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Re: Fractint digest, Vol 1 #367 - 5 msgs
by JackOTradez 20 Jan '03

20 Jan '03

It worx! Yeah-Right! I have figured how to animate the TMan1 Rising 3D Mandelbrot. The program is writ and the images are rendering as I write this. They are slow. It will take a few days at this rate; possibly due to all that extra complex math my poor little CPU has to deal with. I also changed the color palette. It will look like a flaming 3D Mandelbrot arising and forming out of a lake of frothing lava - way cool! Soon as it's done I will post on my web site for download. Mean time, let me check out those Lee Skinner / Guy Marson formulas ... ... ... (one of the nice things about being unemployed is you have lotsa time for these things <g> )

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FOTD 20-01-03 (Bad Boy [6])
by Jim Muth 20 Jan '03

20 Jan '03

FOTD -- January 20 2003 (Rating 6) Fractal visionaries and enthusiasts: Today's image is titled "Bad Boy". This name does not allude to a reggae song; it refers to the fact that at one point there are 12 elements surrounding the central midget, which is quadratic in nature and therefore not expected to have rings that consist of a number of elements that is a non-integral power of 2. The image might also be considered bad because it is unstable. The slightest change in the real(p2) parameter causes the entire scene to vanish. Finally, the two satellites in the northeast and southwest corners have six elements surrounding them, which is another wrong number. This image certainly earns its bad reputation. I don't know what it's going to do when they come for it. The generating formula is unusually simple. It takes Z^3 and adds somewhat more than half as much Z^5 before adding C. The resulting parent fractal is rather routine, except when the value of the parameters is near today's, at which point the area of the fractal where today's image lies becomes unstable. Like everything else in the world of fractals, this localized instability happens because of the things numbers do. Given the nature of complex numbers, it could not be otherwise. I rated the image at a 6, a rating that might be considered generous. The coloring is only moderately impressive, and the math interest is worth only slightly more. But then, a 6 is only slightly above average, so the rating will remain. The attached parameter file renders in under 6 minutes on my tired old P200 machine, which might soon be replaced as my fractal-dedicated unit. Those who would rather not wait 6 minutes to see the image may download it, already completed, from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> I continue to find interesting things in variations I am creating of the recently posted Tman formula. Regardless of the number of dimensions, the images are out of this world. In fact, they're in the fractal world. Some unusual images could be coming in the near-future FOTD's. The Fractal Central weather turned milder, but remained too cold on Sunday for the dynamic cats to venture outdoors. There was some sun, but also flurries of snow, and a temperature that never reached freezing. The dynamic ones were surprisingly pleasant in the midst of their confinement. Today is starting milder yet. Could this be the day when the cats' paws reach the turf of the yard? Check in 24 hours to see. Until then, take care, and go where the fractals take you. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Bad-Boy { ; time=0:05:40.20--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+1.09529517003905100/+0.003871516957443\ 89/856841.9/1/155/2.75135829397310516e-009 params=1/3/-0.599/5/0/0 float=y maxiter=1200 inside=0 logmap=112 periodicity=10 colors=0004EO4FS3GX3H`2Ie2Ji2Jm6HmAGmEFmHEmLDmPBmT\ AmW9m_8mc7mg5mj4mn3mr2mv1my0mw6cvCUpCPkCLfCHaCCXC8\ SC4NC0ME2MF4MG5MH7MI9LJALKCLLELMFLNHLOIJPKIQLHQNGR\ OFSQESRDTSCUUEXVG_XIbYKeZMhYOk`QldUmhYmkcmnhmpnmrs\ mtrhprclrZhrUdrP`qKXqFTqAPq5Lq0HsAEtKCuU9vc7reDofI\ kgNhhTdjYakbYlhVmmSnrRonRokQohQodPoaPoZXbbcRfjEjq2\ np7npCnoHnoLnoQnnVnn_nncnmhnmmnmqninhfkcbiZ_fUWcPT\ aKPZFMWAJU5PT9UTCZTFdSJiSMnSPsSSi3uj5qj7mk9ikBfkCb\ lEZlGVmISmKOmLKnNGnPDoR9oT5oU2nW6nX9nYCmZFm_Im`Lma\ OibPfbPbbQ_bQWcRTcRPcSMcSIdTFdTBdU8dU7bV7`W7ZW7XX6\ VY6TY6RZ6P_6N_6N_7O_7O_7O`7O`7O`7O`7OaKOaLOaMOaNOa\ OObPObQObRObSOcTOcUOcVOcWOdXPdYQfZPd_Pd`PdaPebPecP\ ecPecPfcPfcPfcPfcPfcPgcPgcPgdPgePhfPhgPhhQhiQhjQik\ QilQimQioRjqSjsTjuUjwVjyWkzXkzYkzZkz_lz`lzalzblzcm\ zcnzcozcpzcqzcrzcszctzcuzcvzcxzcyzczzczzczzczzczzc\ zzczzczzczzczzczzczzczzcz } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Re: Fractint digest, Vol 1 #366 - 3 msgs
by JackOTradez 20 Jan '03

20 Jan '03

Most Intriguing. The Russ-Dude strikes again! The rising Mandelbrot is way cool. Now I must figure out a way to animate it and make a viddie - like a Mandelbrot "sunrise" from an ocean horizon.......

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Re: [fractint] FOTD 18-01-03 (Rising mandelbrot [6])
by Lee H. Skinner 19 Jan '03

19 Jan '03

This TMan1 formula can produce some amazing looking 3D-like images. frm:TMan1 { c1=flip(real(pixel)),c2=imag(pixel),c3=p1 z1=z2=z3=0: t1=z1*z1+2*z2*z3 t2=z3*z3+2*z1*z2 t3=z2*z2+2*z3*z1 z1=t1+c1,z2=t2-c2*c2,z3=t3+c3 z=z1+z2+z3 |z| < 8 } The following par produces what looks like midgets intersecting in 3 perpendicular planes: 60118025 { ; 3-Plane Midget t= 0:33:48.68 ; on a P4 2Gh at 1600x1200 Jan 19, 2003 22:43:12 ; Image Copyright 2003 by Lee H. Skinner ver=2002 ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=fractint.frm formulaname=tman1 passes=1 center-mag=-0.14086254709453280/+0.63267349162819330/12556.45/1/-137.500\ 000000003013/1.74807113229036304e-011 params=-0.4/0 float=y maxiter=18000 inside=0 logmap=108 symmetry=none periodicity=10 colors=000d6fX7`Q8U<2>AHV<2>4A9<3>BONCRQEVT<2>JdbLhfOig<12>mttouuqvv<3>z\ zzxzz<16>UcOTaLR`J<3>JV9LY4<11>OG4OF4OD4<2>P94Q74Q86<21>EVmDWoDXq<3>Aaz<\ 2>`Lz<5>lcZnfUpiP<2>vsBxv6xvH<3>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8KJ8<3>MD6N\ C5NA5O94P73<3>aI8eLAhMBiODjQF<3>qeBriAtm9vq8xu7zz5zz4zz3<8>zY4zV5zS5<3>z\ E6<28>jEJiEJiEK<3>fDMhENjFPlLS<3>rdhtilvoqxtuzzz<3>pvzmtzgpz`lzUhz<3>iWz\ mTzrPz<3>z3zs4tk5m } The 3 following images show more 3D-like views: 60118021 { ; Fig Tree Strangling a Mandelbrot t= 0:04:09.58 ; on a P4 2Gh at 1600x1200 Jan 19, 2003 22:43:05 ; Image Copyright 2003 by Lee H. Skinner ver=2002 ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=fractint.frm formulaname=tman1 passes=1 center-mag=-0.14094542272236100/+0.61891532192206370/284916.1/1/-37.4999\ 99999989555/1.37909239583677845e-010 params=-0.4/0 float=y maxiter=18000 inside=0 logmap=63 symmetry=none periodicity=10 colors=000bOvdRqfUlhXgj`c<2>piQrmLsnQ<3>wujxvoyxtzzz<3>jqdfo_blU<3>Mb8<3\ >LQ8KM8KJ8<3>MD6NC5NA5O94P73<3>aI8eLAhMBiODjQF<3>qeBriAtm9vq8xu7zz5zz4zz\ 3<8>zY4zV5zS5<3>zE6<4>xE8wE8wE9<3>tEAsEArE9<11>eE3dE3cE2<2>`E1ZE0_G4<5>j\ YTl`Xnc`<2>tllvoqxtuzzz<3>pvzmtzgpz`lzUhzUhzUhz<44>wxzwxzxyzyyzzzz<33>ai\ s`ir_hr<3>Xfqzsz<24>LezJdzHdz<3>Aaz<2>`Lz } 60118007 { ; Cave of the Fire Pit t= 0:21:46.41 ; on a P4 2Gh at 1600x1200 Jan 19, 2003 22:42:41 ; Image Copyright 2003 by Lee H. Skinner ver=2002 ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=fractint.frm formulaname=tman1 passes=1 center-mag=-0.14109239066731250/+0.63265570738880520/95831.26/1/-44.9999\ 999998383586/-5.38782074510635312e-011 params=-0.4/0 float=y maxiter=18000 inside=0 logmap=139 symmetry=none periodicity=10 colors=000LBUFEVAHV<2>4A9<3>BONCRQEVT<2>JdbLhfOig<12>mttouuqvv<3>zzzxzz<\ 16>UcOTaLR`J<3>JV9LY4<11>OG4OF4OD4<2>P94Q74Q86<21>EVmDWoDXq<3>Aaz<2>`Lz<\ 5>lcZnfUpiP<2>vsBxv6xvH<3>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8KJ8<3>MD6NC5NA5O\ 94P73<3>aI8eLAhMBiODjQF<3>qeBriAtm9vq8xu7zz5zz4zz3<8>zY4zV5zS5<3>zE6<28>\ jEJiEJiEK<3>fDMhENjFPlLS<3>rdhtilvoqxtuzzz<3>pvzmtzgpz`lzUhz<3>iWzmTzrPz\ <3>z3z<4>Q8U } 60118013 { ; Fiery Forest t= 0:07:39.35 ; on a P4 2Gh at 1600x1200 Jan 19, 2003 22:42:51 ; Image Copyright 2003 by Lee H. Skinner ver=2002 ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=fractint.frm formulaname=tman1 passes=1 center-mag=-0.14072100474163920/+0.63232110386355890/380133.7/1/-142.500\ 000001225942/7.55598403290314025e-010 params=-0.4/0 float=y maxiter=18000 inside=0 logmap=110 symmetry=none periodicity=10 colors=000JXzSRz`Lz<3>hXgj`clc_nfVpiQrmL<3>vsewujxvoyxtzzz<3>jqdfo_blU<3\ >Mb8<3>LQ8KM8KJ8<3>MD6NC5NA5O94P73<3>aI8eLAhMBiODjQF<3>qeBriAtm9vq8xu7zz\ 5zz4zz3<8>zY4zV5zS5<3>zE6<6>wE9vE9uEA<3>sEBrEBqEA<13>cE3bE3aE2<3>XD0<3>f\ VMiZSlcY<9>LmoJnpGor<3>4sz<41>MgzMgzNgz<2>OfzPeyOex<63>D_vD_vD_vD_vD_vCZ\ uB_wAaz }

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investigations#3.2
by jos hendriks 19 Jan '03

19 Jan '03

Dear reader I'm not really fond of complex complex functions. They are too complicated for me and I can't follow what they are "doing". So I continued with something much simpler the real valued function f(x)=x^2+c. If you choose c between -2 and .25 then the prisoner set of the orbits of x,f(x), f(f(x),..... is an interval. For c>. 25 all orbits escape and there is no prisoner set. For c<-2 the prisoner set is a Cantorlike set (you can figure these things out by drawing the graph of f(x)=x^2+c for some values of c and then tracing back the orbits of intervals (the prisoner set is invariant not only under forward but also under backward tracing)) So making pictures with f(x,y)=(x^2,y^2)+ (c1,c2) what do you expect? Well choosing c1 and c2>.25 nothing, c1 and c2 between -2 and .25 a rectangular prisoner set. The interesting things are when you choose one or both of c1 and c2 smaller then -2. . If you choose only one of them <-2 then you expect a band-like patron. If both <-2 then you expect a patron with smaller and smaller rectangular parts. Below are some pars. Pictures are indeed as expected. The boogie_woogie pars all have the same value for c1 and c2. But the use of different coloring methods give slightly different but interresting/nice pictures. All the pars renders in seconds, so you don't need to spend much time if you decide to look at them. frm:Jh_square {;Jos Hendriks,2002 if (ismand) z = 0 , c = pixel else z = pixel , c = p1 endif : a=real(z),b=imag(z) z=a*a+flip(b*b)+c real(z)<p2 && imag(z)<p2 } Boogie_Woogie_1 { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=invest~1.par formulaname=jh_square ismand=n passes=1 center-mag=0/0/0.6666667 params=-2.012450635926158/-2.013287548247079/4/0 float=y colors=000zpC<4>zTBzOBzJB<3>z0AzAM<2>z3az0gz0i<3>z0rz0uz0wz0yz2x<14>ziOz\ kMznJ<3>zzA<3>zoEzlFzjGzgHzeJ<8>zUQzSRzRS<3>zLV<19>zVnzWozWp<5>z`uzavzbw\ <2>zeyzfyzgyzhyziy<3>znyzoyzpy<2>zty<3>zoyznyzmx<3>zgpzfnzelzci<19>zrkzs\ kztl<3>zwlztl<3>zbgzZfzUe<2>zHa<4>zHfzGg<3>zAfz8ez7e<19>zkkzmkzok<3>zwl<\ 4>zndzlbzja<2>zeXzcVzcV<5>zZUzYUzXUzXTzWT<8>zRLzQKzQJ<3>zNFzMEzLD<12>zuC } Boogie_Woogie_2 { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=invest~1.par formulaname=jh_square ismand=n passes=1 center-mag=0/0/0.6666667 params=-2.012450635926158/-2.013287548247079/4/0 float=y outside=mult colors=000aJB<4>iMEjNFlNF<2>qPHsQIwYB<4>wRBwPBwOB<3>wIBwKBwNBwPB<15>cYGb\ ZG`_H__HZ`HXaI<10>RQOQPOPOPPNPOMQNKR<25>RaERbDRcD<2>ReBSfATdC<10>cIYdG_e\ Ea<3>i5i<12>FBYDCXACW<3>0FS<8>RDWUDXXDX<3>hB_<15>shdtjduld<2>wrexufxuc<3\ >uuRuuOtuLsuH<14>GfJEeJBdJ<3>0_K<9>XSK`SKcRK<3>qNL<5>WMWTMXPLZ<3>AKf<3>E\ WdF_dGbc<2>JlaETK991<16>_IA } Boogie_Woogie_3 { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=invest~1.par formulaname=jh_square ismand=n passes=1 center-mag=-0.00113141/0.401369/9.887676 params=-2.012450635926158/-2.013287548247079/4/0 float=y outside=mult colors=0000jR<2>0eM0cK0cK<5>0ZJ0YJ0XJ0XI0WI<8>0RA0Q90Q8<3>0N40M30L2<6>0d\ 10g10j1<3>0u1<5>0T00O00J0<3>0000AB<2>03R00X00Z<3>00g00j00l00o<3>0Bf0s1<1\ 1>0O80M80J9<3>08C<22>0ad0be0dg<5>0jn0ko0lp<3>0qu<3>0ZR<2>0lQ<6>0Qd0Mf0Jh\ <3>05q<3>0El0Gk0Ij0Lh0NgFPf<9>FlTFnSFpR<3>EzL<3>Sb9WX6_Q2LUC5YM0aW0ef06f\ <5>0_J<3>0s31x01w0<2>0s00r10p10o20m2<16>0RA0PA0OB<3>0ID<2>0PN0RY<9>0k`0m\ `0o`<3>0wa<5>0lS } Boogie_Woogie_4 { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=invest~1.par formulaname=jh_square ismand=n passes=1 center-mag=0/0/0.6666667 params=-2.012450635926158/-2.013287548247079/4/0 float=y outside=summ colors=0000SA<3>0NC0LD0KD0IE<2>0PO0RZ<9>0ka0ma0oa<3>0wb<4>0nV0lT0jS<2>0e\ N0cL0cL<5>0ZK0YK0XK0XJ0WJ<8>0RB0QA0Q9<3>0N50M40L3<6>0d20g20j2<3>0u2<5>0T\ 10O10J1<3>0000AC<2>03S00Y00_<3>00h00k00m00p<3>0Bg0s2<11>0O90M90JA<3>08D<\ 22>0ae0bf0dh<5>0jo0kp0lq<3>0qv<3>0ZS<2>0lR<6>0Qe0Mg0Ji<3>05r<3>0Em0Gl0Ik\ 0Li0NhFPg<9>FlUFnTFpS<3>EzM<3>SbAWX7_Q3LUD5YN0aX0eg06g<5>0_K<3>0s41x01w0\ <21>0UA } Boogie_Woogie_5 { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=invest~1.par formulaname=jh_square ismand=n passes=1 center-mag=0/0/0.6666667 params=-2.012450635926158/-2.013287548247079/4/0 float=y outside=atan colors=000SG9<10>iMFjNGlNG<2>qPIsQJwYC<4>wRCwPCwOC<3>wICwKCwNCwPC<15>cYH\ bZH`_I__IZ`IXaJ<10>RQPQPPPOQPNQOMRNKS<25>RaFRbERcE<2>ReCSfBTdD<10>cIZdG`\ eEb<3>i5j<12>FBZDCYACX<3>0FT<8>RDXUDYXDY<3>hB`<15>shetjeule<2>wrfxugxud<\ 3>uuSuuPtuMsuI<14>GfKEeKBdK<3>0_L<9>XSL`SLcRL<3>qNM<5>WMXTMYPL_<3>AKg<3>\ EWeF_eGbd<2>JlbETL992<10>QF8 } Boogie_Woogie_6 { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=invest~1.par formulaname=jh_square ismand=n passes=1 center-mag=0.00500626/-0.0250417/4.901961 params=-2.012450635926158/-2.013287548247079/4/0 float=y outside=atan colors=000ISEDSD9RC<3>5P84P73O6<2>0L3<6>Xd2ag2ej2<3>xu2<5>VT1PO1KJ1<3>00\ 0AAC<2>J3SM0YN0_<3>T0hV0kW0mY0p<2>`8iaBg`Cg<17>DXjCYkBZk<3>5cl<17>QGnSFn\ TEnUCnVBnX9o<24>LENLEMKFL<2>JFIIGGKHG<4>ZOGaPGdRG<3>pXGnXJPmn<3>DgfBfdAe\ b8c_<19>mraosartb<3>zwbwtb<3>ibYeZXbUW<2>SHS<3>bHWeHXhGY<3>rAXt8Wv7W<19>\ xkaymayoa<3>ywb<4>tnVtlTsjS<2>peNocLncL<4>i_KgZKfYK<3>bVJ<3>MTF } Boogie_Woogie_7 { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=alle.frm formulaname=Jh_square ismand=n passes=1 center-mag=0/0/0.6666667 params=-2.012450635926158/-2.013287548247079/4/0 float=y outside=imag colors=000<8>000000000<3>000zzz<88>zzz<4>zzzccc<143>ccc } Beach_Tent_Stuff { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=alle.frm formulaname=Jh_square ismand=n passes=1 center-mag=-1.12092/0.549035/5.495472 params=-2.074165287254229/-0.1060234799935393/4/0 float=y maxiter=30 colors=(a)goodega.map } More_Stuff { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=alle.frm formulaname=Jh_square ismand=n passes=1 center-mag=0/0/0.6666667 params=-1.266704348177156/-2.115420862728206/4/0 float=y maxiter=30 colors=000Pmm<3>DgeBfcAea8cZ<19>mr`os`rta<3>zwawta<3>ibXeZWbUV<2>SHR<3>b\ HVeHWhGX<3>rAWt8Vv7V<19>xk`ym`yo`<3>ywa<4>tnUtlSsjR<2>peMocKncK<4>i_JgZJ\ fYJ<3>bVI<3>MTEISDDSC9RB<3>5P74P63O5<2>0L2<6>Xd1ag1ej1<3>xu1<5>VT0PO0KJ0\ <3>000AAB<2>J3RM0XN0Z<3>T0gV0jW0lY0o<2>`8haBf`Cf<17>DXiCYjBZj<3>5ck<17>Q\ GmSFmTEmUCmVBmX9n<24>LEMLELKFK<2>JFHIGFKHF<4>ZOFaPFdRF<3>pXFnXI }

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FOTD 19-01-03 (Maximum Spirals [5])
by Jim Muth 19 Jan '03

19 Jan '03

FOTD -- January 19, 2003 (Rating 5) Fractal visionaries and enthusiasts: Since yesterday's FOTD I have continued to work with a variation of the Tman formula that was posted on Friday. Working with this formula gives the impression that more than three dimen- sions are involved. I can get no clear mental image of slicing through a single 3-D object. And if there is only one dimension in addition to the two on the screen, why are the two variable parameters needed to fully explore it?. Morgan has also commen- ted on this, but for now, we'll assume that we're dealing with a three-dimensional M-set (and a six-dimensional Julibrot?). Today's image lies in the default fractal created by the TMan1 variation, near the point at the northern edge, where the two straight stretched arms criss-cross. I named the image "Maximum Spirals". I have rarely seen an image with so many spirals surrounding a midget. In the parent fractal, the scene is stretched, (foreshortened actually), and skewed. So in order to have a normal image I needed to unstretch and unskew the scene. When this was done, I was left with an image that rates a 5. I could rate the image no higher than a 5 because it duplicates scenes that lie in spirals in many valleys of the classic M-set. I don't expect to find any totally new Mandelbrot features in this formula or its variations. The interest lies in discover- ing which parts of the classic M-set are reflected in which parts of the new-shaped Mandelbrot fractals. I'll continue working with these fractals of ambiguous dimension for a few days, then it will be back to the ever-fruitful M-Mix4 formula. The render time of 9 minutes can be avoided by downloading the GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather was sunny but very cold and breezy all day here at Fractal Central. The temperature in the teens F, around -9C, kept the dynamic cats glued to the warmest spots they could find. They moved around enough to ask for food and eat, but retired as soon as their meal was done. It's cold again this morning, with clouds and a few flakes of snow in the air. But it is not as cold as yesterday. Only time will tell if the snow will turn heavier and if the intrepid cats will venture outdoors. I find myself with nothing to do again today. If I play my cards right, I'll get through the entire day without doing anything that can be considered work. Until next FOTD, take care, and one must work hard to be truly lazy. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Maximum_Spirals { ; time=0:09:08.43--SF5 on a P200 reset=2002 type=formula formulafile=triter.frm formulaname=TMan1 passes=1 center-mag=-0.003218524\ 4524517/+0.7498998373975185/2.623604e+007/4.125/-4\ 6.9647077347951267/-9.94802466789319162 params=0/0 float=y maxiter=4200 inside=0 periodicity=0 colors=000kRElLInRFoXDqaBrg8tm6tt1ur4uq6up9uoBunDu\ mGulIukLujNuiPuhSvgUvfXveZvd`vccvbevahv`jv_lvZovYq\ vXsuWruWquWpuVouVnuVmuUluUkuUjtTitThtTgtSftSetSdtR\ ctRbtRasQasQ`sQ_sPZsPYsPXsOWsOVsOUrNTrNSrNRrMQrMPr\ MOrLNrLMrLLvJJrLLoNMkOOhQPeRRaTSZVUVWVSYXOYXPZYQZZ\ QZZRZ_SZ_SZ`TZaUZaU_bV_bW_cW_dX_dY_eY_eZ_fZ_f_`g_`\ g_ah`ah`ai`bi`biacjacjackbdkbdkbdlbelcemcfmcfmdfnd\ gndgodgoehoehpeipfiqfiqfjqfkrgkrgksglshlshlthlvhlu\ ikwikuikvjkxjkyjkwjjwijuhjsgjsfiqehodgmcflbejadi`c\ g_afZ`dY_bXZaWY_VWZUVXTUWTTUSSTRRRQPQPOOONNNMLMLJL\ JIKIGJHFIGDHFCGDAFC9EB7DA6C94B71C83D95EA7FA9GBBHCD\ IDFJDGKEILFKMGMNGOOHQPISQJUQJVRKXSLZTM`UMbVNdWOfXP\ hYPiZQk_Rm`SoaSqbTscUudVwcWwdVxdVxeVxeVxeUyfUyfUyg\ UygTzgTzhTzhTzhTziUwiVuiWsiXqiYojZmjZkj_ij`gjaekbc\ kcakc_kdYkeWlfUlgSlhQlhOliMmjKmkImlGmmEnoBmmCmlClk\ CljCkiCkhCjgDjfDidDicDhbD } frm:TMan1 { c1=flip(real(pixel)),c2=imag(pixel),c3=p1 z1=z2=z3=0: t1=z1*z1+2*z2*z3 t2=z3*z3+2*z1*z2 t3=z2*z2+2*z3*z1 z1=t1+c1,z2=t2-c2*c2,z3=t3+c3 z=z1+z2+z3 |z| < 8 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 18-01-03 (Rising mandelbrot [6])
by Jim Muth 18 Jan '03

18 Jan '03

FOTD -- January 18, 2003 (Rating 6) Fractal visionaries and enthusiasts: A formula that draws the 3-D triternion Mandelbrot set was posted yesterday to the Fractint list by Russell Walsmith. As posted, the formula draws slices in the XY orientation of the 3-D M-set. After seeing what the formula would do, and being unable to resist experimentation, I made a slight modification to it. I flipped the value of initial c1 from real to imaginary, and named the modified formula TMan1. The change enables the formula to draw what I assume is the YZ orientation. Of course, it could be the XZ orientation, or something in between. I have no idea how triternions work. But regardless of the orientation, the revised formula draws slices with intact midgets. Many of these midgets duplicate scenes in the classic M-set, but some midgets are entirely different, doing strange things even while we watch. Today's image illustrates one of these new and unusual midgets. The midget (or half-midget) appears to be rising above a horizon that consists of part of another, larger midget. The fragment of a larger midget is stretched, most likely because the larger midget lies in a different plane. In the 2-D M-set, midgets are oriented in every possible direction. I assume the same thing happens with an even greater degree of freedom in the 3-D M-set. Overlapping features such as those pictured in today's scene are common in the hypercomplex M-set, but I have never seen both stretched and unstretched Mandelbrot features overlapping. I need to do much more experimenting with this three-dimensional Mandelbrot set. For now however, I'll settle for a FOTD image that rates a 6. The rating reflects the mathematical worth of the image. The artistic worth barely rates a 4. The name "Rising Mandelbrot" was inspired by the impression of one Mandelbrot midget rising above the horizon-like edge of another. The render time of 10 minutes can be avoided by down- loading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather was cold here at Fractal Central on Friday. With a temperature of 25F -4C, brisk winds, and occasional showers of snow waiting for them, the cats didn't even think of going out. They were quite contented lying by their radiators. Today is even colder, (the 8am temperature was 7F -14C), so they will be housebound for at least another day. As for me, I've got a bit of work to wrap up, then a day with little to do but wander through FractalLand. If I find anything worthwhile, it will appear as tomorrow's FOTD. Until then, take care, and when the going gets tough, get a fractal going. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Rising_Mandelbrot { ; time=0:10:14.45--SF5 on a P200 reset=2002 type=formula formulafile=triter.frm formulaname=TMan1 center-mag=-0.33019260452431920/\ +0.53369254258170410/2256.431/3.3373/149.75/-15.93\ 32167459564502 params=-0.4/0 float=y maxiter=18000 inside=0 logmap=94 periodicity=10 colors=000UKATKASKARKAQKAPKAOKANKAMKBLJCKKDJKEIKGH\ KHGLIFLKELLDLNCMODMPDMREMSFNUGNVHNWINYJOZKO`LOaMOb\ NPdNPeOPgPPhQQiRQkSQlTQnURoVRpWRrXRsXRtWSsWSsWSsWT\ sWTsWTsWTsWUsVUsVUsVVsVVsVVsVVsVWsVWsUWsUWsUXsUXsU\ XrUYrUYrUYrTYrTZrTZrTZrTZrT_rT_rT_rS`rS`rS`rS`rSar\ SarSarVbvTatSarR`pQ`nP_lO_jN_hMZfLZdKYbJY`IYZHXXGX\ VFWUEWSDVQCVOBVMAUK9UI8TG7TE6TC5SA4S83R62R41R33Q55\ Q77P89PAAOBCODENFGNGHMIJMJLLLNLMOLOQKQSKRUJTWJUXIW\ ZIX`HZbH`cGaeGcgFdiFflDhjFgiGfhHegIdfJcdKbcLabM`aO\ _`PZZQYYRXXSXWTWVUVTVUSWTRYSQZRP_QN`PMaOLbNKcMJdLH\ dKIeLIeLJeLJeMKeMKfMKfMLfNLfNMfNMfNMgONgONgOOgPOgP\ OhPPhPPhQQhQQhQUfPQhQNiRJjRGkSCmT9nT2oU4qS6pT8pUAp\ VCpVEpWGpXIpYKp_MpaOpcQpeSpgUpiWpjYpk_plapmcpnepog\ pphpqiprjpskptlpumpvmpwmpxmpympzmpzmpzmpzmpzmpzmpz\ mpzmpzmpzmozmozmozmozmozmozmnzmnzmnzmnzmnzmnzmmzmm\ zmmzmmzmmzmmzmlzmlzmlzmlz } frm:TMan1 { c1=flip(real(pixel)),c2=imag(pixel),c3=p1 z1=z2=z3=0: t1=z1*z1+2*z2*z3 t2=z3*z3+2*z1*z2 t3=z2*z2+2*z3*z1 z1=t1+c1,z2=t2-c2*c2,z3=t3+c3 z=z1+z2+z3 |z| < 8 } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] xfractint questions and quirks
by Natalie 17 Jan '03

17 Jan '03

On Wed, 13 Nov 2002 21:14:49 -0600 Jonathan Osuch <osuchj(a)avalon.net> wrote > > 1. ---------- passes=b does not work, it freezes up xfractint. > Yes, it's broke. ?It is on my list of bugs to fix. Good luck! >?> 2. ---------- Why is the initial colormap different from the > Put map=default.map in an sstools.ini file. ?Now, where to > put the sstools.ini file, I don't have a clue. I'll try to figure out where to put it. >?> 3. ---------- Is there no way to use multiple directories in > > xfractint? > Use sstools.ini to define your subdirectories. As soon as I've found out where to put it ;-) > > 4. ---------- In DOS I could move to another dir or to another ?> > drive, xfractint doesn't seem to know there are subdirs in the ?> > default dir. > Hmm, somebody should fix that. ?8-)) Would be great. ?> > 5. ---------- Is it possible to create an xfractint.rc file > Yes, use sstools.ini. Yes, as soon as ... ;-) ?> > 6. ---------- When I use <Page-Up> to call up a zoombox it is not ?> > always visible. I tried <Ctrl-Ins> and <Ctrl-Del> to change the ?> > colors, no effect whatsoever. I tried <Ctrl-I> and <Ctrl-D> too, ?> > still no change of color. When using the mouse, the zoombox is ?> > visible. It makes no difference if I use the left or the right ?> > button. Manipulating the zoombox while using the mouse seems ?> > impossible. As soon as I release the button, the zoom-in is drawn. > Mouse support is not what it should be, yet. ?One of these days > someone will get to working on it. Thank you. And what about the invisible zoombox? And the color changing? ?> > 7. ---------- Sound doesn't work always. Sometimes it beeps > Sound is not implemented in Xfractint. Doesn't really matter. ?> > 8. ---------- In the Helpscreens: Backspace to get to the Last > > Topic dooesn't work. The Helpscreens get scrambled > Other than the top line being scrambled (it's on the list), the help > screens work fine for me. ?Even the backspace works. I've tried another xterm and yes, the Backspace works and the screen does not get scrambled. It seems that the various xterms behave differently. In this xterm the 'image-is-completed' beep uses the internal speaker. In the one I previously used the sound came via the soundcard. Natalie -- Stolen tagline: Linux is like a wigwam, no windows, no gates, apache inside. [ Linux Counter: user 230952 machine: 111180 ]

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FOTD 17-01-03 (Four_Esses [5])
by Jim Muth 17 Jan '03

17 Jan '03

FOTD -- January 17, 2003 (Rating 5) Fractal visionaries and enthusiasts: Though it appears quite weird, today's image was not created with the M-Mix4 formula. It is actually part of the Z^1.93+C fractal, which, when the multi-valued nature of the complex logarithm is taken into account, is infinite in surface area. In today's case, we have examined the fractal as it appears 57 levels down the log spiral. In fractals like today's, the strangest and most interesting things are found along the negative X-axis, where the major split usually exists. This is especially true in the parent of today's image, where things that I would never expect are happening along the X-axis split. There is a fairly normal almost-quadratic midget at the center of today's image, though it lies beyond the limit of resolution. In fact the image itself is so close to the break-up point that I included a mathtolerance=/1 entry in the parameter file to be sure the image renders at the correct magnitude. The image consists of a mixture of inside and outside material. It was rendered with the inside set to < fmod >. It is this inside coloring that creates the effect of concentric rings. I named the image "Four Eesses". There are four almost-perfect letter 'S's in the image. I rated it at a 5. It takes more than a few embedded letters to make an above-average image. The render time of 17 minutes can be avoided by downloading the pre-rendered GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Now let's get to constructing that 4-dimensional 24-cell. To keep things simple, we'll start at the two-dimensional level. It's best to have a glass-topped light table, straight edge, and X-acto knife for this kind of dissection and construction. I did a lot of this kind of play stuff back in the slow times of the good old days of the 70's and early 80's, when I worked at a light table, cutting and pasting by hand. But since light tables are expensive and not everyone has one, the same thing can be done with paper and scissors. As I said in yesterday's FOTD, the 24-cell is the only regular 4-dimensional polytope that has no analog in 3-space. It does however have a corresponding figure in 3-space that is similarly constructed -- the rhombic dodecahedron. To understand the construction of the rhombic dodecahedron we can start in 2-space, with two equal paper squares. Lay the two squares side by side on the table top. Then take one square and cut it along its diagonals, resulting in four right triangles, whose bases are the edges of the square and apexes the center. Now take the four triangles and attach their bases to the four edges of the other square. The result is a larger square, rotated 45 degrees, with twice the area and 1.4142 times the width. Not a very impressive construction, but it is a start. The next step will be a three-dimensional one -- more difficult to perform, but relatively simple to visualize. Lay two equal cubes on the table. Take one cube and slice it into six square pyramids, whose bases are the faces of the cube and apexes the center. Then take the six pyramids and attach their bases to the six faces of the other cube. The resulting polyhedron is a rhombic dodecahedron. It is not a regular figure because its rhombic faces are not regular, and more importantly, because it has two different kinds of vertices -- those where 3 edges meet and those where 4 edges meet. The final step -- the construction of the 24-cell -- cannot be visualized, but the analogy is so clear that it can be followed. To begin, we need an extra dimension. Assuming we have found the extra dimension, we can get started. Lay two equal 4-D hypercubes on the hypertable. Take one hypercube and slice it into eight cubical hyperpyramids, whose bases are the cells of the hypercube and apexes the center. Then take the eight hyper- pyramids and attach their bases to the eight cells of the other hypercube. The resulting figure is the 24-cell. 4-space is the only space higher than 2 in which this construction produces a regular figure. In the higher spaces, there are too many lower- dimensional parts to the figure, which must be shaped and fit together just right. It appears I'm getting so involved in hyperspace that I almost forgot about the Fractal Central weather. The weather was cold again here at Fractal Central on Thursday, with a temperature of 28F -2C and only a hazy sun. The cats chose comfort over adventure. They decided to spend the day indoors. This morning is once again cold, and to make matters worse, about 3cm of fresh snow fell overnight. The cats, who dislike cold wet paws, will not be happy about this. I have a minor pile of work sitting on the shelf to my right, but unlike the fractal duo, I can do more than be unhappy about the situation. So until the next FOTD appears almost by magic in 24 hours, take care, and be moderately happy. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Four_Esses { ; time=0:17:30.18--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-0.4282456346546068/+0.0113573879900267\ 6/5.48016e+012/1/-132.5/0.00936043190115933704 params=1.93/0/-57/0 float=y mathtolerance=/1 maxiter=1200 inside=fmod periodicity=10 colors=000_U2bS2cR2eP2hR2gP2eN2eM2cM2cL2bJ2bI2`I2_\ G2_F2YD2YD2XC2XB2VB2U92U83S74S74R56R47P28N28N1AM0B\ M0BL0CL0EJ0FI0FI0HG0IG0KF0KF0LD0MD0MD0TD5ZF9fDCdDD\ bCGbCIaBLaBM_BPZ9RZ9UX8VX8YW7_W7bU7cT5gT5hR4kR4mQ2\ qQ2rO2vM1wM1zL0zL0zK0zK0zK7z25z25w25t25r25o25k24j2\ 4g24c24b24_24X22V22S22P22N32L42I62G71G70F70F60D60D\ 60C60C20C20C600A00B00C00E00F00F00H01I01K01L02K02K0\ 2L04M04M04L05M05M05N05M07N07P07Q08S08S08T19V19X19Y\ 2BY2B_2BY4CW4CY4Cd5Df5Dg5Di5Di4Ck4Ck4Ck2Ck2Au2Ak2C\ k1Ck1Bl1Bl1Bl0Bl0Bl0Bl0Bl0Ba0Bl09n09n0Sn09n0Sv0Qn0\ 9n09n09n08d08k08o08o08o08o08o08o07o08p09n09n0Bk0Ck\ 1Ch4Dg5Fe7Fe8GbBIaCIZDJXGLUILTJMQMNMNNLV14U24S44R5\ 4P54N73M83L93J93IB3IC2GD2FD2DF2CT27E29I28J27L25M20\ M25T2S`FSlWbqUloUqmTrkTtjTthRvgRveQwcQybQy`Oz_OzYO\ zXMzVMzULzSLzRLzPKzNKzLMzMKzMIzNHzNEwNCtPBqP8oP7kR\ 6hR4eR2cS2RY3SY2VX2XV2YU2 } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] FOTD 15-01-03 (Nest of Tachyons [8])
by Jim Muth 16 Jan '03

16 Jan '03

At 06:49 PM 1/15/03 +0000, John lewis wrote: >And if you could persuade one [tachyon] to travel in a >circle -- it would never overtake itself? Interesting idea. Exactly what would happen? I rather suspect that the tachyon would soon reach infinite speed and disappear from our view, having gone back in time. A tachyon moving faster than light would likely create a shock wave, which would cause it to lose energy and therefore increase its velocity to infinite. At infinite speed, a tachyon would travel backward in time at the same rate we are traveling forward. >>Until next time, take care, and never forget that we >>are made of tardyons. >Especially when we feel lazy? Most especially when we are fractal cats. Jim M.

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