November 2010 - Fractint - mailman.xmission.com

Threaded Julia
by Roger Alexander 05 Nov '10

05 Nov '10

Today's post is another formula by Kerry Mitchell based on the Julia iteration loop. Gif and jpg version available at http://maxitersfractalfollies.blogspot.com Threaded Julia { ; fract499.gif another Julia iteration loop fractal ; blank ; calctime 0:05:22.08 ; created Nov 04, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=kerrym.frm formulaname=km_08 center-mag=-0.730914/0.135225/2.109705 params=0.5243385113071077/0.07968382824182867/-0.8776207770012513/-0.809\ 0762047181616/-0.5746330149235511/0.3112582781456953/-0.8414868617816705\ /0.2847071749015778 float=y maxiter=1500 inside=0 decomp=256 periodicity=0 colors=000734633523422312211101000000100200311411512612723823924A34B35B3\ 5C46D46E46F47G57H58I58J69K69L6AM6AN7BO7BP7BQ8CR8CS8DT9DU9EU9EV9FWAFXAGYA\ GZBH_BH`BHaCIbCIcCJdCJeDKfDKgDLhELiEMjEMkEMlFNlFNmFOnGOoGPpGPqHQrHQsHRtH\ RuISvISwJTwJTwKUwLVwLVwMWwNWwNXwOXwPYwQYwQZwRZxS_xS_xT`xU`xUaxVbxWbxWcxX\ cxYdxZdxZex_ex`fx`fxagxbgxbhxchxdiyejyejyfkygkyglyhlyimyimyjnyknykoyloym\ pynpynqyoqyprypsyqsyrtyrtzsuztuztvzuvzvwzwwzwxzxxzyyzyyzzzzzzzyyzxxzxxzw\ wzvwzvvzuvztuztuzstzrtzqszqszprzorzoqynqympympyloykoyknyjnyimyimyhlyglyg\ kyfkyejyejydiychybhybgyagy`fy`fy_eyZeyZdyYdyXcyXcyWbyVbxVaxUaxT`xT`xS_xR\ _xQZxQZxPYxOYxOXxNXxMWxMWxLVxKUwJTvJTuJTtISsISrIRqIRpHQoHQnHPnGPmGOlGOkF\ NjFNiFNhFMgEMfELeELdDKcDKbDJaCJ`CI_CIZCHYBHYBHXBGWAGVAFUAFTAES9ER9DQ9DP8\ CO8CN8BM7BL7AK7AJ7AI69H69H68G58F57E57D46C46B45A45934834 } frm:km_08 { ; Kerry Mitchell 11may98 ; originally conic-near_jul16 ; tweaked by rjr 2k04 to allow user to directly input ; julia parameters previously hardcoded to 0.2882,0.0106 cc=p4, zc=pixel, maxr=1e12, minr=maxr, iter=1 a=real(p1), b=imag(p1), c=real(p2), d=imag(p2) e=real(p3), f=imag(p3): iter=iter+1, zc=sqr(zc)+cc, x=real(zc), y=imag(zc) conic=|x*(a*x+b)+y*(c*y+d)+e*x*y+f| if (conic<minr) minr=conic end if if ((|zc|>maxr)||(iter==maxit)) iter=-1 t=log(minr) z=cos(t)+flip(sin(t)) end if iter>0 } Roger Alexander

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FOTD 05-11-10 (Order-Three Nonsense [No Rating])
by Jim Muth 05 Nov '10

05 Nov '10

FOTD -- November 05, 2010 (No Rating) Fractal visionaries and enthusiasts: I rather enjoyed the half-and-half view of Seahorse Valley that I posted as the FOTD for yesterday. Today I decided to take it one step further and see what would happen if I calculated the same type of view of North Valley. The result is today's image. The image closely resembles yesterday's, with the outer shape being the familiar Julia set of the area, with the bloated Mandelbrot-valley aspect filling the inside. At first glance, today's image appears to have origin symmetry. A second glance however reveals that it has no symmetry. An even greater change is in the periodicity. In yesterday's image the blunt spirals had two arms; in today's image there are three arms in each spiral. I re-used the same color palette to bring out the similarities in the images. But this makes today's image too much of a repeat for an honest rating. I let it go with no rating. The name "Order-Three Nonsense" refers to the periodicity of the area of the Julibrot pictured in the image. The calculation time of 46 seconds is just about what the image is worth. The most convenient way to view the Julia-Mandelbrot nonsense is to view the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> Heavy clouds, steady rain, and a temperature of 46F +8C spoiled outdoor plans here at Fractal Central on Thursday. Luckily, with no outdoor plans, the fractal cats were satisfied indoors, lying by the heat. My day was tranquil enough, which means enough work to keep my thoughts reasonably free of politics, philosophy and personal opinions in general. Now that gardening season has ended, FL found herself with more spare time than she knew what to do with, but a latin soap-opera soon filled the empty time. (I wish I understood Spanish.) The next FOTD, even higher-order nonsense, will be posted in 24 hours. Until then, take care, and will there ever come a day when someone discovers the last fractal? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= OrderThreeNonsense { ; time=0:00:46.52-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=1 symmetry=none center-mag=-0.0201592/-0.0270368/0.9861933/1/58.5/0 params=87/0/87/58.7/-0.125/0.66/0/0 float=y maxiter=2700 inside=0 logmap=yes periodicity=6 colors=000REQSESUEUWEXYFZ_G`aHbcIeeJigKmiLqkMtmNwk\ OziPygQxeRwcSvaTu_UtYVqWWnUXkSYiQZfOZcMYaKXZIWWGVU\ EURCTOASM8RJ6QG4PE5OF5NF5MF5LF5KG5KG5KG5KG6KH6KH6K\ H6KH6KI6KI6KI6KI8KH9KGALGBNFDQEESEFUDGWDIZCJ`BKbBL\ dAMfAQbET_IWXMZUQbQTeNXhK`kHdnEgoFfoFepFdpGdqGcqGb\ rGarHasH`sH_sH_uL`vO`wR`xVayYaz`asaYlaUebRZbNScKLc\ GEdD7d91d5AdFFdPKeZUeccehmfhlfdiecfdbcca`b`Za_W`ZT\ _YQZWNYVLXUIWTFVSCUR9TQ7TPEXOL`OSdNZgNcdRMlCOpDMlC\ LiCMfCNcCO`CPYBQVBSSBUPBWMBYJB_GAaDAcAAc7Ac4Ac1Ac3\ Cc5Dc6Ec8Fc9HcBIZCJUEKPFMKHNFIOAKP5MR3NS3PT3QU3SW3\ TX4VY4W`4Yc4Zh4`m4ar4cv4ez4fz5iz5jz5lz5nz5oz5oz5pz\ 5pz5pz3qz5qz6qz8rz9rzBrzCszDszFszGtzItzJtzKuzMuzNu\ zPvzQvzSvzTwzUwzWwzXwzZwz_wz_wzawzbwzcwzdwzewzfwzh\ wziwzjwzkwzlwzmwzowzpwzqwzqwzqwzqwzqwzrwzrwzrwzrwz\ rwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrw\ zrwzrwzrwzrwzrwzrwzrwzrwz } frm:SliceJulibrot2 {; 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), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD?
by JackOfTradeZ＠comcast.net 05 Nov '10

05 Nov '10

. I dont see any FOTD posted after Oct 27 2010. ? Is there a problem or did the site move again?? .

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Yesterday's Post
by Roger Alexander 04 Nov '10

04 Nov '10

Today's fractal is the Nov. 2 formula with a new map and different parameters. And at good ole http://maxitersfractalfollies.blogspot.com is yesterday's post re-sampled. Yesterday's Post { ; fract498.gif ; blank ; calctime 0:13:29.11 ; created Nov 03, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=kerrym.frm formulaname=km_10 center-mag=-0.63921378791777690/+0.42946123624707840/231.2811 params=-0.2080599383526109/1.29938962981048/-0.510940885647145/1.6808160\ 64943388/0.2298806726279488/0.8896145512253182/-0.749626148258919/0.4 float=y maxiter=256 inside=0 outside=atan decomp=256 periodicity=0 cyclerange=0/255 colors=sz8sz8rz8rz8qz8py8py8oy8ny8nx8mx8mx8lx8kx7kw7jw7iw7iw7hv7gv7gv7fv\ 7fv7eu7du7du7cu6bt6bt6at6`t6`s6_s6_s6Zs6Ys6Yr6Xr6Wr5Wr5Vq5Uq5Uq5Tq5Tq5Sp\ 5Rp5Rp5Qp5Po5Po5Oo4No4Nn4Mn4Mn4Ln4Kn4Km4Jm4Im4Im4Hl4Gl3Gl3Fl3Fl3Ek3Dk3Dk\ 3Ck3Bj3Bj3Aj39j39i38i28i27i26i26h25h24h24h23g22g22g21g20f10f10e10e10d10c\ 10c10b10a10a10`10_10_10Z10Z10Y10X10X10W10V10V10U10T10T10S10R10R10Q10Q10P\ 10O10O10N10M10M10L10K10K10J10J10I10H10H10G10F10F10E10D10D10C11B01A009009\ 00A00B00C00C00D00E00F00F00G00H00I00J00J00K00L00M00M00N00O00P00P00Q00R00S\ 00T00T00U00V00W00W00X00Y00Z00_00_00`00a00b00b00c00d00e00f10f11f12f13g14g\ 15g16g17h17h18h19i2Ai2Bi2Ci2Dj2Ej2Fj2Fk2Gk2Hk2Ik3Jl3Kl3Ll3Mm3Nm3Nm3Om3Pn\ 3Qn3Rn4So4To4Uo4Vo4Vp4Wp4Xp4Yp4Zq4_q5`q5ar5br5br5cr5ds5es5fs5gt5ht6it6jt\ 6ju6ku6lu6mv6nv6ov6pv6qw7rw7rw7sx7tx7ux7vx7wy7xy7yy7zz8 } frm:km_10 { ; Kerry Mitchell 11may98 ; originally conic-near_juli ; tweaked so user can directly input ; julia parameters (p4) originally hardcoded ; to 0,1 cc=p4, zc=pixel, maxr=1e12, minr=maxr, iter=1 a=real(p1), b=imag(p1), c=real(p2), d=imag(p2) e=real(p3), f=imag(p3): iter=iter+1, zc=sqr(zc)+cc, x=real(zc), y=imag(zc) conic=|x*(a*x+b)+y*(c*y+d)+e*x*y+f| if (conic<minr) minr=conic end if if ((|zc|>maxr)||(iter==maxit)) iter=-1 t=log(minr) z=cos(t)+flip(sin(t)) end if iter>0 } Roger Alexander

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FOTD 04-11-10 (Seahorse Games [7])
by Jim Muth 04 Nov '10

04 Nov '10

FOTD -- November 04, 2010 (Rating 7) Fractal visionaries and enthusiasts: Today's image keeps us in Seahorse Valley. The image is centered on the real(X) axis, just west of the valley itself. The orientation of the slice is double rotated 5 and 5 degrees from the actual Julia direction, which is close enough that the outer shape of the Julia set of Seahorse Valley can clearly be recognized. The multi-colored arms thrusting into the outer Julia shape from the sides are part of the Mandelbrot aspect of Seahorse Valley. The open upper half of the fractal is part of the main period-2 Mandelbrot bud; the lower half is part of the main bay. The colorful decorations are stuff that mostly lies in the perturbed Mandelbrot sets. Due to its fancy colors, I rated the image at a 7. The name "Seahorse Games" was inspired by the colorful trimmings, such as might be seen at a birthday party. The calculation time of 14 seconds is a real bargain. The trip to view the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> is equally brief, and more convenient than running the included parameter file. Wednesday began with fog here at Fractal Central, but by 10am the fog cleared off, leading to a day with total sun, just what the fractal cats needed to keep them happy. The temperature rose from a sunrise 28F -2C until it reached a very typical 54F 12C in mid-afternoon. My day was average, which is pleasant enough but leaves little to discuss. FL had a similar day. The next FOTD, a trip to a different part of the Julibrot, will be posted in 24 hours. Until then, take care, and who's behind those wacko conspiracy theories that the radiation emitted by cell phones is unsafe? If the phones were unsafe, the phone companies would be warning us, just like the tobacco companies warned us about the dangers of smoking cigarettes. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Seahorse_Games { ; time=0:00:14.77-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=1 center-mag=0/-0.025052/0.85034 params=85/0/85/90/\ -0.764/0/0/0 float=y maxiter=2500 inside=0 logmap=yes symmetry=yaxis periodicity=6 colors=000REQSESUEUWEXYFZ_G`aHbcIeeJigKmiLqkMtmNwk\ OziPygQxeRwcSvaTu_UtYVqWWnUXkSYiQZfOZcMYaKXZIWWGVU\ EURCTOASM8RJ6QG4PE5OF5NF5MF5LF5KG5KG5KG5KG6KH6KH6K\ H6KH6KI6KI6KI6KI8KH9KGALGBNFDQEESEFUDGWDIZCJ`BKbBL\ dAMfAQbET_IWXMZUQbQTeNXhK`kHdnEgoFfoFepFdpGdqGcqGb\ rGarHasH`sH_sH_uL`vO`wR`xVayYaz`asaYlaUebRZbNScKLc\ GEdD7d91d5AdFFdPKeZUeccehmfhlfdiecfdbcca`b`Za_W`ZT\ _YQZWNYVLXUIWTFVSCUR9TQ7TPEXOL`OSdNZgNcdRMlCOpDMlC\ LiCMfCNcCO`CPYBQVBSSBUPBWMBYJB_GAaDAcAAc7Ac4Ac1Ac3\ Cc5Dc6Ec8Fc9HcBIZCJUEKPFMKHNFIOAKP5MR3NS3PT3QU3SW3\ TX4VY4W`4Yc4Zh4`m4ar4cv4ez4fz5iz5jz5lz5nz5oz5oz5pz\ 5pz5pz3qz5qz6qz8rz9rzBrzCszDszFszGtzItzJtzKuzMuzNu\ zPvzQvzSvzTwzUwzWwzXwzZwz_wz_wzawzbwzcwzdwzewzfwzh\ wziwzjwzkwzlwzmwzowzpwzqwzqwzqwzqwzqwzrwzrwzrwzrwz\ rwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrw\ zrwzrwzrwzrwzrwzrwzrwzrwz } frm:SliceJulibrot2 {; draws most 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), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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Spirals of Threads
by Roger Alexander 03 Nov '10

03 Nov '10

Today's post uses a formula using a Julia iteration loop producing a spirals of threads design. Ready made at http://maxitersfractalfollies.blogspot.com Spirals of Threads { ; fract492.gif ; blank ; calctime 0:06:08.77 ; created Nov 02, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=kerrym.frm formulaname=km_10 center-mag=-0.550248/0.349382/6.884776 params=0.1263771477401044/0.1877803888058107/-0.8391064180425428/0.67070\ 52827539903/0.1497543259987182/0.7999206518753624/-0.749626148258919/0.7\ 06839197973571 float=y maxiter=1500 inside=0 decomp=256 periodicity=0 colors=000000000000000000000000000000000100100200400500700900B00D00G00I0\ 0L00O10Q10T10W10Z10a10e10h20k20o20r20v20y20z30z50z60z80z90zB0zC0zE0zF0zH\ 0zI0zK0zL0zN0zO0zQ0zR0zT0zU0zW0zX0zZ0z_0za0zb0zd0ze0zg0zh0zj0zk0zm0zn0zp\ 0zq0zs0zt0zv0zw0zy0zz1zz3zz4zz6zz7zz7zy7zx7zx7zw7zv7zv7zu7yt7ys7ys7yr7yq\ 6yq6yp6yo6yo6xn6xm6xl6xl6xk6xj6xj6xi5xh5wh5wg5wf5we5we5wd5wc5wc5vb5va5va\ 5v`4v_4vZ4vZ4vY4vX4uX4uW4uV4uV4uU4uT4uS3uS3uR3tQ3tQ3tP3tO3tO3tN3tM3tL3sL\ 3sK3sJ2sJ2sI2sH2sH2sG2sF2rE2rE2rD2rC2rC2rB1rA1rA1r91q81q71q71q61q51q51q4\ 1q31p20p20o20n20m20m20l20k20j20j20i20h20g20g20f20e20d20d20c20b20a20a20`2\ 0_20Z20Z20Y20X20W20W20V20U20T20T20S20R20Q20Q20P20O20N20N20M20L20K20K20J2\ 0I20H20H20G20F20E20E20E20D20D20C20C20C20B20B20A20A20A2092092092082082072\ 0720720620620520520520420420420320320220220220120120010 } frm: km_10 { ; Kerry Mitchell 11may98 ; originally conic-near_juli ; tweaked so user can directly input ; julia parameters (p4) originally hardcoded ; to 0,1 cc=p4, zc=pixel, maxr=1e12, minr=maxr, iter=1 a=real(p1), b=imag(p1), c=real(p2), d=imag(p2) e=real(p3), f=imag(p3): iter=iter+1, zc=sqr(zc)+cc, x=real(zc), y=imag(zc) conic=|x*(a*x+b)+y*(c*y+d)+e*x*y+f| if (conic<minr) minr=conic end if if ((|zc|>maxr)||(iter==maxit)) iter=-1 t=log(minr) z=cos(t)+flip(sin(t)) end if iter>0 } Roger Alexander

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FOTD 03-11-10 (Valley of Surprise [5])
by Jim Muth 02 Nov '10

02 Nov '10

FOTD -- November 03, 2010 (Rating 5) Fractal visionaries and enthusiasts: Today we enjoy another image from the Z^2+C Julibrot. The image would normally have been discarded as soon as it appeared, but November is the month of salvation for questionable images from the Julibrot, so I decided to give today's image a chance to show its stuff, or its lack of stuff. The rating of a 5 is right in the middle of the rating scale, which ranges from zero to ten. This leaves it to the individual fractal fan to decide whether the 2-1/3 minute calculation time would be worth the effort. The scene lies in the Seahorse Valley complex of the Julibrot. I have totally lost track of the location and orientation, and of the amount of stretching and skewing I did on the scene, but in the end, I was left with an image of a debris-filled hole with a brilliant white stripe in the background, which on the surface has no resemblance at all to anything normally connected to Seahorse Valley. The name "Valley of Surprise" has something to do with the first impression of the image. If one looks closely enough, however, they will see tiny hints of seahorse activity every- where. Finally, the 2-1/3 minute wait for the image to calculate may be avoided by viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> The total sun here at Fractal Central on Tuesday was spoiled by a morning temperature of only 23F -5C and an afternoon high of 48F +9C. The fractal cats, who spent the day in the indoor temperature of 68F 20C fully enjoyed the sun however. My day was average. The next FOTD will be posted in 24 hours. Until then, take care, stay alert, and prepare for a bombshell. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Valley_of_Surprise { ; time=0:02:19.88-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=1 center-mag=-0.512268272656399/+0.0732312476231547/\ 164.2885/5.3623/13.0817225561897121/65.54874842\ 92186195 params=0/0/90/0/-0.76/0/0/0 float=y maxiter=15000 inside=255 logmap=142 periodicity=6 colors=000dWteXsfXqgYohZmi_kj`ikaglbfmbencdodcpebq\ farg`sg`sf_sfZsfZsfYsfXrfXqfWpfWocXn`YmZZlX_kW`jUa\ iSbhScgQdfPeeNfcLgaJh_GiYEjWBkV7nU9lTBjSChREfQFdPG\ bOH`NIXMIXLJVKKTJLRIMPHNNHPLIRJJSHKTFKUDKVBKW9KX7M\ X5OX2QX4SX5UW7SW8QWAOWBMXDKXEIWGGVHEUIDTKCSLCSNCRO\ AQQ9PR7PT6PU2SU5RV8RVBQWEPWHNXKMXNLYQKYTIZWHZZH_ZI\ _ZJ_ZKQZLH_MJ`NKaOLcPMdQNeROfSPhTQiURjVSlWTmUUnUVo\ UWpUXpUYoUZmUYkUXiUWgUVeUUcUTaUS_URYUQWVPVVOUVNTUM\ STLRTKQTJPTIOUHNUGMUFLVEKVDJVCKXBKYAKZ9KZ8KZ7KY6KX\ 7KW7LX8LX8LX9LX9LYALYALYALZBL`BMaCMbCMcDMdDMdEMdEM\ dFMeFMeGNeGNeGNfHNfHNfINfINgJNgJNgKOgKOhLOhLOhMOhM\ OiMOiNOiNOiOPjOPjPPjPPjQPkQPkRPkRjzzczzczzczzczzcz\ zczzczzezzdzzdzzczzczzbzzbzzazzazz`zz_zz_zzZzzZzzY\ zzYzzXzzXzzWzzWzzVzzVzzUzzUzzTzzTzzSzzRzzRzzQzzQzz\ PzzPzzOzzOzzNzzNzzMzzMzzLzzLzzKzzJzzJzzIzzIzzHzzHz\ zGzzGzzFzzFzzEzzEzzDzzuzz } frm:SliceJulibrot2 {; 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), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 02-11-10 (An Undefined Mini [7])
by Jim Muth 02 Nov '10

02 Nov '10

FOTD -- November 02, 2010 (Rating 7) Fractal visionaries and enthusiasts: In my fractal explorations I constantly find interesting and unexpected slices of the Julibrot. Usually I discard these almost as soon as I find them, but now I have decided to make November the month of unexpected slices of the Z^2+C Julibrot, which is the abstract four-dimensional monster that holds the Mandelbrot set as well as all the perturbed Mandelbrot sets and all the Julia sets. Yesterday's image was the first of these slices. At first glance, today's image appears to be a Julia set of Seahorse Valley. But it is not. Seahorse Valley Julia sets have either XY-axis symmetry or origin symmetry. The mini-thing in today's scene has X-axis symmetry, something that is impossible for a Julia set to have. The reason is that it is not a mini-Julia set, it is an Oblate set corresponding to the Seahorse Valley of the large minibrot on the main spike of the Mandelbrot set. The scene of the image is off to the side of the valley in the real(Z) direction at a distance of 0.5477. The entire image has been stretched about 2-3/4 times in the horizontal direction to bring it into what is considered normal relative dimensions. The brilliant line through the center of the image is actually the narrow space between an extension in the real(Z) direction of the two branches of Seahorse Valley of the large minibrot on the main spike of the M-set I put more coloring effort into the image than it deserves, but the effort raises the worth a full point from 6 to 7. The name "An Undefined Mini" means that, as far as I know, there is no generally accepted name for the type of object that appears in today's image. So maybe I'll invent a name. The calculation time of 2 minutes is about what the image is worth. A bargain may be found on the FOTD web site at: <http://www.Nahee.com/FOTD/> where the finished image is posted for near-instant viewing, and if not total, then at least partial satisfaction. The air remained chilly here at Fractal Central on Monday, with a high temperature of only 46F +8C, but the sky was clear and the sun shone strong on the fractal cats' window shelf most all day, keeping them happy as two bedbugs in a flophouse mattress. My day was about average. The next FOTD will be another unexpected slice of the Z^2+C Julibrot. It will be posted in 24 hours, give or take a few. Until then, take care, and our world might be a better place without religion, but what would we replace it with? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= An_Undefined_Mini { ; time=0:02:12.52-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=1 center-mag=-0.\ 00030581/0/269/2.763 params=0/0/90/0/-1.7685291540\ 2387/0/0.5477/0/2/0 float=y maxiter=120000 inside=255 logmap=12 symmetry=xaxis periodicity=6 colors=0007Wb7Wc7Vc7Vc7Vc7Ud7Ud7Ud7Ud9VeAVeBVfCWfE\ WgFWgGWhHXhIXiKXiLYjMYjNYjOYkQZkRZlSZlT_mU_mW_nX_n\ Y`oZ`o_`paapbapcaqdbqecrgdrhesifsjgtkhtmiunjuokvpl\ vqmvrmsrmprmnrmkrmirlfrkdsjasiZshXsgUsfSsePseNseKt\ eHteFteCueAve7we5xe2ye0zd0yd0xc0wc0vb0ub0ta0sa0r`0\ q`0p_0o_0nZ0mZ0lY0kY0jX0iX0iW0hW0gV0fV0eU0dU0cT0bT\ 0bS0aS0aS0`R0_R0_Q0_Q0ZP0_P0ZO0ZO0ZN0ZN0YM0ZM0YL0X\ L0XK0WK0UK0TK0TJ0RJ0RI0QI0QH0PH0PG0OG0NG0OF0NE0NE0\ MD0LD0LC0KC0JB0JB0IA0HA0H90G90F80F80E70E70E60E60E5\ 0E50E40E40F30F30F20E20D10C10B00A00A03A06A09A0CA0DA\ 0EA0EB4HC8KDCMEGOFKRGOTHSVIWYJ__KcaLgYNgVPgSRgPTgM\ VfJXfGZfD`fAaf7`eN`db`cq_boZbmYblXbjWbhVbgUbeTacSa\ bRa`QaZRaYSaWTaUUaTV`RW`PX`OY`MZ`K_`J``Ha_Fb_Ec_Ce\ _Ag_9i_7k_5m_4oZ5qZ5sY5uY6wX6xX6yW6zW7yV7xV7wU7wU8\ wT8wT8wT8wV7wW7wX7wZ7w_6w`6wa6wc6wd5we5xf5xh5xi5yj\ 4yl4ym4zn4zo3zq3zr3zs3zt3 } 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=========================================

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Devil Fractal
by Roger Alexander 01 Nov '10

01 Nov '10

Behold a fractal devil. Actually that's the name of the formula, the same one used in the Oct. 2 post. I zoomed in one of the lobes, rotated 90 degrees giving the image a portrait orientation and re-sized. The rotating of the image takes it from simple anti-aliasing to the level of post-processing. To everybody this blogs first post-processed fractal! Go to http://maxitersfractalfollies.blogspot.com for instant gratification. Halloween Devil { ;fract495.gif ; blank ; calctime 0:07:22.81 ; created Oct 31, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=_d.frm formulaname=devil passes=1 center-mag=0.738924/3.33067e-016/3.908693 float=y maxiter=1500 inside=0 colors=000000000000000000000000000000000100100200400500700900B00D00G00I0\ 0L00O10Q10T10W10Z10a10e10h20k20o20r20v20y20z30z50z60z80z90zB0zC0zE0zF0zH\ 0zI0zK0zL0zN0zO0zQ0zR0zT0zU0zW0zX0zZ0z_0za0zb0zd0ze0zg0zh0zj0zk0zm0zn0zp\ 0zq0zs0zt0zv0zw0zy0zz1zz3zz4zz6zz7zz7zy7zx7zx7zw7zv7zv7zu7yt7ys7ys7yr7yq\ 6yq6yp6yo6yo6xn6xm6xl6xl6xk6xj6xj6xi5xh5wh5wg5wf5we5we5wd5wc5wc5vb5va5va\ 5v`4v_4vZ4vZ4vY4vX4uX4uW4uV4uV4uU4uT4uS3uS3uR3tQ3tQ3tP3tO3tO3tN3tM3tL3sL\ 3sK3sJ2sJ2sI2sH2sH2sG2sF2rE2rE2rD2rC2rC2rB1rA1rA1r91q81q71q71q61q51q51q4\ 1q31p20p20o20n20m20m20l20k20j20j20i20h20g20g20f20e20d20d20c20b20a20a20`2\ 0_20Z20Z20Y20X20W20W20V20U20T20T20S20R20Q20Q20P20O20N20N20M20L20K20K20J2\ 0I20H20H20G20F20E20E20E20D20D20C20C20C20B20B20A20A20A2092092092082082072\ 0720720620620520520520420420420320320220220220120120010 } frm:devil {; Copyright (c) Paul W. Carlson, 1998 ; Based on one of Noel Giffin's formulas w = pixel z = iter = wp1 = wp2 = bailout = 0 : old_w = w w = w * w - wp2 wp2 = wp1 wp1 = real(old_w) - flip(imag(old_w)) IF (|w| > 4) bailout = 1 z = 4 * iter + 30 z = z - real(216) * trunc(z / real(216)) ENDIF iter = iter + 1 z = z - iter bailout == 0 ;SOURCE: 98msg.frm } Roger Alexander

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Halloween Minibrot
by Roger Alexander 01 Nov '10

01 Nov '10

A minibrot in Halloween colors. According to Wikipedia "Black and orange are the traditional Halloween colors and represent the darkness of night and the color of bonfires, autumn leaves, and jack-o'-lanterns" Gif and re-sampled jpg. At the usual http://maxitersfractalfollies.blogspot.com Halloween Colors { ; fract493.gif ; blank ; calctime 0:01:56.33 ; created Oct 31, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=mandel center-mag=-0.04428222277847312/-0.98332827545909710/508323.8/1/170.0000\ 00000846683/-9.35095410825592666e-010 params=0/0 float=y maxiter=2300 inside=0 logmap=163 colors=00000000000000000000000000000000000000000000000000000000100100100\ 100100100100100100100100100100100100100100100200200200200200200200200200\ 200200200200200200200200200300300300300300300300300300300300300300300300\ 300300300400400400400400400400400400400400400400400400400400400500500500\ 500500500500500500500500500500500500500500500600600600600600600600600600\ 600600600600600600600600600700700700700700700700700700700700700700700700\ 7007008KF0OG0SI0WK0_M0cO0gQ0kS0kS0kS0kS0lT0lT0lT0mU0mU0mU0nV0nV0nV0oW0oW\ 0oW0pX0pX0pX0pX0qY0qY0qY0rZ0rZ0rZ0s_0s_0s_0t`0t`0t`0ua0ua0ua0ua0vb0vb0vb\ 0wc0wc0wc0oW0oW0oW0oW0ye0ye0zf0zf0zf0zf0ye0ye0ye0xd0xd0xd0wc0wc0wc0vb0vb\ 0vb0ua0ua0ua0ua0t`0t`0t`0s_0s_0s_0rZ0rZ0rZ0qY0qY0qY0pX0pX0pX0pX0oW0oW0oW\ 0nV0nV0nV0mU0mU0mU0lT0lT0lT0kS0gQ0cO0_M0WK0SI0OG0KF0000 } Roger Alexander

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