November 2010 - Fractint - mailman.xmission.com

Steel Blue Curves
by Roger Alexander 11 Nov '10

11 Nov '10

Another Kerry Mitchell formula fractal. Gif and jpg at the usual http://maxitersfractalfollies.blogspot.com Steel Blue Curves { ; fract283.gif ; blank ; calctime 0:14:50.83 ; created Jun 30, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=kerrym.frm formulaname=km_12 center-mag=0.639399/0.290604/1.173709/1/15.0000000000000018/-3.778227730\ 67748585e-014 params=-1.596484267708365/-0.3024384289071322/1.072847682119205/0.015808\ 58790856655/-0.5392010254219184/-0.1369060335093234/-0.2313303018280587/\ 0.7412945951719717 float=y maxiter=1500 inside=0 invert=0.644093142490921/-0.0506912442396313/-0.962157048249763 decomp=256 periodicity=0 colors=ELLFLLFMMGMMGNNHNNHOOIOOIPPJPPJPPKQQKQQLRRLRRMSSMSSNTTNTTOTTOUUPU\ UPVVQVVQWWRWWRXXSXXSXXTYYTYYUZZUZZV__V__W``W``W``XaaXaaYaaYaaYbbYbbZbbZb\ b_cc_cc`dd`ddaddaeebeebffcffcffdggdggehhehhfiifiigiigjjhjjhkkikkikkjlljl\ lkmmkmmlnnlnnmnnmoonoonppoppopppqqpqqqrrqrrrrrrssssssttttttuuuuuuuuvvvvv\ vwwwwwwwwwxxxxxxyyyyyyyyyxxxxxxwwwwwwvvvvvvuvvuuutuutttsttsttrssrssqrrqr\ rprrpqqoqqoppnppnoomoomoolnnlnnlmmkmmkmmjlljllikkikkhkkhjjgjjgiifiifiieh\ hehhdggdggcggcffbffbeeaeeaeeadd`dd`cc_cc_ccZbbZbbYaaYaaXaaX``W``W__V__VZ\ ZUZZUZZTYYTYYSXXSXXRXXRWWQWWQVVQVVPVVPUUOUUOTTNTTNTTMSSMSSLRRLRRKRRKQQJQ\ QJPPIPPIPPHOOHOOGNNGNNFNNFMMFMMELLELLDLLDKKCKKCJJBJJBIIAIIAII9HH9HH8GG8G\ G7GG7FF6FF6EE5EE5EE4DD4DD3CC3CC3CC2BB1BB1AA0AA0AA1BB1BB2CC2CC3DD3DD4DD4E\ E5EE5FF6FF6FF7GG7GG8HH8HH9HH9IIAIIAJJBJJBJJCKKCKKDLLDLL } frm:km_12 { ; Kerry Mitchell 11may98 ;originally conic-near_jul2 ;tweaked so user can directly input ; julia parameters (cc=p4) originally ; hardcoded to -2 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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Re: [Fractint] FOTD 06-11-10 (Almighty Spiral [6])
by Roger Alexander 10 Nov '10

10 Nov '10

A very impressive fractal Jim. The design is vivid. Roger Alexander

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FOTD 10-11-10 (The Mystical Donut [7])
by Jim Muth 10 Nov '10

10 Nov '10

FOTD -- November 10, 2010 (Rating 7) Fractal visionaries and enthusiasts: Like all images in the month of November, today's image lies in an unfamiliar slice of the Z^2+C Julibrot. I'll not try to describe the location or orientation of the parent-fractal slice, other than reporting that it is centered on Seahorse Valley and is double-rotated halfway between the Mandelbrot and Julia orientations. This is little help, since in the 4-D Julibrot there are countless orientations halfway between the M and J directions. Today's scene is located on the rudimentary main stem of the parent slice. I named the image "The Mystical Donut". I know it's a rather silly name. There is little of a mystical nature in a donut. But I can't help it if I saw a donut in the image. Most of the image's detail was created by rendering it with the outside set to 'real'. The 'imag' and 'summ' options work almost as well. The rating of a 7 makes the image worth the minute required to run the parameter file. Those with over-qualified machines can hopefully find the eye- ball-ready image posted to the FOTD web site at: <http://www.Nahee.com/FOTD/> A mixture of sun and clouds prevailed here at Fractal Central on Tuesday, with the clouds predominating. The temperature of 55F 13C was just a bit too chilly for maximum comfort, though it was about normal for early November. The fractal cats enjoyed the sun when it appeared and sought comfort by the heat when it went behind the clouds. My day was average. Isn't that boring? The next FOTD will be posted in 24 hours. Until then, take care, and do we exist even when we are unconscious? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= The_Mystical_Donut { ; time=0:01:03.50-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 center-mag=-1.41420407/\ 0/724383.1/1.5564/-90/0 params=45/0/-45/0/-0.75/0\ /0/0 float=y maxiter=1400 inside=0 outside=real colors=000JffIeeIddIccIbbIbaIb`Ib_IbZIbYIbXIbWIbVI\ bUKaTLaSNaROaQQaPSaOTaNVcMXeLYgK_iK`kKdmKhoKmqKrsK\ vs2zz2zzzzzzzzzzzzvuzrw2my2hz2ZoCUeMPVWKLfGApCAzB8\ vB6tB4rB3oB3mA4kA4iA5gA6eA6dA7c97b98a98`99_9AZ9AY8\ BX8BW8CV8CU8DT8DS7ER7EQ7FP7FO7FN7GM7GL7GN7HP7HS7IU\ 7IW6IZ6J`6Jb6Je6Kg6Ki6Ll6Ln6Lp6Ms6Mu6Mw8Nv9OuAPtBP\ sCQrDRqERpGSoHTnITmJUmKVlLVkMWjOXiPXhQYgRZfSZeT_dU\ `cV`cSZdQYeOXeMWfJVgHUgFThDRiBQi8Pj6Ok4Nk2Ml0Ll2Nh\ 3Od4Pa5QY6RU7SR8TN9UJAVGBWCCX8DY5BaDAeL9iT8l`AmaBm\ bDmcEmdGmeHnfJngKnhMniNnjOnkQolRomTonUooWopXpqZpr_\ psaptbpucpuensflrgkqhipigojfnldlmcknajo_ipZhqXgrWf\ n_djbcffabi`Zm_VpYRtXOwWNtVMqVLoVKlVJjUIgUHeUGbUF_\ UEYTDVTCTTBQTAOTCPUDQUERUFSUGTUHUVIVVJWVKXVLYVNZWO\ _WP`WQaWRbWScXTdXUeXVfXWgXVeUVcSVbQV`OV_MVYKUXIUVG\ UUEUSCURAUP8UO6SSDQWKP_QNcXMgbKkiJnoKnpKnpKnpKnpKn\ oKnnKmmKllKkkKjjKiiJhhJgg } 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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Field Line Variations
by Roger Alexander 09 Nov '10

09 Nov '10

Today's blog post of Fractint compatible gifs and anti-aliased jpgs is of two versions of the field4_jul formula by Kerry Mitchell. They are identical except for the imaginary P2 values. I calculated with values of 0 and 12. Available at http://maxitersfractalfollies.blogspot.com I've posted only one version of the par file, just vary imag(P2) if regenerating. Field Line Variations { ; fract506.gif ; blank ; calctime 0:03:55.63 ; created Nov 08, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=*.frm formulaname=field4_jul center-mag=0.048197/0.607759/3.404629 params=0.375/0.375/1000000/0 float=y maxiter=1500 inside=0 decomp=256 periodicity=0 colors=00101211312412413523624724825935936A36B37C47D48E48F49F59G5AH5AI5B\ J6BK6CK6CL6DM7DN7EO7EP7FP8FQ8GR8GS9HT9HU9IUAIVAJWAJXBKXBKYBLYCLZCMZCM_DN\ `DN`DOaDOaEPbEPbEQcFQcFRdFReGReGSfGSfHTgHTgHUhIUiIViIVjIWjJWkJXkJXlKYlKY\ mLZnLZnM_oM_oM`oN`pNapOaqObqPbrPcrPcrQdrQdsResRetRftSftSgtTguThuUhuUivVi\ vVjvVjvWkwXkwYlwYlwZmxZmx_nx_nx`ox`oxapyapybqybqycrydryesyeszftzgtzhuzhu\ zivzjvzkwzmwznxzpxzqyzryzuzzuzzuzzryzqyzoxznxzmwzkwzjvzivziuzhuzgtzftzfs\ zesydrycrybqybqyapyapy`ox_ox_nxZnxZmxYmwYlwXlwXkwWkwVjvVjvVivVivUhvUhuTg\ uTguSfuSftRetQesQdsQdrPcrPcrObqObqOapNapN`oN`oM_nM_nMZmLZmLYlLYlKYlKXkJX\ kJWjJWjIViIViIUhHUhHTgHTgGSfGSfFRfFReFQdFQcEPcEPbEObDOaDNaDN`CM_CM_BLZBL\ ZBKYAKYAJXAJWAIV9IU9HU9HT8GS8GR8FR8FQ7EP7EO7DN7DM6CL6CL6BK6BJ5AI5AH59G59\ G48F48E47D37C36B36A35A259248247236135124124113012001000 } frm:field4_jul { ; Kerry Mitchell 20jan98 ; ; Colors Julia sets by nearest approach to ; period 4 field lines ; ; use decomp=256 ; p1 = Julia parameter ; real(p2) = bailout (try 1e12) ; imag(p2) = number of field line to use: 0 - 15 ; 4 iterations per pixel ; variable zc used for calculation, z for coloring ; zc=pixel, c=p1, maxr=real(p2), minr=maxr, iter=1 fieldangle=tan(imag(p2)*2*pi/15): ; ; iteration ; compare tangent of polar angle with desired ; field line angle, update minimum if needed ; iter=iter+4, zc=sqr(zc)+c, zc=sqr(zc)+c, zc=sqr(zc)+c zc=sqr(zc)+c, rzc=|zc|, tanangle=imag(zc)/real(zc), r=cabs(fieldangle-tanangle) if (r<minr) minr=r end if ; ; bailout ; set "iteration done" flag (iter=-1) ; use log of minimum difference of angles as ; decomposition angle ; if ((rzc>maxr)||(iter>=maxit)) iter=-1 angle=log(minr) z=cos(angle)+flip(sin(angle)) end if iter>0 } Roger Alexander

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FOTD 09-11-10 (Hourglass Spirals [7])
by Jim Muth 09 Nov '10

09 Nov '10

FOTD -- November 09, 2010 (Rating 7) Fractal visionaries and enthusiasts: Today's image is (no guarantee) the last of the series of near- Julia Mandelbrot valley images. This one shows the valley of the north bud of the large minibrot on the west branch of the filament that extends from the north bud of the Mandelbrot set. The effect is much the same as the previous images, though there is more decoration around the almost-Julia set. The name "Hour- glass Spirals" refers to the hourglass-like shape of the two spirals on either side of the center. It is tempting to think of these fractal spirals as 3-D things such as short curved lengths of string. But they are actually 2-D slices of 3-D spaces that curve and twist in 4-D space. As with all 4-D stuff, the entirety of the spirals is impossible to visualize. As mere humans, our consciousness is limited to the 3-D experience. I decided to give today's image, which is likely the last of the series, a rating of a 7. We have been mired in this series longer than I had intended, and there are many unusual slices of the Julibrot that we have not yet checked. Tomorrow's image will begin the exploration of these. Today's image calculates in under 7 minutes, not fireball fast, but certainly faster than some FOTD's, which have taken days to complete. The last I heard, Paul was still in the hospital, recovering from an infection. He has enough access to the FOTD web site to post the FOTD discussions. But since he is using a new-fangled laptop machine running Vista, which panics as the sight of the Fractint program, he cannot run the parameter files. I am send- ing the finished GIF images to him while he is in the hospital, from where he can post them to the FOTD web site. Hopefully, the web site will be up to date shortly. As always, the site may be accessed at: <http://www.Nahee.com/FOTD/> A few too many clouds and a bit too little sunshine here at Fractal central on Monday kept the fractal cats from reaching maximum contentment. The temperature of 54F 12C was just about normal. My day was normal also. The next FOTD will be posted in 24 hours. Until then, take care, and I hear that within 25 years everyone will have their own private autogyro for their daily commute. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Hourglass_Spirals { ; time=0:06:51.18-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=1 center-mag=0/0\ /11.7/1/87/0 params=89.9/0/89.9/52.5/-0.15436/\ 1.0371225/0/0 float=y maxiter=40000 inside=0 logmap=8 periodicity=6 colors=000CKVDLUEMSFNWGOTHPRIQOJRMJSJKTIMUJNVIOWIQ\ XHTYGVZGY`F_aFabEdcDfeDifCkgCnhBpjAskAul9wm9zlCzlE\ zlHzlJxlMvlOtlRtlTslWslYsl`rlbrlerlgqljqllqlnokmnj\ lmikkijjhiifhgdhfegedfcbecadcaccaccabcbacc`cc_ccZc\ cZccYccXccWccVccUcbUcaYc`acZecXicWmcVqcUpcUpcUpdUp\ dUpdUpeUpeUoeUofUofUofUogUogUogUnhUnhUnhUniUniUnjU\ nkUmlUlmUkmUjmUimUhmUhmUgmUfmUemUfmUgmUhmUhmUimUjm\ UjmUkmUlmUlmUmmUnmUnmUomUpmUpmUpmUqmUrmUsmUtmUumUv\ mUwmUxmUymUxmUxmUxmTxmSxmRwmQwmPwmOwmNwmMwmLvmKvmJ\ vmIvmHvmGumFumEumDumCumBuiEteHtaKsYNsUQrSRrQSrOTsM\ UsKUsIVsGVsEWtCWtAXt8Xt6Yt4Zu2_u0`u0bz0dz0ez0ez0fz\ 0fz0gz0hz0hz0hz0iz1jz3jz4kz5kz7kz8qzArzBrzCszEszFs\ zHuzIuzKuzLuzMuzOuzPuzRuzSuzSuzUzzVzzWzzXzzYzzZzz`\ zzazzbzzczzdzzezzgzzhzzizzizzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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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Re: [Fractint] Fractint Digest, Vol 93, Issue 4
by JackOfTradeZ＠comcast.net 08 Nov '10

08 Nov '10

. can someone tell me why i can not see the FOTD image post after Oct 27? is it my problem or something with the site - has it moved? thanx .

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FOTD 08-11-10 (Be Forever Fractal [No Rating])
by Jim Muth 08 Nov '10

08 Nov '10

FOTD -- November 08, 2010 (No Rating) Fractal visionaries and enthusiasts: Today's image is what happened when I tried the almost-Julia- valley trick on the valley leading to the large sub-bud on the northwest shore line of the large period-2 bud of the Mandelbrot set. Like the recent images, there are some similarities and some differences. The greatest difference in today's image is the fact that it is only the central part of the entire parent almost-Julia set. I have cropped off a good part of the out- lying areas, but the part that remains is interesting enough. We have the same spirals and the same grossly enlarged view of the Mandelbrot aspect of the valley. Once again I used mostly the same color palette, though in today's image I cut the values and intensity of the stronger hues. I could hardly give just another valley scene a proper rating, though I did name it "Be Forever Fractal", a name that sounds a bit more meaningful than it actually is. The calculation time of only 3 minutes is blessedly brief. (I gave it the blessing myself.) I haven't heard how Paul at the FOTD web site is coming, but the last I heard he was recovering, so it might be worth a look to see if the FOTD web site at: <http://www.Nahee.com/FOTD/> is up to date yet. FL and I managed the shift from daylight time to standard in fine shape here at Fractal central on Sunday. We simply arose an hour earlier. The cats never noticed the change, except in the evening, when they had to wait an hour longer for their treats. A mixture of sun and clouds hung above Fractal Central all day. The fractal cats enjoyed the sun while it was out and the house heat when the sun failed them. The temperature of 45F +7C was chilly for both man and cat. The next FOTD will be posted in 24 hours. There is no escaping the delay. Until then, take care, and resistance is futile. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Be_Forever_Fractal { ; time=0:03:07.19-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=1 periodicity=6 center-mag=0/0/2.16/1/47.5/0 float=y maxiter=42000 params=88.7/0/88.7/77.5/-1.12542/0.21722/0/0 inside=0 logmap=yes colors=00086a97bA8cB9dCAeDBfECgFDhGEiHFjIGkJHlKImL\ JnMKoNMnOOmPQlQSkRUjSVgTWdUXaSY_QZXOZUMYSKXQIWOGVN\ EULCTJASH8RE6QB4P95OA5NA5MA5LA5KB5KB5KB5KB6KC6KC6K\ C6KC6KD6KD6KD6KD8KC9KBALBBNADQ9ES9FU8GW8IZ7J`6Kb6L\ d5Mf5Qb9T_DUXHUULUQOUNSUKWUH_UEbUFaUF`UF_UG_UGZUGY\ UGXUHXUHWUHVUHVULWUOWURWUVXUYXU`XUaTUaPSbMQbIOcFQc\ BSd8Ud4Wd0YdA_dKaeUceZceccfccf_ceZcdYccX`cWZcVWcUT\ cTQcRNcQLcPIcOFcNCcM9cL7cKEcJLcJScIZcIccMMc7Oc8Mc7\ Lc7Mc7Nc7O`7PY6QV6SU6UU6WU6YU6_U5aU5cU5cU5cU5cU5cU\ 7cU8cU9cUAcUCcUDZUEUUFPUHKUIFUJAUK5UM3UN3UO3UP3UR3\ US4VT4WW4YZ4Zc4`h4am4cq4ev4fw5ix5jy5lz5nz5oz5oz5pz\ 5pz5qz3rz5rz6rz8sz9tzBtzCuzDuzFuzGvzIwzJwzKxzMxzNx\ zPzzQzzSzzTzzUzzWzzXzzZzz_zz_zzazzbzzczzdzzezzfzzh\ zzizzjzzkzzlzzmzzozzpzzqzzqzzqzzqzzqzzrzzrzzrzzrzz\ rzzrzzrzzrzzrzzrzzrzzrzzrzzrzzrzzrzzrzzrzzrzzrzzrz\ zrzzrzzrzzrzzrzzrzzrzzrzz } 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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FOTD 07-11-10 (Home of the Spiral [No Rating])
by Jim Muth 07 Nov '10

07 Nov '10

FOTD -- November 07, 2010 (No Rating) Fractal visionaries and enthusiasts: The lateness of today's image is due to a not-so-surprise antiquing expedition that arose not-so-unexpectedly on Saturday. But better late than never. Today's FOTD is the parent fractal of yesterday's 'Almighty Spiral' fractal. The actual spiral that filled yesterday's image lies humbly at the right edge of today's scene. Many other spirals fill the upper half of the image, which lies on the bud side of the Mandelbrot valley that is visible as the two brilliant wedges jutting across the center of the outer shape. The lower half of the image, which is the main-bay side, has no spirals at all. Today's image is not a Julia set, but it comes very close. It is double-rotated 0.04 and 0.04 degrees from the actual Julia orientation. (Double rotation is a mathematical abstraction most difficult to comprehend. Nothing at all like it exists in three-dimensional space.) But the orientation of today's image produces many Julia characteristics and also shows the position of the hairline spirals in relation to the Mandelbrot aspect of the area. With today's image being a near-repeat of yesterday's, I could give it no rating. The name "Home of the Spiral" needs no expla- nation however. The calculation time of almost 10 minutes will need to be endured in nail-biting impatience. I hear that Paul Lee has been in the hospital for over a week, and has been unable to update the FOTD web site. Fortunately, he appears to be on the road to recovery. But a trip to the FOTD web site that he has maintained for over 13 years and that holds the past FOTD images is always a lot of fun. The web site may be accessed at: <http://www.Nahee.com/FOTD/> Heavy scudding clouds, blustery north winds and a temperature of 43F +6C made Saturday quite brisk here at Fractal Central. The fractal cats had enough heat inside that they never noticed the outside chill. When the antiquing was over and done, my day was reasonably settled. The next FOTD will be posted in 24 hours. Until then, take care, and the answer may lie where least expected. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Home_of_the_Spiral { ; time=0:09:52.49-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=1 center-mag=0/0/0.8503401/1/126/0 periodicity=6 params=89.96/0/89.96/0/0.3272613/0.0561252/0/0 float=y maxiter=150000 inside=0 logmap=yes 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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Yet Another Spiral
by Roger Alexander 07 Nov '10

07 Nov '10

Today's post is a spiral, perhaps not as impressive as Jim Muth's FOTD 06-11-10 but incontestably a spiral. Ready made at http://maxitersfractalfollies.blogspot.com Yet Another Spiral { ; fract502.gif ; blank ; calctime 0:10:07.09 ; created Nov 06, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=kerrym.frm formulaname=km_04 center-mag=0.167019/0.535127/24.2564 params=-0.5/-0.5/-0.6354869228186896/-0.3533127842036195/-0.173558763389\ 996/-0.1402325510422071/0.08810693685720389/-0.7196569719534898 initorbit=0.3/-0.6 float=y maxiter=1500 inside=0 decomp=256 periodicity=0 colors=DHVCGUBET9DS8BR7AQ69P57O36N24M13L02K02K13L25M36N47O69P7AQ8CR9DSAE\ TBGUCHVDIWFKXGLYHMZIO_JP`KRaLSbMTcOVePWfQXgRZhS_iTajUbkVclXemYfnZgo_ip`j\ qakrbmscntepufqvgrwhtxiuyjvzjvziuyhsxgrwfqvdoucntblsakr`jq_hpZgoYfnWdmVc\ lUbkT`jS_iRYhQXgPWfNUdMTcLSbKQaJP`IN_HMZGLYEJXDIWCHVBFUAET9DS8BR7AQ58P47\ O36N24M13L02K02K13L25M36N47O69P7AQ8CR9DSAETBGUCHVDIWFKXGLYHMZIO_JP`KRaLS\ bMTcOVePWfQXgRZhS_iTajUbkVclXemYfnZgo_ip`jqakrbmscntepufqvgrwhtxiuyjvzjv\ ziuyhsxgrwfqvdoucntblsakr`jq_hpZgoYfnWdmVclUbkT`jS_iRYhQXgPWfNUdMTcLSbKQ\ aJP`IN_HMZGLYEJXDIWCHVBFUAET9DS8BR7AQ58P47O36N24M13L02K02K13L25M36N47O69\ P7AQ8CR9DSAETBGUCHVDIWFKXGLYHNZIO_JP`KRaLSbMTcOVePWfQYgRZhS_iTajUbkVclXe\ mYfnZho_ip`jqalrbmscntepufqvgswhtxhtxiuyhtxgrwfqveoucntbmsakr`jq_ipZgoYf\ nXdmWclVbkT`iS_hRZgQXfPWeOUdNTcMSbLQaKP`IO_HMZGLYFJXEIW } frm:km_04{; Kerry Mitchell 26aug98 ; tweaked by rjr so user can input julia parameters ; See the end of the formula general_man-2circ for ; Kerry Mitchell's explanation of the "2 circles ; coloring method". ;originally general_jul_test ; "2 general circles" coloring method for Julia sets ; c = Julia parameter, hardcoded originally to (0.65,0.33) ; p1 = x-circle center ; p2 = y-circle center ; real(p3) = x-circle radius ; imag(p3) = y-circle radius ; bailout hardcoded to 10^12 ; use "decomp=256" coloring ; zc=pixel, c=p4, bailout=1e12, iter=1, rmin=1e12 cenx=p1, radx=real(p3), rad2x=radx*radx ceny=p2, rady=imag(p3), rad2y=rady*rady: iter=iter+1, zc=sqr(zc)+c tempx=|zc-cenx|-rad2x tempy=|zc-ceny|-rad2y temp=tempx+flip(tempy), r=|temp| IF (r<rmin) rmin=r, z=temp ENDIF IF ((|zc|>bailout)||(iter==maxit)) iter=-1 ENDIF iter>0 ;SOURCE: 98msg.frm } Roger Alexander

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FOTD 06-11-10 (Almighty Spiral [6])
by Jim Muth 06 Nov '10

06 Nov '10

FOTD -- November 06, 2010 (Rating 6) Fractal visionaries and enthusiasts: Usually, I put little effort into fractal spirals. They're very easy to find and nearly everyone does them. But the spiral in today's image is so unusual that I had to make it a Fractal of the Day. I found the spiral when I tried to extend the trick of the two most recent FOTD's to the valley of the period-10 bud on the northeast shore line of the Mandelbrot set. The trick worked as I thought, producing the anticipated image, but I never expected the image to be filled with such hairline-thin spirals. Today's scene is a blow-up of a small part of the full image, which in itself is quite interesting. (The full image will be the FOTD for tomorrow, November 07.) Actually, images with very fine details such as today's and tomorrow's are improved by anti-aliasing, which helps eliminate the awkward breaks in the finer parts. Because of the fine detail in today's image, I recommend calculating it at the highest resolution available. The name "Almighty Spiral" is overblown. The spiral is not all that great when compared to some that have been found by others, though it is probably the best I have found. If spirals were not so commonplace, I might have rated the image higher. As it is, a rating of a humdrum 6 will have to do. The calculation time of 11 minutes is for a resolution of 640x480. It will be far longer if the image is rendered at a higher resolution than this. But for the true fractal-spiral fan, the result will be worth the wait. The finished image is posted on the FOTD web site at: <http://www.Nahee.com/FOTD/> Sprinkles of rain fell during the morning Friday here at Fractal Central. A few breaks of sun appeared during the afternoon, but not enough to lure the fractal cats to their shelf by the south- west window. The temperature of 52F 11C was about normal for early November. The next FOTD will be posted in 24 hours. Only a surprise antiquing trip could delay it. Until next time, take care, and expect the unexpected. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Almighty_Spiral { ; time=0:11:12.40-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=t periodicity=6 center-mag=-0.448511/-0.894674/9.159484/1/114/0 params=89.96/0/89.96/0/0.3272613/0.0561252/0/0 float=y maxiter=15000 inside=0 logmap=-3 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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