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hurry up angry fish.. and is environment
by Sebastien helie 02 Jan '12

02 Jan '12

The sum of mathematic history cannot be carry by a single individual i hope you taught so. I was wondering if the death last year of Benoit Mandelbrot have something to do with this off and on phenomenon we all observe. Here Jim M. reaction come valide and in-valide following pattern open only to speculation. Anyway i was jealous at one time following popular mathematician, i always taught facing such phenomenon that the popularity of one should be a garanteed for the wealth of all. Nobody even god cannot claim to carry the whole complexe array of the univers of number and following my experience their is nothing better than a formulae comming from a different user (refreshing). Nobody should be best in this world, like in bee no controler just worker in balance. For the rest i never stay in one state long..... and also following my last posted experimente. Do it if you feel adventurous but you will understand that it only livable ion in moderation, experience also skin rash (anaphylactic shock) and hallucination when you woke up, seeing fractal pattern black on wall comming on and off at the speed of imagination. (i recommande beteween 2 and 4 time a month max, for fractal enthusiaste) the reaction also after the sleep get some amplification thru the normalize machine we all are using... I hope my english get better. it's hard to think french and wright in different.. feel free to comment. START PARAMETER FILE=========================== Muth_sh { ; pink star reset=2000 type=formula formulafile=may1997.frm formulaname=Mystic2 function=sin passes=t center-mag=-3.3e-007/9.06e-006/0.8503463 params=7/-5/0.03/-10/-5/-5 maxiter=1000 potential=120/200/4 colors=000<57>000000000<2>000000222<24>nnnppprrr<2>xxxzzzzyy<14>zkkzjjzi\ i<3>zee000zcc<4>zZZzYYzXXzWW<25>C66A55844<3>000<25>nnnppprrr<2>xxxzzzzxx\ <24>zCCzAAz88<2>z22z00x00<22>G00E00C00<2>600400000 } frm:Mystic2 {; Jim Muth a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), k=real(p3), f=imag(p3), g=pixel, z=(pixel)^a+(b*(pixel))^c: z=(fn1(z)+(d*(g)))^k+(f*(cos(g))) g=sqr(g), LastSqr <= 100 } END PARAMETER FILE==================================

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zita and another experiment...
by Sebastien helie 02 Jan '12

02 Jan '12

So to be has short has possible, i set my computer on a fractal who represent a circular channel (every fractint user have one) and set it on color cycle after extensive calculation use. Then i sink 2 or 3 beer and GOTO bed facing the screen, after turning around (cause it set the mind high) i fall in deep sleep, every time i do this i have computer related dream and they are really interesting (mother of computer is the univers of number) Last night my coco III (tandy computer) was in the casting has the master of the univers, i had to find every missing part of it, what a adventure. Yesterday after a check on Jim M. 1997 formulae i end up on a few nice variation, i will go back to the univers master and see the meditator to know if it worthed to post (dual processing) here. Until then be parsing of be nice... START PARAMETER FILE================================== zita { ; only order four star.... reset=2000 type=formula formulafile=2012_1.frm formulaname=zita corners=-9.655069/1.544931/-4.149917/4.250083 params=10/2/10/2/10/2 float=y potential=300/200/4 colors=000LLT<3>SWZUZ`HDP<6>E8UE7UD6V<3>B3YGDP<6>9HN8IN7IN<3>3LLJEN<3>VJ\ FYLD`MB<3>lS3JDQ<7>ZLY<3>fPahQcLjZHFQ<3>JPUJSVKVXHDN<3>FDFFDDECBKJM<3>Zg\ 7bn3ICR<4>Q7cR6eT5h<3>Z0rJER<3>SK_LGR<3>`WZdZahbc<3>xrlGIP<3>BbOJJT<3>Ug\ iWmmZsqazvHDP<6>GFOGFOFFO<3>EHNHCS<4>G7fG6iG5l<3>F0xIGQ<7>WcdYff_ig<3>fu\ oHDR<6>NDiODkODn<3>SCy6xLLFQ<3>bRUgUVkXWp_XubYHIS<3>KafLfjLkmMpqNuuMGS<3\ >hWdn_gtckRFI`HAjJ2KDQ<3>YEUaEVdEW<3>sG_MDN<3>eEFjEDoEBtE9zF6HGO<7>EdDEg\ CEjB<3>Cw5JGR<3>VS`YVb`Yec`gfcjODL<2>kD9IFQsC4 } frm:zita{;sinpix a=real(p1)-imag(p1) b=real(p2)-imag(p2) c=real(p3)-imag(p3) d=a*b*c z=pixel: s=((z^a+z^b+z^c)*d)^(Z*a*b*c) z=s^z+a+pixel |z|<10 } END PARAMETER FILE===================================

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FOTD 02-01-12 (Drunkard's Walk [7])
by Jim Muth 02 Jan '12

02 Jan '12

FOTD -- January 02, 2012 (Rating 7) Fractal visionaries and enthusiasts: Today's image lies in the same parent fractal as yesterday's image, but it is located far west of the main body of the parent, out on a zigzagging filament that springs from the location of yesterday's scene, curves out and around to the left, only to dissolve into chaos as it merges into the chaotic area on the southwest side of the parent's circular main bay. The name "Drunkard's Walk" describes the filaments radiating from the central minibrot, which rather resemble the path a drunkard might take as he stumbles from the tavern, totally tanked. The rating of a 7 keeps us in average territory, though, at least IMO, the image is a small improvement over yesterday's, which was over-rated at a similar 7. The parameter file, in some mysterious manner encoding an infinity of information, runs in 1-1/3 minutes, a time that will bring distress to no one. The fastest and simplest way to see the image is always to check in at the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> where the image has been pre-calculated and posted for instant satisfaction. A higher definition version is posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site is available at: <http://www.Nahee.com/FOTD/> Lots of clouds, a few minor snow flurries and a temperature of 36F +2C made today a typical winter day here at Fractal Central. The fractal cats were more interested in their toy bird-on-a- string than the outside conditions. The humans made it through the day uneventfully. The next FOTD will be posted in 24 hours. Until then, take care, and before you wish for eternal life, give the wish careful thought, but then be prepared. You might get what you wish for. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Drunkard's_Walk { ; time=0:01:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip center-mag=-2.952636809643972/+1.39201736065955/\ 2.782937e+011/1/72.5/0 params=-1.2/-4.4/-2.2/-1.4/\ 0/0/0/0 float=y maxiter=5000 inside=0 logmap=141 periodicity=6 mathtolerance=0.05/1 colors=00040B40C40D40E50F50G60H60I70J70K80L80M90N9\ 0OA0PA0QA0RA0SA0TA0UA1VA3WA5XA7YA9ZAB_AD`AFaAHbAJc\ ALdANeAPgARhATiAVjAXkAZlA`mBbnCdoDfpEhqFirGjpIkoJk\ nLlmMllOmkQmjRniTngUofWoeYpdZpc`qbaqacr`ctZdr_ep_f\ n_gl`hj`ih`ig`jeakcalaam_bnYboWblRgnTdoVbpW_rYYsZV\ t`TvbQwcOxeLzgIyfJxeJweKvdKvdLucLtcMsbMrbMraNqaNp`\ Oo`Oo_Pn_PmZPlZQkYQkYRjXRiXShWSfVSgWShWShXSiXSiXSj\ YSjYSkYSlZSlZSmZSm_Sn_Sn_So`Sp`Sp`SqaSqaSraSrbSsbS\ sbSrXTrRTrLTzDWvEUrFToGSkGQgHPdIO`IMYJLUKKQKINLHJM\ GKJDGMFDPH9SJ6VL1SI2VK3XM3_O4aQ4cS5fU5hW6jY7m_7oa8\ qc8te9vg9xiAzo7zwBztFzrJzpNznRzlXzvUzjRzZdzCPzNNzM\ MzLKzLJzKzzKGzJzzIDzIzzH8zFzzGAzHzzIzzJzzKzzKzzLzz\ MzzNzzOzzPzzFzzKzzPzzTzzYzzbzzfPzkRzpUzuTztSztSzsR\ zsRzrQzrPzrPzqOzqOzpNzpNzpMzoLzoLznKznKzmJzmIzmIzl\ HzlHzkGzkgzZUzeGzkIziKzhLzgNzfPzeQzdSzcUzaVz`Xz_Zz\ Z_zYazXczWdzUfzThzSLz5Mz5 } 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, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 01-01-12 (Generating Colors [7])
by Jim Muth 01 Jan '12

01 Jan '12

FOTD -- January 01, 2012 (Rating 7) Fractal visionaries and enthusiasts: We start the sixteenth year of the FOTD with an image a full point better than the one that appeared yesterday on the final day of last year. But a rating of a 7 is still a rating of a 7, and today's image leaves plenty room for improvement. Luckily, there are 365 days remaining in this leap year to realize that improvement. The parent fractal resulted when I combined 1.2 negative parts of Z^(-4.4) with 2.2 negative parts of Z^(-1.4) on each itera- tion before adding (1/C). This parent consists of a circular main bay surrounded by Mandelbrot buds except on its southwest side, where it is severely eroded. Today's scene lies in the north branch of the valley cutting off a large bud on the west side of the bay. The name "Generating Colors" came to mind when I was struck by the thought that fractals in themselves have no colors. The colors are added by an outside agent, in this case the human fractalists who work with fractals. This corresponds quite well to the 'real' world supposedly 'out there', where the objects themselves have no colors. The colors of the 'real' world are sensations in the mind produced by light waves of various frequencies. The rating of a 7 and a calculation time of 4-2/3 minutes combine to make today's image not much of a bargain. Save the 4-2/3 minutes by viewing the completed image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> Savor the image's finer details on the high-definition web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And remember the original web site at: <http://www.Nahee.com/FOTD/> A sunny morning here at Fractal Central on the first day of the new year was followed by afternoon clouds and showers. The temperature of 52F +6C was mild enough, though the brisk wind kept it from feeling as warm as it might have. The fractal cats seemed undecided, alternating between the window shelf and the shelf by the heat. The humans had an uneventful day today after an active day yesterday. The next FOTD will be posted in 24 hours. It might be better, it might be worse. Until then, take care, and the more we determine about reality, the less real it seems. Maybe the philosophy of Secular Materialism is past its peak. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Generating_Colors { ; time=0:04:40.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=-0.791355305708/+1.621547195972/\ 2952823/1/50/0 params=-1.2/-4.4/-2.2/-1.4/0/0/0/0 maxiter=4900 inside=0 logmap=550 periodicity=6 colors=000F0QF0RF0SF0TF0UG0VH0WI0XK0YL0ZL0_K0`K0aJ\ 0cJ0eL0gK0iI0kH0mF0oD0qC0sA0u90wA0zqtIqtIXYNv74qL9\ mYDijHewLgtIiqFknDllAni7pf5rc2sa0rV6qPBpJGpDLqKRqR\ WqX`qcfqjkqpp2oh3nb3nY3mT3mO3mI3lD3l83l33e83_C3TH3\ NL3HP8HRDHSIHTNHUSHVXHW`HXcMMfRBhW1l_BocKrgUujbnda\ hZ`bU_WOZQJYKDXE8WRJPbUIndBzn4yl4yk4yi4yh4yf4ye4yc\ 4yb4x_7wXAwUDvRFuOIuLLtIOtGQAp4BrDCsLCtTDuaDviEwqE\ xyLsrSnkZidedYl_RrWLgbPYhTOnWEt_4zbHxVUwOfvHruAks7\ er4_q1TnDMlOFj_8hj1fu2hr3ip4km5lk6nh7of8pdBn_ElWHk\ RKiNMhJLdILaHLYGLVFULHaBIYCGVDERECOFAKG8HG7LMBORFS\ WIVaMZfQakTyelyQklPZ`6mS57J5AA4D14G6PiJQdVR`gSXsST\ kWPcZMb2bWCfQMjJVnDdr6nv0wy3nn6ec9XUCOJFG9DNBCUDB_\ FAfG9lI8sK7yLFYOG_TIaZJbcLdhMemUaoaYqhZsccpZbnVckQ\ ciLcgHcdCcb8m`emffmZfmSfmKfmDmz6mzCmzImzOmzUmz_mzd\ mz`mzXmzTzzPzzLzzHzzNzzTzzZzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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word from the univers odd number
by Sebastien helie 01 Jan '12

01 Jan '12

Iran did a nice 2012 show today isn'it. Masculin, missile, and growth i guess. ANyway i was thinking doing the dictionary of fractal word send you a basic frame before we find ourself in Babel...leave a few letter open and so try word every letter is reactive. START PARAMETER FILE======================== alphabet { ; debit reset=2000 type=formula formulafile=2012.frm formulaname=word_frame corners=-0.6035943/-0.34761471/-0.096009672/0.096002042 potential=120/256/4 colors=00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzzzLzzz000555<3>HHHKKKOO\ O<3>ccchhhmmmssszzz00z<3>z0z<3>z00<3>zz0<3>0z0<3>0zz<2>0GzVVz<3>zVz<3>zV\ V<3>zzV<3>VzV<3>Vzz<2>Vbzhhz<3>zhz<3>zhh<3>zzh<3>hzh<3>hzz<2>hlz00S<3>S0\ S<3>S00<3>SS0<3>0S0<3>0SS<2>07SEES<3>SES<3>SEE<3>SSE<3>ESE<3>ESS<2>EHSKK\ S<2>QKSSKSSKQSKOSKMSKK<2>SQKSSKQSKOSKMSKKSK<2>KSQKSSKQSKOSKMS00G<3>G0G<3\ >G00<3>GG0<3>0G0<3>0GG<2>04G88G<2>E8GG8GG8EG8CG8AG88<2>GE8GG8EG8CG8AG88G\ 8<2>8GE8GG8EG8CG8AGBBG<2>FBGGBGGBFGBDGBCGBB<2>GFBGGBFGBDGBCGBBGB<2>BGFBG\ GBFGBDGBCG000<6>000 } frm:word_frame{;sinpix z=pixel: a=sqr(z),b=z^3,c=1/z,d=((-z)^0.707106)+1.4142,e=1/d,f=z+(z-1)^z,g=z-(z-1)^z,h=1.4142^z+0.707106 i=1/h,j=2.26^z/2,k=1/z-z-z-z,l=z^z^z^z,m=flip(z^2)/2,n=tan(z+z),o=tan(sqr(z))/2,p=1/o,q=(1/z+1/z)^2 r=0.707106*z/2,s=1.4142*z/2,t=z^0.707106*4,u=1/t,v=0.66*sin(z),w=1/v z=d+e+b+i+t+z+pixel } END PARAMETER FILE=================================

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8 shell
by Sebastien helie 01 Jan '12

01 Jan '12

To begin 2012, 8 and a shell form. Formulae from Jim indicate that we took a different branch i guess cause, the screen mysteriously indicate plaine. i check your web site, something is to be understood from this difference but i cannot get it. 8_shell is really intersting in the way that playing with parameter can make lot's of different symetrical fractal. have a good 2012. START PARAMETER FILE============================== 8_shell { ; last_of reset=2000 type=formula formulafile=2012.frm formulaname=lastof_2011 corners=-5.309591/13.97041/-8.582258/5.877745 params=-1/0.707106/-2/1.4142/-3/2.2316 potential=120/200/4 colors=000000XeiNReCC`<3>COXBRWPS`bTfqVl`QO<3>JRCES99S64T3<3>bmUXcGQU1Yv\ 8<3>fTEhLGjDIm5KBZG<3>cP`jMfqJkyGqAM_<3>HMOIMLKMIMMFONB<3>BD48A2470RKUnY\ x<3>p`TqaKkeO<2>Ttb<3>SteSteRtfRtgQuhEbP1J4<3>6TN7WS9YXA`aCcf<3>peY<3>u`\ jwZmxYpzWt<3>R8dH1`L7Z<3>cVOh`LmgI<3>A9EpnC<3>XlASlAMk9<3>ZYSbUXeQaiMf<4\ >_RIYSDWT7cHYl5y<2>oEO<3>YUiTYnOatJez<2>3VN8MCDC1<3>byNaGY<2>g0S<2>_c6<3\ >d_GeZIfYLhXO<3>FYR7ZSIb_Tfgdko<3>NjhJjgEieAic5ha<3>`WXhSVeVT<3>UhKQlH3f\ Z<3>FcGJbBKaB<3>SYAUXAWV9<3>cGVeC_h8e<3>fepfmsevv<3>ikajhWkeRmbLrmq<3>gr\ sdttauuZwv<2>S32_65g98<3>Chc4rkBpjIniPlh<2>A8W<2>J_a } frm:lastof_2011{;sinpix a=real(p1)+imag(p1) b=real(p2)+imag(p2) c=real(p3)+imag(p3) z=pixel: z=(z^a)+(z^b)+(z^c)+pixel |z|<10 } END PARAMETER FILE================================

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FOTD 31-12-11 (Critically Different [6])
by Jim Muth 01 Jan '12

01 Jan '12

FOTD -- December 31, 2011 (Rating 6) Fractal visionaries and enthusiasts: Tomorrow begins a new year here at FC, and unless someone is very wrong, (which is most likely the case), none of us will be around to see its end. FL and I, unconcerned about doomsday predictions, passed the day browsing a local antique emporium, which explains the lateness and brevity of the discussion. The image rates a mere 6; its calculation time is 11 minutes -- hardly a bargain, but still worth a look. The name "Critically Different" indicates that the generating expression is the same one that created yesterday's image, but to create today's parent fractal, Z was initialized at the other critical point of the expression, which is 0.7293231403. Today's parent fractal is much the same as the parent of yesterday's image, though in today's parent, only the eastern spike appears to be a critical area. Today's scene is located on the northeast shore line of the third bud out the positive spike of its parent. As can be seen from the image, the law of diminishing returns has already started to set in. The image is basically little more than just another East Valley minibrot with a little extra decoration added. The image is rather slow; the reward is rather small. It's up to the individual fractalist to decide whether the modicum of satisfaction would be worth the calculation time and effort. Save the calculation time by viewing the finished image at: <http://www.crosscanpuzzles.com/Archives.html> And enjoy the bliss, real or imagined, of seeing the image in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Remember the original FOTD web site at: <http://www.Nahee.com/FOTD/> Today here at Fractal Central was marked by lots of clouds, occasional rain showers and even a little sun. The temperature of 50F 10C was mild enough to keep the fractal cats happy, while the humans kept happy in other ways. The next FOTD will appear in 24 hours. Until then, take care, and when will science and religion combine their forces and put an end to the religious conflicts that are causing so much strife in our world? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= CriticalyDifferent { ; time=0:11:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotMix5way passes=1 inside=0 center-mag=+0.89928867757371820/+0.043597207123572\ 44/1.01e+010/1/165/0 params=1/2/-1/3/1/4/-1/5/\ 0.7293231403/0 float=y maxiter=3250 logmap=-418 periodicity=6 mathtolerance=0.05/1 colors=000FAwFAwFAwFAwFAwFAwFAwFAwFAwFAwFAwFAwFAwF\ AwFAxFAzFAzFAzFAzFAzFAzFAzFAzFAzFBzFCzFDzFEzFFzEGz\ CHyFGxDFwFFvGFuFFtEGsDGrBGp9In7Il6Gj8Fh9DfBCdCAbEA\ `FC`HKbIUpPczUmzZpzcszcvzcxzcyzczzUuzKmzCczGUzKKzN\ N5MT5LZ5Kd5Ii4Ho4Gu4Fz4Dr9BkDAcI8cM6cQ5cV3cZ2cbQmR\ TsTVpVXmWZjYagZcd`eaagZcjWdlTfnQgpNirLjlRlfXmabnWh\ oRnphqkztgxqivojtmkrklpimnfnldojbph`qgZrd`oaam_bkX\ ciUegSfePgcMhaKi_HkYElWCmU9nS7oQMnX_mcmmilkjkikjgl\ iemhcngbnf`oeZpdXqcVrbTsbSsiOpoLmuIjpGflEbhDZdBV`9\ RX8NY9QYATZBWZBZ_Ca_Dd_Df`GcaJaaMZbOXcRVcUSdXQeZNe\ aLfdJggGgiEhlBio9iq7er9brBZsDWsESsGPtILtJIuLEuNBuO\ GvoDwkBxg9yd6z`4zX2zU6zVAzVEzWIzWMzWQzXUzXYzXazYez\ YizYezVbzSZzQWzNSzLPzILzGIzDFzBNzFUzIazLhzOozRpzPp\ zOpzNpzLpzKpzJpzIpzGpzFpzEpzDzztyzuyzuxzvxzvwzwwzw\ wzwizpWziIzcJzaJz`JzZJzYHzcGziFzoEzuLzhSzWYzK`zKcz\ KfzKgzGhzDiz9jz6izDhzKczc } frm:MandelbrotMix5way {; Jim Muth z=p5, c=pixel, a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4): z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <= 100 } END PARAMETER FILE=========================================

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the first. flux
by Sebastien helie 31 Dec '11

31 Dec '11

Let fractal-life for year 2012 cause i think fractal is a interesting extension of being. Life can be define for any consciousness who considere communication, creativity and individuality justificative element of being. First must existe a collective consciousness, a cynergic force who developp individual form of creative engine. This mobile form existe by opposition to his history who is immobile and keep withing itself knowledge and memory. The fractal who must be associated with this sentance is somewhere on my disk, you probably had it in your parsing experience, it's circle in circle touching in on point. Where to put fractal univers? i like to think it at the beginning, just after death movement excluded. Attempt to set it in movement end up in really bizzard computer reaction. Wish you all a great year 2012 START PARAMETER FILE============================= flux_flux { ; rich start. reset=2000 type=formula formulafile=test.frm formulaname=super8_1 function=sin corners=-0.2010783/0.9661853/-0.50831914/0.36712939 params=1/1 potential=120/200/4 colors=000ZLv<3>cBwYQv<15>oVhqWhrWg<3>wYcWRuUStWQqTTr<3>MYmLZkJ_jHah<16>\ XggYhgZhg_hg`igaigbjf<10>ZaWY`VY_UXZTXYSWXR<5>XMEXKCYI9<2>YC3ZA0ZA0<10>P\ 83P83O83<3>K75VLz<15>ojWpkUqmS<3>wtK<15>HYYEXZBV_<3>0Pc<9>AWjBXkCYl<2>F_\ nH`oJan<9>dnWfpUiqS<3>rwK<3>doT`lWXjY<2>Mce<14>`OnaNobMpcLpdKqfIr<3>lKrn\ LqoLq<3>vOp<3>UUX<14>KmkJnlIom<2>GspFurGuq<3>Ktj } frm:super8_1{;sinpix a=imag(p1) b=real(p1) c=a/b z=pixel: r=z^ln*c f=z*c^(z-1) ac=e^r+z z=1/fn1(ac^z+t^(sqr(z))) |z|<4 } END PARAMETER FILE======================================

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FOTD 30-12-11 (Diminishing Returns [7])
by Jim Muth 30 Dec '11

30 Dec '11

FOTD -- December 30, 2011 (Rating 7) Fractal visionaries and enthusiasts: Start with Z^2, subtract Z^3, add Z^4, subtract Z^5 then add C on each iteration. The result is a fractal with a mis-shapen main bay and several large sub-bays. Large period-2 buds lie on both the east and west extremities of the parent, with spikes extending outward along the X-axis from both buds. Today's image is located on the spike extending west from the western large bud. Luckily, one of the critical points of today's iterated expression lies at zero, which would have saved some tedious calculation if I had not been curious about other critical points. (A second critical point lies at +0.729323..., which draws a very similar parent fractal. A point of inflection lies at +0.436117..., but this also draws a very similar image.) The name "Diminishing Returns" refers to the nature of fractals. The most interesting Mandeloid is created by raising Z to the power of 2. As the exponent of Z is increased, the Mandeloids start to look ever more similar, and by the time we reach Z^100, there is almost no difference in the overall appearance or in the smaller details. In short, the law of diminishing returns kicks in, and the fractals start to all look the same. The same law of diminishing returns applies to the magnitude. As we go deeper into a fractal such as the Mandelbrot set, the minibrots we find grow ever more interesting at first, but at a magnitude around 10^25 they begin to all look the same, and by the time we reach 10^100, with some few exceptions, little but nearly identical concentric circles surround the minibrots. The same diminishing returns appear as we pile on various powers of Z. Today's parent fractal combines four different powers of Z in each iteration, yet the image falls far short of some of the images created by the MandAutoCritInZ formula, which combines only 2 different powers. Out of curiosity, I have written formulas that pile on up to 15 different powers, only to discover that, once again, the fractals all start to look the same. The rating of a 7 is near FOTD average, but the calculation time of 12 minutes is too high a price to pay for a merely average image. Luckily, rescue from boredom may be found at the FOTD web sites. The official FOTD web site with the completed image is at: <http://www.crosscanpuzzles.com/Archives.html> A more-detailed high-definition version of the image is posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> Another day of uneventful weather prevailed here at Fractal Central today, with mostly cloudy but dry skies, a little sun and an unremarkable temperature of 43F +6C. The fractal cats were satisfied that no draft fell on their shelf by the window. The humans, FL and I, had another in a long string of similar routine days, which are quiet enough, but leave little to report. The next FOTD, the last of the year, will be posted in 24 hours. I'm trying to think of a fractal theme for the month of January, so far without much luck. Until next FOTD, take care, and only 357 days remain before the world ends. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= DiminishingReturns { ; time=0:12:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotMix5way center-mag=-0.764203\ 8506481917/+0.00004122174900695/1.586226e+012/1/\ -83.25/0 params=1/2/-1/3/1/4/-1/5/0/0 float=y passes=1 maxiter=3750 inside=0 logmap=460 periodicity=6 mathtolerance=0.05/1 colors=000mCcmCcmCcmCcmCcmCcmCcmCcmCcmCcmCcmCcmCcm\ CcmCcmCcmCcnCcnCcnCcnCcoCcoCcoCcpCcpBcpAcp9bq8`q7Y\ r6Vr2Tr3Vr3Wr4Xr4Yr5Zr5_r6`r6ar7br7cr7dr8er8fr9gr9\ irAjrAkrBlrBmqBnqCoqCpqDqqDrqEsqEtqFuqFvrDyqFwqHvq\ JuqLtqNspPqpRnpTkpUhpUeoUboU_lUXhUUcUUZUUUUUPUUNRU\ ONXOJ_PFbPBeQ7hQ3kO5nN7qL9qKBnIClHEjFGhEIfCKdBLeCK\ fCJfCIfCHfCGfCGfCFfCEfCDgCCgCCgCBgCAgC9gC8gC8gCAaB\ CXBERAGLAHGK4UH5QE5NC5K96G76D46A05A48AABAFEAKHAPKB\ UMCZODcQEcSFcRGcQHcPIcOJaNK_MLZLLSIOMGRGETACW4AY7C\ WAEVCGTFISHKQKMPNONPQMSSKUUJXWHZYGYVHXTHWRHbbAdb5g\ a6j`7l_8o_8qZ9tYAvYApV9jS9dP9ZM8TJ8NG8HD8VU9gj9tz9\ ryIpyRox_mxhlxpiahfG`WOgMWmCcs2kyGfuTareXodPecHXbA\ OaGK`MH_REZXBYa8Xc5Wc2Uc3Tc4Rc5Qc6Pc7Nc8Mc9Lc9FcBA\ cDGcELcFQcGVcH_cIdcJicKccSZc_UczZczcczhczmczqczmcz\ iczemzamzYmzUmzRmzZmzemzmnztzzmzzfzz`zzUzzNzzHzzAz\ z4zzLzzLzzVzzVzzUzzTzz_zz } frm:MandelbrotMix5way {; Jim Muth z=p5, c=pixel, a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4): z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <= 100 } END PARAMETER FILE=========================================

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FOTD 29-12-11 (Total Breakdown [?])
by Jim Muth 29 Dec '11

29 Dec '11

FOTD -- December 29, 2011 (Rating ?) Fractal visionaries and enthusiasts: The rating of today's FOTD image is a question mark. I'm not sure how to rate it. I think this is the first FOTD image to actually make the breakdown of definition its main feature. The magnitude of 4*(10^9) is not all that great, but something like a quantum uncertainty principle must exist in Julia sets, which prohibits any trick that might reveal detail beyond the standard Mandelbrot magnitude limit of 10^12. Actually, such attempts merely shift the decimal point rather than add the imaginary extra precision of extra decimal places to the math. Curiously, when today's image is calculated by the standard math routine used by the type=julzpower formula, the breakdown is notably more severe. Today's image is actually part of one of the Julia sets of yesterday's image. This parent Julia set is filled with variations of today's scene, some of which are worth FOTD status in themselves, and might appear in a future FOTD. The name "Total Breakdown" exaggerates the situation quite a bit. A total breakdown would be either a flat color covering the screen or a screen full of featureless fractal sand. The calculation time of 1-3/4 minutes is reasonably brief for an image whose rating is a mystery. Those who do not enjoy mysteries yet do enjoy fractals may view the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition version posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> will reveal even more of the breakdown of precision, though I doubt that any new stuff will be revealed. Perfect resolution may be achieved only by calculating the image with the type=julzpower formula, which does support arbitrary precision math. But doing this will increase the calculation time from seconds to days. The original, now classic, web site may be accessed at: <http://www.Nahee.com/FOTD/> The day began with a brilliant sunrise and a temperature of 21F -6C here at Fractal Central. But clouds moved in during the morning, and hung around for the rest of the day. The high temperature of only freezing was near normal, but compared to the well above-average weather we have had so far this season, felt quite cold. Luckily the wind was light. The fractal cats spent the day seeking warmth, finally finding it on the shelf over the radiator in the hallway. The humans passed the day wondering when everything will fall apart. With the government paralyzed and unable to switch from hand-out-the-benefits mode to cut-the-benefits-and-raise-the- taxes mode, the day of collapse can't be too far off. The next FOTD will be posted in 24 hours, unless the collapse comes before then. Until next time, take care, and be ready to bite the bullet. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Total_Breakdown { ; time=0:01:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=slices.frm formulaname=JuliaN center-mag=-0.0089014397\ 2939820/+0.01721564886246437/4.252493e+009/1/-10/0 params=2.0001/0/0/0/-1.940345965619678/7.483135796\ 9939e-008 float=y maxiter=5000 inside=0 periodicity=6 mathtolerance=0.05/1 colors=000zOEzLCzKJcUIc3Hz3zW3FZ3Fa3Ed3Dh3Ck3Bn3Aq\ 39t38w37z37v26s26p25o23m25j25g24c14`14Y13V13S13P12\ M12Im2Fm1Lm19z1zz030zcm2_m1Wm1SG1OD1KA1I91mUzE70C6\ 0A508406304202109VI8RG7OE6KC5HA4D83A6264132F_mDWgB\ SaAOX8KR6GM5CG38B145T0RQ0NN0KK0HH0DE0AC09B07906705\ 503302101jzY`lTLePI_MGUJDOGAJC8E9596243EzzCpmBkcAf\ R9aO8XL7TI5OF4JC3E9296143BlM9cI7WE5OB3G7183K2rE1oD\ 1cC1eB1ZA1WA1U91R81P71M60U50M50I40F30D207105002zvz\ UUc31z20k20k20c20X20V20T10R10O10M10K10I10F00D00B00\ 9006004002IYKGWMFVNETODSPBRQAPR9OS8NTGVYObaViebqii\ xmciYYVITG2XUA_fIbsQ9Jl8Sh8`d8h`8qX8yT9iNAVHBGBZcT\ eZTlTSsOSuUPvZNwcKxhIymFzrDniHbaLRTPFLT4DWp70q60r5\ 0s40t40u30v20w20x10y00zKHzKEzKBzU8zK5z7Hz6Gz6FzUEz\ 5Dz5Cz5Cz4Bz4Az4cz38z38zc7z26zc5z2mz14z13z1mz01z00\ zAzz80z7zz7Zz6Xz6Wz6Uz5Sz5RzKPz4Nz4Mz4Kz3IzKGzUFz2\ Dz2Bz2Az18z16z15z03z01zRG } frm:JuliaN {; Jim Muth b=p1, z=p2+pixel, c=p3: z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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