January 2005 - Fractint - mailman.xmission.com

FOTD 31-01-05 (The Beast Itself [6])
by Jim Muth 31 Jan '05

31 Jan '05

FOTD -- January 31, 2005 (Rating 6) Fractal visionaries and enthusiasts: Today's FOTD is an image of a beast -- a fractal beast no less. The beast is a midget located in a spiral on the southern shore of the period-4 bud on the northeast shore of the main bay of the Mandelbrot set. It is a rather handsome midget, with well- defined spiral arms that are twisted to just the right degree, and many sub-spirals to add fractal excitement. The spirals resemble both elephant trunks and seahorse tails -- kind of a blending of the two. One would never imagine that an elephant and a seahorse would make a couple that could produce hybrid offspring, but in today's image they apparently have. I consider the midget a beast because it is an impostor. It is not the animal it first appears to be. Look carefully at the parameters and you will see that the value of Z has been initial- ized to the same value as C, and not to zero, as would be the case when calculating the true M-set. Also notice that the orientation of the slice has been double-rotated half way from the Mandelbrot direction toward the Julia direction. We are looking at a scene in what I call the shadow set -- a second Mandelbrot set with dimensions sqrt(2) times those of the true set. Since today's midget is actually a beastly impostor, there can be nothing wrong with distorting it. And why not? After all, the image is a slice of the Julibrot, which is a 4-dimensional thing that can be sliced in more directions than can be imag- ined, and some of these slices do quite unexpected things to the beastly midget. But we will leave the distortions and variations to the next few FOTD's. Today's image shows the beast as its undistorted self. I have therefore named the image "The Beast Itself". I took some extra time with the coloring, but such scenes have been pictured so many times that they have become hackneyed. As a result, I could rate the image no higher than a 6, which is still a little above average. How high, or low, the coming variations of today's scene will rate has yet to be determined. The render time of under three minutes is true on my fractal- dedicated machine, which is almost ten years old. The image will likely finish in under one minute on most present-day units. But some present-day units don't know what they are missing, and will choke on the VESA video modes used by Frac- tint. For the convenience of those with such handicapped units, the finished GIF image has been posted to the FOTD web site, from where it may be downloaded in a video mode all computers can display. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Light snow continued into the early afternoon here at Fractal Central on Sunday, keeping the fractal cats confined to the porch. But fractal cats are known for their stoicism, and the duo took their confinement without complaint. Today is starting sunny and chilly, with a warming trend forecast for this after- noon. The cats should be happy. I have a moderate amount of work before me, which will bring happiness my way when it is behind me. Until next FOTD, when the true or false, take your choice, philosophy will resume, take care, and be wholly fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Beast_Itself { ; time=0:02:49.71--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 center-mag=0/0/719412.8\ /1/90/-1.23373533611470521e-014 params=45/0/45/0/\ 0.288136932805/0.482645405409/0.288136932805/0.482\ 645405409 float=y maxiter=5000 inside=0 logmap=288 periodicity=10 colors=000SYsSXrSWqSVpSUoSTnSSmSQlTOkUMjVKiWIhXGgY\ Ef_CeaAdcAceAbgAaiA`kC_mEZoGYqIXrKWsMTrOSqQRpSQpUP\ oWOnXNnYMmZLl_KlaJkcIjeHjgHkhGkgFlfEldDmbCm`BnZAnX\ 9kV8hT8eR8bP7_N7XL7UJ6RH6OF6LD5IB5FC5CC49D46D43D45\ E57F59G6AH6CI6EJ7FK7HL8JM8KN8MO9OP9QQARRATSAVTBWUB\ YVC_WC`XCaYEbZGbZHc_Jd`Kd`MeaNebPfbQgcSgdThdVheWif\ YjgZjh`kiakjclkdmlfmlgmmimminmjomjpmjqnjrojtpjuqjv\ rjwsjxtlxujwtivshurgtqftpdsocrmbqlapk`oj_oiYnhXmgW\ lfVkdUjcTjbRiaQh`Pg_OfZNfYMgXKgVJgUHhTGhREhQDiPBiN\ AiM8jK7jJ5jI4kG2kF1kE0gH1dJ1aM2ZO2WR3TT3QY4Na4Kf5U\ o5cs2mz5mz8mzBhtEcrHZqKUoNPnQLmTMkWNjZOiaPidQhgRhj\ SgmTgpShsTgrTfrTfqTeqUepUbpU_pUZoUUoVTnVTnVSnVSmVR\ mWRnWQoWQpWPqWPsXOuXOwXNxXNzXMzYMzYLzYLzYKzYKzVOzS\ SzQWzN_zLczPgzUkzZozcszhvzmuzmwzmvzmvzmuzmuzmtzmtz\ mszmszmrzmrzmrzmqzmqzmpzmpzmozmozmnzmnzmmzmmzmmzml\ zmlzmkzmkzmjzmjzmizmizmiz } 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 30-01-05 (The Sin of Eve [5])
by Jim Muth 30 Jan '05

30 Jan '05

FOTD -- January 30, 2005 (Rating 5) Fractal visionaries and enthusiasts: Today's image is a scene in the four-dimensional Julibrot created by the formula (Z^1.1)*(C^-0.1)+C. It is neither a Mandelbrot set nor a Julia set. It is a slice through the Julibrot in what I call the Oblate direction, which is the plane determined by the imag(c) and real(z) axes. Don't let the name "The Sin of Eve" lead you to believe that the image is in any way . . . um . . . dirty. I gave it this name because one of the early color palettes that I tried reminded me of an apple with a bite removed. The coloring I finally chose produces an effect more of a splash than an apple. The rating of a 5 is about right for such an average image. The render time of a very brief 1/2 minute means that little time will be required to see the fractal splash appear onscreen. The completed GIF image is available for download on the FOTD web site faithfully maintained by Paul Lee at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Partly cloudy skies and a temperature of only 34F 2C kept the fractal cats' time in the yard limited to less than 1/2 hour on Saturday. The duo remained in a surprisingly good mood however, and were satisfied with only the usual amount of tuna for their evening treat. Today is starting with 2inches 5cm of new snow on the ground, with light snow still falling. It looks to be a poor day ahead for the duo. For me, the main task will be clearing away the ice. I'll start the job in an hour or so. The next in the unending series of FOTD's will appear right here in only 24 hours, plus or minus a few hours. If I feel extra energetic, I might include some new and thought-provoking philosophy in the philo-fractal version. Until then, take care, and sleep secure within the great cosmic fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Sin_of_Eve { ; time=0:00:34.49--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multXYZWcompjb-min function=ident/flip center-mag=0.844885/1.42109e-014/0.05969098/1/-90/\ 3.885780586188e-016 params=0/90/1.1/0/0.9/0/0/0/0/0 float=y maxiter=1200 inside=0 periodicity=10 colors=0000051032513A04F16H29K2BM3EP4GR4JU5LW5OZ6R\ `7Uc7We8Zg8`h7bi7cj7ek6fl6hm6in5ko5lp5mq4nr4os4pt3\ qu3rv3su5tu7uu8vtAwtBxtDysFzsGzsIzsJDnsGipJdnM`kOW\ iRRgUNdXIbZE`YGaXHbWJcVKcVMdUNeTPeSQfRSgRTgKbZDkQ6\ tI8rIAqICoIDmIFkIHjIJhILfINdIOcILaNI_SGZWDX`BWdCUe\ CSeCQeCOeDMeDKeDIfDGfEEfECfEAfE8fE6fG9hHCiIFkJIlLL\ mMOoNRpOTqPUnPUlPUjPUhPUfPUdPUbPU`PUZPUXPUVPUTPURP\ UPPUNNVOLVPJVQHVQFVRDVSBVS9VT7VU5VU7TP8RLAPGBNCCL8\ HQGMVOR_WWdc_ij6LcDN_KPXQQUXSRbTOiVLoWIjYOfZTQGdOJ\ fNMgMOhKRiJTjIWkGYlF`nEboCepBgqAjr8ls7ot6qu9orCmoF\ klIjiLhgOfdQeaTcZWaWZ_UaZRdXOgVLiUJeTKbTKZSKWSKSSK\ PRKLRKIRKPVJVZJ`bIfeIliHrmHxpHpfBhY6iWDjVJkTPlSVlR\ `kPZkOYkNXkMWkLVjKTjJSjIRjHQjGPjFOhEMfDLdCJcBIaAG_\ 9FZ9DX8CV7AT69S57Q46O34N33P54R65T75U86W96YA7_B7`C8\ bD8dE9fF9gGAiHAkIBlJBbZZUmvWjrXhoZel_ciaafbZcdX`eU\ YgSVhQSjNPkLMlJJkLHkMGkNF } frm:multXYZWcompjb-min {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p4, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p5: z=(-z)^(p2)*(c^(p3-1))+c, |z| < 400 } END PARAMETER FILE=========================================

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FOTD 29-01-05 (Copper Terraces [4])
by Jim Muth 29 Jan '05

29 Jan '05

FOTD -- January 29, 2005 (Rating 4) Fractal visionaries and enthusiasts: With today's image we return to that old warhorse, the overused MandelbrotMix4 formula. But the return is not a noble one, for we have again fallen below fractal average. Try as I might, I could rate today's "Copper Terraces" image, with its muddy terraces, no higher than a 4. The formula that wreaked this minor havoc combines portions of Z^(-1.2) and Z^(2.1) before adding C. I tried to add a little interest by rendering the scene with the inside set to 'bof60' and the outside set to 'fmod', but the improvement was minor. In the end I decided to be stoic and post an image that was not up to FOTD standards. After all, this is hardly the first time a deficient FOTD image has been posted. Thankfully, the image renders in under 6 minutes on my machine, which must be a decade old. In the computer world, this is about as state-of-the-art as a cave-man. On a modern unit, the image will render in a minute or so. And if even one minute is too slow, the completed image can be downloaded from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A bit of philosophical rambling is included in the philofractal version of today's message. The sun was bright, but the cold temperature of 23F -5C and the solidly frozen snow pack kept the cats confined to the porch all day Friday here at Fractal Central. When evemnong came, they demanded extra tuna. Today is starting with hazy sun, cold temperatures, and snow again in the forecast. I suspect the duo will not enjoy the outside conditions. I have a little work to finish and a lot of fractal exploration to do. Until next time, take care, and don't fear the dark. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Copper_Terraces { ; time=0:05:46.15--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+0.84253097446520620/-0.105017701083716\ 60/3.373927e+007/1/87.5/6.71509495994704331e-008 params=-0.25/-1.2/0.5/2.1/0/0 float=y maxiter=1200 inside=bof60 proximity=1 outside=fmod periodicity=10 colors=000KyfVDlUGlTJkSMkRQjQTjOWiNZiMbhLehKhgJkgH\ offCvHofGpfFqgErgDsgCthCthBuiAvi9wi8xj7yj6yk7yk9yk\ BxkDwkFvlHvlJulLtlNslPrmUpmZmmcjlhhlmekrbks_jp`gq_\ frZdsXesWbsUYsTWtRTtPRtOPuMMuLKuJHuIFvGDvFAvD8wB5u\ E8tF9sG9rHAqIAoJBnKBmLClMCkNDiODhPEgQEfRFeSFcTGbUG\ aVH`WH_XIYZJXfOWnUrsFrtEquDrqItlOvhUxc_zZeub_q`ZnZ\ YjYXgWWcUV`TUXRTUPTQOSNMRJKQGJPCHO9FN5DM9HN9JN8LN8\ NM8PM7RM7TM7VL6XL6_L5aL5cK5eK4gK4iK4kJ3mJ3oJ2rI2rI\ 2qI0qH2pH2pG2oG2nF3nF3mE3mE3lD3kD3kD3jC4jC4iB4hB4h\ A4gA4g94f95e87a89Y7EYDKYJQXQWXWaXagWheXhcYgaZf_`eY\ aeWbdUdcSebQfbOgaMi`Kj_Ik_GmZEnYCoXAqWBoXCmYDj_Eh`\ GebHccI`eJZfKXgMUiNSjOPlPNmRKoRKnRKmRKlRKjRKiRJhRJ\ fRJeRJdRJcRJaSI`SI_SHYSHXSGWSGVSETSESSDRRDPQCOPCNO\ BLNBLMBKLBJKBIKAIKBHLCGMDFNEEOFFPGFQHFRIFSJFTKFULF\ VMFWNFXOFYPGZQI_RK`SMaUObWQcYSd_UeaWfcYge_hgaiicjk\ ekmgloimqjnrjosjptjqujrvj } 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 PARAMETER FILE=========================================

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Fwd. -- Fractal Calendar
by Jim Muth 28 Jan '05

28 Jan '05

This is an open call for you to submit your fractal artwork for consideration for inclusion in the Fractal Universe ® Calendar 2007. All the information you will need is detailed on the following website: http://www.fractalforum.com Please make your submissions and any additional enquires you may have via the contact form on the above website. This message has been posted to some of the fractal art mailing lists and forums. If you think it may be of interest to others please feel free to forward it, as it is written here, to other 'net sites where fractal artists meet to share and discuss fractals. Thanks and good luck! Linda Allison and Panny Brawley

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FOTD 28-01-05 (Snail on Mushroom [6])
by Jim Muth 28 Jan '05

28 Jan '05

FOTD -- January 28, 2005 (Rating 6) Fractal visionaries and enthusiasts: There are everyday snails and there are snails of the Wonderland variety, which, along with the caterpillars, sit on mushrooms, smoking water pipes and blowing smoke letters into the air. Today's image shows a highly decorated snail of the latter variety, at a time when he is not smoking his pipe. The curious little critter was created by the same formula that gave us the orb that appeared in yesterday's FOTD. But in today's version we slightly shift the direction of the slice +3 and -3 degrees from the Julia aspect. This small rotation opens the figure and reveals considerable 'inside' area. The 'fmod' fill, with the proximity set to 1, adds the chaotic detail to the 'inside' areas. The final step in the creation of the snail was to stretch the image in the vertical direction. When this was done, the little fellow came to life for all the world to see, sitting on his abstract mushroom, wondering what happened to his pipe. Snails are not my favorite animals. They make quite boring pets, and they don't taste good either, so a rating of 6 was the best I could do with the image. But the rendering takes less than a minute, so it is worth the little bit of effort required to see the snail on his mushroom. The name "Snail on Mushroom" is the only name that could have been given to an image like today's. For the convenience of those who dislike rendering snails, the image is available in all the glory it can muster on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The next round of enlightening philosophy is a few days off. But be patient. The best (or craziest) part is yet to come. It was colder than a w-----'s t-t here at Fractal Central on Thursday. The wind was up and the temperature never rose above 21F -6C, but the sun was strong, and just enough sunlight struck the porch to make conditions bearable for the cats, who spent a full 45 minutes chasing the moving sunbeams that filtered through the upper branches of the holly trees. When the sunbeams were gone, the duo came inside without the need to be called, to enjoy their treat of tuna. Today is starting even colder. Luckily, the sun is once again strong. The cats should have another acceptable day. My other work is light, which means more time for fractals and more time to prepare the next eagerly awaited outburst of philosophy. Until we meet again in 24 hours, take care, and I still have not decided whether fractals truly exist or whether they are inventions of the human mind. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Snail_on_Mushroom { ; time=0:00:38.89--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=mult-xy-zw-compjb function=ident/flip center-mag=-0.789184/1.12102/0.7198814/0.8175/2.04\ 299432563946048/1.01592002781501933 params=87/93/1.4142/0/1.4142/0/0/0/-0.542983266/0.\ 017693381 float=y maxiter=5000 inside=fmod proximity=1 periodicity=10 colors=000O8UQCWSGYUK_WOaYSc_Wea_gcciegkgkmiooksqm\ wspzutzzzzzLVPBLE1B36E4BH4GK5KN5PP5US6YV6bY7g_7kb7\ pe8uh8yj8tf7pc7k_6gX6cU5ZQ5VN4RK4SL8SLCTLGTMKTMOUM\ SUNWVN_VNcVNg`UYf`PlgGqm7lk9hjAdhB`gDXfETdFOcHKaIG\ `JC_L8YM4XN0WO6OYBHgGAqK9nO9kR9hV9eZ9ba9_e9Xh9Vc8V\ _8VW7VS7VO6VK6VI9WHBWGDWEFXDIXCKXAMY9OY8QYBPXEPWGP\ VJPULPTOOSQORTORVOQYOP_NObNNdNMgNLiNLjLOkJRmHUnGXo\ E_qCbrAes9hu7kv5nw3qx2sq7mkCheHc_MZBdETRTNWOH`JSmS\ PkQNjOLiMJhLHgJFfHDeF3PX4QW4RV5SU5ST5TS6US6UR6VQ7W\ P7WO7XN8YN8ZM8ZL9_K9`J9`IAaIAbHAbGBcFBdEYGtXHsWIrW\ IqVJpVJoUKnULmTLlTMkSMjSNiRNhROgQPfPPePQdOQcORbNSa\ NS`MT_MTZLUYLUXKVWKWVJWUJXTIXSHYRHZQGZPG_OF_NF`ME`\ LEaKDbJDbICcHCcGBdFZBAYCBXDBXEBWEBWFBVGBVGBUHBTIBT\ IBSJCSKCRLCRLCQMCQNCPNCOOCOPCNPCNQCMRDMSDLSDLTDKUD\ JUDJVDIWDIWDHXDHYDGZEGZEF_EE`EE`EDaEDbECbECcEBdEc7\ NYELSLJMSHGZF3k94jAUdURaS } frm:mult-XY-ZW-compjb {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p4, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p5: z=z^p2*(c^(p3-1))+c, |z| < 400 } END PARAMETER FILE=========================================

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FOTD 27-01-05 (Orb [7])
by Jim Muth 27 Jan '05

27 Jan '05

FOTD -- January 27, 2005 (Rating 7) Fractal visionaries and enthusiasts: Today's image is a Julia set of the fractal that results when both Z and C are raised to the power 1.4142 and multiplied together, and then C is added. It consists of gaudily colored but broken concentric circles with an interesting area of chaos toward the center. Most of the effect was achieved by calculating the formula with the outside set to 'tdis'. The chaotic parts of the image are filled with curious but hard-to-find Julia basins, one of which appeared two days ago as the 'Hairy Caterpillar' FOTD for January 25. I gave the image the name "Orb". The name was inspired by the nature of the image itself, which basically consists of nothing but circles. After a modicum of consideration, I rated it at a not-bad 7. The colors are a bit too brilliant, but still striking. The 'passes=b' option is fastest with this image, rendering the entire scene in only 11 seconds. This option often is the fastest, but it must be used with caution because it can easily miss important isolated features. The render time of under 11 seconds is true only when the image is rendered with the passes set to 'b'. I have discontinued the overall worth rating, which was weighted too heavily in favor of the render time. No one paid much attention to it anyway. The only important thing is the appear- ance of the completed image, which is covered in the rating that appears in the subject line of every FOTD. The image is a very fast one. By the time this letter is read, it should already be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The continuation of the philosophy that we have been waiting for appears in the philofractal version of today's FOTD discussion. The sky was mostly cloudy, but the temperature reached a high of 47F 8C here at Fractal Central on Wednesday. Only the wet sloppy snow kept the fractal cats on the porch. Today is starting sunny but much colder. The temperature is down to 10F -12C, and the snow has frozen rock hard. I wonder what the dynamic duo will make of it. My only problem is where to find the next FOTD. The search will begin in a few hours. Until that next FOTD appears, take care, and be serene as a fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Orb { ; time=0:00:10.82--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=mult-xy-zw-compjb function=ident/flip center-mag=-0.00542788/-0.101983/0.1702254/1/40/\ -3.21104948186601e-011 params=90/90/1.4142/0/1.4\ 142/0/0/0/-0.542983266/0.017693381 passes=b float=y maxiter=5000 inside=255 outside=tdis periodicity=10 colors=000sCzqEzoGzmIzkKziMzfOycRx`UwYXvU_xRbwNdvK\ epLdnMbjM_fNXbNVZOSWOQSPNOPLKQIGSGDWFBaE9gF7kC5jH8\ hMAfRDdVFbYHeZFhZEkZDnZCqZBsZAUVG4RL8VKBYJF`IIcHMf\ GPiFQkHQlJRmLRnNSoPSpRSrTTsVTtXUuZUv`UwbSscQodOkeM\ gfKcgI_gGWhESiCOjAKk8Gk7Fj7Fi7Fh6Fg6Ff6Ee5Ed5Ed5Ec\ 4Eb4Da4D`3D_3DZ3DY3DY9EWFFVLGURHSXHRbIQhJOnKNtKMsL\ OsLQsLSsLUsLWlRXeWYZ`YSeZLjZEo_7t_CrYHqWMpUQoSVnQ_\ mOclMhkKmjIqiHbaoeaqhaskau6Oi7Oo7OuCQtHStMTsQVsVXs\ _Yrd_rh`rbdmXhiRkdLo`FsW9vSLoZXieifogcleajc_gaYe_V\ bYT`WRYUPWSNTQKROIOMGMKEJG9IICHKFHMIGNLGPOFRRFTUEU\ XEW_DYbD_eC`hCbkBdnBfqALHRgsAdeCaTEWDFZGGaIHdLIgNJ\ jQKxNMlSL`WKQ`KEdJ3hJ8eKDcLHaLMZMQXMVVNeZTZTNTNHMH\ BGB5A50D72F83H94KA5MB6OC8RD9TEAVFBXGC_HIbHOeHUhH_k\ HenHkw8xpHpjQhcY`YfTSnMXhS`bXeXaiSgnMlrGqz7yvBvrEs\ nIpjLmfPjlOrcSgVVYMYOIOCE`EE`EEaEDaEDbEDbECcECcECd\ EBdEBeFBeFKKkKNiKQfKTdKWb } frm:mult-XY-ZW-compjb {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p4, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p5: z=z^p2*(c^(p3-1))+c, |z| < 400 } END PARAMETER FILE=========================================

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FOTD 26-01-05 (A Nothing Set [7])
by Jim Muth 26 Jan '05

26 Jan '05

FOTD -- January 26, 2005 (Rating 7) Fractal visionaries and enthusiasts: I wrote another quick new formula since yesterday's FOTD, and gave it the impressive name 'multXYZWcompjb-min'. The only difference from yesterday's formula is that today's calculates (-Z) instead of (Z). The difference in the formula is small, but the change in the appearance of the fractals with fractional exponents of Z is great. Today's fractal shows a scene in the four-dimensional Julibrot of the formula (-Z)^1.4142*C^0.03+C. The orientation of the slice is very close to the Julia direction. But being close does not make today's image a Julia set, so I have named it "A Nothing Set". The true Julia set may be seen by changing the value of (p1) from 81,90.2 to 90,90. The Mandelbrot aspect of the scene appears when (p1) is set at 0,0. The point that corresponds to today's image lies in the disconnected triangle in the M-set. The other values of (p1) draw various oblique slices through the Julibrot, some of which are quite interesting, while others have little to offer. The image relies mostly on intense coloring for its effect. As a result I limited its rating to a 7. But the render time is a fast 2-3/4 minutes, which boosts the overall worth to 257. And don't forget the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the completed GIF image has or soon will be posted for the convenience of those who would prefer to leave the rendering to someone else. The clouds hung tough most all day on Tuesday here at Fractal Central, but the temperature rose to 36F 2C, which was comfort- able enough for the fractal cats. Unfortunately, the warmer temperatures started melting the snow, which then wet the paws of the duo, sending them scurrying back to the porch, where they sat for nearly an hour watching the birds fly by. The evening treat of tuna was a bit larger than average. Today is starting warmer with lots of clouds. But with so much snow still on the ground, it looks doubtful that the duo will have a good day. Since the work is still caught up, my day will be good. And when 24 hours have passed, the next FOTD will appear in all its glory and wisdom. Until then, take care, and be awe-struck in the presence of a fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Nothing_Set { ; time=0:02:43.52--SF6 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multXYZWcompjb-min function=ident/flip passes=1 center-mag=-0.306729/0/1.253133 params=81/90.2/1.4142/0/1.03/0/0/0/-0.76/0 float=y maxiter=2000 inside=0 symmetry=xaxis logmap=yes periodicity=10 colors=0004AA6AA8AAAAACAAEAAGAAIGLKKPMNTPQXST`VWdY\ Zh`alcdqfgtiixikyikzhkzgkzflzelzdlzclzbly`mx_nwZov\ YpuXqtWrsVsrUtqTtpStoRtnQtmTrlVpkXnlZkm`hnbeodbmf`\ khYijVglSelPcjMagJ_dGYaDWZAUW7SS5QP4OM4MO3KQ2ISCGU\ EFVGGWIHXJIYKJZKK_KK`KKaKKbKKcKKdKKdKKdKKdKHdKEdKA\ cK7bK4aK6`K7_K8ZIAYGBXFCWDEVBFUAGT8IS6JR5KP3MN1NK0\ OKh8ervdsodthdzaccXcYScMNcAJcFNcJQcNTcRWcVZcZacbda\ fgZjjWnmTrpQvsOupNtnMskLriKqfJpdIpaHo_GnXFmVElSDkP\ CkMPhKKeKFaK0ZH3WI6TH9VGCXGFZGI`FLbFOdERfETgEUcDV_\ DWWDWSDXODYKDYGDVJKTLRROYPQdTPgWOi_NkbMmeLoiKqlJso\ IujGmfEfaC_YBT`AWb9Ye8_g7ai6cl5en4gq3is2ku1ml4fc7`\ VAVMDPQCRTCTWBVZBWaAYdA_gA`hGXhLUiQQiVNj_JjdGkiCkn\ 9elF`jLWhRRfWMdaHbgCalHZjLXhQVfUTdYRbbPafN_jLYoJWs\ HUwFTsHSpISmKSiLSfNScOS`PS_UO_YL_aH_eE_jB_n7_r4_v1\ buBetLgtVjsdmrnorxnmumhrlhpkkmknkmqcotXqwPszIuzBqz\ LSzbUzfXziZzl`zoTznLzmDzm } frm:multXYZWcompjb-min {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p4, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p5: z=(-z)^(p2)*(c^(p3-1))+c, |z| < 400 } END PARAMETER FILE=========================================

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FOTD 25-01-05 (Hairy Caterpillar [8])
by Jim Muth 25 Jan '05

25 Jan '05

FOTD -- January 25, 2005 (Rating 8) Fractal visionaries and enthusiasts: It is rare that a hairy caterpillar comes squirming out of the fractal computer (unless it is an Apple, that is), but this is exactly what happened last evening, and today's image is the evidence. The object in today's image is a Julia basin in one of the Z^1.4142 sets. It looks so much like a big fat squishy caterpillar that I could not resist the urge to name it "Hairy Caterpillar". The image was created by the new 'mult-XY-ZW-compjb' formula that I recently wrote. The same scene could have been found with a simpler formula, but I prefer today's formula, which can switch between the Mandelbrot and Julia, as well as the other aspects of a scene, with little difficulty. The rating of an 8 does not imply that I enjoy hairy caterpil- lars. Actually, I am neutral about them, and it is hardly the time of year when caterpillars are out and about in this part of the world anyway. I gave the image such a high rating because of the extraordinary definition of the basin at the center, with its odd set of holes. When the rating is combined with the render time of 19 minutes, the overall worth registers a 42. Somehow, the image seems better than that. In fact, I'm less than satisfied with this whole overall worth thing. I think I'll stop rating the FOTD images for overall worth, or start figuring the rating in a different manner. The present method gives far too much impor- tance to the render time. And the overall worth rating really is pretty useless. The render time becomes just a curiosity when the completed GIF image is downloaded from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The Morning sun on Monday turned to clouds by 1:00pm and snow by 4:00pm. Only about 1/2 inch (1cm) fell, but it proved to the cats that a trip outdoors was out of the question. Their excite- ment was limited to watching the snow from their shelf by the window. The boredom was eased by a treat of tuna mixed with bits of cheddar cheese. Today is starting milder, but it is still below freezing and the sky is cloudy. Let us hope for better things for the fractal duo. For me, only a little commercial work waits to be accomplished, and then it's back to the fractals. Until 24 hours have passed, take care, and a fractal a day is better than tuna at keeping boredom away. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Hairy_Caterpillar { ; time=0:19:07.28--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=mult-XY-ZW-compjb function=ident/flip passes=1 center-mag=+0.77150925485208020/-0.441181\ 37588527820/1770.401/1/55/1.95960608850853646e-012 params=90/90/1.4142/0/1.4142/0/0/0/-0.542983266/0.\ 017693381 float=y maxiter=5000 inside=0 logmap=200 symmetry=none periodicity=10 colors=000IF8KI9KK9KK9KF9KE9KG9KK9KH8KH9KK9KK9KK9K\ G9KK9KH9KJ9KI9KJ9KPAKKAKMAKKAKKAKKAKKAKMAKKAKKAKOA\ KPBKPBKQBKMBKNBKNBKOBKOBKPBKSBKQBKRCKRCKRCKRCKSCKS\ CJTCJTCJUCIUCITCIVDIWDHWDHXDHXDGYDGYDGZDFZDFZDF_DE\ _EE`EE`EEaEDaEDbEDbECcECcECdEBdEBeFBeFAfFAfFAfF9gF\ 9gF9hF9hF8iF8iF8jG7jG7kG7kG6lG6lG6mG5mG5nG5nG6mE5n\ F5nG5nG5nH5nH5nI5oI5oJ5oJ5oK5oK5oL5oL5pM4pM4pN4pN4\ pO4pP4pP4qQ4qQ4qR4qR4qS4qS4qT4rT4rU3rU3rV3rV3rW3rW\ 3sX3sY3sY3sZ3sZ3s_3s_3t`3t`3ta2ta2tb2tb2uc2uc2ud2u\ d2ue2ue2uf2vg2vg2vh2vh2vi1vj1vk1wk1wl1wm1wn1wn1wo1\ wp1xq1xq1xr1xt1xt1xu0xu0yw0yw0yx0yx0yy0yy0yz0zz0zz\ 0zz0zz0zz0zz0zz5mtAamFQhKAcLCZMEUOGPPHQQJQSLQTNQUO\ RWQRXSRXTRYVRYXRYZRZ_SZaSZcS_eS`fSahSbjSckRdkSgkSj\ kSmkSokSqkSskSukSwjSzjSzjSzjSzjSzjSzjSzjSzjSziSziS\ ziSziSziSziSziTziTziTzhTzhTzhTzhTzhTzhTzhTzhTzhTzg\ TzgTzgTzgTzgTzgTzgTzP8zO8 } frm:mult-XY-ZW-compjb {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p4, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p5: z=z^p2*(c^(p3-1))+c, |z| < 400 } END PARAMETER FILE=========================================

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FOTD 24-01-05 (Complex Diversion [5])
by Jim Muth 24 Jan '05

24 Jan '05

FOTD -- January 24, 2005 (Rating 5) Fractal visionaries and enthusiasts: Over the long weekend I began wondering what some of the 'cmplxmarksmand' type fractals look like in the odd planes of the Julibrot. A few minor changes to one of my Julibrot formulas enabled me to investigate the mystery. I named the new formula 'mult-XY-ZW-compjb' and included it in my 'allinone' file of most active formulas. At the present time, I have done almost no exploring with the new formula, so I cannot comment on what it might hold, but I did find one rather interesting, if not great, image in my first trial run that appeared good enough to be an average-rated FOTD. The parent Julibrot is that of the Z^100+C fractal, which has been reduced to one lobe. The angle at which it is sliced is 30 degrees from the Julia orientation. Quite a bit of stretching was needed to bring the image to a roughly circular shape. The outer circular ring is the Julia part of the overall Julibrot fractal. The Mandelbrot part has been stretched in one direction to infinity, and appears as the horizontal bands filling the circle. I named the image "Complex Diversion". There is nothing outstanding about the image; it simply exists to be looked at as a diversion. Since everything about it is average, the rating of a 5 seems proper. The superman-like render speed of under 6 seconds gives the image an unrealistic overall worth of 5574. The image is not really worth this rating. I must do something to avoid such artificially high overall worths. As has been the case almost from the day the FOTD first appeared, the finished image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> I'll do some further exploring in this new formula later today. I am sure it has better things in it than the image that passed for today's FOTD. Arctic cold and roaring winds kept the dynamic duo ensconced safely indoors all day Sunday. The high temperature on the almost-accurate fractal thermometer reached only 18F -8C, while the wind gusted to near 50mph 80kph, blowing the powdery snow around in great clouds. The duo watched all this from their window shelf, thankful that they were inside. In the evening I put extra tuna in their dish to reward them for their patience. Today is starting sunny and just as cold, but the wind has died down, which makes it feel far less harsh. The cats might sneak an hour or two on the porch. For me it's time to finish the job of clearing away the drifted snow. If I accomplish that, I will be home free. The commer- cial work is caught up. The next FOTD will appear in 24 hours. The enlightening philosophy might be included, or it might not. Until then, take care, and if this is the age of enlightenment, why are we so ignorant of so many important things? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Complex_Diversion { ; time=0:00:05.38--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=mult-XY-ZW-compjb function=ident/flip passes=g center-mag=0.000367865/3.88578e-014/1.229\ 082/1.3647 params=60/90/100/0/-99/0/0/0/-0.50878/0 float=y maxiter=10000 inside=253 symmetry=xaxis logmap=yes periodicity=10 colors=000K84SB5bU6ELUDYbBTUAYU8aU7eU0460350340230\ 1261C215I8GXERkKafNdbQfZTiUWkQZnMapIdrNbsSasW_s`Zs\ dYs_ZqV_oQ_mM`kHaiCag7be3bdWQZwDU0Nb4MT8LJCK9GJ08O\ Q1SnWGdy4V1l92mV2moZ6LRMWJafCppImjOkdUhZZfTdcNjaHp\ ZBuX6m_EeaMYdUQfaIiiAkq2myAhrdvFfwFixFkyFq_8wB2sF5\ oJ7kN9gRBcUD_YFWaHSeJPhLReSSbZT`dUYkVWqQPpMJoICnE6\ mA0m`G7bJ8Zvm`xmcqlejlhcljYkmRkoKkqEkoIjnMilPhkTgi\ Wfh_efcdefccjbbma`q`_t_YsaXscWreUrfTrhSqjQqlPpmOpo\ MpqLosKotInvHnxGnyIltKjpMhlOfhQddSb`U`XWZTYXP_VLaT\ HcRDeP9gN5hL10pX1lY1hZ2e_2a`3Z`3Va3Sb4Oc4Kd5Hd5De6\ Af66g63gTRQnm8jk7fi7cg6_e6Wd5Tb5P`4LZ4IX3EW3AU27S2\ 3Q10P1a4FZ3CW39T27Q24N22Q53eM9hOAjRBmUCpXDrZEuaFxd\ GzfHycKxaNw_QwXTvVWuTZuQatOdsMgsKjeMoTOsGQwBYb6eJA\ dcEcxF_tGXpHTlHQhIMdJJ`KFXKCTIEOGFKEHGCICAJ8FIAJIB\ NICRIDVIEZIFcHGgHHkHIoHJsHKwHLrFLnDLjCLeALa9LY7LT6\ LP4LL3LJ8IHCGGGEHwzOZfVU` } frm:mult-XY-ZW-compjb {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p4, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p5: z=z^p2*(c^(p3-1))+c, |z| < 400 } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD 23-01-05 (Mysterious Triangle [9])
by Fr. Jim Lacasse 24 Jan '05

24 Jan '05

Yes, this is for sure a 9. Great fractal Fr. Jim >>> jamth(a)mindspring.com 01/23/05 06:59AM >>> FOTD -- January 23, 2005 (Rating 9) Fractal visionaries and enthusiasts: I am not sure that today's image truly rates the 9 that I have given it, but it is certainly one of the better FOTD's. The image, which shows the entire parent fractal, was created by the JimsCompMand formula. This formula can increase the number of arms in Mandel-type fractals, and it can also reduce the number of arms, as it has done in today's image, where the Z^(-1000) Mandeloid has had its arms reduced from 1001 to merely 3. This reduction in the number of arms brings out the delicate intricacy of the high-order fractals with negative exponents and large escape radii. The natural delicate effect was enhanced in today's image by the softly-glowing background, which was created with the 'bof60' inside fill and a bit of applied color theory. The black-to-orange shading of the foreground elements was achieved by setting the outside to 'fmod' and the proximity to a very high 1650. The effect of delicacy can be made stronger by increasing the escape radius beyond the 1100 that was used in the image. When this is done, the foreground elements gradually grow smaller. I assume they would eventually disappear entirely, though I have not taken the escape radius this far. Changing the inside and outside fills also creates interesting effects. The 'bof61' and 'atan' inside fills are particularly effective, as are several of the other outside options. I named the image "Mysterious Triangle", though there is really nothing very mysterious about it -- except that it is a fractal -- and we know how mysterious they are. The rating of a cosmic 9 and the brief render time of 1-1/2 minutes combine to create an image with an overall worth of 577. This is not the highest overall worth of all time, but those higher worths are somewhat artificial, having been achieved by render times of only a few seconds. As always, the finished image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy snow fell all afternoon Saturday here at Fractal Central, piling up to a depth of 6in 15cm. The temperature reached a high of only 16F -9C. The fractal cats took one brief smell of the outside air and decided that their adventure would be more comfortable on the window shelf. A treat of extra tuna in the evening insured their contentment. Today is starting cloudy. The snow has ended, but the temperature is 12F -11C, and the high winds are blowing the snow into drifts. The duo have already accepted that it will be another inside day. For me, the task is to clear the driveway and sidewalk, but before tackling that job I will wait for the drifting snow to settle down. The delay will give me a chance to find another fractal hopefully as good as today's. The next FOTD will appear in 24 hours. The vaguely fractal philosophy might or might not be included. Until then, take care, and see the light. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= MysteriousTriangle { ; time=0:01:33.60--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=JimsCompMand passes=1 center-mag=1.64342/2.84649/0.08912656/1/30/-1.233\ 73533611470521e-014 params=-1000/0/999/0/1000/0 float=y maxiter=2500 inside=bof60 proximity=1650 outside=fmod logmap=yes periodicity=10 colors=0000AHAAHLAHTAHXAHaAHeAHhAHjAHlAHkAHoAIqDJs\ HKuKLpOMpRNpVOpYPp`PpcQpfRpjSpmTqqUrtVswWuyXwzXxzW\ yyVzsUzwUzvTzuSztSwsRtqQqqQnpPknOhmOhlNgjMfiMfgLef\ KeeK`iRWlXRocMsiHvpCyvEvqFtmGrhHodJm_KkWLhSMfNOdJP\ aEQ_ARY6QZBQZGQZLP_QP_VP__u6Ks5Jr5Iq5Hp5Hn5Gm5Fl5F\ k5Ei5Dh5Dg5Cf5Bd5Bc5Ab49a48_48Z47Y46X46V45U44T44S4\ 3Q42P42O41N40M40N54O67O7BP8EQ9HQALRBORBRVFPZJObNMf\ RLjVJnZIlXHkWHjUHiTHhRHgQHfOHeNGdLGcKGbJGaHG`GG_EG\ ZDFYBFXAFW8FV7FU5FT4FS3GU5IV7JW9KXBMYDNZFP_HR`JSaL\ TbNVcPWdRXeTZfV_gX`hZbi`djbfkdilfkmgmngoohpohrpitq\ iurjvrjwskwtkxtlyulyvlzvlzulytlxskwrkwqjvqjupitoit\ nhsmhrlgrlgqkfpjfoieohengdmgdmfcleckdbjcbjbaibaha`\ h``g__fZ_eYZeYZdXYcWYcVXbUXaTW`TW`SV_RVZQUYPTYOSXO\ RWNQWMPVLOUKNTJMSJLRIKQHJPGIOFHNEGMEFLDEKCDJBCIABH\ 9AG99F88E77D66C55B44A439328017206105004zR1yQ0xQ0wP\ 0vP0uP0tO0sO0rN0qN0pN0oM0 } frm:JimsCompMand {; Jim Muth z=c=pixel: z=z^p1*(c^(p2-1))+c, |z| <= p3+100 } END PARAMETER FILE========================================= _______________________________________________ Fractint mailing list Fractint(a)mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint

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