FOTD -- December 09, 2012 (Rating 5) Fractal visionaries and enthusiasts: Today's image of a strange spiral is located in the Scepter Valley area of the Z^2+C Julibrot. It is sliced in a direction halfway between the Oblate and the Rectangular, and has been stretched and skewed to a rather large extent to bring it to a recognizable shape. The name "Broken Hyperspiral" refers to the infinitely divided nature of the features in the image. This unlimited division, known as 'Cantor Dust', is typical of the Julia sets of points outside the Mandelbrot set, but as today's image shows, it also exists in the odd planes and angles. The image consists totally of points, with no two points being connected. A zoom into one of the sub-spirals will reveal a never-ending chain of similar broken spirals, and this series continues all the way to infinity, which is not an end point or a very large number, but an abstract idea that can never be reached. The rating of a 5 is pretty pathetic by FOTD standards, but it's all I could give the image, which has little more than a bit of pop-math interest going for it. More effort on the coloring might have raised the rating a point or two. The calculation time of 1-3/4 minutes is about average, but perhaps a bit slow for an image with so little reward. The situation is resolved on the web sites. The completed image is posted for instant viewing at: <http://www.crosscanpuzzles.com/Archives.html> with high-definition variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are online at: <http://www.Nahee.com/FOTD/> Clouds ruled the sky today here at Fractal Central, while the temperature of 45F +7C kept things feeling seasonal. The forecasted rain held off until sunset however. Both the cats and humans had a typical uninteresting day. The next FOTD will be posted when it is ready. Until whenever, take care, and if humans ever populate the galaxy, how will they agree on a universal galactic time? (IMO, we will never populate anything but planet earth, so there is no problem.) Jim Muth jimmuth@earthlink.net START PARAMETER FILE======================================= Broken_Hyperspiral { ; time=0:01:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=1 center-mag=+0.03264445237728411/+0.172536526663781\ 00/8438.382/0.1402/79.9353442340639617/73.17794208\ 35490413 params=45/90/0/90/-1.25/0/0/0/2/0 float=y maxiter=2200 inside=255 logmap=-126 periodicity=6 colors=000knUknUloUloTmpTmpSmqSmqRmrRmrRmsQmsQmtPm\ tPmuOmuOmuNmvMmvLkvKiwKhwJfwIdxHcxGaxG_yFZyEXyDVzC\ ayIcyMeyQgyUiyYky`mydoyhqylpykoyjmygjxdhxafxZcwWaw\ T_vQXuN`sT_qSZoRYmQWkQViPUgOTdNSbMQ`MPYLOWKNUJMRIK\ PIJMHIKGHIFGFEEDEGBDI8CK6BM3AO8HQ7MS6RU5WW4`Y3eZ2j\ Z4kZ6kZ8kZAkZCk_EkaGlbIncKodMqfOseQsdSrcUqbWq`Xp_Y\ oZYoYYnWZmVZmUZlTZkSZkQ_jP_iO_iN_hL`gK`gJ`fI`eH`eF\ adEacDacCabAba9ba8b`7b_5cZAbaBcaDdaEdaGeaHfaJgaKga\ MhaNiaOiaQjaRkaTlaUl`Wm`Xn`Zo`_o``p`bq`cq`er`fs`ht\ `it`ku`lv`nw_nw_mw`mw`lwalwakwbjwbjwczzczzdzzdzzez\ zezzfzzfzzgzzgzzhzzhzzizzizzjzzjzzkzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================