October 2010 - Fractint - mailman.xmission.com

FOTD 31-10-10 (Shadow of the Wind [6])
by Jim Muth 31 Oct '10

31 Oct '10

FOTD -- October 31, 2010 (Rating 6) Fractal visionaries and enthusiasts: Today's rather harmless image lies in a valley of the fractal that results when various negative parts of Z^(-4.5) and Z(-1.7) are mixed together and (1/C) is added. Like most fractals of this double-negative type, this parent fractal cannot be des- cribed, though it may easily be seen by backing out of today's image. I rated the image at a 6. I searched for something to justify a higher rating, but nothing is there. The name "Shadow of the Wind" has nothing to do with an old radio hero who could make himself invisible. It's simply a phrase that came to mind from apparently nowhere. The calculation time of 9 minutes means that the time required to run the parameter file is more than the resulting image is worth. The problem may be eliminated by viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> Too many clouds and a temperature of 54F 12C kept the fractal cats suppressed here at Fractal Central on Saturday. My day was relaxing enough, though for some reason the Halloween trick-or- treaters were out one evening early. The next FOTD will be posted in 24 hours. Until then, take care, and if a spook spooks you, spook him back. (They do exist, you know. Whether they are real is another question.) Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Shadow_of_the_Wind { ; time=0:09:02.88-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=+0.56620315067701/+0.03728036351951/\ 8.3e+009/1/2.5/0 params=-0.6/-4.5/-3.6/-1.7/0/0/0/0 maxiter=10000 inside=0 logmap=1140 periodicity=6 colors=000HChCAkF7mE5oE3qD4oD5nC6mC7kB8jB9iAAgABf9\ Ce9Cd9Db8Ea8F`7GZ7GY6IX6JVCHU5LT5LSFHU8JVAIWHGYDGZ\ EF_JEaHDbJCcMBeLBfNAgP9iQ8jR7kS6mU5nW4oQ3kZ2r_1sN3\ iU2mO3gI3aC4V65P05JA7EJ8ASA5`B1bD2cF3dH4fJ5gL6hN7i\ P8kR9lTAmVBnXCpZDq`ErbFsdGufHvhIwjJxkKuiLrgMoeNlcO\ iaPf_QcYR`XRYVSVTTSRUPPVMNWJLXGJYDIYDIdDIkDIrAXm7k\ h4zdCqcJhcQ_bXRbcIaj9aq1ao3`n4_m5_k6Zj7Zi8Yh9XfAXe\ BWdCWcDVaEV`FU_GTZHTXISWJSVKRULRTMQTMQTNP1BF19G8CI\ EEKKGMQIOXKQbMShOUnQVlTWjVWhXWf_WdaWccWdeTefQfhNgi\ LhkIilFjnCkoAbf8VY6MQ4EH26905EA4JK4NU3Sc2Xm2`w4Xr6\ Un7Ri9OeBKaCHXEETFBPEJXDRcDYjLdXSkJEU8KTBPSEVRH_RK\ Vw8RvANvCJuDFuFBuG9qP8mY7if6eoRShkEacH_XKYQNWJQUCT\ S5WR6YX6Zb6_g6`m6arKVhXPZiIPvCGsSGqfGouGgqN`nUTk`M\ ggEdn7au5dm3fe1hY0jQEfTRcWd`ZqY`y8FtIMoRTfYZYddPki\ Gzo8ztAzmBzfCz_DzTEzMFzFBzQ8z_5zi2zsKzr`zrqzrmzliz\ ffz`bzVZzPWzK1zB1zC1zD1zE } frm:MandAutoCritInZ {; 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)+(p4)), k=real(p3)+1, esc=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < esc } END PARAMETER FILE=========================================

1 0

Plant Scales
by Roger Alexander 30 Oct '10

30 Oct '10

I let my imagination run wild when I generated today's post and I thought I saw scales on a plant. The Oct. 28 post (Swirly Wallpaper) formula with different parameters. Ready made at http://maxitersfractalfollies.blogspot.com Green Scales { ; fract491.gif ; blank ; calctime 0:00:42.19 ; created Oct 29, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=kerrym.frm formulaname=LKM-quiltm2 function=cos/cosxx center-mag=-0.899274/-0.684337/0.3272439/1/180 params=1.75/-0.875/0.375/-0.375 float=y maxiter=1500 inside=0 decomp=256 periodicity=0 colors=0F00F00F00F00F00G00G00G00G00H00H00H00H00H00I00I00I00I00J00J00J00J\ 00J00K00K00K00K00L00L00L00L00L00M00M00M00M00N00N00N00N00O00O00O00O00O00P\ 00P00P00P00Q00Q00Q00Q00Q00R00R00R00R00S00S00S00S00S00T00T00T00T00U00U00U\ 00U00U00V00V00V00V00W00W00W00W00X00X00X00X00X00Y00Y00Y00Y00Z00Z00Z00Z00Z\ 00_00_00_00_00`00`00`00`00`00a00a00a00a00b00b00b00b00b00c00c00c00c00d00d\ 00d00d00e00e00e00e01e01e01e02e02f02f03f03f03f04f04g05g05g05g06g06g06g07h\ 07h07h08h08h08h09i09i0Ai0Ai0Ai0Bi0Bj0Bj0Cj0Cj0Cj0Dj0Dj0Dk0Ek0Ek0Fk0Fk0Fk\ 0Gl0Gl0Gl0Hl0Hl0Hl0Il0Im0Im0Jm0Jm0Km0Km0Kn0Ln0Ln0Ln0Mn0Mn0Mo0No0No0No0Oo\ 0Oo0Po0Pp0Pp0Qp0Qp0Qp0Rp0Rq0Rq0Sq0Sq0Tq0Tq0Tr0Ur0Ur0Ur0Vr0Vr0Vr0Ws0Ws0Ws\ 0Xs0Xs0Ys0Yt0Yt0Zt0Zt0Zt0_t0_t0_u0`u0`u0`u0au0au0bv0bv0bv0cv0cv0cv0dw0dw\ 0dw0ew0ew0ew0fw0fx0gx0gx0gx0hx0hx0hy0iy0iy0iy0jy0jy0kz0 } frm:LKM-quiltm2 {; Kerry Mitchell ; quilted backgrounds ; uses 2 iterations of 2 mandelbrot variables with different c's ; c1 and c2 are tiled periodically, with different frequencies ; z1 & z2 are multiplied together to add their angles ; use "decomp=256" coloring ; r=bailout=0 for swirly exteriors and no interiors ; real(p1), imag(p1) = x1, y1 frequencies for c1 ; real(p2), imag(p2) = x2, y2 frequencies for c2 ; try different fn1 and fn2 for added joy x=real(pixel), y=imag(pixel) a1=pi*real(p1), b1=pi*imag(p1) a2=pi*real(p2), b2=pi*imag(p2) x1=2*cos(a1*x), y1=2*cos(b1*y) x2=2*sin(a2*x), y2=2*sin(b2*y) c1=x1+flip(y1), c2=x2+flip(y2) z1=c1, z2=c2, r=0: z1=sqr(z1)+c1, z2=sqr(z2)+c2 z=fn1(z1)*fn2(z2) |z| < r ;SOURCE: lkm.frm } Roger Alexander

1 0

FOTD 30-10-10 (Reciprocal World [6])
by Jim Muth 30 Oct '10

30 Oct '10

FOTD -- October 30, 2010 (Rating 6) Fractal visionaries and enthusiasts: Today's image is an afterthought. On Friday I was exploring the (-Z)^(1.5)+C Mandeloid, with no thought of finding a FOTD there, but when I stumbled upon today's image, it struck me as so unusual that I decided to declare it FOTD for October 30. Actually, what we have here is a scene in the Mandeloid that results when the formula is iterated with Z initialized at -0.5. I named the image "Reciprocal World" because of the apparent negative curvature of the surface at the bottom of the frame. If this were a real planet, it would be in the shape of a pseudo- sphere. The rating of a 6 makes the 4-1/2 minute calculation time barely worth the effort. I recommend viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> Friday turned blustery here at Fractal Central, with alternating periods of sun and heavy clouds, and even a few light showers. The temperature of 48F +9C was too chilly for the fractal cats, who grew tired of watching the blowing leaves and spent most of the day sleeping near the heat or asking for their treats. My day was slightly busy, but nothing to get excited about. The next FOTD is due to be posted in 24 hours. But if an unexpected antiquing trip comes up on Saturday, it could be dalayed how- ever. Until whenever, take care, and be filled with wonder. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Reciprocal_World { ; time=0:04:26.88-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot5 passes=1 float=y center-mag=-0.0079014/+0.7369293/90/1/-72.5/0 params=0/0/0/0/0/0/-0.5/0/1.5/0 maxiter=24000 inside=0 logmap=-120 colors=000KAHKAIKAJKAKKALKBMKCNJDOIENHFMGGLFHKEIKD\ IJCIIBIHCIHAIIDHJEGKEFLFEMFEMHFNJFNLGQNHUPKZRMcSOh\ UQmWSrYUv_VzaWzbWzdWzfXzhXzjXzlXzmXzlYzlZzl_zk`zka\ zkbzkczjdzjezjfzifzigzihziizhjzhkzhlzgmzgnzgozgozh\ pzipzipzjpzkqzkqzlqzmqzmrznrzorzorzpszqszqszrszztz\ ztzztzztzzuzzuzzuzzuzzpzzkzzfzzazzYzzXzzWzzWzzVzzV\ zzUzzTzzTzzSzzSzzRzzQzzQzzPzzPzzOzzNzzNzzMzzMzzLzz\ LzzJzzHzzFzzEzzEzzEzzEzzEzzEzzEzzAzzEzzHzzKzzOzzRz\ zUzzYzz`zzczzgzzjzzmzzqzzszzrzzpzzozznzdmzekzfjzfi\ zggzgfzheziczibzjazj`zkZzlYzlXzmVzmUznTznSzlUzkVzj\ XziYzhZzg`zfazebzddzcezbfzahz`iz_jzZlzYmzXnzWpzVqz\ UrzSqzRqzPpzOpzNozLozKnzJnzHmzGmzFlzDlzCkzBkz9jz8j\ z6kz7jz8jz8jz9jzAjzAizBizCizCizDizEhzEhzFhzGhzGhzH\ hzIgzIgzJgzKgzKgzLfzMfzMfzNfzOfzOfzPfzPgzQgzQgzHdz\ QgzZjzgmzppzxszxqzxpzxnzxmzxkzxjzxhzxgzxfzxdzxczxa\ zx`zxZzxYzxXzuYzsYzqYznYz } frm:SliceJulibrot5 {; 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=========================================

1 0

Swirly Wallpaper
by Roger Alexander 29 Oct '10

29 Oct '10

A Fractint generated fractal with nary a minibrot in sight! Fractint - a little something for everybody. And for those who the whole point of the internet is clicking on links for instant satisfaction try http://maxitersfractalfollies.blogspot.com Swirly Wallpaper { ; fract486.gif ; blank ; calctime 0:00:41.91 ; created Oct 28, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=kerrym.frm formulaname=LKM-quiltm2 function=tan/sinh center-mag=1.33227e-015/-4.44089e-016/0.4644958 params=0.1115146336252937/0.4293343913083285/1.394390697958312/1.4464552\ 75124363 float=y maxiter=1500 inside=0 decomp=256 periodicity=0 colors=05F05F05F16G16G16G16G16G27H27H27H27H27H38I38I38I38I38I49J49J49J49\ J49J5AK5AK5AK5AK5AK6BL6BL6BL6BL7CM7CM7CM7CM7CM8DN8DN8DN8DN8DN9EO9EO9EO9E\ O9EOAFPAFPAFPAFPAFPBGQBGQBGQBGQBGQCHRCHRCHRCHRCHRDISDISDISDISDISEISEJTFJ\ TFKTGKUGLUHLVHMVIMVINWJNWJOWKOXKPXLPYLQYMQYMRZNRZNSZOS_OT_PT_PT`QU`QUaRV\ aRVaSWbSWbTXbTXcUYcUYcVZdVZdW_eW_eX`eX`fYafYafZbgZbg_ch_ch`ch`diadiaeibe\ jbfjcfjcgkdgkdhlehleilfimfjmgjmgknhknhlniloimojmpjmpknpknqloqloqmprmprnq\ snqsorsortpstpstqtuqturuuruvsvvsvwtwwtwwuxxuxxuxxvyyvyywzzvyyvyyuxxtxxtw\ wsvwsvvruvquuqtupstostorsnqsnqrmprlpqloqknpjnpjmoimohlnhkngkmgjmfjleileh\ kdhkcgjcfjbfibeiaeh`dh`cg_cgZbfZbfYaeX`eX`dW_dW_cVZcUYbUYbTXaSWaSW`RV`RV\ _QU_PTZPTZOSYNSYNRXMQXLQWLPWKPVKOVJNUINUIMTHLTGLSGKSFKRFJREIQDIQDHPCHPBG\ OBFOAFN9EN9EM8DM8CL7CL6BK6AK5AJ49J49I38I37H27H16G16G05F } frm:LKM-quiltm2 {; Kerry Mitchell ; quilted backgrounds ; uses 2 iterations of 2 mandelbrot variables with different c's ; c1 and c2 are tiled periodically, with different frequencies ; z1 & z2 are multiplied together to add their angles ; use "decomp=256" coloring ; r=bailout=0 for swirly exteriors and no interiors ; real(p1), imag(p1) = x1, y1 frequencies for c1 ; real(p2), imag(p2) = x2, y2 frequencies for c2 ; try different fn1 and fn2 for added joy x=real(pixel), y=imag(pixel) a1=pi*real(p1), b1=pi*imag(p1) a2=pi*real(p2), b2=pi*imag(p2) x1=2*cos(a1*x), y1=2*cos(b1*y) x2=2*sin(a2*x), y2=2*sin(b2*y) c1=x1+flip(y1), c2=x2+flip(y2) z1=c1, z2=c2, r=0: z1=sqr(z1)+c1, z2=sqr(z2)+c2 z=fn1(z1)*fn2(z2) |z| < r ;SOURCE: lkm.frm } Roger Alexander

1 0

FOTD 29-10-10 (Offside [6])
by Jim Muth 29 Oct '10

29 Oct '10

FOTD -- October 29, 2010 (Rating 6) Fractal visionaries and enthusiasts: Today's scene lies off to the side of the large period-2 bud of the Mandelbrot set at an angle of 90 degrees. But since there is a complete 360-degree circle of lines in the Julibrot perpen- dicular to the M-set, we must be more specific. Today's image lies in the direction of the imag(Z) axis, and is centered at the point 0.78615 on that axis. The image is not a perturbed Mandelbrot set. It is rotated at an angle of -19.37 degrees from the Mandelbrot orientation, the angle at which it is tangent to the edge of the Julibrot in the Elliptic orientation. When rendered in the conventional manner, today's image is a rather boring fractal. The Fractint program cures this monotony with its various inside and outside fills. I rendered today's image with the outside set to 'real' and the inside set to 'bof61'. I could rate the image no higher than a 6. It has too much program magic and not enough true fractal stuff for any higher rating. I named the scene "Offside" because it lies off to the side of the large bud on the main stem of the M-set. The calculation time of under 6 seconds is brief enough to hold disappointment at bay if the resulting image is seen as lacking. The easiest way to view the image is to visit the FOTD web site at: <http://www.Nahee.com/FOTD/> where it is posted already calculated and ready to be appreciated at leisure. With a temperature of 68F 20C and sunny skies, Thursday was pleasant enough here at New Fractal Central, though the wind was a bit too blustery for absolute comfort. The fractal cats spent most of their time in the window, watching occasional flurries of leaves that fluttered past on the gusts. My day was uneventful; FL's day was the same. The next FOTD will be posted in 24 hours. Until then, take care, and a month ago my broker told me I could make a pile in the guano market, but I must have done something wrong because I dropped a load. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Offside { ; time=0:00:05.59-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=0/-0.0000596\ 847054883/272487.8/0.0009874/90/0 params=-19.37/0/\ 0/90/-1/0/0/0.78615/2/0 symmetry=none inside=bof61 float=y outside=real maxiter=1500 periodicity=6 colors=000WuVTtYQt`NtcKsfHsiEskDGyCleAe_8ZU7SO5LIz\ uCzr6xoJrfFhYCXQ9QH6J83d38Y26R25K14D126mzNRzI`mDS`\ 9IP49CTnyPwzLaiIVaEPVAJN7CF367eJdaidU_WMROFIG798Zt\ DNa8BJ4I1cF0YC0SA0M70H50B205AWz8Sr7Oj6Kb5GV3CN28F1\ 47I1OueoaSYJEHhVxaQoWMfPHYJDQC8H648IP3EK2AF17A1350\ YO9MG6B834Xw2Mc1BKcUIGoqYFkYYxTTpPPhLLaHHUCCM88F44\ 7iswWtbGSJeMyRkOLaJGSEAJ9594Lg4AM2bQcXMYRISMEMiTWi\ QXgS_`_m`Zn`Yo`Xn`Wm_VkYUiVRfTQbQO_cMWmPhzWHyVHzbI\ v`IrbImeJhhJcjJZlIUnHPpGRrFYtEcuEanL`hSZaZYWdRRYLN\ RFIK9EDHJHPOLXTPdYTlaX_bONcFAd69c58b47a42SF8SNDSVB\ OQ9KM7GH5CD388144CIR5_e4SX3LP2EG178XorShkObdKWYGQR\ CJK8DD466cdpUUbKKQAADJlUE_M9OF4C7PT8IL6CE46721Q30L\ 20H20D1081040gF_ZCSQ9LH6E837ZZtQQeHHS88ETs9Oi7J`6E\ S49I3491sNGgICXD9M96B43nRdPDKMSLGLFBEA575B`zip3UZ2\ FH15OC3G8184hKHUDBF65cKveQrgWnhajbYeYVaSSYNPUHLQCI\ M6FI1CE9MHHVJOdLWmNbvPZuS } 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=========================================

1 0

Spheres Within Spheres
by Roger Alexander 28 Oct '10

28 Oct '10

Today's fractal is from Fractint's built in formula fn(z*z). The design is of spheres within spheres colored in blue and cyan. Ready made at http://maxitersfractalfollies.blogspot.com Cyan Spheres { ;fract487.gif ; blank ; calctime 0:00:31.09 ; created Oct 28, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=fn(z*z) function=log center-mag=1.56626/-0.0173035/0.7732086/1.0031/90/3.88578058618804789e-0\ 16 maxiter=3000 inside=0 outside=atan cyclerange=0/255 colors=hzzgzzfzzezzdzzczzbzz`zz_zzZzzYzzXzzWzzVzzTzzSzzRzzQzzPzzOzzMzzLz\ zKzzJzzIzzHzzGzzEzzDzzCzzBzzAzz9zz7zz6zz5zz4zz3zz2zz0zz0zz0yz0yz0xz0wz0w\ z0vz0uz0uz0tz0sz0sz0rz0qz0qz0pz0oz0oz0nz0nz0mz0lz0lz0kz0jz0jz0iz0hz0hz0g\ z0fz0fz0ez0dz0dz0cz0bz0bz0az0az0`z0_z0_z0Zz0Yz0Yz0Xz0Wz0Wz0Vz0Uz0Uz0Tz0S\ z0Sz0Rz0Qz0Qz0Pz0Pz0Oz0Nz0Nz0Mz0Lz0Lz0Kz0Jz0Jz0Iz0Hz0Hz0Gz0Fz0Fz0Ez0Dz0D\ z0Cz0Cz0Bz0Az0Az09z08z08z07z06z06z05z04z04z03z02z02z01z00z00z00z00y00y00\ x00x00w00w00v00v00v00u00u00t00t00s00s00r00r00r00q00q00p00p00o00o00n00n00\ n00m00m00l00l00k00k00j00j00j00i00i00h00h00g00g00f00f00f00e00e00d00d00c00\ c00b00b00b00a00a00`00`00_00_00Z00Z00Z00Y00Y00X00X00W00W00V00V00V00U00U00\ T00T00S00S00R00R00R00Q00Q00P00P00O00O00N00N00N00M00M00L00L00K00K00J00J00\ J00I00I00H00H00G00G00F00F00F00E00E00D00D00C00C00B00B00A } Roger Alexander

1 0

FOTD 28-10-10 (Curious Coincidence [No Rating])
by Jim Muth 27 Oct '10

27 Oct '10

FOTD -- October 28, 2010 (No Rating) Fractal visionaries and enthusiasts: Today's image gets no rating. Why? Because it's a virtual repeat of yesterday's image. The difference is that, while yesterday's image was sliced in the Oblate direction, today's is sliced in the Rectangular direction, which consists of the imag(Z) and imag(C) axes of the Julibrot. IMO, what made yesterday's scene so curious is the fact that the fractal terminates on the left and right at values of plus and minus 1.618...., (the golden ratio), while the large valleys meet at plus and minus 0.618...., the reciprocal of the golden ratio). This is curious enough, but when I checked the horizontal terminal points of today's image, I found a value of plus and minus 0.78615.... What an incredible coincidence it is that this is the reciprocal of the square root of the golden ratio. (The two large valleys in today's image meet at plus and minus 0.521555...., though I have yet to find anything significant in this value.) Mathematical interest aside, today's image is simply a variation on yesterday's image, with the same color palette. Those who enjoyed yesterday's will enjoy today's almost as much. Those who thought yesterday's image was boring will be no more impressed by today's. The name "Curious Coincidence" refers to the mathematical aspect of the image. The calculation time of only 3 seconds is mercifully brief. The best way to view the image is to enjoy it already calculated on the FOTD web site at: <http://www.Nahee.com/FOTD/> Wednesday began with clouds here at Fractal Central. But the clouds broke up by midday, leading to a sunny afternoon with a temperature of 72F 22C. These conditions were perfect for the fractal cats, who spent several hours in the sun that streamed in the southwest window. My day was average; FL had a similar day. The next FOTD will be posted in 24 hours, and is likely to be another mathematical curiositiy, though one with far more artistic impact. Until then, take care, and why does the number epsilon equal minus one when it is raised to the power of imag(PI)? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= CuriousCoincidence { ; time=0:00:03.35-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=0/0/1.398/1/\ 90/0 params=90/0/0/90/-1/0/0/0/2/0 float=y inside=0 maxiter=300 inside=0 outside=real periodicity=6 colors=000KZzJXwJVsJTpJRmJQjJPgJNeJMbJL`IKYHJVGISF\ HPEGMDFJCDFBBCA8A958GQKJYKMeKPmKUmKZmKcmKhmKmmIrmF\ vmCzjHzhNzeSzcXzbTzaPz`Lz_HzZDzZ9zSCzLFzEHz7Kz1Mz6\ OzAPzFRzJSzNTzSSzXSzaRzfRzhRzjRzlRzmRzoRzqRzrRzzOz\ zLzzIzzFzzKzzOzzTzzXzzVzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ 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=========================================

1 0

Twilight Colors Reprised
by Roger Alexander 27 Oct '10

27 Oct '10

Today's fractal is a remix of my Oct. 24 post. Same formula and palette, different parameters. Like the Oct.24 post ready made at http://maxitersfractalfollies.blogspot.com Twilight Remix { ; fract484.gif ; blank ; calctime 0:17:07.88 ; created Oct 26, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=kerrym.frm formulaname=hermanm_man-polar center-mag=-1.89610111352240000/+0.00222840388810970/9616.574/1/22.49999\ 99999827232/-2.86882184674652763e-011 params=4/2/1/60/3/0 float=y maxiter=1500 inside=0 proximity=1 outside=fmod decomp=256 colors=000302403503504604705805806907A07B08B08C09D1AE1AF1BF1BG1CH1CI1DI1\ EJ1EK1FL1FL1GM1GN1HO2IN2KM2NK2QJ2TH2VG2YE2`D2cB1fA1i81l71n51q41t21w00z03\ z07z0Bz0Fz0Jz0Nz0Rz0Vz0Zz0bz0fz0jz0nz0rz0vz0zz0xz0vz0tz0rz0pz0nz0lz0jz0h\ z0fz0dz0bz0`z0Zz0Xz0Wz0Uz0Sz0Qz0Oz0Mz0Kz0Iz0Gz0Ez0Cz0Az08z06z04z02z00z00\ y10x20v20u30s40r50p50o61n71l81k91i91hA1gB1eC1dC1bD1aE1_F1ZF1YG1WH1VI1TJ2\ SJ2RK2PL2OM2MM2LN2JO2IM2GJ2EH2CE1AC18916614312000101302503605806A07C19D1\ 9E1AF1AF1BG1BH1CI1DI1DJ1EK1EL1FL1FM1GN1HO2IO2JQ2IS2HV2GX2F_2Da2Cd2Bf2Ah1\ 9k18m17p15r14u13w12z00z20z50z70zA0zC0zF0zH0zK0zM0zP0zR0zU0zX0zZ0za0zc0zf\ 0zh0zk0zm0zp0zr0zu0zw0zz0zw0zu0zr0zo0zl0zj0zg0zd0za0z_0zX0zU0zS0zP0zM0zJ\ 0zH0zE0zB0z80z60z30z00x01v02s03q04n06l07i08g19e1Ab1B`1CY1EW1FT1GR1HO2JN2\ IM2HK2GJ2FH2DG2CE2BD2AB19A18817715514413212000000101201 } frm:hermanm_man-polar { ; Kerry Mitchell 16feb98 ; ; real(p1) = z exponent (use integer >= 2; m=n-1) ; imag(p1) = g exponent (integers) ; real(p2) = alpha magnitude (try 1) ; imag(p2) = alpha polar angle (try integers) ; real(p3) = critical point selector (>0 for positive root) ; imag(p3) = unused (<0 for negative root) ; use decomp=256 ; zero and infinity bailouts hardcoded to 1e-6, 1e6 ; coloring speed hardcoded to 4 ; c=pixel, iter=1, n=real(p1), m=imag(p1), nfac=2*n-1 maxr=1e6, minr=1/maxr, speed=4*pi/128 r=real(p2), t=imag(p2), alpha=r*(cos(t)+flip(sin(t))) oln=1/log(n), fac=log(0.5*log(maxr)) c2=sqr(c), hypnum=sqr(n)+sqr(m), pn=1 hypden=sqr(n-m), hypfac=hypnum/hypden if (real(p3)<0) pn=-1 end if if (real(c2)>hypfac) pn=-pn end if if (imag(c)<0) pn=-pn end if afac=c*n, bfac=c2*(n-m)+(n+m), cfac=c*n d=sqrt(bfac*bfac-4*afac*cfac) z=(bfac+pn*d)/(2*afac) : g=(z-c)/(1-c*z), z=alpha*z^n*g^m iter=iter+1, r=|z| ; ; orbit trap around 0 ; renormalize iteration count via decomp angle ; set "iteration done" flag (iter=-1) ; if (r<minr) angle=(iter+oln*(fac-log(log(cabs(z)))))*speed z=cos(angle)+flip(sin(angle)) iter=-1 end if ; ; orbit trap around infinity ; renormalize iteration count via decomp angle ; add pi to angle to separate from 0 orbit trap ; set "iteration done" flag (iter=-1) ; if (r>maxr) angle=(iter+oln*(fac-log(log(cabs(z)))))*speed angle=angle+pi z=cos(angle)+flip(sin(angle)) iter=-1 end if iter>0 } Roger Alexander

1 0

FOTD 27-10-10 (A Golden Slice [5])
by Jim Muth 27 Oct '10

27 Oct '10

FOTD -- October 27, 2010 (Rating 7) Fractal visionaries and enthusiasts: The formula behind today's image is Z^2+C, the same formula that creates the Mandelbrot set and all its associated Julia sets. But today's image is obviously not the M-set, nor is it any recognizable Julia set. It is something I call an Oblate set, a hybrid set half-Mandelbrot and half-Julia. The X-axis of the image is the real(Z) axis of the Julibrot, while the Y-axis is the imag(C) axis. The image has a Mandel- brot nature in its vertical direction and a Julia nature in its horizontal direction. The center of the image is the center of the large period-2 bud of the M-set. No shape manipulation such as stretching or skewing was done in the creation of the image, though I did add a bit of life by rendering it with the outside set to 'real'. A most curious relation exists in the location of the elements along the X-axis of the image. The fractal terminates on the left and right at the points plus and minus 1.61803398875.... which of course is the Golden Ratio, while the two major valleys closest to the center meet at plus and minus 0.61803398875.... which is the reciprocal of the Golden Ratio. There must be a logical reason why this is so, though I have not been able to find it. I rated the image at a 7, a good part of which is due to the mathematical interest. Artistically, the image rates a 5 or 6. I named the image "A Golden Slice" because of the appearance of the Golden Ratio in it. Despite all the golden glitter, the image is blazingly fast, finishing on my machine in under 3 seconds, almost as fast as the display can switch to super-VGA mode. The trip to see the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> may not be quite as fast, but it will involve much less set-up work. Rain fell most all Monday night here at Fractal Central. The remaining clouds blocked the sun on Tuesday, but the temperature of 70F 21C was mild enough that the lack of sun was never noticed. The fractal cats spent an hour chasing a mechanical toy mouse we picked up Monday evening. Nicholas finally killed it when its battery went flat. The rest of the day was occupied with routine work. Remembering yesterday, I dared not ask FL what was happening on the Spanish channel. The next FOTD will be posted in 24 hours. It should be no surprise if another odd slice of the Z^2+C Julibrot shows up. Until then, take care, and let your negative side shine through. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= A_Golden_Slice { ; time=0:00:02.85-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=0/0/0.7544715 params=0/0/90/0/-1/0/0/0/2/0 float=y maxiter=300 inside=0 outside=real periodicity=6 colors=000KZzJXwJVsJTpJRmJQjJPgJNeJMbJL`IKYHJVGISF\ HPEGMDFJCDFBBCA8A958GQKJYKMeKPmKUmKZmKcmKhmKmmIrmF\ vmCzjHzhNzeSzcXzbTzaPz`Lz_HzZDzZ9zSCzLFzEHz7Kz1Mz6\ OzAPzFRzJSzNTzSSzXSzaRzfRzhRzjRzlRzmRzoRzqRzrRzzOz\ zLzzIzzFzzKzzOzzTzzXzzVzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ 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=========================================

1 0

Benoit Mandelbrot, Mathematician, Dies at 85
by Paul N. Lee 26 Oct '10

26 Oct '10

His death was caused by pancreatic cancer: http://www.nytimes.com/2010/10/17/us/17mandelbrot.html Sincerely, P.N.L. -------------------------------------- http://www.Nahee.com/PNL/Fractals.html http://www.Nahee.com/Fractals/

1 1