/1/0/0/0 maxiter=2000 inside=0 periodicity=6 colors=vQ1h_FViSIsdGnREiDCe0Ec8GaGI_OKYW000MWcOUkQ\ SrTUrWWrZYra_rdargcridrjYokSlkMjlGglAej9Zh8Sf8Ld7E\ c77_A8WD8SG9PJ9RELSAXT5hU1tha9VaLIaX8GHEURBNLIuBGn\ CEgDD`EBUF9NG7ct8S_I53G86EA9CCBAEEGkOCWKSk8NcAIWCD\ OE80P84N87L8AJ8DHhWEaTFWQFQOFKLGEIGdNYOJPaz3NbAPVV\ KRRGNNCJJ1CO5EKLcNJ`MHYLGVKESJCPIBMH9JGqtjknfeib_d\ ZV_VPVRJQNDLJ5_n6Wh6Tb7QX7MR8JL1Cr3Dj4Eb6FV7GNxfdm\ `_bWVTQQILLQCcLDYHESCFMVHHRGGOGGLGGHGGEGGBGG9je8VT\ ipUXcPKSKcRe_PaWOZSMWOLTKKPGIMCHJxa4pY6hV8aSAUPBNM\ DFJFHZBJ44G77E99CCCAEEhMBWKDKIFhnVahSWbQQXNKRLELIh\ G7cG9ZGAVGBQGCLGDHGECGFiIkaHdUHZNGSFGMhJkZIcQHWHGO\ lpmfkhafdXb`SYXNTSIPODKKyiRBmhAd`9XU8ONM_9JWBHTCFQ\ DCMEAJFlf6ea8ZYASTBLPDEKFhW60cw4Savl3XWAulFdaGhlEh\ q7c3vZ9nUEfQJZLOSHTKCYC8b5E_6KX7QU7WR8aO8gL9mJ9lIC\ lIFlIHlHKlHMlHPlHRdKPXNNQQLITJBWIJUNQTSXRXcQajOfqN\ kxMosKhoIbkGWgEQcCJ_BDkJ7 } frm:F_20160221_1004 { ; Similar to the parallel resistance formula a=real(p1),b=real(p2),d=imag(p1),f=imag(p2), z=0,c1=pixel-p3,c2=pixel-p4: cs=z*z*cos(z)*sin(z), z=1/(1/(cs+c1)+1/(cs+c2)), |z|<100 } -- Mike Frazier www.fracton.org
Mike, Thanks for posting the nice images. I zoomed your first image out in maximum "unzoom"-sized steps to your parent fractal in Richards Fractint for Windows beta 5, and saw lots of pleasant scenery on the way there. - Hal Lane ######################## # hallane@earthlink.net ######################## -----Original Message----- From: Fractint [mailto:fractint-bounces@mailman.xmission.com] On Behalf Of Mike Frazier Sent: Sunday, February 21, 2016 2:18 PM To: Fractint and General Fractals Discussion <fractint@mailman.xmission.com> Subject: [Fractint] Shortarm Castle This fractal mixes two copies of z * z * cos(z) * sin(z) at slightly different locations. The area around the fractal has lots of short arms interconnecting the features. If you zoom in more on the main feature on the right it looks like a castle with six towers. The zoomed in images need arbitrary precision math but the first image works fine with double precison. Here is a link to an image: http://dl.dropboxusercontent.com/u/33642054/image/pr_3cossin-3cossin_BC_1200 _5.jpg A deep zoom into the feature on the left using arbitrary precision math and a different color palette: http://dl.dropboxusercontent.com/u/33642054/image/pr_3cossin-3cossin_CD_640_ 2.jpg A zoom into the castle feature on the right using arbitrary precision math and a different color palette: http://dl.dropboxusercontent.com/u/33642054/image/pr_3cossin-3cossin_DD_640_ 5.jpg The FractInt compatible PAR file for the first image is: Shortarm_Castle { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20160221_1004 passes=1 float=y center-mag=-0.6417820664871355/0/9172173044.248877\ /1/0/0 params=1/1/0/0/-1/0/1/0/0/0 maxiter=2000 inside=0 periodicity=6 colors=vQ1h_FViSIsdGnREiDCe0Ec8GaGI_OKYW000MWcOUkQ\ SrTUrWWrZYra_rdargcridrjYokSlkMjlGglAej9Zh8Sf8Ld7E\ c77_A8WD8SG9PJ9RELSAXT5hU1tha9VaLIaX8GHEURBNLIuBGn\ CEgDD`EBUF9NG7ct8S_I53G86EA9CCBAEEGkOCWKSk8NcAIWCD\ OE80P84N87L8AJ8DHhWEaTFWQFQOFKLGEIGdNYOJPaz3NbAPVV\ KRRGNNCJJ1CO5EKLcNJ`MHYLGVKESJCPIBMH9JGqtjknfeib_d\ ZV_VPVRJQNDLJ5_n6Wh6Tb7QX7MR8JL1Cr3Dj4Eb6FV7GNxfdm\ `_bWVTQQILLQCcLDYHESCFMVHHRGGOGGLGGHGGEGGBGG9je8VT\ ipUXcPKSKcRe_PaWOZSMWOLTKKPGIMCHJxa4pY6hV8aSAUPBNM\ DFJFHZBJ44G77E99CCCAEEhMBWKDKIFhnVahSWbQQXNKRLELIh\ G7cG9ZGAVGBQGCLGDHGECGFiIkaHdUHZNGSFGMhJkZIcQHWHGO\ lpmfkhafdXb`SYXNTSIPODKKyiRBmhAd`9XU8ONM_9JWBHTCFQ\ DCMEAJFlf6ea8ZYASTBLPDEKFhW60cw4Savl3XWAulFdaGhlEh\ q7c3vZ9nUEfQJZLOSHTKCYC8b5E_6KX7QU7WR8aO8gL9mJ9lIC\ lIFlIHlHKlHMlHPlHRdKPXNNQQLITJBWIJUNQTSXRXcQajOfqN\ kxMosKhoIbkGWgEQcCJ_BDkJ7 } frm:F_20160221_1004 { ; Similar to the parallel resistance formula a=real(p1),b=real(p2),d=imag(p1),f=imag(p2), z=0,c1=pixel-p3,c2=pixel-p4: cs=z*z*cos(z)*sin(z), z=1/(1/(cs+c1)+1/(cs+c2)), |z|<100 } -- Mike Frazier www.fracton.org _______________________________________________ Fractint mailing list Fractint@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint --- This email has been checked for viruses by Avast antivirus software. https://www.avast.com/antivirus
If anyone wants to explore this fractal I would suggest using this PAR file instead of the Shortarm Castle one because this one has a color map that works at any zoom. I also made the starting zoom show the search area with all the good stuff. I usually just search along the x axis to save time (there are also some minibrots between the spirals off axis too). The left side has cubic minibrots at the center of the 3 way symmetry features. The right side has some quadratic minibrots and both sides have places that zoom to infinity. Curiously, this fractal is an exception to the pattern I have seen in the past where all the minibrots are the same order. This fractal has the expected cubic minibrots that go with the z^3 terms in the formula and unusual quadratic minibrots that I didn't expect. Here is a link to an image: http://dl.dropboxusercontent.com/u/33642054/image/pr_3cossin-3cossin_AS_640_... The FractInt compatible PAR file for the image is: pr_3cs-3cs_AS { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20160222_0854 passes=1 float=y center-mag=-0.2449348958171875/0/2.237762266986161\ /1/0/0 params=1/1/0/0/-1/0/1/0/0/0 maxiter=2000 inside=0 periodicity=6 colors=000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O\ 40C10000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40\ C10000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C1\ 0000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C100\ 00C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000\ C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C1\ 0O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O\ 40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40\ ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA\ 0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0h\ I0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0\ oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS\ 0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0u\ a0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0ua0\ ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0ua0ym\ 0zy0ym0ua0oS0hI0ZA0O40C10 } frm:F_20160222_0854 { ; Similar to the parallel resistance formula a=real(p1),b=real(p2),d=imag(p1),f=imag(p2), z=0,c1=pixel-p3,c2=pixel-p4: cs=z*cos(z)*sin(z), z=1/(1/(cs+c1)+1/(cs+c2)), |z|<100 } -- Mike Frazier www.fracton.org
participants (2)
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Harold Lane -
Mike Frazier