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Another Newton Mandelbrot Mash-up
by Roger Alexander 15 Nov '10

15 Nov '10

Today's post is another newton mandelbrot mash-up. Ready made at http://maxitersfractalfollies.blogspot.com fractt517.gif { ; another newton-mandelbrot mash-up ; blank ; calctime 0:09:56.44 ; created Nov 15, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=_m.frm formulaname=mandel-newton-2 passes=1 center-mag=-0.61577/4.44089e-016/0.7788162 params=12/0 float=y maxiter=1500 inside=0 periodicity=0 colors=00000000100300400600800900B00C00E00G00H00J00K00M00O00P00R00T00U00\ W00X00Z00`00a00c00d00f00h00i00k00m01m03m04n06n07o09o0Ao0Cp0Ep0Fq0Hq0Iq0K\ r0Lr0Ns0Ps0Qs0St0Tt0Vu0Wu0Yu0Zv0`v0bw0cw0ew0fx0hx0iy0ky0mz1mz3mz5nz7nz9o\ zBozDozFpzHpzJqzLqzNqzPrzRrzTszVszXszZtz`tzbuzduzfuzhvzjvzlwznwzpwzrxztx\ zvyzxyzzzzyzzxzzwzzuzztzzszzqzzpzzozzmzzlzzkzzizzhzzgzzezzdzzczzbzz`zz_z\ zZzzXzzWzzVzzTzzSzzRzzPzzOzzNzzLzzKzzJzzIzzGzzFzzEzzCzzBzzAzz8zz7zz6zz4z\ z3zz2zz0zz0yz0xz0wz0uz0tz0sz0qz0pz0oz0mz0lz0kz0iz0hz0gz0ez0dz0cz0bz0`z0_\ z0Zz0Xz0Wz0Vz0Tz0Sz0Rz0Pz0Oz0Nz0Lz0Kz0Jz0Iz0Gz0Fz0Ez0Cz0Bz0Az08z07z06z04\ z03z02z00z00y00x00w00v00u00t00s00r00q00p00o00n00m00l00k00j00i00h00g00f00\ e00d00c00b00a00`00_00Z00Y00X00W00V00U00T00S00R00Q00P00O00N00M00L00K00J00\ I00H00G00F00E00D00C00B00A009008007006005004003002000000 } frm:mandel-newton-2 {; Sylvie Gallet [101324,3444], 1995-1996 ; Formula designed for Fractint 19.2 and modified for Fractint 19.3 limit = real(p1), test0 = 1, test3=0, iter = 1 z = pixel, c = z, b1 = 16 rad = 6, pix = (10*pixel+(8.0,-5))*(-0.1,-0.95) center = (1.0,0.1), zn = center+rad/(pix-center), b2 = 0.0001 : test0 = 1-test0, test1 = (iter<limit), test2=(iter!=limit) z = (z-zn)*test2 + zn z2 = z*z, z4 = z2*z2, z1 = (z4*z-1)/(4*z4 + (z==0)) z = (z2+c)*test1 + (z-z1)*(1-test1) test3 = (test3 || (|z|>b1)) z = z*(1-(test3 && test0 && test1)) iter = iter+1 ((|z|<=b1)*test1) || ((|z1|>=b2)*(1-test1)) ;SOURCE: gallet-n.frm } Roger Alexander

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Re: [Fractint] <Paul> I hope you're feeling better, Paul.
by Paul.N.Lee＠att.net 15 Nov '10

15 Nov '10

Hal Lane wrote: > > I hope you're feeling better, Paul. Yes, somewhat better. But very drained and tired. Hopefully, the doctors will think I have recovered enough to go home from the hospital in about 6 days or so. Jim Muth wrote: > > The finished image might be posted on the FOTD web site..... > ....but I am not sure Paul has the site up-to-date quite yet. And under my current health state, it explains why I only have finished the Oct.27th through Nov.07th web pages to get them up-to-date for the FOTDs. The rest will soon be up and available as I finish them over the next 36 hours. Sincerely, P.N.L. -------------------------------------- http://www.Nahee.com/PNL/Fractals.html http://www.Nahee.com/Fractals/

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Henon_JKO
by Mike Frazier 15 Nov '10

15 Nov '10

While looking through a used book I bought (Fractals Images of Chaos by Hans Lauwerier) I saw a formula I wasn't familiar with. The formula was discovered in 1969 by French mathematician M. Henon. I entered it into Fracton, played with it a bit, and found a few fractals I liked. Henon is listed in FractInt's built in formula list but I have never seen anyone use it. I have no way to tell if FractInt's Henon is the same as this one. Here is a page with an image: http://www.fracton.org/fmlposts/henon_jko.html Here is the par file used to generate the fractal: Henon_JKO { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20101115_0906 passes=1 float=y center-mag=0.32/0.15/0.53333334/1/0/0 params=-0.0235/0.488/4.6/0/0/0/0/0/0/0 maxiter=190 proximity=0 colors=000aaateOthNtjNtlMtnMtoLtqLtsKtuKswJswJsvJs\ uJsuJstJssJssJsrKsqKspKspKsoKsnKsnKsmKslLslLskLsjL\ siLsiLshLsgLsgMsfMseMseMsdMscMsbMsbMsaNs`Ns`Ns_NsZ\ NsZNsYNsXNsWOsWOsVOsUOsUOsTOsSOsSOsRPsQPsPPsPPsOPs\ NPsNPsMPsLQsLQsKQsJQsIQsIQsHQsGQsGRsFRsERsERsDRsCR\ sBRsBRsASs9Ss9Ss8Ss7Ss7Ss6Ss5Sr4Tq4Tp4To5Tn5Sl6Sk6\ Sj7Si7Rh8Rf8Re9Rd9QcAQbAQ`BQ_BPZCPYCPWDOWDOWDOWDOW\ DOWDOVDOVDOVDOVDOVDOUDOUDOUDOUDOUDOTDOTDOTDOTDOTDO\ TDOSDOSDOSDOSDOSDORCORCORCORCORCOQCOQCOQCOQCOQCOQC\ OPCOPCOPCPPCPPCPOCPOCPOCPOCPOCPNCPNCPNCPNCPNCPNCPM\ BPMBPMBPMBPMBPLBPLBPLBPLBPLBPKBPKBPKBPKBPKBPKBPJBP\ JBPJBPJBPJBPIBPIBPIBPIBPIBPHAQIBQJDQLEQMGQOHQPJQRK\ QSMQUNQVPQWQQYSQZTQ`VRaWRcYRdZRf`RgaRhcRjdRkfRmgRn\ iRpjRqlRsnSrnSpnSnnSmnSknSinSgnSfnTdnTbnTanT_nTYnT\ WnTVnTTnURnUQnUOnUMnUKnUJnUHnUFnVEnVCnVAnV8nV7nV5n\ V3nV1oW1oW1oW1oW1oW1pV1pV } frm:F_20101115_0906 { ; Henon's Expression ; From Fractals Images Of Chaos by Hans Lauwerier p126 ; x' = y ; y' = -x +2ay + by^2 ; Time = 0.4 sec at 640 x 480 with no anti-aliasing ; using Fracton on Mac Pro 2 x 2.8 GHz Quad-Core Xeon x=real(pixel),y=imag(pixel), a=2*real(p1),b=imag(p1),; p1 - Julia constant bailout=real(p2),; real p2 - bailout @beginloop, temp=y, y=a*y+b*y*y-x, x=temp, z=x+flip(y), |z|<=bailout } -- Mike Frazier www.fracton.org

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FOTD 15-11-10 (Troubled Julia Set [7])
by Jim Muth 14 Nov '10

14 Nov '10

FOTD -- November 15, 2010 (Rating 7) Fractal visionaries and enthusiasts: Today's image is an almost Julia set of the 4th valley beyond Seahorse Valley out the main spike of the Mandelbrot set. I call it an *almost* Julia set because its orientation is rotated 0.4 degree toward the Rectangular direction. The valley itself appears as the open stripe down the center of the image. The north and south branches of the valley are seen edge-on, and appear as the brilliant blue-white areas flanking the open area and filling the outer Julia shape. The name "Troubled Julia Set" indicates that the Julia set is askew. This close to the over-extended Julia orientation of the Julibrot, a small rotation makes a big difference. The rating of a 7 might not fully justify the calculation time of just under 6 minutes, but the image is still an interesting one. The finished image might be posted on the FOTD web site at: <http://www.Nahee.com/FOTD/> but I am not sure Paul has the site up-to-date quite yet. Sunday turned into a perfect day here at Fractal Central. The blue sky, mare's-tails cirrus and temperature of 61F 16C kept both cats and humans happy. I passed some time walking to the nearby Susquehanna River, where a large number of Canada geese were resting on the water before flying south. FL kept busy doing other things. The next FOTD will be posted in 24 hours. Until then, take care, and old age is the time when a person has the money to do what he always wanted to do but is no longer able to do it. (Hey, don't tell me my attitude is negative. That's the way I see it and I'm not the one who designed it.) Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Troubled_Julia_Set { ; time=0:05:58.08-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 center-mag=0/0/26.83367\ /1.0692 params=90/0/89.6/90/-1.3996313761/0/0/0 float=y maxiter=250000 inside=0 logmap=35 symmetry=yaxis periodicity=6 colors=000REQSESUEUWEXYFZ_G`aHbcIeeJigKmiLqkMtmNwk\ OziPygQxeRwcSvaTu_UtYVqWWnUXkSYiQZfOZcMYaKXZIWWGVU\ EURCTOASM8RJ6QG4PE5OF5NF5MF5LF5KG5KG5KG5KG6KH6KH6K\ H6KH6KI6KI6KI6KI8KH9KGALGBNFDQEESEFUDGWDIZCJ`BKbBL\ dAMfAQbET_IWXMZUQbQTeNXhK`kHdnEgoFfoFepFdpGdqGcqGb\ rGarHasH`sH_sH_uL`vO`wR`xVayYaz`azaYzaUzbRzbNzcKzc\ GzdDzd9zd5zdFzdPzeZyecxehwfhvfduectdbscarb`qa_p`Zo\ _YnZWmYVmXUmWTmVSmURmTQmTPmXOm`OmdNmdNmdRlcCkcDjcC\ icChcCgcCfcCecBdcBccBcbBcbBcbBcbAcaAcaAcaAc`Ac`Ac_\ Cc_DcZEcZFcYHcYIZXJUXKPWMKWNFVOAVP5UR3SS3RT3RU3SW3\ TX4VY4V`4Wc4Wh4Xm4Xr4Zv4`z4az5dz5ez5gz5iz5jz5jz5lz\ 5mz5nz3pz5qz6qz8rz9rzBrzCszDszFszGtzItzJtzKuzMuzNu\ zPvzQvzSvzTwzUwzWwzXwzZwz_wz_wzaxzbxzcxzdxzexzfyzh\ yziyzjzzkzzlzzmzzozzpzzqzzqzzqzzqzzqzzrzzrzzrzzrzz\ szztzzuzzvzzwzzvzzuzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ 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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FOTD 12-11-10 (Deep-Blue Computer [!])
by Jim Muth 14 Nov '10

14 Nov '10

FOTD -- November 12, 2010 (Rating !) Fractal visionaries and enthusiasts: Today's image is a slice through the Julibrot oriented halfway between the Mandelbrot and Julia directions. It is not the one- and-only halfway slice. There is no single slice. The Julibrot is four-dimensional, and today's slice is but one of an infinity of slices oriented halfway between the M and J directions. Today's image is actually the entire parent fractal of the past two days' FOTD's. With minor tweaking, I have used basically the same colors on all three images. I named the image "Deep-Blue Computer". I think this is the name of the computer than beat a grand master at chess a number of years ago. I rated the image with an exclamation mark. (Called a 'bang' in the printing trade.) I surprised myself when I tried the 'real' option on the 'outside' parts. The calculation time of 5 seconds makes whatever comes up worth the effort. But all effort may be eliminated by checking the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> I usually avoid discussing politics, but today I must make an exception. While FL and I were taking a break watching the news at lunch time on Thursday, they showed a 10-second clip of a certain un-named congressman declaring that something must be done about the country's out-of-control financial deficit. A few minutes later, when some effective but painful actions were suggested, the same congressman declared that the suggestions were unacceptable, unworkable and totally out of the question. The resulting laugh from FL made my day. The Thursday weather here at Fractal Central was a repeat of Wednesday's, with a slight drop in temperature to 57F 14C. The fractal cats spent the afternoon basking in the sun on their window shelf. My day was quite busy but still acceptable. The next FOTD will be posted in 24 hours. Until then, take care, and does anyone know how to reduce the deficit without raising taxes or cutting benefits? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Deep-Blue_Computer { ; time=0:00:05.05-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 center-mag=-0.000556425\ /0/0.6726457 params=45/0/-45/0/-0.75/0/0/0 float=y maxiter=1000 inside=0 outside=real symmetry=xaxis colors=00075H76I77K78M79P7AR7BT7CW7DY7E_7Fb7Gd7Hf6\ Ii6Jk6Jm6Jp6Kr6Kt6Lw6Ly6Lz6Oz6Qz6Sz8Uz9VzAUzBSzCQz\ DRzERzGSzHTyITxJUxKVwLVvMWuOXtPXsQYrRZqSZpT_oU`nV`\ nSZoQ_pO`pMaqJbrHcrFcsDctBct8cu6cv4cv2cw0cw2cx3cy4\ cz5cz6cz7cz8cz9czAczBczCczbcz_czYczWczUczSczQczOcz\ MczKczJczHizGszLozQlzTczVczXczZcz`czbczfcziczmczpc\ ztczwczzcz0cz1cz1cz1cz1kzAizJhzRgzTjzUlzWnzXpzYrzT\ ozPlzKizGfzBcz7`z3YzIazXdzjgzjfzjfzjezjezjdzjdzjcz\ jczcYzXSzQMzJGzDBzOIzYOzhUzr_zfYzVWzJUz8Tz9Pz9Lz9H\ zADzA9zA5zA2zH9zOFzULz`SzgYzmczkfziizhlzfnzeqzctzb\ vzLWz36zELzOZzYlzgzzavzWrzQozKkzEhz8dz2az7XzBTzFPz\ JKzNGzRCzV8zRKzNWzJgzJfzIezIdzIczIbzIbzIbzIbzIbzIb\ zIbzIbzIbzIbzKazLazNazOazQazSazTazVczXezYgz_iz`kzd\ mzhozmqzrszvszzzzzzzzzzzzzzzzvuzrwzmyzhzzZozUezPVz\ KLzGAzCAzB8zB6zB4zB3zB3zA4zA4zA5zA6zA6zA7z97z98z98\ z99z9Az9Az8Bz8Bz8Cz8Cz8Dz } 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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<Paul> I hope you're feeling better, Paul.
by Hal Lane 14 Nov '10

14 Nov '10

I hope you're feeling better, Paul. - Hal Lane ######################### # hallane(a)earthlink.net # #########################

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Newtonish Mandelbrot
by Roger Alexander 13 Nov '10

13 Nov '10

According to the formula writer this formula is a newton mandelbrot mash-up. Regular bailouts, inverse bailouts it can be so confusing at times. Pre-rendered at the usual http://maxitersfractalfollies.blogspot.com And finally welcome back Paul, keeper of the FOTD! Newtonish Mandelbrot { ;fract515.gif a minibrot ; blank ; calctime 0:34:08.17 ; created Nov 13, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=_m.frm formulaname=man-newt-man center-mag=-0.78353162878688400/+0.06835193132850351/2185.907/1/44.99999\ 99999986215/-4.14705769724577067e-012 params=0/0 float=y maxiter=1500 inside=0 logmap=42 colors=0Sm000000000000000000000000000000100100200400500700900B00D00G00I0\ 0L00O10Q10T10W10Z10a10e10h20k20o20r20v20y20z30z50z60z80z90zB0zC0zE0zF0zH\ 0zI0zK0zL0zN0zO0zQ0zR0zT0zU0zW0zX0zZ0z_0za0zb0zd0ze0zg0zh0zj0zk0zm0zn0zp\ 0zq0zs0zt0zv0zw0zy0zz1zz3zz4zz6zz7zz7zy7zx7zx7zw7zv7zv7zu7yt7ys7ys7yr7yq\ 6yq6yp6yo6yo6xn6xm6xl6xl6xk6xj6xj6xi5xh5wh5wg5wf5we5we5wd5wc5wc5vb5va5va\ 5v`4v_4vZ4vZ4vY4vX4uX4uW4uV4uV4uU4uT4uS3uS3uR3tQ3tQ3tP3tO3tO3tN3tM3tL3sL\ 3sK3sJ2sJ2sI2sH2sH2sG2sF2rE2rE2rD2rC2rC2rB1rA1rA1r91q81q71q71q61q51q51q4\ 1q31p20p20o20n20m20m20l20k20j20j20i20h20g20g20f20e20d20d20c20b20a20a20`2\ 0_20Z20Z20Y20X20W20W20V20U20T20T20S20R20Q20Q20P20O20N20N20M20L20K20K20J2\ 0I20H20H20G20F20E20E20E20D20D20C20C20C20B20B20A20A20A2092092092082082072\ 0720720620620520520520420420420320320220220220120120010 } frm:man-newt-man {; Sylvie Gallet [101324,3444], 1995 +R.B. ; tiny mod on original Mandel-Newton by Sylvie ; tweaked brainlessly by Robin Bussell ; to give a hybrid mandel-newton fractal z = pixel, c = z, iter = 1, test1 = 1 rad = 3.1, center = (1.0,0.1) pix = (10*pixel+(5.0,-3.4))*(-0.1,-0.95) zn = center+rad/(pix-center) limit = real(p1), b1 = 16, b2 = 0.0001 : test1 = (1-test1), test2=(iter!=limit) z = (z-zn)*test2 + zn z2 = z*z, z4 = z2*z2, z1 = (z4*z-1)/(4*z4) z = (z2+c)*test1 + (z-z1)*(1-test1) iter = iter+1 ((|z| <= b1) * test1) || ((|z1| >= b2) * (1-test1)) ;SOURCE: forummsg.frm } Roger Alexander

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Re: [Fractint] FOTD 06-11-10 (Almighty Spiral [6])
by Paul.N.Lee＠att.net 13 Nov '10

13 Nov '10

Lloyd Garrick (JackOfTradeZ) wrote: > > I dont see any FOTD posted after Oct 27 2010? > Is there a problem or did the site move again?? > Sorry for the delay in getting these uploaded, but it seems that old age is not what it is cracked up to be (or maybe it is a matter of way too many cracks). Anyway, I got admitted to Emergency unexpectedly, and am just now getting caught back up with my emails, and other issues. Mike Frazier wrote: > > I made a 1200x900 pixel image with 5x5 > anti-aliasing which can be downloaded.... > Very nice example of what Jim's FOTDs have within them, especially when one takes the time to explore and render at such larger image sizes. The details in the lower portion sure stand out much better. Sincerely, P.N.L. -------------------------------------- http://www.Nahee.com/PNL/Fractals.html http://www.Nahee.com/Fractals/

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FOTD 14-11-10 (Glimmer of Hope [8])
by Jim Muth 13 Nov '10

13 Nov '10

FOTD -- November 14, 2010 (Rating 8) Fractal visionaries and enthusiasts: Today's image is not exactly a slice of the Z^2+C Julibrot, but it is certainly a slice of some other Julibrot, and at least in my opinion, it is well worth being declared FOTD for November 14. The rating of an 8 includes 2 full points for the coloring, which creates most of the effect of the image. But I cannot take too much credit for the colors. They were created by the Fractint program with a random strike of the <enter> key. The brilliant spot at the center of the image is a point of anti- bifurcation, or as I call such things, an anti-minibrot. While naming the image I was undecided between "Light at the End of the Tunnel" and "Glimmer of Hope". I finally decided on the latter name, since it was the one that fit in the allotted space in the parameter file. The image is a super fast one, finishing in a speedy 36 seconds. The way to avoid the calculation might be to check the FOTD web site at: <http://www.Nahee.com/FOTD/> I say 'might be' because I have not heard from Paul for a week or so, and the last I checked, the web site was not yet up to date. If for some reason, Paul is unable to continue with the FOTD web site, I could probably take it over myself. We are also considering setting up our own web site here at FC. Maybe we could incorporate the FOTD web site into our own site. After a chilly start, Saturday here at glorious Fractal Central turned into another near-perfect day, with a temperature of 61F 16C. Only a few delicate streaks of cirrus marred the unbroken blueness of the sky, while the strong sun in the southwest window gave the fractal cats all the pleasure they needed while the humans were away antiquing. Our day was occupied by the antiquing trip to Richfield. Maybe I'm going soft, because these trips are actually starting to become rather enjoyable. The next FOTD will be posted in some- thing like 12 hours. Until then, take care, and if the best has not already happened, it is yet to come. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Glimmer_of_Hope { ; time=0:00:36.30-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip center-mag=-0.7352361863561826/+0.2917224444576193\ /5293406/1/82.5/0 params=7/100000000000.0/0/0 float=y maxiter=1500 inside=0 periodicity=6 colors=000VULTSKRQIOOHMLFKJEIHCFFADD9BA79866644432\ 21000hhOddM``KXXIUUGQQEMMCIIAFF8BB6774332647A23E6C\ HCGjsKhqJgpIfnIemHckHbjGahG`gFZeFYdEXbEWaDU_DTZCSX\ CRWBPUBOTANSAzzzzzzzzzzzzzvzzrzzozylzxivwervbouZlt\ UisPfrJcqEbp9ao5`n0_m0Zl0Yk0Xj0Wi1Vh1Ug1Tf1Se1Rd1Q\ c1Pb1Oa1N`1M_1LZ1KY1JW1IV1HU1HT1GS1FR1FQ1EP0EO0DN0\ DM0CL0BK0BJ0AI0AG09F08E08D07C07B06A059058047046035\ 024023c12b11a0D`4CZ3CY3BX3BW3BV3AU3AT39S39R29Q28P2\ 8N28M27L27K26J26I26H15G15F14E14D14B13A139138027026\ 0150140130020010oTqiQkdNf_K`VHWQERKBLF8GA5A5254_93\ Z83Y83Y83X83W83W83V73U73U73T73S73S73R62Q62Q62P62O6\ 2O62N52M52M52L52K52K52J42I42I41H4BXrAYsAYtAYuDXsGW\ qJVoMUnPTlSSjVRhXRgWQfVPeVPdUOcTObTNaSN`RM_RM_QLZP\ LYPKXOJWOJVNJVNIUMITLHTLHSKGRJGQJFPIFOHENHEMGDMFCL\ FCKEBJDBIDAHCAGB9FB9EA8E98D97C87B76A75965854754743\ 6335324223112111000_ZPXWN } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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Thermal Emission
by Roger Alexander 12 Nov '10

12 Nov '10

The map suggests heat and flame. Fire-along with air,earth, and water one of four elements to the ancients. Ready made at http://maxitersfractalfollies.blogspot.com. Thermal Emission { ; fract510.gif ; blank ; calctime 0:02:00.94 ; created Nov 12, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=kerrym.frm formulaname=range-y-3_jul center-mag=0.127469/0.618401/13.64778 params=0.5/0.5/4/1/1/1 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:range-y-3_jul { ; Kerry Mitchell 23jan98 ; ; colors Julia set by real part of iterate, only when ; imaginary part of iterate falls in certain range; ; range specified in terms of c ; use decomp=256 ; ; p1 = Julia parameter ; real(p2) = bailout (try 4) ; imag(p2) = decomposition scale factor (try 16) ; real(p3) = center of range (try 1) ; imag(p3) = width of range (try 0.1) ; center of range is multiplied by imag(sqr(sqr(c)+c)+c) ; calculation done on variable zc, z used for coloring ; zc=pixel, c=p1, maxr=real(p2), scale=imag(p2), iter=1 angle=0, fac=imag(sqr(sqr(c)+c)+c) lo=(real(p3)-imag(p3)/2)*fac, hi=(real(p3)+imag(p3)/2)*fac if (hi<lo) temp=lo, lo=hi, hi=temp end if : ; ; iteration ; if imaginary part of iterate falls into range, ; scale real part into decomp angle ; iter=iter+1, zc=sqr(zc)+c, r=imag(zc) if ((r>lo)&&(r<hi)) angle=scale*real(zc) end if ; ; bailout--escape and maximum iterations treated the same ; set "iteration done" flag (iter=-1) ; decomposition method will color according to last time ; imaginary part of iterate was within range ; if iterate was never in range, angle was initially set ; to 0, so decomp with use color 0 ; if ((|zc|>maxr)||(iter==maxit)) iter=-1 z=cos(angle)+flip(sin(angle)) end if iter>0 } Roger Alexander

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