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FOTD 02-01-08 (Aurora Fractalis [9.5])
by Jim Muth 01 Jan '08

01 Jan '08

FOTD -- January 02, 2008 (Rating 9.5) Fractal visionaries and enthusiasts: In yesterday's FOTD I did much talking and little coloring. In today's I have done much coloring and little talking. But then, an image that rates a 9-1/2 and calculates in one minute doesn't need words to get its message across. The image is an oblique slice of Seahorse Valley. The orienta- tion is halfway between the Oblique and Rectangular directions. A moderate amount of skewing and a slight stretching was neces- sary to create the cold mystical effect. The rating of 9-1/2 might be a bit liberal, but I really do think the image rises above the normal mass of FOTD fractals. The name "Aurora Fractalis" is a phrase that came to mind as I studied the image. The calculation time of 1-1/4 minute will be no problem for even the most hurried fractalist. And as always, the finished image is or soon will be posted for instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Tuesday was really not such a bad day here at Fractal Central. There was lots of sun and the temperature reached 43F 6C. Only a brisk wind kept the day from being near perfect for early winter. The fractal cats did not worry about the weather. For some reason, they were too busy sulking at each other. My day was slow, which gave ample time to find and work on the FOTD fractal. The next FOTD will be posted in 24 hours. By then the familiar old work-day routine will be back in effect. Until next time, take care, and be at peace with the universe. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Aurora_Fractalis { ; time=0:01:14.43-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 center-mag=-0.155155/\ 0.643015/3.45136/1.0763/-90/20.2819418025888787 params=45/90/0/90/-0.7505/0/0/-0.35 float=y maxiter=32767 inside=0 logmap=5 periodicity=10 colors=000EPSFKSFKSFKSGKSGKTHKTHKTIKTIKTIKUJKUJKUK\ KUKKUKKVLKVLKVMJVMJVMJVNJWOKWOLWPLWPMWQNWQNXROXRPX\ SPXSQXTQXTRXURYUSYVTYVUYWVYXVYXWYYXZYXZZYZZY__Z`__\ a`_b`_ca`daaebafbbgcdhbfiahhcjieljhnkkqlnqnqtqtvtw\ wwzzzwxwtutqtqoqnmpmkpmiomholgnlfmkemkdljckjbkjaji\ `ji_ihZhhYhgXggWggVffUefTeeSdeRcdQcdPbdObcNacM`bL`\ bK_aJZaIZaHY`GY`FX_EW_DWZCVZ9WYBVZCV_DU`EUaFTbGTcH\ SdISeJRfKRgLRhMQiNQjOPkPPlQOnROoSNrTNtUNvVNuUNuTNu\ TMsSLqRLoRKmQKkPJiOIhOIgNHfMHeMGdLFcKFbKEaKE`KD_KC\ ZKCXKBWKAVKAUK9TK9SK8RK7QK7PK6OK6NK5MK4LK4KK3JK3IK\ 2HK1GK1FK0EK0DK0EK0EK0EK0EK0EK0EK0EK0EK0EK0EK0EK0F\ K0FK0FK0FK0FK0FK0FK0FK0FK0FK0FK0GK0GK0GK0GK0GK0GK0\ GK0GM0GO0GQ0GS3HS5HS7HS9HSBHSDIRFIRHIRJIRLIRNJRPJR\ RJQTJQVJQXKQZKQ`KQbKQcKQdKZOVYPTXPSWQRWQQVROURNTRM\ TSLSSJRTIQTHQTGPUEOUDNVCNVBMW9LW8KW7KX6JX4IY3HY2E_\ 0GZ1HY1IY2JX2DRRDQRDQREQR } 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 01-01-08 (No Name [No Rating])
by Jim Muth 31 Dec '07

31 Dec '07

FOTD -- January 01, 2008 (No Rating) Fractal visionaries and enthusiasts: I have been lagging in the FOTD discussions recently, and giving too much attention to the images, so what better day than the first day of a new year to begin a discussion of the fourth dimension as it relates to the section of Seahorse Valley that appears as today's FOTD. What do I mean when I claim that today's image is a new view of perhaps the best known of all fractal 'objects', Seahorse Valley of the Mandelbrot set? It bears no resemblance at all to the valley or its Julia sets. Despite appearances, I mean exactly what I say. Today's image shows part of Seahorse Valley. What then is Seahorse Valley? The first impression is that it consists of two tapering wedges that approach but never actually reach the point at -0.75 on the real axis of the M-set. This much is true, but these two wedges are only a small part of Seahorse Valley. What about the Julia set of the point -0.75? This Julia aspect is as much a part of Seahorse Valley as the Mandelbrot aspect. And when we consider Julia sets, what of the countless other Julia sets associated with the other points of Seahorse Valley? They are also a part of the valley. We now find ourselves with a unique two-dimensional Julia image associated with every point of Seahorse Valley, and all these Julia images stack together in four-dimensional space to form a single four-dimensional assemblage, which is the hyper-Seahorse Valley area of the four-dimensional Z^2+C Julibrot figure. Since it is a 4-D object, the full Seahorse Valley cannot be visualized in its entirety at a single moment of time, but it can be analyzed and statements can be made about it that can be demonstrated to be true. In its full 4-D aspect, Seahorse Valley consists of two tapering hyperwedges that approach but never quite reach the plane of the Julia set of the point -0.75 of the M-set. Instead of terminating in two sharp points, as do the two branches of the familiar Seahorse Valley of the M-set, these two hyperwedges terminate in two sharp planes, which are cuttingly sharp over their entire 2-D surfaces. In our three-dimensional space, sharp planes are an absurdity. Planes are flat and there is nothing sharp about a flat surface. In 4-D space however, an unlimited plane does not form an impassable barrier, and one may simply step around the plane and continue on. If the two additional dimensions of the plane are extremely small, the plane will act in 4-D space as a razor edge does in 3-D space, slicing through any reasonably soft 4-D object it comes in contact with. So the full Seahorse Valley consists of two hyperwedges terminating in two sharp planes. What shape then is the eastern surface of the valley, which faces the main bay of the M-set? Like the surface of any other 4-D object it is a surface with three dimensions, and the buds that appear to be flat circles are actually 4-D hyper-cylindrical shapes with two extended Julia dimensions and two small Mandelbrot dimensions. Like regular 3-D cylinders, these hypercylinders may be sliced in two dimensions to give circles, ellipses and parallel-edged stripes. In today's image the eastern surface of Seahorse Valley has been sliced in the Oblate direction, which shows the buds there as black stripes. To make the stripes more clear I have stretched the image quite a bit in the vertical direction. And to add interest I moved the center of the slice 0.35 in the imag(z) direction. For some reason the whole thing ended up rotated 180 degrees. Oh well, nobody's perfect. Since today's image is more a study than a finished piece of art, I gave it no name or rating. And its calculation time of 20 minutes is admittedly slow for a mere 4-D study. I seriously recommend visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. But it is New Year's time, so be patient if Paul has not yet posted it. Three wet slushy inches or 7cm of snow fell overnight Sunday here at Fractal Central. Monday was sunny with a temperature of 41F 5C, which melted a good part of the snow. The fractal cats noticed the snow with curiosity, then returned to their normal activities. The next hyper FOTD will be posted in 24 hours. Until then, take care, and to find the fourth spatial dimension, look sideways to your inside. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= FOTD_for_Jan_01_08 { ; time=0:20:13.47-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=Oblate passes=1 center-mag=+0.02067323\ 061209259/+0.01838987041970301/1425.157/0.002231/\ -180/-32.619243071192308 params=0/-0.35/-0.7498/0 float=y maxiter=32767 inside=0 logmap=325 symmetry=none periodicity=10 colors=000cpaco`cn_cmZclXcjWciVchUcgTcfScdRccQcbPb\ aNb`MbZLbYKbXJbWIbVHbTGbSEbRDbQCbPBbNAbM9bL8bK7aH1\ bJ6bLAbMFbOJbPOcRScSXcU`cVecXicYmdZldZkdZjeZieZheZ\ gfZgfZffZefZdgZcgZbgZahZahZ`hZ_hZZiZYiZXiZWjZWjZVj\ ZUjZTkZSkZRkZQlZQlZPlZOmZNmZMmZLmZKnZKnZJnZIoZHoZG\ oZFoZEpZEpZDpZCqZBqZAqZ9qZ9pYAoYAnYAmYAlYAkYBjYBiY\ BhYBgYBfYBeYCdYCcYCbYCaYC`YC_XDZXDYXDXXDWXDVXEUXET\ XESXERXEQXEPXFOXFNXFMXFLXFLXFMWEMWENWENWEOWDOWDPWD\ PWDQWCQWCRVCRVCSVBSVBTVBTVBUVAUVAVVAVVAWU9WU9XU9XU\ 9YU8YU8ZU8ZU8_U7_U7`T7`T7aT6aT6bT6bT6cT5cT5dT5dT5c\ S4dT5dT6dU7dU8dV8dV9dWAeWBeXBeXCeXDeYEeYEeZFfZGf_H\ f_Hf`If`Jf`KfaKgaLgbMgbNgcNgcOgdPgdPgdUfdZfccfcheb\ mebrdavdazc`zc`zc_zb_zbZzaZzaYz`Yz`Xz`Xz_Wz_WzZVzZ\ VzYUzYUzYTzXTzXSzWSzWRzVOzWRzXTzYWzYYzZ_z_bz_dz`gz\ aizakzbnzcpzcrzbqzaqzaqz`qz`qz_pzZpzZpzYpzYpzXozXo\ zWozVozVozUnzUnzTnzTnzSnz } frm:Oblate {; Jim Muth real(z),imag(c) z=real(pixel)+p1, c=flip(imag(pixel))+p2: z=sqr(z)+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 31-12-07 (Good-Night Irene [6])
by Jim Muth 30 Dec '07

30 Dec '07

FOTD -- December 31, 2007 (Rating 6) Fractal visionaries and enthusiasts: With today's image, we say good-bye to the overworked and underpaid parent fractal that has been the source of all but a few images in the month of December. To say good-bye we delve deep into what appears to be the East Valley of the parent, where we find today's scene. The most notable feature of the image is the small bailout radius, which has been lowered to the point where the entire image is about to be swallowed up. This broadens the elements of the outside parts and is exactly the opposite of evaporating an image, where the bailout radius is increased and the outside elements shrink and eventually vanish. The entire image has also been slightly stretched to fit artistically onto the 4x3 screen. In my opinion the final result rates a 6. The name "Good-Night Irene" is my way of saying good-bye to a parent fractal that most likely will never again be seen. The calculation time of 8 minutes is a bit slow, but this can be avoided by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunday began clear and sunny here at Fractal Central, but thick clouds moved in at midday and light wet snow arrived in the afternoon. The fractal cats spent the day watching for trouble. None arrived. I spent the day recovering from the rush job on Saturday. If all goes well, the next FOTD will be posted in 24 hours. Until then, take care, and by their nature, fractals are always incomplete. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Good-Night_Irene { ; time=0:08:02.36-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=-1.918948862109704/-15.57003563522107/\ 88811.98/1.0585/137.5/-1.5198849193099e-009 float=y params=-2.475/-1.05/-0.275/-5.5/0/-86.5/0/0 maxiter=20000 inside=0 outside=tdis periodicity=10 colors=0008a06U26OG4HR4Aa40s40n42l46i4Ad4Ga4JY4MU4\ PR4UO4XJ4_G4cB2d14f84gD6iJ6jO6lT8nX8naApfArjAsnBts\ BvwBvzDsyDrwDpvDntDlrDjpDinDgnDflDciDagD_fDYdDWaDU\ _DTYDRXDPWDMTDKRDJPDHOADJDGMGGOHHPJHRKHTMJUOJWPKXR\ KYUKaWMcXMdYMf_OgaOicPjdPlfPngRnjRrlRsnTtnTvpUwrUy\ sUztWzvWzwWznYwfarXdjOgd8l_DiYHfYMcYP_XUYXXWXaTWdP\ WiMWlKUpHUsDUwATz6Tz4TsAOjDKaJGTMBJR88U20Y00a00c11\ d48fAGgDMiJTiMYjPdlUjnXpnavpdzpgsnjjnlztyzszzszzsz\ zrzzrzzrzzy0zrzznzznzzlzzjzzizzfzzdzzczzawz_vzXszW\ rzUnzTnzRjzOizMfzKdzJazH_zDXzBWzATz8Rz6Oz0Oz1Mz4Mz\ 8KzBKzGKzJJzMJzPJzTHzWHzYGzaGzdGzgDzjDzpHznGznDylB\ wjAvi8sg6rf4pd2nc1na0j_0iY0gX0fW0dU0Ji0Ua0cU0nO0vG\ 0z60z00z22z66z88zBBzDGzHHwJKvMOsPPrRTnUWlWXjY_g_af\ cdcdg_giYjlWlnUnpRpsOsvMtwyzzhzzHzzHzzHtzHwzGzyGvw\ GrvGnvDjtDnsDnrDlpBjnBinBglBflAdjAciAagA_f8Yd8Xc8W\ a8Ua6T_6RY6PX6OW4MU4KT4JR } frm:AutoCritInZ {; 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 30-12-07 (No Name [No Rating])
by Jim Muth 30 Dec '07

30 Dec '07

FOTD -- December 30, 2007 (No Rating) Fractal visionaries and enthusiasts: Today's very late and super hurried image is a half-evaporated scene in the parent fractal that is created by mixing various negative portions of Z^(-1.1) and Z^(-5.9). The new inside parts that have appeared are rendered with the 'zmag' inside fill, which adds the fine diagonal striations to the image. The parent fractal features one of the most convoluted main bays I have yet seen in a fractal. Today's scene is located near the north shore of the cove on the northwest shore of the bay. I gave today's image neither a name nor a rating. The calculation time of 2-1/3 minutes can be avoided by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Saturday proved to be a very pleasant day, and the fractal cats agreed. The next FOTD fractal will appear in about 7 hours. Until then, take care, and fractal things are never simple. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= No_Name { ; time=0:02:22.97-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-6.920117649021531/-0.2690318440929521/\ 8508315/1/-165/-2.26411326827158366e-006 params=-1/-1.1/-0.1/-5.9/0/82900000/0/0 float=y maxiter=750 inside=zmag periodicity=10 colors=000hRRhUQgXQg_PgcOgfOgiNglMgoMbkYYgiUaxTcuS\ dsSfpRgnQhkQjiPkgOldOnbNo_MpYMrVLsTNzPLtRKnSJiTIcU\ HYWGTXFNYBLaEIZHGXKEVNCTQ9QT7OW5MZ0GY3KX5OW8SVAWUD\ _TFbSHfRKjQMnPPrORvDPzNTyXXyf_yaShdOafLWiIPkFJmCDk\ GDiJDgNDeQDcUDaXD__DYcDWfDUjDSmDQqDOtDMwDJoKGhQDaW\ AVa6Pn8OgAN`CNVEMOGMIILBJL5JO9JQDJSGJVKJXOJZRJaVJc\ YJeaJheJjhJllJopJqsJswJuzZbbnLFlKGkJGiIGhHGgGGeFHd\ EHcDHaCH`BHZAIY9IX8IV7IU6IT6IV8JW9KXALYCMZDN_EO`GP\ aHPbIQcKRdLSeMTfOUgPVjPShQVfQXdR_bRaaRc_SfYShWTkUT\ mPWrTToXQl`NiYJdcLfhNhnPj000sRkpUlmXmjZngaocdp`gqY\ irVlsSotPqtRnpTllVihWgdYd`_bXa_R``U`aW_bY_b`ZcbZdd\ YefYeiXfkXgmXgoYdoZbo_`o`Yo`WoaUobRocPocNodKoeIofG\ ovKHfEo`IT`LV`OX`QZ`T``Wb`Yd``f`ch`ej`hl`jnckkfkii\ kglkdokbrk`ofcmaeicgedhaeiYfjUgkQhlMjmIknEloAmp6nq\ 3or4mo5ll6ki7jf8hc9g`AfYBeVCdSDbPYkZ_hZ`e_bb_d__eX\ `gU`heghS`iAVhEUhHThKShNS } 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 29-12-07 (Chaos of a Misfit [5])
by Jim Muth 28 Dec '07

28 Dec '07

FOTD -- December 29, 2007 (Rating 5) Fractal visionaries and enthusiasts: I fear we're coming to the end of the line for the December parent fractal. Only two more images to go before we launch out on a new fractal project. I'm getting a renewed interest in four-dimensional stuff. It's been quite a while since I last discussed the curiosities of the fourth spatial dimension. But I'll make no decision until the new year arrives. Meanwhile, today's image takes us the the East Valley of the large minibrot in the chaos extending from the large period-13 bud of the parent fractal. The East Valley characteristics are quite prominent, even though the countless rings associated with the parent are equally prominent. My waning enthusiasm for the children of this particular parent is visible in the rating of a merely average 5. And the name "Chaos of a Misfit" confirms my increasing boredom. The calcula- tion time of 6-1/4 minutes is about what would be expected of such an image. Viewing the finished image on the FOTD web site is faster. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A sunny morning gave way to a cloudy afternoon and a rainy eve- ning here at Fractal Central on Friday, while the temperature reached a pleasant 48F 9C. The fractal cats grabbed as much sun as they could in the morning, and wondered where it went in the afternoon. My day was average; tomorrow promises to be quite busy. The next FOTD is due in 24 hours, but don't be surprised if it appears 12 or more hours late. Until next time, take care, and if the observation *is* the fractal, where does the fractal go when it is not being observed? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Chaos_of_a_Misfit { ; time=0:06:16.68-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=-152.7771462778378/-55.57885459963332/\ 56686.04/1/127.5/1.44225563644684307e-008 params=-2.475/-1.05/-0.275/-5.5/0/0/0/0 float=y maxiter=4800 inside=0 logmap=736 periodicity=10 colors=0007MK8NK9OKAPKBQKCRKDSKETKFUKGVKHWKIXKJYKK\ ZKLYLMXLNWLOVLPULQSLRRLSRLTPLUNLWNKXNKYLKZKK_JK`HK\ aGKbFKcDKdCKeBKg7JfAKeCLeFMdHNdKOcMOcPPbRQbURaWSaZ\ T``T`cU_eV_cWZjXZbXbgZe_`i_blVcpResNgwKkvJhuIftHcs\ GarGZqFXpEUoDSnCPmCNlBKkAIj9Fk8Bi9Dg9Fe9Gd9Ib9J`9L\ _9NY9OW9QV9RT9TR9VP9WO9YM9ZK9`J9bH9cF9eCAdE9fG9gI8\ iK8jM7lO7mQ6oS6pU5rW5sY4u_4va3xa1zb3yb4yb5yb6xb7xb\ 8xb9wbAwbBwbCwcEvcFvcGvcHucIucJucKtcLtcMtgQwcNt_Kq\ WHnSEkPBhOEiOGiOIjOLjONkOPkOSlOUlOWmOZmO`nNbnNeoNg\ oNipNlpNnqNpqNsrNurNwsNysMvrMtrMqrLoqLlqLjqKhpKepK\ cpJ`pJZoJXoIUoISnIPnHNmHKlHIjGGiGDhGBaF8`F6_A4ZB5W\ C6VD7U98TA9NBANCBN8BN9CNADNBENCFMpOWrHWoJWlLViOUfP\ TcVSeWRgaQibPjgOjgOWT7VU9UVATWBSWDSXERYFQZGPZIO_JO\ `KNaLMaNLbOKcPKcQHcQEcPBdO8dO5dN3eN5fL6gJ7hH8iG9jE\ FkCKlAPm9Un7Zo5cp3hq2mr4rs5vt6zu7zv8zw9zxFzyKzzPzz\ UzzZzzczzhzzmzzqzztzzwzzz } 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 28-12-07 (Redevelopment Plan [6])
by Jim Muth 27 Dec '07

27 Dec '07

FOTD -- December 28, 2007 (Rating 6) Fractal visionaries and enthusiasts: Today, in contrast to yesterday, I have posted the correct parameter file. I have no idea how the parameter file with the rough colors got posted yesterday, but I finally discovered the error, and it will not happen again, (most likely). Today's journey into the parent fractal of December takes us deep into the edge of the chaos field on the west side of the main bay. We are so deep that the resolution is actually starting to break down, which requires the mathtolerance entry to assure that the image calculates at the correct magnitude. Actually, the magnitude of 9.4*(10^9) is quite moderate, but in today's image the decimal point has been shifted several places to the right, reducing the upper limit of resolution. Since I could find nothing of exceptional interest in today's image, I rated it at a 6, which is just the tiniest bit above average. As for the name "Redevelopment Plan", I wish someone would tell me what it has to do with fractals. It simply came to mind first as I searched for a name. The calculation time of 4-1/3 minutes is within reason, provided the devoted fractalist has nothing more pressing to do. But if time is of the essence, the finished image may be viewed without delay on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Thursday began with heavy clouds and sprinkles of cold rain here at Fractal Central. At 2pm the clouds suddenly broke, giving a couple hours of partial sunshine before the early sunset around 4:50pm. As the temperature topped at 45F 7C, the fractal cats enjoyed the brief sunlight that streamed in the southwest window. My day was much calmer than yesterday. And tomorrow might be calmer still. The next FOTD will appear in 24 hours. Until then, take care, where does space end, and when did time begin? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Redevelopment_Plan { ; time=0:04:21.66-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-114.0062226111369/+14.12163053608614/\ 9.435573e+009/1/-99.5/0 params=-2.475/-1.05/-0.275\ /-5.5/0/0/0/0 float=y maxiter=1600 inside=0 logmap=448 periodicity=10 mathtolerance=0.05/1 colors=000dJYcKZcK_cL`bMbbNcaOdaOeaPf`Qg`RhaQl`Ri_\ SgZTeYUcXVaXV_WWYVXWUYUTZSTZQS_OR`MQaKPbIOcGOcENdC\ MeALf8Kg6Hi0Kg4Ne8QcCTbGU`KUZOUYRUWVUUZUSbURfUPjUN\ nUPrUJoUKpUGnUGnVEmVClXAlYCmZEm`GnaIncKodNofOpgSpi\ SqjWqmVqnZrpZrqbssbstetvftwhuyjutirtirohojfleej`cg\ WbdR`aM__HYXCWU4TO7USAZVC_YFdaHgdKjgMmkPpnRsqStrSu\ rSusSvsSwtSwtSxuSyuSyuSyuVwnYuh`sacqWfoPimJmnCkkDi\ hEgeFecFc`GaYH_WHYTIXQJVNKTLKRILPFMNDMLANJ7OI5Oz_U\ w`Uu`UqaUmaUibUebUacUYdUVeURgUOiUKlUHnUDqUAsU6vT7v\ U7tU7rU7pU7nU7lV7jV7hV7gV7fV7eV7dW7cW7bW7aW7`W7`WA\ aUCbTFcSHcQKdPMeOPfMRfLUgKWhIZiH`iGcjEekDhlCjlBhjD\ fhEefGcdHbbJ``KZZLYXNWVOVTQTRRSPScKUmLVzTXzmYmZ_cD\ `UBaKKzDPzCUzAXz9YzC`zFczHezKhzNUePKeSAdUBdXDd_EcL\ ZkN_jQ_hS`gU`fXadZac`bbcb`ec_gcZme_igYeiXakWYmVUoU\ QqTMrSIsREtQ6uQBvPGwOLxOQyNVzM_zMdzLizJhzLhzMgzNgz\ OgzPfzQfzRfzSezUezVdzWdzX } 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 27-12-07 (Correct Coloring [No rating])
by Jim Muth 27 Dec '07

27 Dec '07

FOTD -- December 27, 2007 (No Rating) Fractal visionaries and enthusiasts: Due to an unexpected emergency rush job, I posted the wrong file of the FOTD for Dec 27 to the lists. This post includes the correct (I hope) coloring. The first and wrong posting has an overall bluish cast, which this version corrects (I again hope.) Today's discussion must be so short as to be virtually non- existant. But I do have time to explain that it is an evaporated scene near the origin of the December parent fractal. The name "Totally Evaporated" means just what it says. An image with so little effort behind it could hardly be rated. The calculation wait of 5 minutes may be avoided by viewing the finished scene on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Wednesday was a cloudy and cold day here at F.C. The fractal cats kept warm by the heat. The next FOTD will be posted in 24 hours, along with a longer discussion. Until then take care, and what ever happened to the land-fill crisis? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Totally_Evaporated { ; time=0:05:06.29-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+3.389200514565685/+0.2627706206541682/\ 5.323121e+009/1/-171.5/-3.59915041934014135e-005 params=-2.475/-1.05/-0.275/-5.5/0/1e+100/0/0 float=y maxiter=2500 inside=bof61 periodicity=10 colors=000Af68k67pA7wD6uE6tE6rF6qF6pF6nG5mG5lH5jH5\ iH5gI5fI4eJ4cJ4bJ4aK4_K4ZK3YK3WK3VK3TK3SK3RK2PK2OK\ 2NK2LK2KK1DK2JK3PK4VM5`O6fQ7lS8rUgzX8z_`xZ9vYStXBq\ XBoWCmVCkUDhUEfTEdSFbRF`RGYQHWPHUOISNJPNJNMKLLKJKF\ GGGEGGCGHAGH8HK9IL9JM9KN9KOALPAMQAMSANUBOWBOYBP`BQ\ aBQbCRcCSdCSeCTfDUgDUhDViDWi8XjBWjDWjFWkHVkJVkLVlN\ VlPUlRUmUUmWTmYTn_TnaTncSwklsgSzztpmUzzzohQofNodLo\ cJoaHn_EoZCnXAnV7nU6mS6mR60863A66C68E6BF6DH6GJ6JK6\ LM6OO7QQATRDWTGYVI`WLbYOe_Rg`TbYOYWKUUGNRCJP8FN6EM\ 6DL6CM67O70SD2RE5RF7RGARHCRIFRJHQKKQLMQMPQNSQOUQPX\ PQZPRaPScPTfPUjOWhPVgPUfPTdQTcQSbQR`RR_RQZRPXSPWSO\ VSNTTNSTMRTLPULOUKNUJMUJOWKPYKQ_LSaLTbMUdMVfNXhNYj\ OZkO`mPaoPbqQeqRcrQarQ`rPZrPXrPWrOUsOSsORsNPsNNsNM\ sMKtMJtLHtLFtLEtKCtKAuK9uJ7uJ5uJ4uI2uI1uI2sJ2qK2oL\ 2mM2lN2jN2hO2fP2eQ2cR2aR3_S3YT3XU3VV3TW3RW3QX3OY3M\ ZAmAAl9Al99l89l89k78k78k6 } 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 27-12-07 (Totally Evaporated [No rating])
by Jim Muth 26 Dec '07

26 Dec '07

FOTD -- (No Rating) Fractal visionaries and enthusiasts: Due to an unexpected emergency rush job, today's discussion must be so short as to be virtually non-existant. But I do have time to explain that it is an evaporated scene near the origin of the December parent fractal. The name "Totally Evaporated" means just what it says. An image with so little effort behind it could hardly be rated. The calculation wait of 5 minutes may be avoided by viewing the finished scene on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Wednesday was a cloudy and cold day here at F.C. The fractal cats kept warm by the heat. The next FOTD will be posted in 24 hours, along with a longer discussion. Until then take care, and what ever happened to the land-fill crisis? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Totally_Evaporated { ; time=0:05:06.29-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+3.389200514565685/+0.2627706206541682/\ 5.323121e+009/1/-171.5/-3.59915041934014135e-005 params=-2.475/-1.05/-0.275/-5.5/0/1e+100/0/0 float=y maxiter=2500 inside=bof61 periodicity=10 colors=000HaMFfREkVErYDpZDoZDm_Dl_Dk_Di`Ch`CgaCeaC\ daCbbCabB`cBZcBYcBXdBVdBUeATeAReAQfAOfANgAMg9Kg9Jh\ 9Ih9Gi9Fi88g9EiAKjBQlCWmDaoEgpFmrExuFutGssGqrHoqIl\ qIjpJhoJfnKcnLamL_lMYkMWkNTjORiOPhPNgQKgQIfRGeREdS\ BdT9cT7bU5aU3aW4bX4cY4dZ4d_5e`5fa5fb5gc6hd6he6ig6j\ h6ji7kj7lk7ll7mm8nn8no8op8pp3qq6pq8pqAprCorEorGosI\ osKnsMntPntRmtTmuVmuXmuZlzflzblznlwhnyrlvcjuagt_et\ ZcsXarVZrUXqSVpQSpPQoNOoMM733A56D79F9CIAFKCHNEKQFN\ SHQVJSXLV_MYbO`dQbgReiThlVknWmiThdRd`P`WMXSKTNIPU9\ 7ODEJGLEJS6NY9MZCM_EM`HMaJMbMMcOLdRLeTLfWLgZLh`Lic\ KjeKkhKljKmmKnqJpoKonKnmKmkLmjLliLkgMkfMjeMicNibNh\ aNg_OgZOfYOeWPeVPdUPcTPcVRdWTdXVeZXe_Yf`_faagccgde\ hefhghihjiiljllkjmjhmjgmiemicmibmh`nhZnhYngWngUngT\ nfRofQoeOoeMoeLodJodHpdGpcEpcCpcBpb9pb8pb9nc9ld9je\ 9hf9gg9eg9ch9ai9`j9Zk9XkAVlATmASnAQoAOpAMpALqAJrAH\ sHhVHgUHgUGgTGgTGfSFfSFfR } 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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Re: always expect the unexpected
by JackOfTradeZ＠comcast.net 25 Dec '07

25 Dec '07

. . soooo ... after so many years of using fractint I finally get around to checking out the "evolver" function. and it's awesome! now what can I do with it .... . .

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FOTD 26-12-07 (Emergency Fractal [No rating])
by Jim Muth 25 Dec '07

25 Dec '07

FOTD -- December 26, 2007 (No Rating) Fractal visionaries and enthusiasts: Christmas turned hectic here at Fractal Central when my sister unexpectedly dropped in from Old Fractal Central, with tales of the old fractal cats, making for a total of four guests at the same time. Somehow I managed to get away from the chatter long enough to find a fractal minibrot deep in the valley centered on the positive Y-axis of the cubic Mandelbrot set. It's a rather slow one, and notably un-impressive, but at least it keeps the current unbroken string of daily FOTD's intact. I named the image "Emergency Fractal" because that's what it is. I gave the image virtually no coloring effort. The calculation time of over 25 minutes is far too slow for such a mongrel fractal. A far better way to view the image is to go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and see the finished scene there. But due to the holiday, it may be best to wait a bit to give Paul a chance to post it. A perfectly average day graced Fractal central on Tuesday, Christmas Day. Check the average conditions for central Pennsylvania in late December, and you'll have an accurate description of the day's weather. In keeping with the weather, the fractal cats' behavior was average also, as they vigorously attacked the bows on the gifts. My behavior was less serene than I would have liked, but still peaceful enough. The next FOTD will appear in 24 hours. Until then, take care, and if Christmas is supposed to be all about peace on earth, why do we intentionally go out of our way to make it so hectic? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Emergency_Fractal { ; time=0:25:47.52-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotCube center-mag=-0.000000289\ 53107351/+1.088681187267954/1.340348e+010/1/-92.5/\ -2.8133834276376779e-005 params=0/0/0/0 float=y maxiter=130000 inside=0 logmap=3679 periodicity=10 colors=000GLNKPQNTSQXUT`WXdZ_h`blbeodinemmeqleuleh\ mkXmpLmuJnoIniHncGoYEoSDoMCpGBpAAp4Dm6Gj8JgAMeCPbE\ R_FUYHXVJ_SLbQNdNOgKQjISmFUpCWrAXmHWiNWeTW`ZVXdVTj\ VPpVQkWQfWQbWRYXRUXRPXSLYSGYSCYTB_TAaUAbU9dV8eV8gW\ 7iW6jX6lX5mY4oY4pS3iN3bH3XC3Q73KB5NE6QH7TL8WOAZRBa\ UCdYDg`EjcGmgHpjIsmJvpKxlTa9GHQw5obpkaY9VvIXkRY`__\ QpHNmOKjVHokXh5ghLTa5RJat54`jGQiMNiRKhWH5RfFU_PWTZ\ ZMrpmnjakeQswFmkFT00ZD5cPAEcKPbIZaGzyZurUqlPlfKywn\ 1K0NT8D6cFrHNmGUiGadFCaoL`eT`X``OQXEXWLdUSkTZsSezR\ lwQkuPjsOipNhnMglLfiKegJdeIcbHb`GaZF`WE_UDZSCY0UcT\ CXWCXYCW`CWcCVeCVhCVkCUmCUpCTsCTuCSxCSzCSzhYNSc4Zi\ I_ZW`PBxbNpVYhNVZ6__9d`CVAc0byLb1hrfhm_hiThdMHNQRS\ M_XIKDKXPH3XQHZMV_IVMjZQbaUVeYNmi6kf9icCnrFjrvimki\ i`hdQKUuRWjXY_b_PfqNghJpNXnRSlUOjYJvaCo`Ehf5hd8hcA\ haD1wICqHNkGYeFJ64WMA1vEGnFVgFVaaMPKEC2PUGZkT7Bl9D\ XBFHCG13AD37E35E79HADJDHL } frm:MandelbrotCube {; Jim Muth real(c),imag(c) z=p1, c=pixel+p2: z=z*(sqr(z))+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 25-12-07 (Any Which Way You Will [7.5])
by Jim Muth 24 Dec '07

24 Dec '07

FOTD -- December 25, 2007 (Rating 7.5) Fractal visionaries and enthusiasts: Today's quickie image was found in the main spike area of the parent fractal for December. I have little time to write a proper discussion, so I'll let the image speak for itself. (Listen closely.) I named it "Any Which Way You Will". The name means basically nothing, but it does attract a bit of attention. The rating of 7.5 includes an extra half-point for my coloring prowess. The calculation time of 3-1/3 minutes will pass in a flash, but downloading the image from the FOTD web site will make an even bigger flash. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Monday turned into a rather pleasant day here at Fractal Central, with some clouds, but still lots of sun, lighter winds, and a temperature of 41F 5C. The fractal cats celebrated by ripping the bows from several carefully wrapped gifts and getting themselves shut out of the room. My day was about average for the day before Christmas. Tomorrow is likely to be rather hectic, but I'm sure the usual fractal will prevail. The prevailing fractal will appear at this same spot in 24 hours. Until then, take care and where are the 12 fractal days of Christmas? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= AnyWhichWayYouWill { ; time=0:03:21.80-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-4.233475702321023/+0.2624673820988766/\ 3.28613e+008/1/-17.5/-0.000788236459404886847 params=-2.475/-1.05/-0.275/-5.5/0/0/0/0 float=y maxiter=2400 inside=0 logmap=321 periodicity=10 colors=000OGcOIdOGZOKeNFXMNhOIUMRmRKRMWrTMNMbvYPML\ hzcUFLmzmY1Lrzva0Lwzzf0Xwzzn0hzzzv0szzmy0hy3by7YyB\ SyENyIHyMCyQ6yU1yX6sZAm`FgbJadOWfSQhWKjVMhUOfTPeSR\ cRTaQU`PWZPXYOZWN`UMaTLcRKePJfOIhMIiLSmN`pPisRepXa\ nbYkhVinbe`iaNpY9oPNnG_m7lIKXLLTNMQPNMRNJUOFWPCYQ9\ _Q5bR2dS0fT0hT0gV0fX0eZ0e`2db5cd7cf9`k5Zp1Xu0Vz0Sy\ 0Px1Nw4Kv7IzAFtDCwGArJ7tM5pP2pS0oV3lW6gW9gXC_XFXYI\ TYLPZOLZRI_UE_XA`_6`a3`O5cP7_P8XQATQBQQDMREJRGGRHC\ SJ9SK5SM2TN0TP0TQ0SR0SS0RT0RT2RU5QV7QVAQWCPXFPXHOY\ KOZMOZPN_RN`UN`WLWVJRVHMVGIVILSJOPLQMMTKNWHPYEQ`BS\ c9Te6Uh3Wk0Xm0Zp0_s0`u0ds0hq0lp0pn0tm2wr4zw6zr8zqA\ zlGzjMyoSwrYuucsr`roYpmVnjSlhPjeMhcJg`GfZDf_Ef_Ef`\ Ff`FfaGfaGfbHfbHfcIfcIfdJfdJbeOZfS_gT`hTaiTbjUckUd\ lUemVenVfoVgpWhqWirWjsXktXluXlvXlw`lxclyflzilzllzo\ mzlnziozfpzcqzalz_hzZczY_zXYzWWzWUzWTzVRzVPzVOzUMz\ UKzUJzTHzTFzTEzTDzQDzNDzL } 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 24-12-07 (Dried-Out But Good [8])
by Jim Muth 23 Dec '07

23 Dec '07

FOTD -- December 24, 2007 (Rating 8) Fractal visionaries and enthusiasts: Our two-day diversion into the depths of the Mandelbrot set ends today, as we return to the parent fractal for December, a very rich fractal indeed. I named today's rather unusual image "Dried-Out But Good". The name reflects the evaporated state of the image. Images with negative exponents of Z will evaporate whenever the imag(p3) parameter is set to an extremely large number, such as the one- googol in today's parameter file. With such a distant escape radius, every point is trapped, resulting in a screen full of inside stuff. Though the outside stuff evaporates and vanishes when the value of the escape radius is increased, the inside stuff that takes its place retains a memory of the outside stuff it replaces. This is where Fractint's various inside fills become very useful. The active inside fills, such as bof61, can bring out the hidden detail in the remnant inside stuff. This is exactly what has happened today. Before I applied the bof61 inside fill, I was faced with a most disappointing blank black screen. But this fill made the ghost of the vanished image reveal itself to the world. The scene is located inside a ring in the extreme western exoburbs of the parent fractal for December. The rating of an 8 includes a whole point for the coloring, which I put almost an hour into, and which makes the entire scene. The calculation time of today's image, just over 2-1/2 minutes, is a vast improvement over the hours-long time of yesterday's very deep Mandelbrot scene. And as always, relief is at hand on the internet at the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is or soon will be posted for instant gratification. Heavy clouds and heavy showers, along with a temperature of 61F 16C, made Sunday here at Fractal Central unusually warm but fit for neither man nor beast. The fractal cats, being neither men nor beasts, but cats, whatever cats are, showed not the slight- est concern. I kept occupied most of Sunday making the final preparations for the holidays. And there was also one tiny job to wrap up. The next FOTD will appear in 24 hours. Until then, take care, and if absolute time doesn't exist, as relativity implies, what is it that appears to pass between one day and the next? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Dried-Out_But_Good { ; time=0:02:39.26-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-294.475271301/+33.1264441037/118788/1/\ 177.5/0 params=-2.475/-1.05/-0.275/-5.5/0/1e+100/0\ /0 float=y maxiter=1600 inside=bof61 periodicity=10 colors=000chEccCUZ9UY7KR4KO2AM05I00I00H00F00H10H20\ I41I51E727925A45C47E57F79H7AI9EK9FLAIMAKOCMPCOSERV\ ESYFVaFVdCXgAYe9Zd7Zc4``2aV1aP0cL0dK0eK0eI0gH0hF0h\ F0gH0gI0dK0eK0dL00M0cO1cO2cP4aR5aS7`S9`UAZVCZXEZXI\ `ZMa`RacUcdYdgadheekhgllgophptiswitzkwzlxzlzzkzxiz\ shzogziezedz`czXazR`zM`zMazMczMdzMezMgzMhzMizMkzMl\ zMnzMozMpzMrzMszMtzMvzMvzOwzPwzPwzRwzRwzSwvUwsUwpV\ wlVwiXweXwcYw`ZwXZwU`wR`wMawKawHXsASo4Mk0Ig0Ed0Fc0\ Hc0Ia0Ka4La7L`AM`FO0IPZLRZPRZSSYVUYZVXaXXdYXhYVkZV\ n`VraUtcUwcUzYVlSXZMYLIZ7KYALYCMYEOYHPYIRYKSYMUYOV\ YPXYRYYUZYV`YXaYZcY`dYaeYccZa```YaZVcYSiZRpZOw`Mz`\ KzaIzaKz`KzZKzYKzYKzXKzVKzVLxULvSLsSLrRLoPLnOLkOLh\ MMgLMdLMcKM`IMYIMXHgz`dz`cz`az``z`PvLFc4C`29Y15X04\ U01R00P00M00L05PIISaFXdEZgCahAdkFglKioPlpUosZstcvv\ cxxhzzhzzmzzizzrzzizzmzzezzZzzUzzezz9vxCswFptInsLk\ pOhoRdnUakXaicXgkUenRdmXh } 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 23-12-07 (Circles of Numbers [6])
by Jim Muth 22 Dec '07

22 Dec '07

FOTD -- December 23, 2007 (Rating 6) Fractal visionaries and enthusiasts: As promised, today's image shows the minibrot that lay invisibly at the center of yesterday's image. One glance shows why such deep minibrots are disappointing. The elements around the mini- brot are intricate enough, but they are so finely divided as to be almost meaningless, and they are arranged in perfectly boring perfect circles. This circularity explains the name "Circles of Numbers". In fact, it appears that, as we approach the minibrot, the circu- lar bands of elements start to take the shape of the equal itera- ion bands of the parent Mandelbrot set. It could be interesting to check if this is true, but the calculation would be extremely slow, and will have to wait until another day. The rating of a 6 indicates that I was much more pleased with the scenery on the way to today's minibrot than I was with what I saw when I got there. This is true of all extremely deep mini- brots. The most interesting parts of the basins are so far out from the center that the minibrots at the center are usually in- visible. Another drawback of course is the extreme calculation time, which in today's image is over an hour on the fast machine and over 4 hours on the slow one. But this will be no problem for those who view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy clouds and a temperature of 43F 6C made Saturday just an- other first day of winter here at Fractal Central. The fractal cats made the most of the brief daylight hours by watching all afternoon for intruders. In that time, they saw one dog pass by. My day was occupied by holiday preparations. The next FOTD will appear in 24 hours. Until then, take care, and a few nights ago I dreamed of a mountain. Then someone told me that the mountain was not real; it was all inside my head. This might be true, but my head is much too small to hold a moun- tain. I am now totally confused. What is the real size of the mountain I dreamed of? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Circles_of_Numbers { ; time=1:06:19.02-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-0.825815776368296644495089770635123369\ 097730630839395359625564/0.18537815042145875449626\ 1784978523032875728204898436494525519/2.602102e+05\ 5/1/-148.75/1.3107570584481e-014 params=0/0 float=y maxiter=30000 bailout=100 inside=0 periodicity=10 colors=000XLLWNMUOMSPMRQMPRMNSMMUNKVNIWNHXNFYND_OD\ _OD`PCaQCbRBcSBdSAeTAfUAgV9hW9iW8jX8kY7lZ7m_6n`Cj`\ Ie`OaaVXa`TafOblKbsFcnJaiOZcTWZYTTbQX_TUbSReRPhRMk\ QJnPzqPztOzwNzzMztNzqNzmMzjMzfLvcLr`LmXKhUKcQJZNJU\ KJPGIKDIK9HK6HK2GK5GK8FKBEKFDKICKLCKOBKSAKV9LY8Na7\ LX9LWBLVCaQOcPPeORfNShMTjKUlJWnKXpM_rObpQenShkUkhV\ neWpeWndVkdVhcUebUbbT_aTW`ST`SQ_SM_SJZSGYSCYT9XU6W\ V2VW2TX3RY4Q`4Oc5Kf6Kj6Km7Kq8Km7Km8Jn8Kn9Mo9OoAQpA\ SpBUpCWqCYqD_rDarEcsEesFgsGitGktHmuHmuImvImvJmw0mw\ LmvMmuNmtPmsQmsRmrSmqUmpVmoWmoXmnZmm_hl`ckaZjcVhaR\ e_PbXN_VLXSJUQHROFOLDLJAIGBJGDKHEMIGNJHOKJQLKRLMSM\ NUNPVOQWPSYQTZRV_RWaSYbTZcU`eVafWchXbgZaf``ec_deZc\ gXbjWalV`nU_qTZsRYvTZsS_sR`sQasQZsPXsOWtNYtNZuM`uL\ bvKdvKewJgwIixHjxHjyGkyFlzEmzEmzDnzCozBpzEqzGryJnw\ LjuNfsQbqSZoUWkXTgZRc`O_cMWeJTgHRjEOlCMn9Kq6HmAKkB\ KjCKhDKfEKeGLcHLaIL`JLZKL } END PARAMETER FILE=========================================

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FOTD 22-12-07 (Halfway to Nowhere [8.5])
by Jim Muth 21 Dec '07

21 Dec '07

FOTD -- December 22, 2007 (Rating 8.5) Fractal visionaries and enthusiasts: Today and tomorrow we take a brief break from scenes in the December parent fractal to dive quite deep into the Mandelbrot set for a view of one of the most unusual scenes I have yet discovered there. The location is on the northeast shore line of the large period-2 bud of the M-set, at a location near the border of Seahorse Valley where the Seahorse Valley character- istics are just starting to take shape. By the way, don't exert to much effort diving down to see the minibrot at the center. It's a long slow trip, and I am almost there myself. Tomorrow's FOTD will be a picture of that tiny atom. I named today's image "Halfway to Nowhere" because the scene lies about halfway to the unseen minibrot at the center. But even though we are only halfway to the goal in today's image, the magnitude of over 8.4(10^47) is not to be sneezed at, or coughed at either. The rating of 8-1/2 has nothing to do with an old Fellini movie. It indicates that, in my opinion, not only is the image much above average, but my coloring is worth another half point as well. The down-side is the calculation time, which, due to the extreme magnitude, is a dragged-out 22 minutes on the fast machine and over 1-1/2 hours on the slow one. Slow images like this make a fractalist appreciate the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the image will soon be posted for viewing without the hassle of calculation. And to speed things up I have sent the finished image on ahead to Paul to save him the time it would take to run the parameter file. Of course, those who enjoy long calculations may always run the parameter file themselves. It works quite well. Friday here at Fractal central started cloudy, turned sunny by 11am, clouded up at 2pm and cleared at 5pm, while the tempera- ture reached 43F 6C. Since this was the shortest day of the year, I think we did pretty good. The fractal cats must have agreed, for they passed the day watching squirrels. My day was on the busy side, but still well under control. The next FOTD fractal, a close-up of the invisible minibrot at the center of today's image, will be posted in 24 hours. Until then, take care, and how deep can you go? Check back tomorrow for a demonstration Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Halfway_to_Nowhere { ; time=0:21:55.90-SF5 on P4-2000 reset=2004 type=mandel center-mag=-0.8258157763682\ 966444950897706351233690977306308393979/0.18537815\ 04214587544962617849785230328757282048984375/\ 8.4e+047/1/-158.75/1.31e-014 params=0/0 float=y maxiter=10000 bailout=100 inside=0 periodicity=10 colors=000Z9Vt9XpKVlVUheSeoRclUajX`h_ZfbYdeWagV_jT\ YmSWpQUsOTzPSuQSpRSkSSfTSaUSXVRTWROXRJYREZR9_R4_R0\ WO5SL9OIEKFI96BGCMNHWTMeWNbZO``PZcQWeRUhSSlROjSQhS\ RfTSeTTcTUaUV`UWZUXXVYVVZUW_SW`QWaPXbNXcLXdJYeIYfG\ ZgEZhDZiB_j9_k9Zo8_l8_i7_g7_d7_b6__6_Y6`V5`S5`Q5`N\ 4`L4`I2_H4`G6aF7aF9bEAbECcDEdDFdCHeCIeBKfBLfANgAPh\ 9Qh9Si8Ti8Vj7Wj7WhAWgCWfEWeGWdIWbKWaMW`OW_RWZTWYVW\ WXWVZWU`WSbWRdWPfZLjWLgULdRLbPL_NLYKLVILTGLQDLNBLL\ 9LI6LG4LD2LB6PAAT9EX8I`7Md6Qh5Ul4Yp3at2ew2fx4gx5hx\ 7ix8jx9kxBkxClyDmyFnyGoyIpyKqyMqyOowQmuSksUiqWgoYe\ m_ckaaib_hgYieWidUicSibQiaPi`Si_WiZZiYbiXeiWiiVliU\ piTsiSqcToYUnSVlMWjGXiAYg9Uf9Re9Od9Lb9Ha9E`9B_98Z9\ 5`B7bD9dEAfGChHEjJFlKHnMJpNKrPMsQNqROpROoROmROlROk\ RPjRPhRPgRPfRPeRQcRQbRQaRQ`RQbTRcUSdWTeXTfYUg_Vh`V\ ibWjcXkdXlfYmgZnhZmhXmhVlhTceI`aJYYKVULSQMPMNMIOJE\ PGAQiLagNbeQcr`kcSdQJZCAT } END PARAMETER FILE=========================================

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FOTD for Dec. 22
by JimMuth＠aol.com 21 Dec '07

21 Dec '07

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FOTD 21-12-07 (No Ambiguity Here [7.25])
by Jim Muth 20 Dec '07

20 Dec '07

FOTD -- December 21, 2007 (Rating 7.25) Fractal visionaries and enthusiasts: I found today's image on a side filament of the main spike of the December parent fractal. Of course, it's questionable whether a feature so small that a microscope is needed to make it visible can actually be considered anything main. I named the image "No Ambiguity Here". Your guess is as good as mine as to the meaning of the name. I rated the image at a 7. I almost gave myself an extra half point for the coloring, but then I decided I didn't like the off-green, which gives the whole picture a rather unpleasant feeling. I rather enjoy the celestial blue areas behind the earthy green however, so I finally relented and rewarded myself a full quarter point for the coloring. The calculation time of a brisk 32 seconds means near instant satisfaction for all those who run the included parameter file. Those who do not run parameter files may still enjoy the image by surfing to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing it in finished form there. Thursday turned out notably un-notable here at Fractal Central, with partly cloudy skies, a temperature of 41F 5C and melting ice. The fractal cats spent the day in meditation;I spent the day in work. The next FOTD will appear in 24 hours. Until then, take care, and avoid redundancy. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= No_Ambiguity_Here { ; time=0:00:32.07-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-2.832783439347563/+0.5032633458298688/\ 1.989567e+008/1/155/0.000454344359649368201 params=-2.475/-1.05/-0.275/-5.5/0/0/0/0 float=y maxiter=380 inside=0 logmap=48 periodicity=10 colors=058bWz`WzO7qYWzUPQUWzWPLRWzUOKVRITNHSOCRMBO\ M6PL3IO0MK0ER0KI0KXKRcnXzzzzRibqkoqzdhwRqr9iw0qw0i\ w0qw0qw2qw6qwBqwGqwLqwNquRqoVqmZqdbqckqbpqWPqO2qQ0\ qO0qJ0qE0q80q20q20q40q20q50q83qEEqJKqPTqU`qZnhbqZi\ qRnqLnqEmqNnjUjPbd9n_0qZ0qT0qO0qN5qIFoHQnEbl9kd5qa\ 2qY2qU2qS2qO2qN2qN6qNCqPKqOQqQZqReqTsqUwkWweVwXVwQ\ UwKWwIWwFLqGD`H3MJ0VR0cX4kaBqiDwoJwqNwqPwqTwq_wqfw\ qhwqnwqqwnqrmqliqhlqgmqfnqfnqegqecqg_ql`qq`quXqvTn\ vQcuNYuMPuJIvEBuB2uA0wB0wF0wH0wH1wK1wK4wJ6wL6wO8wO\ 8uK6qH5nG3kB1h70e50a7D`7PW8_Q6hK5oH4q75q64q24q23q2\ 3q26q5BqMKqbSquaYwhGwn0wq0wq0wqIwqXrqkfqqaqqeqqfqq\ hdqu`qwUqwMqwBqw3qw0qw0pw0nw0iw6dwJ_wYZwkXwqUwqU2m\ 5Vq0wq0wq3wq8wqCwqFwqJwqNwqQwqTwqXwqZwqbwqewniwcnw\ _qwUquMqoFqi7qd0qZ0qZ0qb0qi0ql0qs0qw0qw0qw0iw0bw0U\ w0Mw0Lw2Dw6CwE9wH8wO6wS1wa0wc0wi0wp0wq0wq0wq0wq0wq\ 0wq0DNqDEqD6qE0qI0qI0qI0q } 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 20-12-07 (As Far As It Goes [6.5])
by Jim Muth 19 Dec '07

19 Dec '07

FOTD -- December 20, 2007 (Rating 6.5) Fractal visionaries and enthusiasts: I passed an hour or so Wednesday afternoon pondering the much sought after theory of everything (except self-awareness, that is). I have lost track of the current leader of the pack of theories, but the last time I checked, M-theory, which is sup- posed to explain everything including the cause of the 'big bang', was coming on strong. I think this theory requires 11 dimensions, though I heard somewhere that a 12th dimension, which would be a second dimension of time, might be needed to get the numbers to add up. What would it be like to live in a universe with two temporal dimensions. We would no longer be trapped on a line moving ineluctably into the future. We would be able to move sideways in time, to circle around and experience the same event again and again, from different directions. Of course, it would be impossible to predict the future, if there even was a past and a future, because we would be able to choose any part of the future we preferred. And what would happen to fractals such as the Mandelbrot set in a 12-dimensional world? Speaking of fractals, today's image takes us to the southernmost fringes of the parent fractal for December, all the way to the terminal ring of the filament extending from the period-14 bud. The image is nominally interesting, and I have named it "As Far As It Goes". The name refers to the magnitude, which has just exceeded the limit of resolution. 5*(10^9) is not an unusually large magnitude, but the decimal point has been shifted several places in the calculation, making this magnitude as large as resolution will permit. Considering the lack of sharpness and the lack of oomph in the colors, I rated the image at a 6-1/2. My coloring is not included in this rating; the basic image earns the entire 6.5 points. The parameter file is quite a fast one, finishing as it does in a supersonic 1-3/4 minutes. And if even this is too slow, the completed image is or soon will be available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy clouds all morning, light flurries of snow all afternoon, and a temperature that hung around freezing all day made Wednes- day of questionable worth here at Fractal Central. The fractal cats wondered why the dog that hung around the neighborhood for several hours did not go home and get warm. I had another notably average day. The next FOTD will be posted in 24 hours. Until then, take care, and when I posted the first FOTD to the Fractal Art list almost 11 years ago, I expected to post one or two more before I grew tired of it. I guess I was wrong. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= As_Far_As_It_Goes { ; time=0:01:45.12-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=-56.69915584369026/-148.8951750514287/\ 5.10025e+009/1/-2.5/2.26305686272451623e-005 params=-2.475/-1.05/-0.275/-5.5/0/0/0/0 float=y maxiter=1200 inside=255 logmap=162 periodicity=10 mathtolerance=0.05/1 colors=000BBNBBMDDRBBLDERBBJDGQB9IDGQBBLJEGBDB4E80\ N20a00Y00n1Bi8QtEbqJqzQstXzzazxdzzfxtgwwipqklqldln\ blpXgsRftNdwIaxD_z8Xz2Tz0Rz0Vx0Xq0Yk0ad0bY0dR0gL0i\ E0k80n10p00q00s00p04n0Dl0Ji2Rg8qfEgdJxaOw_TzYYzXbz\ NgTDl84pB9aEENIJ8GIEGIJEGQEGVEE_DEfDDkDDpLJqRQsYXs\ datkgtqnwxtwzzxzzxzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzznzfTObQOaOO_NOYJOVIOTGORDOQBON9OL6OJ4OD4N\ I1OJ1QN1TO1TR0VT0YX0_Y0aa0ab0bf0fg0fk0gl0ip0kq0lt0\ nw0px0qz0sz0tz0wz0xz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz\ 0zz0zz1zz4zz8zx9zwBzsDzpGznIzkJzgLzdOxaQx_RxXTwTXw\ QYwN_tLatIdtDfs9gs4iw8isBgpEglIfiLffOdbQdaTbYXbTYa\ QaaNd_Jf_IdXJdVJdTLbRLbQNbONbNNaLOaJOaIQaGQ_ET_DT_\ BT_9TY8TY6VY4VY1VX0YX0YX0_X0_V0aV0aV0aV0aT0aT0bT0b\ J0fO0fT0bY0ab0ag0_l0Yq0Vw0VzELzTBzi2zw0zz0zz0zz0zz\ 0zz0zz0zz18GV9EVDBTE9TG6T } 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 19-12-07 (Iterating Anvils [7])
by Jim Muth 18 Dec '07

18 Dec '07

FOTD -- December 19, 2007 (Rating 7) Fractal visionaries and enthusiasts: Today's image has been totally evaporated. Every point is 'trapped'. All 'outside' stuff has long since dried out and blown away, yet the image is still visible. It is visible because it was resurrected by the 'bof61' inside fill. The scene is located deep on the wrong side of the south branch of East Valley of the December parent fractal. The wrong side is the east side, which forms the southwestern shore line of the extra bay east of East Valley. The rating of a 7 was easy to decide on. The image seemed to be a perfect 7 from the first time I saw the top half of it. The calculation time of 8-1/3 minutes could be shorter, but relief is at hand on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image may be viewed without effort. Much improved conditions prevailed here at Fractal Central on Tuesday. Sunny skies, light winds, and a temperature of 37F 3C set the ice melting process into high gear. The fractal cats spent much of the day at their window, though they were a bit startled when a cluster of icicles fell from the roof next door. A generous treat of tuna quickly soothed their ruffled nerves. My day was typical and tomorrow will likely be a repeat. The next FOTD will be posted in 24 hours, more or less. Until then, take care, and watch for signs of life in the world of fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Iterating_Anvils { ; time=0:08:18.94-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=-1.973719968089898/-14.660171066901/\ 1.290328e+007/1/-122.5/-3.81178635387724452e-006 params=-2.475/-1.05/-0.275/-5.5/0/1e+100/0/0 float=y maxiter=5200 inside=bof61 periodicity=10 colors=000Ak6Ck6Dk6Fk6Hi5Ii5Ki5Mi5Nh4Ph4Rh4Sh4Ue4V\ e4Xe4Ye4`d4ad4cd4dd4fd4gb4ib4kb4lb4na4oa4qa4ra4t_4\ u_4w_4y_4zZ4zZ4zZ4zZ4zZ4u_6l_Ic_UVaeMapCasAas3as4b\ s4bs6ds6ds8ds8es8esAhsAhsChsCisDisDksDkszXhzXkzZpz\ Zsz_sz_szaszaszaszbswbsobkibdabXUbNNbFFb56b40d40b4\ 0b40b41b41b43b43b44b46b46b48b48b4Aa5Aa5Ca6Ca8DaAFa\ BFaDHaFHaFIaGIaIKaKM_LM_NN_ON_OP_QP_RR_UR_VS_XU_YU\ _YV__VZ`XZbXZdYZe`Zg`ZgaZhaZjcZkcZmdZnlXsgZsdZna_m\ __lZ_kY_k`Kk0BsI8s`8sq8sz8sz8pz8nz8mz8kz8jz8hz8gy8\ ew8bu8`t8_r8Yq8Xo8Vn8Ul8Rk8Oi8Ng8Lf8Kc8I`8GX8FU8DS\ 8DR8BP8BN8BN8BM8BH8BI8BI8BH9BFBBFCBFPAFQAFRAHSA0Nc\ FUADVADWACXAAYA3Y86_A8_AA_A0PhF_AH_AIaAKaBMaBP`BR_\ BSZBU_B0IVYZD`ZDaZDcZDf_Dg_Di_Dk_Fn_Fo_FqaFraFtaFw\ aFyaGzaGzbGzcGzdGzgGzkGzgNzkKzdIzbGz`FzXDxVBwPArO8\ oG6lC5i84d84a84Y84V84U84S84S84R84P94PB4NE4MI4ML4KP\ 4IS4IU4HX5F_5Fb5De6Ci68l8 } 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 18-12-07 (Squeamish Squirming [6.5])
by Jim Muth 17 Dec '07

17 Dec '07

FOTD -- December 18, 2007 (Rating 6.5) Fractal visionaries and enthusiasts: Today's glorious (IMO) image lies in the decoration surrounding the large northwestern ring of the parent fractal for December. I named it "Squeamish Squirming" because the words sound rather comical when used together, and the image actually is a bit on the comical side. The rating of a 6-1/2 includes the usual half-point reward for my superb (once again IMO) coloring. And why not? After all, it really is difficult to achieve reasonably smooth gradations with only 256 colors to work with. After yesterday's fractal, which calculated about as fast as silly putty flows, today's image, with its FTL calculation time of 46 seconds, will seem like a well-earnrd reward. So why not reward yourself? Save this entire message in your Fractint directory in text format with a .par extension and run it like any other parameter file. Unfortunately, in this advanced computer age, DOS applications and the trimmings that go with them are about as up-to-date as magic lanterns. If your machine is over-qualified for Fractint, leaving you in the dark, the image may be viewed on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Cold biting winds, ice-covered pavements, and a temperature just below freezing made Monday a day to be forgotten here at New Fractal Central. The fractal cats forgot the day before it was half finished. They were more interested in keeping as warm as possible and being fed as often as possible. For me the day was uneventful. The necessary work was behind me by lunch time, leaving the afternoon for the un-necessary work of finding fractals. Today's image shows that I was moderately successful. The next in the long series of FOTD images will appear here in 24 hours. Until then, take care, and here on earth the universe is 13,700,000,000 years old. But in a proto- galaxy 12,000,000,000 light-years distant from earth it is only 1,700.000.000 years old. What then is the true universal age of the universe? (I suspect the question is meaningless.) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= SqueamishSquirming { ; time=0:00:46.48-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=-162.263/97.246/36.71293/1/-165/0 params=-2.475/-1.05/-0.275/-5.5/0/0/0/0 float=y maxiter=1000 inside=255 logmap=56 periodicity=10 colors=000dVKdVKfWKfXKhYKhZKj_Kj`KlaKlbKncKndKpeKp\ fKrgJrhHtjEskCvmAtn7upQvp3wqXxq7yq_zqBzqYyqEyrRwrI\ urLsrLrrNorPmsRmsTlsUlsWksYks_jtajtbitditfhthhtifq\ heogcmfbjfahe_fdZddXacW_bVYaTVaST`RRZPPZOMXMKVLITK\ FSIDQHBPG9QJ8TL7VN6XR6ZW5aa4bj4ch3dm2fo2go1hm0ii0j\ e3da5ZV7TP9NP9NP9OO9PP9PQ9QR9RR9RS9ST9TU9TU9UV9VW9\ VW9WX9XY9YZ9YZ9Z_8_`8_`8`a8ab8ac8bc8cd8ce8de8ef8fg\ 8fh8gh8hi8hj8ij8jk8jl8km8lm8ln8mo8ns1ur3sq5qp6po8n\ nAmmBklDjkFhjGgjIeiJdhLbgNafO_eQZdSXcTWbVUcbPb_RbY\ SbWTbUUbRVbPWbNYbLZbI_bG`bEafGhdEfcDdbCbaB``CZYDVZ\ EW_FX_GX`HY`IYaJZaKZbL_bM_cN`dOadPaeQbeRbfScfTcgUd\ gVdhWeiXfiYfjZgj_gk`hkahlbilcigcdcc_Zc`WcaVcbVccVc\ cVccVccVccUccUccUccUccUccUccUccTccTccTccTccTccTccS\ ccSccSccSccSccSccSccRccRccRccRccRccRccQccQccQccQcc\ QccQccQccPccPccPccPccPccPccOccOccOccOccOccOccOccNc\ cNccNccNccNccNccMccMcczzz } 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 17-12-07 (Around the Rim [6.5])
by Jim Muth 16 Dec '07

16 Dec '07

FOTD -- December 17, 2007 (Rating 6.5) Fractal visionaries and enthusiasts: Today's sojourn into the December fractal takes us to a spurious little valley in the interesting area around the origin. At first glance, this valley appears to have no right to hold minibrots. But right or wrong, minibrots are there, and today's image gives rock-solid proof of their presence. To give the image its finished appearance, I needed to partially evaporate the scene and render it with the inside parts set to 'bof61'. Actually, with the logmap set to -1842, any of the inside fills would have worked equally as well. They all simply add a flat color. Perhaps with a bit too much enthusiasm I rated the image at a 6-1/2. The colors really are not all that great. The name "Around the Rim" refers to the brilliant ring surrounding the somewhat obscured central minibrot. The calculation time of 14 minutes is slow for such a moderately worthy image. I recommend viewing the image instead on the FOTD web site at. I will send the image on ahead to Paul, so it should be already posted by the time this FOTD hits the cyber- way. The world-famous FOTD web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sleet fell all night Saturday here at Fractal Central. At daybreak Sunday it changed to a cold rain, which made a really sloppy mess of things. Then at noon on Sunday the rain changed to snow. When the snow ended at 5pm a high wind arose, with gusts to 50mph 80kph, making the day near a total loss. The fractal cats had no sympathy. They demanded extra treats of chunk tuna and sharp cheddar cheese. My day was kept busy by the task of clearing the heavy slop from the walk ways. The task was finished however in time for the fractal. The next fractal will be posted in 24 hours. Until that glorious moment arrives, take care, and when reason proves to be the answer, question the question. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Around_the_Rim { ; time=0:14:02.17-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=+3.526047700159351/-4.440263736170335/\ 2.066656e+010/1/112.5/0.000131874278297368364 params=-2.475/-1.05/-0.275/-5.5/0/17000000.0/0/0 float=y maxiter=8000 inside=bof61 logmap=-1842 periodicity=10 mathtolerance=0.05/1 colors=000UczcFvjDwqAyrc0iMqteLIm_vfRMrJthBtd4mb7f\ aA``DU_GNZJHYLGKEEQBDW8B`5Af29k05n71qE0eF0VF0NG08G\ 7KEEWCLhASs9NvKJyVEzemzpzznzyvzukmsiLqhPgdS``LLX8E\ LDHIDACMHLHEPDLW9TW5VW4dV3`V8aXQKQRJRSHRTGSUETVDUW\ BVWAVYBWZCW`DXaEXcFXdGYfHYgIY_RSSZMKfGCnBHmHMmMRmR\ WmW`m`elfjlkolptluylzxguxbqxYmxUiwPdwK`wFXwBTuDStF\ SsHRrJRpLQoNQ5FP4S_3dj8fcCgYGiSLjMPlGTmASoDSpGSrJR\ sLRuORvRRwTStSSqSSnSSlSTiSTfSTcSTaSYXUaSWeOYiJZmF`\ qAbu6coFXiORcXKYdEWfDUhDTjDRlDPnDOpDMrDLsDZdHlRKyD\ NzEMzFMzGLzHLzIKzJKzKJzLJzMVWTI1Z6BaLLd_VfnWbgWZ`W\ VUWSOVPMUMLTJKSGJSDILOSFZ`9hiGejNbkU`l`YlgWmnTntRn\ pWhm_bjdXfhScmM`qGYuB`M`USdNXgGbk9gnOWhbKcp8Zr5Zn4\ `j4bg4cc4e`4fX4hU4iQ3kM3mJ3nF3pC3q83s53t8VUAv39t29\ s28r28q28p27n17m16l16k16j1Eg8LeFSbM_`TfY_mWftUmiM_\ ZFNP8AR79T79V78X78Z77`77b77d76f76h75j75l74n74o74lB\ 6jE7hH9fKAdNCbRD`UFKNqRLs } 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 16-12-07 (Alien Enterprise [No Rating])
by Jim Muth 15 Dec '07

15 Dec '07

FOTD -- December 16, 2007 (No Rating) Fractal visionaries and enthusiasts: Two days ago Lee Skinner posted a picture of an alien that he found in December's parent fractal. This alien is obviously from outer space, most likely from the Alpha Centauri system. On Saturday I started wondering what the alien has been up to. I soon found that he, she, or whatever, has been very busy since he was discovered, re-iterating his fractal self. His effort is apparent. I found a whole flock of Minibrots hidden in his depths, one of which appears as today's FOTD. Since the alien is such a busy one, I named the image "Alien Enterprise". I have no idea why the Alpha Centaurian alien has been so busy or what type of work he performs, but all living entities, dead ones also I suppose, need energy to exist, so he must have a good reason for his efforts. I could hardly give a fair rating to an image that lies in an image that was created by someone else, especially since I re-used basically the same color palette. The calculation time of 1-2/3 minutes is brief enough to cause no one any fractal pain. And as always, the finished image is or soon will be available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Saturday began clear here at Fractal Central, but the clouds moved in steadily through the day, and by late afternoon it was heavily overcast, with snow, sleet and freezing rain expected soon. The temperature hung just below freezing all day, keeping the fractal cats close to any source of heat. My day was busy because of preparations for the holiday season. But with the help of Lee, I did manage to find an image of FOTD value. Unless we get snowed or iced in, tomorrow will likely be another busy day. The next FOTD will be posted in 24 or so hours. Until then, take care, and string along with those super- strings and supermembranes. They're the best we've got until someone dreams up a better idea. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Alien_Enterprise { ; time=0:01:19.45-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=+3.195327586826916/+4.972744855053525/\ 27562.94/1/-130/6.71482591751981772e-011 params=-2.475/-1.05/-0.275/-5.5/0/0/0/0 float=y maxiter=2000 inside=0 logmap=64 periodicity=10 colors=000a0gc0ce7_jFRpNIuV9zb0zj0zr1zz1zzCzzTzzpz\ zzzzzrvonsjjqdfo_blUZjPVgJQeEMb8M_8MX8LT8LQ8KM8KJ8\ JF8zC8I88z44G00z31N53z84TA5zD6ZF7zI8fLAhMBiODjQFlU\ EnYDoaCqeBriAtm9vq8xu7zz5zz4zz3zw3zt3zp3zm3zj4zg4z\ c4z`4zY4zV5zS5zP5zL6zI6zE6wE6tD6tD8uDAuCBuCDuBEvBG\ vAIvAKw9Lv9Lu9Lu9Lt9Ls9Lr9Lq9Lq9Kp9Ko9Kn9Km9Km9Kl9\ Kk9Kj9Ki9Ki9Kh9Kg9Kf9Ke9Ke9Jd9Jc9Jb9Ja9Ja9J`9z_9KZ\ 9zY9KY9zX9KW9zV9JU9JU9IT9IS9IR9IQ9IQ9IP9IO9IN9IM9I\ L9IK9HK9HJAIJCIIDJIFKHGLHHLGJMGKNFMNFNOEPPEQPDRQDT\ RCUSCWSBXTAYUA_V9aW9bX8dX7eY9e`BdbDdeFcgHcjJblLboN\ aqP`sS_vVbvYdv`gvcivflvinvlqvotvswwuxxxyyzzzxyzvyz\ txzrwzozzhzwazsVzpNzlGzh8zd8za8zZ8zW8zS8zP8zL8zIDz\ GIzFNzDSzCXzAaz9fz7kz5pz4uz2zz0xz0uz0sz0pz0nz0kz0i\ z1fz1dz1az1_z1Xz1Vz1Sz1Qz1Nz1Lz1Iz2Gz2Dz2Fz3Iz4Kz5\ Nz7Pz8Sz9UzAWzBYzC`zEczFezHhzIdzMazQYzTUzXRz_NzcJz\ gFzpAzzEzwIzuLzrPzoSzlWzi } 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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Formula functions (fnx)
by David M Fisher 15 Dec '07

15 Dec '07

Anyone: Need information about the number of functions allowed per formula. I have been doing some experimenting with writing formulas, and have hit a snag with the <function> part. There seems to be a limit of four function entries per formula, and yet I distinctly remember seeing formulas with six (6) functions. I eyeballed the docs but came up blind, whence this e-mail. Is it possible that the version of fractint I am using is the problem? If so, which earlier version allowed six functions? If there is an obvious answer (solution) to this I would appreciate finding out. And while I have your attention......has anybody figured out yet how to sort .map files, regardless of rotation? I got a python script from Edwin Young, but can't get the thing to run. Keeps telling me there is an error. Any help or information would be greatly appreciated David M Fisher sunfish(a)intercom.net

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FOTD 15-12-07 (Going-Going-Gone [8])
by Jim Muth 14 Dec '07

14 Dec '07

FOTD -- December 15, 2007 (Rating 8) Fractal visionaries and enthusiasts: Today's image is named "Going-Going-Gone". I gave it this name when I watched the inside-outside first version slowly evaporate as I raised the bailout radius from 100 to 1-googol. The rating of an 8 indicates that I was quite satisfied with the evaporated version. The first version would have rated only a measly 6. The scene is located in an 'elephant trunk' deep on the southern branch of East Valley of the December parent fractal. I call it the southern branch because this East Valley consists of two sep- arate branches, much like Seahorse Valley of the Mandelbrot set. Since the scene is evaporated, it consists entirely of inside stuff made visible by the bof61 inside fill. This fill is what creates the textured detail throughout the image. The calculation time of 5 minutes is exact to the 1/100th of a second. This time is not as fast as I would like, but still fast enough to make running the parameter file only a minor chore. A faster way to see the image is to stop in at the FOTD web site, where the finished image is or soon will be posted. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Friday turned out cloudy but rather mild here at Fractal Central, with a temperature of 41F 5C melting much of the icy slop that fell on Thursday. The fractal cats spent the day trying to stay out of trouble. My day was average, which is nearly as good as a day can be. The next FOTD will be posted in about 24 hours. Until then, take care, and some of my ideas are crazy, that much is certain. But I wonder if they are crazy enough to answer the questions. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Going-Going-Gone { ; time=0:05:00.00-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-1.2439905615/-30.5803099973/9227.23/1/\ 81.5/0 params=-2.475/-1.05/-0.275/-5.5/0/1e+100/0/0 float=y maxiter=7500 inside=bof61 periodicity=10 colors=000HvvHpmHihHliHXWHheHNKHaaHDBHWWHC9HQQJHDL\ KKPMGTOHYQIaTKgWNl_PqaQxeSzhVzhWzhVyeTucSq`RmYRiWQ\ dTPaQOZPOYNNTKMTLNNHKTKOPKNQLQRclSMRTQSTPTUTWWTXWW\ YYW_Z_a__c`cdacebfhchidikfllgmohopirrkssluvmvvovvS\ 5RT6TU8VWBXWDYYF`ZHa_Kc`OeaRfcTidXkf`mgdohhpikskou\ lsvmvvh8`j6_j5`j5ai5Yj5Xj5Uk7RuBOuDNvGHuKBwN7wQ5yT\ 5sW5rY5pa5md5kf5gk5cm5ap5Zu5Wv5Tv5TlCS`MRPXQGiQ8vS\ 9sTBpUCmWDlWEiZGf_He`HcbK`cKYdMXgOVhPSiQRgOSfNTdKV\ cKVbHWaHX`FY_EYZD_YB`WBaW9aU8cTcmT6eS5eR6fQ7fQ7hP7\ hO8iO9iN9kN9kNBlLBlLBmLCmLCmH7eH5YH5XJ6WL7VP8TS9SU\ BSaHXhQap_exikzsoH5XcOecPfdQhdShdTifVkfXkgYlovvL5K\ I5HH5EH5BH59H5BH5BI5CL7DO7DS9EWBF`BGdDHiEHoGHtHIyI\ KzKKzMKzKOzKRzKVxKYuKaqKeoKilKmiKrgKvhQphWlhafiici\ pYivVdkK`_DWP7TH5RH5qPhNK7pQhKKBoRiHNHmSkHOMlTlHQS\ kWmWXBkYokf5k`pmhCkcroiOiesqlaghutmrdkvoovbmvfpv`p\ v_rvUsvTsvPuvNuvKvvHvvJsr } 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 14-12-07 (The Whole Universe [No Rating])
by Jim Muth 14 Dec '07

14 Dec '07

FOTD -- December 14, 2007 (No Rating) Fractal visionaries and enthusiasts: Well, here it is in all its glory -- the parent fractal for the month of December -- the universe we have been exploring all this month. And what a world it is. To begin, its size is deceptive. The magnitude of an unusually small 0.0068 makes its area 10000 times the area covered by the Mandelbrot set. The center point of the image, -128,-30, is no mistake. We actually are this far from the origin. Studying the image, we notice that it is filled with rings, as have been most of the images so far this month. Every filament terminates in a decorative ring. Then we notice the main bay, if that's what it is. This nearly circular feature bears little resemblance to the cardioid shape of the classic Mandelbrot main bay. Where is East Valley, and where is Seahorse Valley? Actually, these features are in the fractal, though well hidden. We next notice the largest bud on this circular bay. Intuition says that it is the main bud, and would therefore have a periodi- city of 2. But actually, its periodicity is 13, as can easily be checked by counting the number of arms in its star. If there is a main bay in this parent fractal, it is very distorted. And look at the shape of the chaotic area leading from the large bud to the largest ring. It does rather resemble an East Valley elephant. The elephant resemblance is even more pronounced in the chaotic area of the slightly smaller bud north of the large one, which strangely enough has a periodicity of 12. It appears that nearly the entire shore line of the circular bay is the southern shore of the main bay of this fractal, and the farther we travel counter-clockwise, the deeper go into an East Valley environment. It is now simple to find the actual period-2 bud and Seahorse Valley. Simply count clockwise around the buds from the period-13 bud until the count reaches 2. There is our main bud, complete with Seahorse Valley and the main spike, all of them so small that a blow up is needed to make them visible at all. As we continue beyond the period-2 bud, the periodicity rapidly increases until we find ourselves deep in the north side of East Valley. This area of the fractal is actually the most interesting. The smaller circular bay just to the east is something entirely new. Nothing like it appears anywhere in the M-set. It is highly fragmented, and at first appears to be non-critical. But its shore is dotted with tiny irregular buds in which some very curious minibrots are well hidden. The fractal is also peculiar in that the orbits of the points diverge so fast as to be virtually invisible. Occasionally a single dot appears, but this is a rarity. Such rapidly diverging orbits are likely true of all fractals created with negative exponents of Z. I named the image "The Whole Universe", and so it is. I gave it no rating because I did virtually no work in producing it. But no one can complain about the calculation time of a superlumi- nal 28 seconds, which is about the time it will take to view the completed image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Thursday was most unpleasant here at Fractal Central, as wet sloppy snow and cold rain fell most of the day, while the temper- ature hung just above freezing. The fractal cats spent the day by the heat, ignoring the weather. My day was uneventful. The next FOTD will be posted here in 24 hours. Until then, take care, and even though the concept of an ultimate reality might be a human invention, I really do believe in the virtual reality of fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Whole_Universe { ; time=0:00:28.17-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=-128.674/-30.6294/0.006811989 params=-2.475/-1.05/-0.275/-5.5/0/0/0/0 float=y maxiter=7500 inside=0 periodicity=10 colors=000tNitRgsLesUcsXbrW`rZZqYXq`VqZUpaSpZQo`Po\ YNnZLnXKmXImWHlWFmVDkVClUAkU9mU8lU7mU7lU6mU6lU5mU5\ lU4kU4lU3iU3iU4eU4eU4_U4aT4UT6YR7OR8SR9OPAPQBPNCRP\ DQNEROFQNHSNIRNJUMKSNLUMMTNNWMOUNPYMTUMV_MZbFddLek\ KmiMnsOvoTlo`bmfTklJirAlnIojPqfWtbcwZjyWqo`ifdbYiV\ PmOGrG7v9AsBDpDGnFJkHMiJTbQ_WWePalIgsBmy4sx5qx5ox5\ nx5lx5kx5ix5hx5fx5ew6cw6bw6`w6_w6Yw6Xw6Vw6Uw6Sw6Rx\ 7Sx7Tx7Ux7Vx7Wx7Wx8Xx8Yx8Zx8_x8`x8`x9ax9bx9cx9dx9e\ x9euBfsCgqDhoFilGjjHkhJkfKldLmaNn_OoYPpWRpUSqRTrPV\ sNTzLPqJKrLFjMmmOzjzzfzzbzz_zzWVzSXoPYqL_sH`tEasFb\ rFbqGcpGdoHdnHemIelIemHfnFfoDfoCdmBblB`kBZjBXiBVhA\ TgARfAPeAOdAPdBQdCRdDTdEUdFVdGXdIYdJZdK`dLadMbdOdd\ PedQfdRhdSidUjdVldWmdXLeuNfsPgrQhqSioUjnVkmXlkZmj_\ niaogcpfdqefrchsbitaku_mvZkwtlxplylmzhmzdnz`ZzU`zc\ bzmczrezvfzzhzzjzzkzzmzzVzzZzzazzdzzhzzkzzVzzWzzQz\ zSzzUzzYzzazzezzizzmzzpzz } 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 13-12-07 (Abstract Concrete [7.5])
by Jim Muth 12 Dec '07

12 Dec '07

FOTD -- December 13, 2007 (Rating 7.5) Fractal visionaries and enthusiasts: Today's scene is found in the north branch of the valley of the largest bud on the main bay of the parent fractal for December. This is by no means a period-2 bud however. Despite being the largest bud, its periodicity is 13. I have been doing so much with this mysterious parent fractal for December that I think I'll post it as the FOTD for December 14. Ring-like elements from the parent fractal are mixed with typical high-order valley stuff to make an image that rates a 7.5, which includes the usual half-point for my coloring. I named the image "Abstract Concrete". The name makes little sense, but sounds rather interesting, and gives the impression that something unusual might actually turn up when the parameter file is run. Running the parameter file will take 6-3/4 minutes. Viewing the GIF image on the FOTD web site will be even faster. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> It turned reasonably pleasant at noon Wednesday here at Fractal Central, when the sky cleared and the temperature reached 50F 10C. The fractal cats, (cats are also fractal in nature), enjoyed the afternoon sun streaming in the southwest window. They did their enjoying while they could. The pleasant weather is not expected to continue. My day was ambiguous. I hope tomorrow will be better defined. Regardless, the next FOTD image will appear in 24 hours. Until then, take care, and why ask such unsolvable questions? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Abstract_Concrete { ; time=0:06:46.57-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=-95.2881705491/-35.6398109077/15408.88/\ 1/-162.5/0 params=-2.475/-1.05/-0.275/-5.5/0/0/0/0 maxiter=15500 inside=0 logmap=773 periodicity=10 colors=000oNioRgnLenUcnXbmW`mZZlYXl`VlZUkaSkZQj`Pj\ YNi_LiXKhYIhWHgXFhVDfWCgUAfV9hU8gV7hU7gV6hU6gV5hU5\ gV4fU4gV3dU3dV4`U4`V4VU4XU4PT6TS7JR8NQ9JPAJOBKNCKL\ DLLELJFLHHMGIMFJNEKNDLOCMOBNPAOP9PP8QUBVYD_bFdfIhk\ KmoMrsOvqVlo`bmfTklJirAlnIojPqfWtbcwZjyWqo`ifdbYiV\ PmOGrG7v9AsBDpDGnFJkHMiJTbQ_WWePalIgsBmy4sx5qx5ox5\ nx5lx5kx5ix5hx5fx5ew6cw6bw6`w6_w6Yw6Xw6Vw6Uw6Sw6Rx\ 7Sx7Tx7Ux7Vx7Wx7Wx8Xx8Yx8Zx8_x8`x8`x9ax9bx9cx9dx9e\ x9euBfsCgqDhoFilGjjHkhJkfKldLmaNn_OoYPpWRpUSqRTrPV\ sNTzLPqJKrLFjMmmOzjzzfzzbzz_zzWVzSXoPYqL_sH`tEasFb\ rFbqGcpGdoHdnHemIelIemHfnFfoDfoCdmBblB`kBZjBXiBVhA\ TgARfAPeAOdAPdBQdCRdDTdEUdFVdGXdIYdJZdK`dLadMbdOdd\ PedQfdRhdSidUjdVldWmdXLeuNfsPgrQhqSioUjnVkmXlkZmj_\ niaogcpfdqefrchsbitaku_mvZkwtlxplylmzhmzdnz`ZzU`zc\ bzmczrezvfzzhzzjzzkzzmzzVzzZzzazzdzzhzzkzzVzzWzzQz\ zSzzUzzYzzazzezzizzmzzpzz } 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 12-12-07 (A Raspy Assemblage [8.5])
by Jim Muth 11 Dec '07

11 Dec '07

FOTD -- December 12, 2007 (Rating 8.5) Fractal visionaries and enthusiasts: I rated today's scene in the December parent fractal at an 8.5. I gave it this rating because I like it. It has a freshness that rekindles my enthusiasm for the parent, which was starting to become boring. No more do we see the endless display of terminal rings that have adorned so many of the previous images for December. In their place we see . . . well, I'm not sure what we have. I guess it's up to the individual fractalist to decide what today's image holds. The scene is located on the eastern side of the parent, in about as unlikely a place as is ever checked. I named the image "A Raspy Assemblage" because of the raspy texture of the elements along the edge. The wedge-shaped bluish background sections of the image consist of inside stuff made visible with the bof61 inside fill. The shredded arms in the foreground are outside stuff rendered with the outside set to imag. The little over 3 minutes it takes to run the included parameter file will pass in a flash once the image starts to take shape. And if running a parameter file is too much trouble, the image is, or soon will be available for viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Another miserable day's weather passed unappreciated here at Fractal Central on Tuesday. When the cold morning drizzle became a steady afternoon rain, and the temperature quit at 36F 2C, the fractal cats rolled over, took a quick glance, and went back to sleep. Cats don't like cloudy chilly days. My day was busy enough to prevent boredom. Tomorrow is likely to be the same. The next FOTD will appear in 24 hours. Until then, take care, and if the mind is in the brain, and the brain is a sense-created image in the mind, how do we get off this wheel of circular reasoning without arbitrarily assuming that physical material is the ultimate reality? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Raspy_Assemblage { ; time=0:03:06.91-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+5.63047998949/+10.0389614258/131879/1/\ 25/0 params=-2.475/-1.05/-0.275/-5.5/0/-78/0/0 float=y maxiter=1950 inside=bof61 outside=imag periodicity=10 colors=030b_m`_m`_mY_mWXmWXmUXmSXmS\ XmQVmQVmOVmLVmLVmJSmGSmGSmESmESmGXmJ_mJamLemLgmOjk\ QnbQpVSsMSxDUz4Uz0JxAAsQ2nb2jm2em2fr2_m2_m2_mA_mJX\ mQXmYXmgXmoVmsVmsVmsVmsSmsSksSisSgsVksVmsXmsXms_ms\ _msamsamsdmsdmsemsemsgmsgmsjmsjmslmslmsgmmdmg_m`Vm\ UQm20WGHkJKgJMbLMZLOVLQSOQOOSKQVFQVAQX8S_4S_0Ua0Ud\ 0Ud0We0Wg0Yg0Yj0Yj0bl0gl0kn0mn0qp0sp0ss0ss4su8suDs\ xIsxMszQszSsuQspOshMpbMnXKkRIgLFfKFeJDdIAcH8bG8aF6\ `E4`D2WC2SB0OA1J92L87G7CE6IA5N54R23X25a27f29j2Bn2H\ r2Kr2Mr2Qr2Sr2Vr2Xr8KrQ7qg3ps3ks3fs3as3Xs3Ss3Os3Ks\ 3Fs3Ds38s34s30s30s30s30s30s30s30s70sE0sM0sS0s_0se0\ sl0ss2sz2sz4sz6sz8sz8szAszAszDszDszFszFszFszIszIsz\ KszKszKszQszXszaszgszk2Km2Qm2Xm2dm2jm2pm2sm2sm2sm2\ um5umCukJxeQxaWxVbxQhzKozFsz8sz4sz0sz0sz0sz0szAszK\ szVszbszmszmszmszmmziGzF2z02z02x08s0Gn0Qj0We0da0mV\ 0sQ0sM0sH0sB0s70s30s30sQ0sp0gz0gamdamb_m } 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 11-12-07 (On the Half-Shell [6.5])
by Jim Muth 10 Dec '07

10 Dec '07

FOTD -- December 11, 2007 (Rating 6.5) Fractal visionaries and enthusiasts: Today's image is named "On the Half-Shell". At one time, some- thing about it must have reminded me of a shell, but all I can see in it at this time is a variety of fractal stuff, which is just adequate for being the FOTD for today. And no, there is no picture of the Goddess Venus hidden in the depths. The image lies in the parent fractal that has been the source of every image so far in December. It is located at the junction of a very large ring in the western extremities of its parent. and when I say extremities, I mean extremities. The X-coordi- nate of the image is greater than negative 203. The rating of a 6.5 is rather above average. It could have been higher, but somehow, the images of December are starting to look too similar, and the similarity knocked a point or two off the rating. I gave myself the usual half-point bonus for a coloring job that makes more of the fractal than it has in it. The calculation time of 3-1/3 minutes might or might not be rea- sonable, depending on the definition of the word 'reason' when applied to fractals. But why worry with definitions when the completed image may be viewed almost immediately by surfing to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and enjoying the fractal glories there. The very unpleasant weather of Sunday continued on Monday here at Fractal Central. The fractal cats spent the day ignoring the weather and watching for the squirrels that never appeared. My day was about average. The next FOTD image will be posted in 24 hours. Until then, take care, and be skeptical of skeptics who don't believe in fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= On_The_Half-Shell { ; time=0:03:20.14-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-203.3558256303423/+6.838992380291351/\ 2907653/1/-132/8.6468522646904189e-007 params=-2.475/-1.05/-0.275/-5.5/0/0/0/0 logmap=315 float=y maxiter=2000 inside=0 periodicity=10 colors=000C0pD0kF0`H0`F0WK0RM0PN0HP0HR02T00T00Y00`\ 00f00i04k07m0Cn0Hr0Mq0Rq0Vp0Pp0Kp4Hp7CpC7pF4pK0pK0\ pL0pM0pM0oL0oM0oI0oK7nHCoDIpANq6Vr2`q0fr0mq0rt0ys0\ wr0zp0zn0zm0zi2zh6zf9zdCz`Dz_KzYKzWPzTRzRTzPYzNWzP\ `vR_pR`mTbgVbbVb_WbVYdPYdM_dH_bDYbCW`CV`CT_CRYAPYA\ NWAMVAKVAFYDAbH6fK0kN0iP0iN0_N4`N6RN7RNAMNCINTKNHA\ N`GFM2NiR9P0Ns_9Tv0pm0Nb0fz0zz2fz4zz7xz9zzCzzDizHz\ zIzzDiv9fp4dk0`f0_`0WW0VR0YW0_`0`f0dk0fp0gt0dz__vY\ VrYRnWMkWHfVDbV9_T4WT0RR0NR0KP0HP0KR0NR0RT0TT2WV6_\ V9`VCdWFgWHkYKmYNp_Rt_Tv_4Rp00z00z00z00z20m70gC0bH\ 0YM0VR0PW0K`0Ff0Ck07p02v00nkzidzd_z`VzWPzTIzNDxK9t\ F4pC0mF0MI00M70ND6RKATRFWYKYdNbR`gFpm4zk7ziAziDzgF\ zgIzfMzdNzdRzbVzbWz`_z`bz_dzYgzYkzWmzWpzVtzVvzRrzP\ pzNnzMmzKkzHizFgzDfzCdzAbzC`zF_zIYzMWzPVzTTzWRz_Rz\ bRzfRziRzmRzpRztTzxWzx_zxbzxfzxfzxfzxfzxfzxfzxfzxf\ zxfzxfzxfzxfzxfzxfzxfzxfz } 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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Re: [Fractint] Just wondering if I'm still alive on the list
by david 09 Dec '07

09 Dec '07

Maryetta Campbell wrote: > David wrote: >> >> Don't remember seeing any mail for a while, so just wondering ... >> > > Apparently you are. And Jim still posts the FOTD regularly. > > If you have missed postings, then you can see what has come through by > visiting the website: > > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint and Richard wrote off-list reply: > In article <475C10B1.1010005(a)hawaii.rr.com>, > david <gnome(a)hawaii.rr.com> writes: > >> Don't remember seeing any mail for a while, so just wondering ... > > I got this message; you should be getting fractal of the day messages > every day. That's about the only traffic on here. Thanks, Tim said that my account had been blocked due to excessive bounces, so he cleared it. Strange, this email stuff - nothing else has been bouncing! -- David gnome(a)hawaii.rr.com authenticity, honesty, community

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FOTD 10-12-07 (Quest for Reality [5.5])
by Jim Muth 09 Dec '07

09 Dec '07

FOTD -- December 10, 2007 (5.5) Fractal visionaries and enthusiasts: Today's image is named "Quest for Reality". Actually, I have been questing for reality, if such a thing exists, since I was old enough to quest. I was never satisfied with the assumption that the material universe is the ultimate reality, and I remain unconvinced that the success of science proves that materialism is true. We very possibly could be tweaking our experiments until the results fit neatly into the classical Newtonian world- view of science, thereby reinforcing our faith in materialism. Perhaps the experiments that fail so disappointingly in this uni- verse fail because they are performed in the wrong universe. Experiments that fail in this 'questionably real' universe might prove to be surprisingly true in certain other 'questionably real' alternate universes. This is most certainly the case with fractals, where reality is what one chooses to make of it and one can never be sure what will be found at a certain place until that place is actually reached. Today's image makes this very clear, lying as it does at a spot that at first appears to hold nothing. Today's image is located beyond the ring on the eastern side of the huge December parent, in a spot that, unless it is blown up, appears to be a flat blank area. But like a virus that can be seen only under a powerful microscope, today's image, once it becomes visible, is well worth the trip. The image is a semi-evaporated one, with interest added by ren- dering it with the inside set to 'bof61' and the outside set to 'fmod'. Since it closely resembles several recent FOTD images, I could rate it no higher than an average 5. I rewarded myself the extra 1/2 point for the coloring. I might have added another half point or so for the warp-8 speed of the image, which, with a calculation time of only 47 seconds, almost finishes before it starts. This will make it a pleasure to run the parameter file and watch the numbers almost magically do their thing. But some S.O.T.A. machines and O.S.'s are not Fractint friendly. Those burdened with such uncooperative units may still see the image by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing it without effort there. Sunday was most unpleasant here at Fractal Central, with heavy clouds, slushy streets, and a temperature hovering just above freezing. A cold mist that fell all day added to the unpleasant- ness. The fractal cats spent most of the day stretched by the heat, but perked up when Cassie noticed a squirrel burying a nut in a large flower pot on the back porch. I kept busy taking by it easy. Work permitting, I'll take it easy again on Monday. The next FOTD will be posted in 24 hours. Until then, take care, and if the world is not real, don't worry about it. It's not about ready to go away. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Quest_for_Reality { ; time=0:00:47.73-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=+15.2444272778/+18.1832540939/55113.14/\ 1/-127.5/0 params=-2.475/-1.05/-0.275/-5.5/0/\ 101529000000000.0/0/0 float=y maxiter=1700 inside=bof61 outside=fmod logmap=yes periodicity=10 colors=000cvz_tzWrzSpyOnwKluGjsEhqDfoDdmCbkB`iBZgA\ Xf9Ve9Ud8Sc7Qb6Oa6M`5K_4IZ4GY3EX2CW2BV3AU4AT5AS5AR\ 6AQ7AP7AO8AN99M99LA9KB9IB9GC9GD9GD9GE8GF8GF8GG8GH8\ HI8HI8HJ8HK7HK7HL7HM7HM7HN7HO7IO7I06IQ6IQ6IR6IS6IS\ 6IT6IU6IU09U6IUCRUIZUOgTVrUUpUUoVUnVUmWTlWTkXTjXTi\ YSgYSfZSeZSd_Sc_Rb`Ra`R`000aQYULVbQWbQVcQUcPTdPSdP\ QePPeOOfONfOMgOLgOKhNJhNHiNGiNFjMEjMDkMCkMBnK8kMAi\ OBgQCeRDbTE`VF00GXYHccIS`JQbKOdMUeNzgOziPFjQDlRAnS\ 8oT6qU4sV2tW6uV9uVCuVGuVJuVMuUQuUTuUWuUzvWzuVzuUzu\ UzuT00TzuSzuSztRztRztQztPztPztOztOztNWsNWsMVsMVsLV\ sKVsKUsJUsJUrIUrITrHTrHTrGTrFSrFSrESqESqD00DRqCRqC\ RqBRqAQqAQp9Qp9Qp8Pp8007Pp7Pp6Pp6Qo5Qo5Qo5Qo5Qo5Qo\ 5Ro5Ro5Ro5Ro5Rn5Rn5Rn5Sn5Sn5Sn5Sn5Sn5005Sn5004Tm4T\ m4Tm4Tm4Tm4Um4Um4Um4Um4Ul4Ul4Ul4Vl4004Vl4Vl4Vl4Vl4\ Vm3Wm2Vl4Ul6Tk7Sk9RjAQjCPiEOiFNiHMhILhKLgMKgNJfPIf\ QHeSGeTFeVPZpO_pN`pLaoKbo } 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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Just wondering if I'm still alive on the list
by david 09 Dec '07

09 Dec '07

Don't remember seeing any mail for a while, so just wondering ... -- David gnome(a)hawaii.rr.com authenticity, honesty, community

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FOTD 09-12-07 (A Fractal in Need [No Rating])
by Jim Muth 09 Dec '07

09 Dec '07

FOTD -- December 09, 2007 (No Rating) Fractal visionaries and enthusiasts: Computer troubles raised their ugly heads here at Fractal Central on Saturday, which is the day I work on Sunday's FOTD. The problem was finally solved, but as a result of the trouble, I had very little time for a fractal. I did manage to find one however. I found it on the eastern extremity of the parent fractal for December. I added a bit of interest by half evaporating the scene, then rendering it with the outside set to 'mult' and the inside set to 'atan'. I could not rate the image, which served mostly as a distraction from the day's irritations, but I named it "A Fractal in Need", which describes it pretty well. The calculation time of 53 seconds is blessedly brief. Even more blessed is the instant viewing of the image on the FOTD web site, which may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A cloudy chilly morning gave way to a sunny but chilly afternoon here at Fractal Central on Saturday. The fractal cats disap- proved of the temperature of only 37F 3C. They did approve of the sun streaming in the southwest window however. My day was frustrating, but the problem was solved and things are now back on track. Until next FOTD, take care, and befriend a fractal in need. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Fractal_in_Need { ; time=0:00:52.92-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=+11.13329149909284/-13.96584710674004/\ 4.837861e+011/1/20/0 params=-2.475/-1.05/-0.275/\ -5.5/0/4461700000000.0/0/0 maxiter=2000 inside=atan outside=mult periodicity=10 mathtolerance=0.05/1 colors=000bjYbjXbiVciTciSchQchOchNaeQ`cS_`VZZXXXZW\ UaVScUQeTQcTQbW9bWA_XAWXBTYBQZBNZCK_CH_CEXEGUFHRGI\ PHKMILJJMHLOEMPBNQ9OS6PT3QU1RV6UXZWzzmzI_bMadRceVe\ gZgibikfkmjmnddfZW_TOTNFMI7FE7FA6G76G65H65I65J55J5\ 4K54L44M44M43N33O33P33P2KSz_c0oY6mUBkRGiOLgKQeHtki\ ulowmtxmyvlwulvtlusktrksqkrpjqojpnjnmimlilkikjhjih\ ihhhghgiiakiWliQniKpiEqi8leHgaPbYXYUeTQmPNuSQsVTqY\ Wo`Ymc`kfciieghfcgg_fhWeiSdjOdkKclGbmCan8`o4`p1cj7\ eeCg`HiWNlQSnLXpGbrBgt6lo8ejAZeCS`ELWGERI7NJ0FIU8H\ wBIoEIgHJ`KJTNKLQKEQOIQSMQWQQ_TQcXQg`QkcQogQskQwnO\ haMVPKGCI20NA7RHDVPK_WQccXgjbkqhlqflqelqdmqcmqbmm0\ nq_nqZnqYoqXoqWoqVoqUipVdoW_nWVmXQlXLkYGjYIkXKkWLl\ VNlVPlUQmTSmSUnSVnRXnQZoP_oPapOcpNdpN74hC9cHD_MHWR\ LSWPO`UKeYGjaCoe8ti4sW9sJDmLHgMLbOPXPSSRWMS_GUbBVf\ 5Xj0YmCbnNfnZkniontsnrrmpqmoqlmpllpkjokhnkgnjemjdm\ iblialialgalfakdakbbkabj_ } 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 08-12-07 (Minibrot With Teeth [7.25])
by Jim Muth 07 Dec '07

07 Dec '07

FOTD -- December 08, 2007 (Rating 7.25) Fractal visionaries and enthusiasts: Today's image lies in a tiny insignificant dot in the eastern exoburbs of the parent fractal of December. My first impulse was to bypass this dot, but before doing so, I gave it one quick check, knowing that in the world of fractals, dots may hold an infinity of detail. As today's image shows, I made a wise decision. The image is actually an 'evaporated' one made visible by the 'bof61' inside fill. The name "Minibrot With Teeth" is a description of the central midget, which, due to the active inside fill, appears to have teeth. The rating of 7-1/4 includes a small reward for my coloring efforts. The coloring is not the best however, which is the reason I did not reward myself the full 1/2 point. The fireball calculation time of 55 seconds should remove all fear of wasting time doing the calculation. But if other obstacles prevail, the completed image is available on the FOTD web site for instant download. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The Friday weather featured chilly temperatures hovering just below freezing, cloudy skies, and occasional light snow here at Fractal Central. The fractal cats spent the day trying to stay warm. My day was spent wrapping up a small but complex job. The next in the long series of FOTD images will appear in 24 hours, Mindspring willing, that is. Until then, take care, and I wonder in how many parallel multiple universes fractals do not exist. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= MinibrotWithTeeth { ; time=0:00:54.94-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=+15.2444272778/+18.1832540939/64384.51/\ 1/-127.5/5.8e-007 params=-2.475/-1.05/-0.275/-5.5\ /0/1e+100/0/0 float=y maxiter=1500 inside=bof61 logmap=87 periodicity=10 colors=000A03A03A04A04A05A05A0AA0KAAUAKcAUmAczAmzK\ swUzzbxwaut`rr_ppYmnXjlWhiUegTceS`cQYaPWZOTXMQVROT\ KLRQEKNLRQJPTPTTOV_TWbUXeUYgSWhRViQUjPTkQRlQQnQPoQ\ OpRMqQLtRKwUJzXIz_JzbKzeKPjCPlDOnEOpFNrzLuzNtzOszP\ zhRqISUJTUKVULWULXUMZUN_lO`kObjPciQdiQbjUakY`la_me\ ZmiYnmXoqWpuXrwVpxTnxRlxPkxNiyLgyJeyHdyFbzDazB_z9Y\ z7XzDVwIUtNTqSSnXRkaQhfPekOb_SgPVlQXjRZiS`hTbgTdfU\ feVhdWjbXlaXn`Yp_ZrZ_tY_uXYsVWrUUqTSoRQnQOmPMlOLjM\ JiLHhKFgJDeHBdG9cF9a68bE8cM8dT8d`8eg8fo8fvMik_ladg\ cibenYgsTizNkwPjtRjrTjoVjlXijZig_ieaibch_ehYghVihT\ jhUnYUrNUvCUy1Xx5Zx8`xCbxFewJgwMiwPkwTmwWpv_rvbtvf\ vvixvluwkrwjpwjmwijxhhxhexgcxgduiesjfqkfolgmmhknih\ oifpjdqkbrl`slZtnVnoRipOdqKZrGUsDPpEQnFQkGRiHRfISd\ JSaKT_LTXMUVNUSOVQPVNQWLRWAsIJSWNSSQSPTSLWSIVTGUTF\ UUETUDTUCSVBSVARV9RW8QW7PV6QW6QX6QX6RaIU_GYYE`WCcU\ AgS8jQ6nO4qM2tK0oI1kH2gF2 } 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 07-12-07 (The Truth Lies Within [9.5])
by Jim Muth 06 Dec '07

06 Dec '07

FOTD -- December 07, 2007 (Rating 9.5) Fractal visionaries and enthusiasts: Only rarely do I find a fractal image worthy of an ionospheric rating of 9-1/2, but today I have one. (at least IMO) It is a scene in the East Valley of the largest midget on the main spike of the fractal that will be the parent for the rest of December. Don't think that this main spike is anything like the very prominent main spike of the Mandelbrot set. This main spike, along with its entire period-2 radical, is misplaced so far to the right that it actually lies in kind of an East Valley, and it is so small as to be invisible unless it is magnified. The extra half point rating was earned by the semi-expert (IMO) coloring. As for the name, "The Truth Lies Within", I chose it because it sounds kind of new-agey, and the world of fractals is close to the same age as the 'New Age', (read age-old), ideas. And there is also something a bit mystical about the calculation time of 4:44.44 on the P4. I notice another peculiarity in the image. There are 12 purple elements forming the square, rather that the 2,4,8, . . . that would be expected. I could go into detail about why I consider the image so good. It has something to do with the large expanse of near-neutral colors. But the best way to see the reason for the astronomical rating is to ponder the image, which speaks loudly for itself. (Hmmm . . . we seem to have a talking fractal!) The calculation time of 4-3/4 minutes is a bit slow, but relief is at hand on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the completed image is posted for instant viewing. The Wednesday snow ended, and the sky cleared at nightfall here at Fractal Central. The clear skies and light winds let the temperature drop to 12F -11C by sunrise Thursday. The rest of Thursday was chilly, but with light wind and full sun the after- noon temperature of 32F 0C felt rather pleasant. The fractal cats, whose motto is 'the warmer the better', hung out by the radiators all day. Once I finished the small amount of work on Thursday, the day was pretty good, with lots of spare time, as the quality of the day's fractal shows. I expect a repeat tomorrow. Until next time, take care, and if the earth were turning in the opposite direction, the stars would still rise in the east. We would have to switch the names of the east and west directions. We would also have to switch the names of the northern and southern hemispheres, and redraw our maps upside-down, which would make Australians and New Zealanders very happy. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= TheTruthLiesWithin { ; time=0:04:44.44-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=-3.216611489264438/+0.5748460602506118/\ 3.553654e+011/1/66.5/3.88578058618805e-016 inside=0 params=-2.475/-1.05/-0.275/-5.5/0/0/0/0 float=y maxiter=2000 periodicity=10 mathtolerance=0.05/1 colors=000hfcfdbecadb`ba_a`Z`_YZZXYXWXWVVVUUUTTTSS\ SRQRQPQPOOOMNNLMMKLLIKKHJJGIIFHHHJJJLKLMMMONOPOQRQ\ RSRTUSVWUWXVYZW__YaaZbb_ddaffbggciielkgnniqpltsnww\ wwwwwwwwwwwwwrrrrrrmmmmmmamlemljmlnhlrhlmhlihmfhmc\ hm`imYimVinSjnPjnLjnIknFkoCko9lo6lo3lo0lo2kn4jn6jm\ 8imAhmChmEgmFfmHfmJemLemNdmPcmRcmSbmUamWamY`m__ma_\ mcZmdZmbYlaXk`Wj_WiZVhYUgXUfVTeUSdTScSObRQaQM`PF_N\ LZMAYLJXKAWJHTIAUHARGASDA9FACHFFKGKMHPRIUUKZYLc_Lh\ cMmfMrhNvjNzmOzpOzsOzvOzuOzlHtgGobFiYEdTDZOBUKAOG9\ JC8D87846355555655855955A55C55D54F54G54H54J54K54M5\ 4N54OA8PFCQKGRPKRUOSZSTcWUgZUfYTfYTb_W_`YWa_TcbPdd\ MefBSIBTJBUJAUKAVKAWLAXLAXLBWMCVNCUNDTODSPERPEQQFM\ RGIR0ES0AT00T00A00A00A00A00A00ALEmMDZMCmLDYKUzJDYJ\ EmIEYHUzGFXGFmFFXEUzDGXDGmDESDDmDCmDBmDAmD96D82F76\ H79J6CL6FN5IP5LR4OT4RV3UX3XZ2_`2bb1ec1hb3ga5f`7e_8\ d_AcZCbYEaXFaeRSfVVgZYhb` } 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 06-12-07 (Murmuring Ghosts [7.5])
by Jim Muth 05 Dec '07

05 Dec '07

FOTD -- December 06, 2007 (Rating 7.5) Fractal visionaries and enthusiasts: Today's scene in the parent of the month is titled "Murmuring Ghosts". The image actually does have a hauntingly supernatural feeling about it. And yes, I have heard that ghosts do not exist, at least they are not supposed to. They are mere wish- fulfillment delusions -- kind of an evolved biological defense mechanism against the thought of inescapable final oblivion. But do the ghosts know that they do not exist except in the minds of wishful believers? I doubt it. The shimmering spirit things are everywhere, and as today's image shows, they have even invaded the world of fractals. In fact, in my lifetime I have encountered several things that, if they were not ghosts, certainly gave good imitations of one. I put enough work into coloring the image to add the extra half point to the rating of a 7. We'll forget that I discarded the color palettes that I put all the work into, and used one that came about at the tap of the 'enter' key. With a calculation time of 50 seconds, today's parameter file could hardly be faster. But the fastest way to see the image, as always, is to give Paul a chance to render it and post it to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it may be enjoyed at leisure. Light and occasionally moderate snow fell all day Wednesday here at Fractal Central. By the time it ended at nightfall, about 2 inches or 5cm of fluff had piled up on the sidewalk. A broom and a bit of salt took quick care of the stuff. The fractal cats watched the flakes drift down with puzzlement. My work day was on the slow side. Had it not been for the snow removal, the day might have bordered on boredom. The next FOTD will be posted in 24 hours, maybe a bit later if I can't connect to Mindspring. Until next time, take care, and never trust a spirit that doesn't murmur. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Murmuring_Ghosts { ; time=0:00:50.43-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=-2.800551481860207/+0.8244168043957928/\ 1.420862e+007/1/102.5/-2.41406359750839794e-006 params=-2.475/-1.05/-0.275/-5.5/0/0/0/0 float=y maxiter=1250 inside=0 logmap=118 periodicity=10 colors=00065K64I53G52E51C50A63D65G68I6AL6DO6FQ6HT6\ KW6MY6P`6Rc6Ue6Wh6YjBYeFY`KYWOYRSYMXYH`YCdY8f_Dg`H\ haLjbPkdUleYnfaogephimgkjflgemednbco_bpXaqV`rS_sPZ\ tMYuKXvHWwEVxBUy9Uz8Rx8Pv7Nu7Ls6Jr6Hp6En5Cm5Ak48j4\ 6h44g56f57f58e5Ae6Bd6Cd6Dd6Fc6Gc7Hb7Jb7Ka7La7Ma6TU\ 6_M5fE5l77m98nAAnCBoDDoFEpGGpIHqJIqKJjQJcVJY`KReKK\ kKEpIGmHHjGJgFKeDMbCN_BOXAQV8RS7TP6UM5VK6VF7VB`blZ\ akYajX`iW`hV_hU_gSZfRZeQYePYdOXcNXbMXbOW`PVZQVXSUV\ TUTUTRWTPXSOYSM_RK`RIaQGcQEdPCePBZXLScVMjcFqm9xvCo\ wEfwHYwJPwLHwKIuKJtKKsKLrJMqJNpJOnJPmIQlIRkISjITiH\ RjHPkHNkGLlGJlGHmFFmFDnFBnE9oE7oE5pD3pD1qD0qG1nJ1k\ L1hO2eR2bT2_W3XZ3U`3Rc4Of4Lh4Ik5Fn5Cp59n7Em9IlBNkC\ RjEWZFtYIuXMuXPuWTuVXvV_vUcvTfvTjwSmwRqwRtwUnwXiw_\ cwbZwRduGjsUOvg1xa9jXGYSNKNU7LRBKPFJMJIKNHIRGFVFDZ\ EAbD8fC6jD9hEBfFDdGFbGI`HKZIMXJOVKQTKTRLVPMXNNZLN`\ KOaJOaJPaIPaIQaI79R68P67N } 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 05-12-07 (Inside-In [8])
by Jim Muth 05 Dec '07

05 Dec '07

FOTD -- December 05, 2007 (Rating 8) Fractal visionaries and enthusiasts: The FOTD is late again, which means that I was unable to get connected to Mindspring in the evening once again. When I find more spare time than expected, I sometimes write short science-fiction and fantasy stories. One story I wrote a few years ago concerned voice communication with a humanoid alien on a planet in a distant galaxy. (For convenience we forget the cosmic speed limit of light.) The problem was to communicate our earthly directions. Communicating which directions are up and down was easy for our earth man. Up is toward the sky; down is toward the center of the planet. Communicating east and west was almost as easy. East is where the sun rises; west is where it sets. But then the man on earth tried to think of a way to communicate north and south. He told the alien that when he faces east, north is on his left side. But the alien didn't know which hand was his left hand, and to make matters worse, the bodies of his race had perfect left-right symmetry. When the man on earth then said that the north pole is the one around which the sky appears to rotate in a counter-clockwise direction, the distant alien asked which way is counter-clockwise. And so it went until both men gave up in frustration. I have been wondering ever since if a way actually exists to communicate the left and right directions to someone on a distant planet, who has no objects common to both parties to refer to. A non-symmetrical sub-atomic reaction might work, since it would give an objective reality to these directions, but this would raise a whole new series of technical problems. In deep space the situation would be worse, but with no planets in the vicinity, directions such as up-down, east-west and left- right would have little meaning. Well, I seem to have gotten off the fractal track, and we have a fractal to be concerned about. It's another scene in the parent fractal, which I have decided will be parent of the month. Today's scene falls in the 'half-evaporated' category. The bailout radius has been raised just to the point where the 'outside' stuff has been caught halfway through the evaporation process. I have rendered the scene with the 'inside' set to 'atan' and the remaining outside still set to 'iter'. In my opinion, the image is different enough to rate a lofty 8, so that's where I rated it. The name "Bad Day for Fractals" can mean anything the viewer wishes. The calculation time of 1-1/2 minutes may be avoided by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished GIF image there. Chilly, blustery weather with freezing temperatures and flurries of snow prevailed here at Fractal Central on Tuesday, making the day unpleasant for outside activity. The cats ignored the snow and crowded by the large radiator in the hallway. My day was busy enough to keep boredom at bay. The next FOTD fractal will be posted in 24 hours. Until then, take care, and what's left is right. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= BadDayForFractals { ; time=0:01:36.43-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+9.941892031369065/+16.90580804773217/\ 9285827/1/-20/0 params=-2.475/-1.05/-0.275/-5.5/0/\ 12500000000000.0/0/0 float=y maxiter=2000 inside=atan periodicity=10 colors=000KOYIOWIOVHNTGNRENQENQGRTGVWGYZH`aHcdHfhI\ ikInlIqoKtsKxvKzyLzzLzzLzzQzzVvvWqqYlnZhk`cf`ZcaV`\ cQWdLTdHQfDLh9Ii4Gi0Dl0Ko0Qs0Yv0cy0kz0qz0xz2yyBzvK\ zsTzq`znizkszhzzfzzTszGcs2Ok0Ac0Df0Gh6IkALlGOoKRqO\ VsLRqKQzHOqGNqDLqBKq9Iq7Hq4Eo2Do0Bo0Ao09o07o06o04o\ 06h06a06W07Q4Y26Y47Y69Y79Z9AZABZBDZDDZDB`OA``zz07a\ yzx0NnqzsncykkzhszdxzaztZzlYzdVzYTzd0ta0kZ0aW0TT0L\ Q0W0dT0cR0aQ1aO4`L6`K7ZIAYHBYEDWDGWBHVAIV9HY9HZ7H`\ 7Ha7Hc6Hd6Hf6Hh4Hi4Hk4Hl2Hn2Ho2Hq1Iq0Iq0Iq0Iq0Iq0K\ q0Kq0Kq0Kq0Kq0KqBQfRWWhaNaYLWVLQQKKNKEIIAGIDKLGOOI\ TRLWVO`YRd`VicYlf`qicvlfzohzqlqhof`sWTxLLzBEz17o4A\ c6BQ9DtAE1DG0EH0IK0sL0RN4WO7ZQAcRDhTHlWKqYNtZRy`Vz\ aYzc`zddz`hzWlzRozNszIxzEzzAzz7zsAzlBzcDzVEzNGzGHz\ 9IzDQtGWkIcaLi`Oh`Tf`WdZZcZaaZd`Zh``iW`kRalOanKcoH\ cqDdqAds6ft1fv0hx0hy0iz0iz0Z`2QBLRDOTDQTDTVDVVDYWD\ ZWDaYDcYDfZDhZDkflOknOnoO } 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 05-12-07 (Bad Day for Fractals [8])
by Jim Muth 05 Dec '07

05 Dec '07

FOTD -- December 05, 2007 (Rating 8) Fractal visionaries and enthusiasts: When I find more spare time than expected, I sometimes write short science-fiction and fantasy stories. One story I wrote a few years ago concerned voice communication with a humanoid alien on a planet in a distant galaxy. (For convenience we forget the cosmic speed limit of light.) The problem was to communicate our earthly directions. Communicating which directions are up and down was easy for our earth man. Up is toward the sky; down is toward the center of the planet. Communicating east and west was almost as easy. East is where the sun rises; west is where it sets. But then the man on earth tried to think of a way to communicate north and south. He told the alien that when he faces east, north is on his left side. But the alien didn't know which hand was his left hand, and to make matters worse, the bodies of his race had perfect left-right symmetry. When the man on earth then said that the north pole is the one around which the sky appears to rotate in a counter-clockwise direction, the distant alien asked which way is counter-clockwise. And so it went until both men gave up in frustration. I have been wondering ever since if a way actually exists to communicate the left and right directions to someone on a distant planet, who has no objects common to both parties to refer to. A non-symmetrical sub-atomic reaction might work, since it would give an objective reality to these directions, but this would raise a whole new series of technical problems. In deep space the situation would be worse, but with no planets in the vicinity, directions such as up-down, east-west and left- right would have little meaning. Well, I seem to have gotten off the fractal track, and we have a fractal to be concerned about. It's another scene in the parent fractal, which I have decided will be parent of the month. Today's scene falls in the 'half-evaporated' category. The bailout radius has been raised just to the point where the 'outside' stuff has been caught halfway through the evaporation process. I have rendered the scene with the 'inside' set to 'atan' and the remaining outside still set to 'iter'. In my opinion, the image is different enough to rate a lofty 8, so that's where I rated it. The name "Bad Day for Fractals" can mean anything the viewer wishes. The calculation time of 1-1/2 minutes may be avoided by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished GIF image there. Chilly, blustery weather with freezing temperatures and flurries of snow prevailed here at Fractal Central on Tuesday, making the day unpleasant for outside activity. The cats ignored the snow and crowded by the large radiator in the hallway. My day was busy enough to keep boredom at bay. The next FOTD fractal will be posted in 24 hours. Until then, take care, and what's left is right. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= BadDayForFractals { ; time=0:01:36.43-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+9.941892031369065/+16.90580804773217/\ 9285827/1/-20/0 params=-2.475/-1.05/-0.275/-5.5/0/\ 12500000000000.0/0/0 float=y maxiter=2000 inside=atan periodicity=10 colors=000KOYIOWIOVHNTGNRENQENQGRTGVWGYZH`aHcdHfhI\ ikInlIqoKtsKxvKzyLzzLzzLzzQzzVvvWqqYlnZhk`cf`ZcaV`\ cQWdLTdHQfDLh9Ii4Gi0Dl0Ko0Qs0Yv0cy0kz0qz0xz2yyBzvK\ zsTzq`znizkszhzzfzzTszGcs2Ok0Ac0Df0Gh6IkALlGOoKRqO\ VsLRqKQzHOqGNqDLqBKq9Iq7Hq4Eo2Do0Bo0Ao09o07o06o04o\ 06h06a06W07Q4Y26Y47Y69Y79Z9AZABZBDZDDZDB`OA``zz07a\ yzx0NnqzsncykkzhszdxzaztZzlYzdVzYTzd0ta0kZ0aW0TT0L\ Q0W0dT0cR0aQ1aO4`L6`K7ZIAYHBYEDWDGWBHVAIV9HY9HZ7H`\ 7Ha7Hc6Hd6Hf6Hh4Hi4Hk4Hl2Hn2Ho2Hq1Iq0Iq0Iq0Iq0Iq0K\ q0Kq0Kq0Kq0Kq0KqBQfRWWhaNaYLWVLQQKKNKEIIAGIDKLGOOI\ TRLWVO`YRd`VicYlf`qicvlfzohzqlqhof`sWTxLLzBEz17o4A\ c6BQ9DtAE1DG0EH0IK0sL0RN4WO7ZQAcRDhTHlWKqYNtZRy`Vz\ aYzc`zddz`hzWlzRozNszIxzEzzAzz7zsAzlBzcDzVEzNGzGHz\ 9IzDQtGWkIcaLi`Oh`Tf`WdZZcZaaZd`Zh``iW`kRalOanKcoH\ cqDdqAds6ft1fv0hx0hy0iz0iz0Z`2QBLRDOTDQTDTVDVVDYWD\ ZWDaYDcYDfZDhZDkflOknOnoO } 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 04-12-07 (Inside-In [7])
by Jim Muth 03 Dec '07

03 Dec '07

FOTD -- December 04, 2007 (Rating 7) Fractal visionaries and enthusiasts: I would have rated today's image at an 8 if it had not been rendered with the inside set to 'fmod' and the outside set to 'tdis', thereby spoiling the purity of the image. As it is, the rating of a 7 is adequate for the day's effort. The parent fractal is the same one that has been the source of the four most recent FOTD images. In fact, this indescribable parent is so rich in its depths that I might devote the rest of the month to its exploration. To find today's image I ventured to an area that could possibly be the East Valley of the parent, if it has an East Valley, that is. I checked the shore line of a small out-of-place bay there. This shore line is dotted with very small semi-buds filled with broken fractal stuff. Today's image shows a minibrot I found in the stuff in one of the buds. I named the image "Inside-In". I must have had a reason for the name, but the reason has long since been forgotten. The calcula- tion time of 13-3/4 minutes on the fast machine is rather slow. But I have sent the finished image on ahead to Paul at the FOTD web site, where it will likely be waiting for immediate viewing by the time you read this. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The winds blew at 30mph (50kph), the snow showers flew, and the temperature hovered just above freezing here at Fractal Central on Monday. The fractal cats don't like wind, they don't like snow, and they don't like cold. It was lucky for them that the radiators were comfortably warm. For me the day was quite un-notable, and I have no reason to expect that tomorrow will be different. The next FOTD will appear right here in 24 hours. Until then, take care, and stay tuned for more exciting revelations. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Inside-In { ; time=0:13:44.76-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-1.429354931270962/-15.39071435264147/\ 3276.279/1/-50/0 params=-2.475/-1.05/-0.275/-5.5/\ 0/0/0/0 float=y maxiter=2000 inside=fmod proximity=1 outside=tdis periodicity=10 colors=0005t05t05r05r05p05p05m05m07k09g0Bc0DZ0FV0H\ R0IN0KI0NF0P90R70T50X30Z10c00e00i00k00p00r00w00y00\ z00z00y01t05r09m0Bk0Fg0Ie0Nc0PZ0TX0XT0aR0cN0gK0kH0\ pa0gw0Xz0Nz0Rp7VZPZKgc7zg0zm0zi0zc0mXzzezzpzzpwypi\ rpXkpNepBZp0Tp0Np0XpDipRtpezmazkVzgPzcIzZDzV7zT1zP\ 0zK0zH0zD0z90yH0ZP0DZ00g00r00p00m00k00i00g00e00a01\ Z07X0BV0FT0KR0PP0VK0VP0TT0RX0Pc0Pg1Nk5Kp9Iw1Fk0BZ0\ 5N03R00X70cF0iK0pT0wa0zi0zr0zk0zc0zV0zN5zHBz9Iz1Rz\ 0Xz0ey0kw0tt0zr0tr0kt0ct0Vw0Nw0Fy07y00z00z00y00t00\ p00k00g00c00Z00V00R00N00I00F00B00700100300501707B0\ DD3KF5RH9ZK3cT0gc0kk0pw0tz0yz0zz0mz0Zz0KzB7zP0zc0z\ r0zp0zk0zi0ze0ta3pZBkVIeRRaPZXKgTHpNFyIBzF7z9t00VR\ 05z00000000000z00e1KKIi1az0tz0rz0mz0iw0er0am0Xi0Te\ 0Pa0KX0HZ0Kc1Pg7TiBZmHcrNgtTkyXrzcwzizzpzztzzzzzzz\ zzzzzzzzzzzzzwzzrtzmmzigzeZzaTzXNzTHzPBzK5zH0zB0ea\ 05z05z05z05z05y05y05w05w0 } 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 03-12-07 (Somewhere Sometime [8])
by Jim Muth 03 Dec '07

03 Dec '07

FOTD -- December 03, 2007 (Rating 8) Fractal visionaries and enthusiasts: Today's image lies in the same parent fractal that gave us the images of the past two days. This parent is indescribable, but I can state with perfect confidence that the scene of today's image is located in the valley leading to a period-13 bud. Despite its high periodicity, this bud is the largest on the circular main bay of the parent fractal. (The normally largest period-2 bud is located far around to the northeast, actually lying on the edge of a valley.) Since I consider today's image a notable improvement over the past two days' efforts, I rated it at an 8. The name "Somewhere Sometime" has whatever meaning the viewer chooses to see in it. The calculation took 1/100 of a second less than 4 minutes on the fast machine. On the slow one it would take about 20 minutes. The trip to the FOTD web site, where the completed image is posted, will be even faster. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> About 2 inches, 5cm, of snow fell overnight Saturday here at Fractal Central, but above freezing temperatures on Sunday melted it quickly. Otherwise, the day was cloudy and raw. The fractal cats spent the day huddled next to the radiators. My day was slow and uneventful. If tomorrow is the same, I'll be thankful. The next FOTD will be posted by me in 24 hours. Until then, take care, and what time is it at this moment in the Andromeda Galaxy? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Somewhere_Sometime { ; time=0:03:59.99-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=-87.959320712298/-51.493685900047/72224\ 08/1/-60/0 params=-2.475/-1.05/-0.275/-5.5/0/0/0/0 float=y maxiter=5000 inside=0 periodicity=10 colors=000cuYu0xeoYcu_eoYelYghYgdYgZYiVYiSWjOWjIWj\ FWlAWl7Wu0Yp0Wl2WgHWcSW_dUUoUPoUKoU8oWDoUHoUKoURoS\ UoSYoSaoQgoQjoQnoOroOuoOuoNuoNuoEuoJuzNuzSuzWuzauz\ euzkuzntztrzwpzx_ztJzn2zi0zk0zg0zc0x_2lWAqUCfQCnOD\ jLDlJDlFFnEFoAFo8Hq4Hs2Ju0Ju0Jv0Kx0Kz00z0Cz0Kz0Wl0\ eX0pI0u20u00u00u00u00u80uH0uM2tT4r`6pf8lnAjuClzAiz\ EguHeoLajO_dSY`UWVYTQaRKePFiK2nN7lNAkNDiNHgNIePMcP\ QaPS_PVYPXWR`URdSRfQRjOezJYvLRlNJ`OCQQ3FS02U00U00W\ 04Y0I_6X_CjaHvcNzcRzeTqeUheYZe_QeaHeu0xr2xc7ePDJCI\ 0AH08F48DC6AH68O37W24c22i00p00w00x00n0cx0cx3cxUcxP\ cxKcxHcxCcx8cx3cx0cx0cx0cx0cx0cx0cx0cx0cx0cx0cx0cx\ 0cx0cx0Mx0Mx0Mx0Ox0Ox0Ox0Ox0Ox0Qx0Qx0Qx0Qx0Qx0Qx0Q\ x3Sx8SxDSxJSxNSxTSxUOxWSxWMxYLxYKx_Ix_Hx_Fx`Dx`8x`\ 7x`4x_2x_2x_2xY2xY2tW2tW2kW2kU2cU2aU2VW2SU7JY2JT8A\ Y0ASA0_70UF0aH6XICaOHYMNcXS`RYgdccXilnnfbpuoukhwtu\ xjlxpzxlpxjzxgsxczxexnWzx } 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 02-12-07 (Followed the Rules [5.5])
by Jim Muth 01 Dec '07

01 Dec '07

FOTD -- December 02, 2007 (Rating 5.5) Fractal visionaries and enthusiasts: There is not much to be said about today's fractal image, which lies in the same parent fractal as yesterday's image, except that I found it in less than 2 minutes. The rating of a very modest 5-1/2, including 1/2 point for the coloring, shows that great fractals cannot be found in a time as brief as 2 minutes. The name "Followed the Rules" means nothing at all. To find the name I opened a book randomly and used the first three suitable words I came upon. The calculation time of under 3 minutes is brief enough to make the less-than-stellar image worth the effort. Even less effort is needed to view the image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Mostly sunny but very chilly weather prevailed at Old Fractal Central, where I spent the day Saturday with the old fractal cats Thomas and Tippy, who, in their advanced age, are now being looked after very well by my sister. The trip back to NFC went smoothly, leaving just enough time for a quickie fractal. The next fractal, not such a quick one, will be posted in 24 hours. Until then, take care, and never give up. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Followed_the_Rules { ; time=0:02:42.10-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=-203.6012450004701/+8.529657248892084/\ 1140440/1/-62.5001563856791336/0.000164812558466585 params=-2.475/-1.05/-0.275/-5.5/0/0/0/0 float=y maxiter=2000 inside=0 periodicity=10 colors=000jMrkLqlKqmJpnIooHnpGnqFmrElsDltCkuBjvAiw\ 9ix8hy7gy6gw9huBhtDirGipIioKjmNjlPkjRkhUkgWleYld_l\ aXk_UkOGkWOjNEjRIjMCjNCiLAiKBhKBhKBhKBgKBgKBgKBfKB\ fKBfKBeKCeKCeKCdKCdKCdKCcKCcKCcKCbKCbKCbJBaJAaJAaJ\ 9`J8`J8`J7`J7_J6_J5_J5ZJ4ZJ4ZJ3ZJ2YJ2YJ1YJ1YL3WN5V\ P7TR9STBQVDPWFNYHM_JKaLJcNHePGgREhTDeVGcXI`ZLZ_NXa\ QUcSSeVQfXNhZLjaIlcGmfEohBqk9sm7toFpqNlrUhtaduh`wp\ XxwTyk_n_edOlUCrK1xA9vDHuFPtHWsJcrMkqOspQzoSjkbWgm\ HdwLftPhrTjpXlm`nkdoi`mgXlfTjePidLgcHfaDd`9c_5aZ2`\ Y4ZX6YW8XV9VUBUTDTSFRSGQRIPQKOPMMONLNPKMRIMTHLUGKm\ EJmDImCHmBHzCIzCJzDKzcLzcMzcMzcNzcObFPbFQcGQcGRcGS\ cHTcHUcHUbIVbJWbKWbKXbLYbMYbNZbNZbO_bP`bP`bQabRabS\ bbScbTcbUdbUdcTedSedReeQeePefOefNegNegMehLehKeiJei\ IejHejGekGekFelEelDemCemBenAenAenAcoAbpA`pAZ`kj_kj\ ZkjYkkXkkWkkVkkUkkTkkSklRklQklPklOklNklQhnSeoVcpX`\ qZYsaWtcTueRvfQugPthOsiNs } 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 01-12-07 (Condensation [6.3])
by Jim Muth 30 Nov '07

30 Nov '07

FOTD -- December 01, 2007 (Rating 6.3) Fractal visionaries and enthusiasts: The unlikely parameters of today's image are a sign that I found the parent fractal with the aid of the Fractint evolver feature. This parent fractal is of gargantuan size and totally beyond description, but when it is finally squeezed onto the screen, it is a most interesting thing, with more interesting places to explore than one can shake a fractal at. Most likely, it will be the source of quite a few FOTD images in the future. The imag(p3) parameter of one-googol indicate that the image has been evaporated, with the resulting blank screen brought to life by rendering the scene with the inside set to 'bof61'. The name "Condensation" came to mind when I pondered the way this inside fill made the invisible visible. The rating of a 6.3 includes a 0.3 point reward for my coloring effort. I did not give myself the usual 1/2 point because I am not totally satisfied with the result. The calculation time of 3-2/3 minutes is slightly slow, but why not go ahead and run the included parameter file. Only satisfac- tion can result. Another way to see the image is to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it is posted for near-instant viewing. Sunny but chilly weather prevailed here at Fractal Central on Friday. The fractal cats disapproved of the temperature, which reached no higher than 37F 3C, while I disapproved of the size of the latest heating bill. The next FOTD might not appear in 24 hours. I will spend most of Saturday back at Old Fractal Central with the old fractal cats, Thomas and Tippy. If I get back to new F.C. in time, there will be a FOTD for December 2, if not, there will be none until December 3. So until next time, whenever that may be, take care, and what does the string theory of everything predict about the fate of the universe? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Condensation { ; time=0:03:39.98-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-30.13938465488174/+47.99141598338133/\ 2.00769e+008/1/-37.5/0 params=-2.475/-1.05/-0.275/\ -5.5/0/1e+100/0/0 float=y maxiter=2000 inside=bof61 logmap=284 periodicity=10 colors=000m_7nX9oVCpSFqQHrNKrLMbZYNkh8xsAweBvSCvFJ\ tFPsFWqFapFgoFnmFtlFthHseIVMKgWMSLKVMHPHESJIUKHWLL\ YMP_OOaPNcQNeRMgSLiUKkVJmWInXHoYHpXHqWHrUHsSHtQHuO\ HsKHqGHoCIm8Ik4Ii5Jh6Jc6JZ7KU8KP8KK9LKALKALPGPTMTX\ RX`X`eadighmllqrpuwszzzynsygptWipXemXajYYgYUdZQ`ZM\ Y_IV_ES`AP`6M`3LZCKYLKWTJVaJTiISrIRzLQuNQpPQlRQgTQ\ bVQZXQUZQP`QLbQGdQC_YSVdfQkuRjpRjkSifSiaSiXThSThNU\ gIUgDUg9Re8Pd8Nb7La7I_7GZ6EX6CW59U57T55R43Q41P42T8\ 2WB2ZF3aI3dL3gP4jS4mW4pZ4sa8rZCqXGpVJoTNnRRmPUlNYk\ LajJdiHhhFlgDofBse9wd7zc5xd6we6ue6tf6sg7qg7ph7oi7m\ i7lj8kk8ik8hl8gl8`iCVfFPdJJaMDZQ7XTCUWGRYLP_PMaUJc\ YHebEgfBik9ko6ms4op7qnAslDuiGwgJyeMz`SvXXrTanPfjLk\ fHpbDu_FqbHmdIjfKfiLckN_mPWpQTrSPtTMvbTwl_wjVqhQkf\ MecLf`LgYKhVKhSKiQJjNJkKJkHIlEImCImBKjBMgBOdBQaBSZ\ AUWAWTAYQA_NAaK9cH9eE9gB9i89k59m2Bg5Db7FY9HSBJNDLI\ FNDHOHIOKJPOKPRLkb4kd1la4 } 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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Re: Fractint Digest, Vol 57, Issue 10
by Marcus e Adriana 29 Nov '07

29 Nov '07

Thanks Ken! Excellent site!! I´m still amazed !!! Marcus From: Ken Childress <kenc(a)bww.com> > Hi, > > "The Algorithmic Beauty of Plants" is available as a PDF download. > > http://algorithmicbotany.org/papers/ > > It's at the bottom of the page. > > > > Ken...

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FOTD 30-11-07 (The Spikes of Life [6])
by Jim Muth 29 Nov '07

29 Nov '07

FOTD -- November 30, 2007 (Rating 6) Fractal visionaries and enthusiasts: I have been having trouble getting connected to Mindspring in the evenings lately, which is why I sometimes post the Fractint version of the FOTD through AOL and do not post the philofractal version until the next morning. (The philofractal list does not like AOL's HTML e-mail encoding.) Earthlink says it is a lack of capacity in this area -- a rather shameful statement for a leading ISP to make. Oh well, we'll give them a chance and see how it goes from here. They have been quite reliable for over 10 years. We end the month of November with another fractal that rates a 6, not that a 6 is a bad rating, it's just so bland. The day's fractal lies in the main spike area of the Z^(2.001)+C Mandeloid as it appears 0.01 level up the complex logarithmic ladder when calculated by the MandelbrotBC1 formula, with no function used in the calculation. The spiky effect was achieved by rendering the image with the outside set to 'fmod' and the proximity set to 0.09. I named the image "The Spikes of Life" for no sensible reason. Since the name is senseless, the calculation time had better be brief. And indeed it is. The 29 seconds will try the patience of not even the most impatient fractalist. And as always, a trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> will be equally fast and even more exciting. Despite brisk winds, Thursday was really quite pleasant here at Fractal Central. The temperature reached a high of 54F 12C and there was ample sunshine. The fractal cats must have agreed, for one of them celebrated by pulling up a corner of the carpet in the living room. They both looked guilty but claimed innocence. In my department, normality prevailed. The day's fractal might have been worth a higher rating, but what the heck, nobody is perfect. The next FOTD fractal will be posted in 24 hours. Until then, take care, and what if the theory of everything turns out to be a theory of nothing? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Spikes_of_Life { ; time=0:00:28.98-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=ident center-mag=-1.769052618204596/-0.00000154115427465\ /5.532635e+008/1/-134/6.49684421322946348e-005 params=2.001/0/0.01/0 float=y maxiter=1800 inside=0 proximity=0.09 outside=fmod periodicity=10 colors=000jezjezjezjezjezleznfzphyrixtkwvmvxouzptw\ ksufrraqpXpmTokOnhJmfEldAkhWFiYHi_Ii`JibLicMieNifP\ ihQiiRikTilUinVioWgkZegadcdb_g`Wj_SlYOoWKrVGuTCxS8\ zSCvSGrSKnSOjSSfSWbSZ_SbWSfSSjOSnKSrGSuDLSLMTMMTMM\ TMMTMNUMNUMNUMNUMLRRKOWJL_IIdGFiFCmE9rD6vJG7LK9MOA\ NRBOVCPYDQaERdFShGTkHUoIVrJWvKXyLYvJZtIZqG_oF_lE`j\ C`gBaeAbb8b`7cY6cW4dT3dR2_S5VS8RSAMSDISF_HKp7Ol8Ri\ 9Tf9VcAX`AZXB`UCbRCeODgLDiHEkEFmBFo8Gq5GsAIqEKpILn\ MNmQOkUQjYRhaTgeVeiWdmYbqZau`_yaZsYYnUYiQYdMY_IXVE\ XQAXL6XG2XI3YJ4ZK4ZL5_M5_N6`O6aQ7aR7bS8bT8cU9dV9dW\ AeXAeQEVJIKDL9ENCEPEERGISFMSEQTDUTCYUBaUAeV9iV8mV7\ iW8eW8aX8YX8UX8QY8NY8JZ8FZ8BZ87_83_80_85a9Ac9FeAKg\ APiAUkBZmBcoBhqCmsCquCjtDcsEYrFRqFLpGEoH8nHFhJMbKS\ YLZSMeMOkHPrBQx6RhVfTrvRnsPkpNhmMejK`gIWeGS_FOXDJT\ BEP99L85ICBMFGQIMTMRXPW_S`cVefZhialkdongrphqnhplho\ jhnhhmfildikbijaii_ihYjgW } 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 PARAMETER FILE=========================================

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FOTD 29-11-07 (Curly Evaporation [6])
by Jim Muth 29 Nov '07

29 Nov '07

FOTD -- November 29, 2007 (Rating 6) Fractal visionaries and enthusiasts: Today's image lies in the parent fractal that is generated when 4 negative parts of Z^(-1.2) are combined with 1 negative part of Z^(-4.8), and (1/C) is added. This parent consists of the typical large round bays with filaments extending from the buds and terminating in rings. Today's scene lies on one of these filaments near the point where it reaches a terminal ring. The name "Curly Evaporation" indicates that the scene is an evaporated one with the resulting expanse of 'inside' stuff brought to life by the 'bof61' inside fill. The colors are a bit too muddy to add to the rating, but the image is still worth a look. The calculation time of 2-3/4 minutes means that it will not take too much effort to run the included parameter file, but if for some reason running parameter files is impractical, the completed image may be viewed on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Bright sun and chilly temperatures around 39F +4C prevailed here at Fractal Central on Wednesday. The fractal cats made the best of things by sleeping most of the day. My department was busier than expected, but still under control. The next FOTD will appear in 24 hours. Until then, take care, and have reasonable faith in reason. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Curly_Evaporation { ; time=0:02:44.72-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-4.535005682551917/-17.02949523595395/\ 9.386122e+007/1/-127.5/0 params=-4/-1.2/-1/-4.8/0/\ 1e+100/0/0 float=y maxiter=1800 inside=bof61 periodicity=10 colors=000th6pi8mjAikCflEbmG_oJWpLTqNPrPMsRItTFuVG\ rXHpZIm`JkbKhdLfeMdgNaiO_kPXmQVoRTpTVjVWdXXZZYT`ZN\ b_IaaGacE`eC`gB`i9_k7_m6Zo4Zq2Zr1Yl7YgDYaJYXOYRUXM\ _XGdXBjX5pX0uGPXJNULMSNKQPJNSHLUGJWFHYDE_CCbAAd97f\ 75h63j51g62d63a63Z74W75U75R76O87L87I88G88QlVUe`XZe\ _TkbMpeGu`FsXErTDqPCoLBnHAmD9k98j57i16h37g58f79f9A\ eBBeCCdEDdGDcIEbKFbLGaNHaPI`RJ`TK_UK_VMXWNVXPTYQRZ\ SPZTN_VL`WJaYHbZFc`DcaBOv6Ms6Kp6Im6Gj6Eg6De6Bb69_6\ 7X65U64S6GPDRMKaJQ_HNZGKYFHWDEVCBUB9XCAZCB`DBbDCdD\ CfEDhEDjEElFEnFFpFFoEGoEHnDHnDImCImCJlBJlBKkALkALj\ 9Mj9Mi8Ni8N`tWJioNgoQdpTbpW_qZXrbVreSshPtkNtnKuqIu\ jJdcJOYJ7bK9fLBkMDoNFqRIrUKsXMt_OucQvfSwiUxpWztYzu\ ZzwZzvZysZwpZumZsjZqhZpgZogZkdVgXRcUO_KKWAHSADOAAK\ F6GK3FQ6FU9FYCFaFFeIFzLzzOzzzzzUzzzzzYIv_JraKmcLhd\ NccJZZFUUBPP7KKDLPJOUPRZVUcWXcX_cYbcZec_hcUk_OnXIz\ zKzzKzzKzzKzzKzzKmzKm8Km3 } 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 for November 29, 2007
by JimMuth＠aol.com 28 Nov '07

28 Nov '07

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FOTD 28-11-07 (Forever Reset [No Rating])
by Jim Muth 28 Nov '07

28 Nov '07

FOTD -- November 28, 2007 (No Rating) Fractal visionaries and enthusiasts: I see in the December 3 issue of Time Magazine that according to science, mankind inherits his good and evil tendencies through his genes and these tendencies manifest as behavior as a result of brain activity. I haven't thoroughly read the article yet, but I suppose it is another pop-scientific 'love is just a brain chemical' type of article. It probably reports that when we think or do good things, a certain part of our brain becomes active, and when we think or do evil things, a different part becomes active. So far so good, but we did not choose our genes, and our brain activity is beyond our control, so how then can criminals be held responsible for their evil behavior? In fact, if genes and brain activity are the ultimate source of human behavior, then we should immediately free all criminals. The poor fellows are innocent, imprisoned for something they had no power to avoid doing. Their genes and brain activity are responsible for the crimes. The preceding conclusion is not to be taken seriously, but it does show how little faith I put in the things that materialis- tic 'science' pronounces about human behavior. I place much more faith in the reality of fractals however, particularly the Mandelbrot set, an infinitesimal part of which is displayed in today's image. The scene is on the main spike, a short distance east of the largest minibrot. The location is in the East Valley area of a larger minibrot in the East Valley area of a larger minibrot . . . Add about 5 more ever-larger minibrots and you'll get the idea. There is a perfect minibrot at the center of today's image. I have been down there to see it. But it is about 15 orders of magnitude deeper and not worth the time spent calculating it. The best scenes along the way are in areas where the number of surrounding elements resets itself to two, as it does in today's image. This resetting repeats quite a few times on the way down to the minibrot, which explains the name I gave the image, "Forever Reset". I could not rate a fractal which is just another scene deep on the main spike of the M-set, so I let it go un-rated. The calculation time of 6-1/2 minutes is true on the 2000mhz machine. On the 200mhz unit, it takes 1/2 hour to finish. So why not avoid the wait and check in at the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the completed image is posted for instant and effortless viewing. Fairly seasonal conditions prevailed here at Fractal central on Tuesday. The fractal cats approved of the temperature of 43F 6C but complained about the clouds that intermittently blocked their warm sunlight. A treat of tuna and cheese restored their good moods. My day was once again busy, and the fractal was once again found too hastily for top quality. The next in the long line of FOTD fractals will appear in 24 hours. Until then, take care, and keep those brain chemicals under control, or you might turn into a fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Forever_Reset { ; time=0:06:28.76-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.7397130566441\ 43559619196/0/2.541631e+021 params=0/0 float=y maxiter=3600 bailout=100 inside=0 symmetry=xaxis colors=000HeuKanNYhQUas66lBDeGJZLQxgyC3CG9HKFMOLRh\ tYclX_dXWXWBPtKQggVscTm_SgWRasJpZOgXPdVPaTQZ4uJAmN\ GeQMYTAuw0yWWFqULfUqFgJ0aMBXOMjSVcRWYQW6LZHOXsWHiU\ M`SR`9bYE`WIZUMX1fUA`VJVWyyjmmeba`oAzVsUUkVTdVSXW1\ 1nNu9PmFQeLRYRCzMKgRilh``aU9uTFlSLcNAhPGcRL_bu7XeK\ mmObaS1vfFe`MtsOlmPdgRXatS9eRL_XhXUcUS_dIpYMePJ5QM\ ERONHarHKYBhu1LhKKWbJJr55tJ6vW7xi8zv9sm6le4eY2d0bb\ Bg`LlaEkV3ga8kgDomIssNwpQsmSpkUmqONgTMZYLQaLQbKQbK\ yffgdVQbKKCxEPZ8a99OJWfsAATGFUMLVrV`iTZ`RXV3KuPQsI\ DiLK`OQgIlcKg_McWO_vQonQjfQeZQ`51rB8lHEfNK`MHgOKcQ\ N_9oNEhQJbSOWUCraGj_KcZOXXEUwITpLSiPRbqGahK__NYq4y\ BCMHHQNMT5PIBQMHQPNQTmMPeOSZPUk14aEIPAfQGbRLZvsyki\ oa_eOEAPHGQKLRNRVbHOTWQRWqR35oykbndYgYUa6_PHVTEkmy\ JHfSqZRfK_0MX8OVGQSO4i6AdDG_JMVQ4yFE6ut7OeHSMBvi2A\ YyEVgNKGONKRQNUVobTbZ4ZmAWhGUdMS_Ko4tI2lKAeMHZOP_6\ GXDMUKRGKlKMfOO`EXCJUJOSQ } END PARAMETER FILE=========================================

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FOTD 28-11-07 (Forever Reset [No rating])
by JimMuth＠aol.com 27 Nov '07

27 Nov '07

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Fractal books.
by John Wilson 27 Nov '07

27 Nov '07

Andy Kotlinski was the first to request these books, so I've asked for a snail mail address to where they should be delivered. Interesting. I had five requests and most were interested in The Algorithmic Beauty of Plants by Przemyslaw Prusinkiewicz. However, I'm sending out only one package to Andy... I don't want to go into competition with Amazon, by sending individual books hither and yon. I think that this book was also Andy's primary interest, and he may do a deal for the others. Try him out. John W.

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Re: Fractint Digest, Vol 57, Issue 9
by Marcus e Adriana 27 Nov '07

27 Nov '07

I would like to receive the book The Algorithmic Beauty of Plants ; Przemyslaw Prusinkiewicz If i´m the lucky one, please, contact me marcusadriana(a)mls.com.br Marcus Rezende

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Getting old and...
by John Wilson 27 Nov '07

27 Nov '07

I'm disposing of some books which I no longer wish to keep, and thought that someone in this group might want to own these Fractal classics: 1) The Fractal Geometry of Nature : Benoit B. Mandelbrot. 2) Fractals Everywhere : Michael Barnsley 3) The Algorithmic Beauty of Plants ; Przemyslaw Prusinkiewicz All in pristine condition, and you pay only the shipping costs. I don't know how I will determine the future owner if more than one of you respond to this offer! John W.

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Re:I am interested, please! [Fractint] Getting old and...
by Jacopo Longo 27 Nov '07

27 Nov '07

Hi, my name is Jacopo Longo, I live in Italy and I am definitely interested in those books of yours! Please, would you tell me what I have to do? I mean, how to send you the money etc etc? 'pirtine condition' = very good one? Thank you very much indeed, Sincerely Jacopo Longo, Roma (Italy) > I'm disposing of some books which I no longer wish to keep, and thought > that someone in this group might want to own these Fractal classics: > > 1) The Fractal Geometry of Nature : Benoit B. Mandelbrot. > > 2) Fractals Everywhere : Michael Barnsley > > 3) The Algorithmic Beauty of Plants ; Przemyslaw Prusinkiewicz > > All in pristine condition, and you pay only the shipping costs. > > I don't know how I will determine the future owner if more than one of > you respond to this offer! > > > John W. > > > > > _______________________________________________ > Fractint mailing list > Fractint(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >

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FOTD 27-11-07 (Orchid Orcas [No Rating])
by Jim Muth 26 Nov '07

26 Nov '07

FOTD -- November 27, 2007 (No Rating) Fractal visionaries and enthusiasts: I have little to say about today's very hasty Fractal of the Day except to advise the viewers to enjoy it as much as possible. It's a scene in the parent fractal that results when 4.5 nega- tive parts of Z^(-1.4) are combined with 1.4 negative parts of Z^(-4.5) and then (1/C) is added. This parent fractal is an overblown thing consisting of numerous bays and rings. Today's scene is located in a valley separating the two largest bays. I put too little effort into the image to give it a rating, though I did name it "Orchid Orcas". But do not bother to ask the meaning of the name. It makes no sense to me either. The parameter file takes a little over 3 minutes to finish. The best way to see the image is to go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view it there at leisure. An all-day rain made Monday most unpleasant here at Fractal Central. The temperature of 43F 6C was fair enough, but no one was able to enjoy it. The fractal cats enjoyed the rainy day however . . . from the comfort of the warm radiator. My day turned unexpectedly busy when a rush job came in, but the work was accomplished and delivered with little difficulty. The next FOTD fractal will be posted in 24 hours. Until then, take care, and make it real. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Orchid_Orcas { ; time=0:03:09.00-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=+0.592202073746/-1.866035687073/4977594\ /1/-62.5/0 params=-4.5/-1.4/-1.4/-4.5/0/0/0/0 maxiter=3200 inside=0 logmap=429 periodicity=10 colors=0000AR09X0BW0DX0FY0HX4JYBLZHNYKP`QRcWTd`Uff\ VglWfpYftYflYgdYjYYlQYmIYo9Yp1Yr0Zt0`v0bx0dr0fo2gj\ BjfKg`SfYZbSf`OmZKYM9H9000000000000910M90ZF0lK0xQ0\ zS4zSBzSHzUOzUUzUZzUdzWlzWpzWvzYzzYzzYzzYzzdrzlSzr\ 1zo1zl0zf0zb0zZ0zW0zQ0zM0zI0yF0x90v40t10r00r40oD0m\ K2lQ9jYFgdKflQdpUbjS`dSZYQYSQWKOUFOS9OQ1MO0MM0KK0K\ I0KIzDYzB`zBdzBgz9lz9oz9pz7tz7xz7zz4zz4zz4zz2zz2zz\ 2zz2zx7zv9zrDzpFzmIzlKzgOzfQzbUz`WzYZzW`zSdzQfzOgz\ SlzWmzZpz`rzdtxgxrjymmzgpzbrzYvzSyzMzzHzzBzz4zz0oz\ YWzzYztZzmZzf`xZ`xSbqKbrDdi4dm0Zj0Wg0Sd0Ob0KZ0HY0D\ U09Q04K01H00B00700100100700D00I00O00U00Y00`00b20gH\ 0mO0rY0xf0zo0zx0zz0zz0zz0zz0yz0vz0pz0lz0gz0dz0`z0Z\ z0Yz1Yz9WyHWvMUrUUo`SlgSgoQdtQ`pSYmSUlUQgUMfUIbWF`\ WBYY7WY2SY0QZ0MZ0KZ0Mb0Mf0Mg2Ol9OoFOpIOtOQxUQyYQzb\ SzgSzlSzpSztZzodzljzfozbtzYyzUzzOzzKzzHxzSgzbSzmIz\ v9zz0zz0zzHzzBzz2zy0zv0zt } 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 24-11-07 (Mossy Fractal garden [7.5])
by Jim Muth 26 Nov '07

26 Nov '07

FOTD -- November 24, 2007 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image in the Z^(1.618034)+C Mandeloid looks quite like a real three-dimensional scene. The three-dimensional effect was created by the coloring, but when I saw it, I started pondering the nature of reality. The question "What is the ultimate reality" can be logically answered in several ways. The specific answer depends on the world view and mind-set of the one who gives the answer. A materialist will confidently state that the material universe is the one and only reality. A true religious believer will agree that the material universe is real, but he will just as confi- dently add that there is a second reality, a spiritual reality where spiritual things such as God, angels and the spirits of the dead exist. A mystic will answer that both the material and spiritual worlds are basically illusions and that only conscious- ness is real. A fractalist will ask where fractals fit in. And I wonder where I fit in. Returning to the topic, I named today's image "Mossy Fractal Garden". Something about it reminds me of a pleasant little garden at the edge of a brook that I used to visit as a child. I can still remember the mossy rocks piled along the banks. The rating of 7-1/2 includes 1/2 point bonus for the coloring, which creates the mossy effect. Actually, the image is one of the better minibrots I have found in the Mandeloids with exponents between 1 and 2. Today's exponent, 1.618034, is the golden ratio, not that it makes much difference in the resulting fractal. What does make a differ- ence is the fact that I now use the function 'ident' instead of 'floor'. Using 'ident' is the same as using no function at all. I made the switch because the images created with the 'floor' function jump about in an irregular manner, while those created with 'ident' move smoothly up the logarithmic ladder, making animations feasable. (Not that I have any plans of creating any animations.) Today's image was created at ground level of the logarithmic ladder, where the parent fractal resembles an overturned turtle, with the scene of today's image located on a filament extending from the turtle's belly. The calculation time of 2-3/4 minutes is quite reasonable, as also is viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Much colder weather moved into the Fractal Central area on Fri- day. With the winds, the temperature of 36F 2C felt more like 25F -4C. The fractal cats kept close to any available source of heat for most of the day, while I kept as far from the local shopping mall as possible. The next FOTD fractal will appear in 24 hours. Until then, take care, and reality is all around us, if only we had eyes to see. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= MossyFractalGarden { ; time=0:02:43.18-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-0.694457057472/+0.729050695061/1536961\ /1/-72.5/-1.2758e-005 params=1.618034/0/0/0 float=y maxiter=5000 inside=0 outside=tdis periodicity=10 colors=00008Y06_06a04b02d01f00g00i00k00l00n00nzXpz\ TnzRntQlpOikNgfJfaI_OGXLETGDRBBO68N26L04I02G01G00G\ 02G06I09J0DL0GO0JR0LV0OY1Ra4Va6_bDfdTkdiqdzxdzzdzz\ dzzdzzdzzbiwaTn_DdYBXX9NV8ET69R42Q20Q06_0Ei0Nq0Vz0\ bz0iz0gz0gz0fz0fz0dz0dz0bw0bt0aq0an0_k0_g0_d1Ya1YY\ 2XX4XT4VQ6VN8TJ8TG9RDBR9BR8DT9EV9EX9GY9GY9I_BJaBJb\ BLdBLdBNfDOgDOiDQkDQkDRlETnETpEVqEzqEzpGzpGznGznGz\ nGzlGzlGzlIzkIzkIzkIziIziIzgIzgJzgJJfJJfJJfJIdJIdJ\ IdJJfIJfGJgGJgEJiDJiDJkBLk9Ll9Ll8Ln6Ln6Lp4Lp2Lp2Tq\ RaqpiqznftsXdxNOzD8z20z60z80z91wD4tE8sGBpIEnLIlNLi\ OOgRRfTVbVYaXa__dXagVbkTdlnJQz04x40n90dB0_G0VJ0QN4\ LQ9ITEDXL8_Q2bV0f_0kd0ia0g_0gY0fX0fV0dT0dR0bO0aN0a\ L0_J0_I0YG0YE0VD0RB0Q91N84J68I4BI4EI2IJ1JJ0NJ0OI0Q\ E0RB0T90R60R20V10X00R00V10Y60b90gE0lJ0qN1wR2zX4z_8\ zd9ziBzlEzqGzwIzzLzzNzzOzzRzzTzzVzzYzzazzbzzfzzgzx\ kzsnznpziszftzax0BV0BX09Y } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-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 PARAMETER FILE=========================================

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FOTD 26-11-07 (Take it or Leave it [?])
by Jim Muth 25 Nov '07

25 Nov '07

FOTD -- November 26, 2007 (Rating ?) Fractal visionaries and enthusiasts: Today's fractal image has texture, and lots of it. In fact, it might set a new record for texture. The scene of the action lies in the Z^(1.44225)+C Mandeloid as it appears a single turn up the logarithmic hyperspiral when the function is eliminated by setting it to 'ident'. The value of the exponent--1.44225--happens to be the cube root of 3. I chose it because I dislike absolutely random exponents. The parent fractal consists of a single large bay with an almost equally large triangular bud on its north side. Today's scene with its jagged and poorly defined minibrot at the center is located near a larger minibrot that lies on a filament extending east from this triangular bud. The near-ridiculous amount of texture was achieved by rendering the scene with the outside set to 'imag'. A high-contrast color palette increased the effect. I have no idea how to rate an image that I went out of my way to sabotage, so I let it go with a question mark for a rating. The name "Take it or Leave it" implies that I do not expect everyone to approve of such a harsh image. But the image is not a total loss. A careful examination reveals a subtle pattern amid the chaos, which just might make a worthy, more convention- al image if I were to emphasize it by more appropriate coloring. The included parameter file takes 3-1/2 minutes to run on the fast machine and 12 minutes on the slow one, a reasonable time by any standards. But if reason fails, do not panic. Simply rush to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> If the image is not already posted there for instant viewing, it soon will be. With 100-percent sunshine and light winds, the high temperature of 46F 8C here at Fractal Central on Sunday felt quite pleasant. The fractal cats agreed as they stretched on their shelf in the sunniest window. Except for a customer who for some reason called about his job at 11am, my day was totally without incident, the weird fractal notwithstanding that is. And speaking of fractals, the next one will appear in 24 hours. Until then, take care, and the philos- ophy of materialism is quite rational, and it makes good common sense, but what if the world does not obey the rules of reason and common sense? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Take_it_or_LeaveIt { ; time=0:03:36.83-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=+0.46417761748/+1.46578697867/211500.7/\ 1/65/0 params=1.44225/0/1/0 float=y maxiter=2500 inside=0 outside=imag logmap=202 periodicity=10 colors=000GS3DQ59N8BKBCIDEFGFDNAKLKQTGXUB_U5_U7ZU9\ ZUAZUCZUDZUFYUGYUIYUKYULYUNYUOYTQYQRYOTZLV_KUZJTYJ\ SYJRXIQXIPWIOWINVHMUHLTHKRGJQGIOGFOHINGLMFOMFRLEUK\ DXKD_JCbIBeIBhHAkG9nG9qF8tE7vE7uF8uF8tG8tG9tG9sH9s\ HAsHArIArIBqJBqJBqJCXKCQKCWKCoNDfPDmSDfUD`QEeOEdUE\ eZEgfFfhFekFdmFcoF`pKZpPWpUUpYZlXbhXfdXj`XnYXkWViV\ UgTTeSRcRQaPP_ONYNMWLLUKJSJIQHHOGFMEE852KDDICBGAAE\ 99C87A66855043422211IhBGdAFa9DY8CV7BR69O58K56H45D3\ 4A2261130cDD5CC5CC5BB5BB4AA4AA499499c8838c3c737736\ 63662662K5255244144133133122122011011000000zvBzsA0\ zA0z90z90z8zh82e72a70Y62W62T51Q51O4FL4JI3MG3PD2PA2\ U8UZ51t0zzzzzuntpiojdie_c`V`XSb_VVSOTQMQOKNLILJGUG\ EFECcCAA98c76544c22ZjHcVBBF5cKIGGFcDCAA9c66333wdCU\ `AwX9UT8wQ7UM6cI5UE4cB3U72U31muUmvUmwUmxUmmUmmUmmU\ mmUzzUzzzzzzzzzzzzzzzzzzzzzzzUzzUzzUzzUzzUzzUzzUzz\ UzzUzzUzzUzzUzzUzzUzzUzzU } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-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 PARAMETER FILE=========================================

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FOTD 25-11-07 (Imaginary Wilderness [5])
by Jim Muth 24 Nov '07

24 Nov '07

FOTD -- November 25, 2007 (Rating 5) Fractal visionaries and enthusiasts: Today's merely average fractal was found in the parent fractal that results when the formula Z^(2+0.01i)+C is iterated two levels up the logarithmic ladder. This parent at first appears to be a normal Mandelbrot set rotated so that its main spike faces southeast. But the surface appearance is deceiving. There is a split on the positive X-axis and the period-5 bud normally on the southwest shore of the main bay lies right on this split. It should come as no surprise that the features in the vicinity of the split are distorted. The minibrot in the center of today's image is a typical example. It appears to have gotten its north and south halves out of phase, with the two branches of Seahorse Valley no longer lining up. I named the image "Imaginary Wilderness" because fractals with complex and imaginary exponents are virtually unexplored -- at least by me. The rating of a 5 seems fair for a fractal done in such haste. The calculation time of just under 3 minutes may be avoided by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. The sun was bright here at Fractal central at sunrise on Saturday morning, but the temperature of 21F -6C promised a cold day. The fractal cats slept until it warmed to above freezing. My day turned busier than expected when I let F.L. talk me into a trip to a local antique mall to see the stuff that someone else threw away. (Actually, I kind of enjoyed it.) When we returned around sunset however, the cats were sulky at having been left alone for most of the day. The next FOTD will be posted in 24 hours, for all it is worth. Until then, take care, and search for the secret. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= ImaginaryWildernes { ; time=0:02:54.25-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=+0.8488258557/-0.0209973644/15601.18/\ 1/82.5/-3.5510218377e-010 params=2/0.01/2/0 float=y maxiter=5000 inside=0 logmap=203 periodicity=10 colors=0008FA9FCAGDAGEAHEAHFAIFBIGBJGBJHBKHBKICKJC\ LJCLKCMKCMLDNLDNMDOMDONDPNEPOEPPEQPEQQERQFRRFSRFSS\ FTSFTTFTTFTTLYWRbZYh`cmcirfowhlsgjpfhmefiddfcbcb``\ aZX`XU_VRZTOYRKXPHWNEVJATLBUNCVODWQEWRFXTGYVHZWIZY\ J_ZK``LaaMacNbeOcfPchQdiRekSflTfnUgpVhqWisXitYjvZk\ xYlwZkvZkuZktZjsZjsZjrZiqZipZioZhnZhnZhmZglZgk_gj_\ fj_fi_fh_eg_ef_ee_de_dd_dc_cb_ca_ca_ca_ca_ca_cb`ac\ a_dbYecWfdUgeSgfQggOfgMffKffIeeGedEddCdcAdc8cb6ca6\ ca6b`6b`5a_5a_5aZ5`Y4`Y4`X4_X3_W3ZV3ZV3ZU2YU2YT2_U\ 0YT2XS4VS5UR7TR8RQAQQCPPDNPFMOGKOIJNJIMLGMNFLOELQC\ KRBKT9JV8JW7IY5IZ4H`0Gb3Ha5Ia7J`9J`CK_EL_GMZIMZLNY\ NOYPPYRPXUQXWRWYSW_SVbTVdUUfVUiUUhVWgVYfV_eVadVccW\ ebWgbWiaWk`Wm_XoZXqYXsXXuWXwVYyWXzXWzXVzYVzYUzZTzZ\ Sz_Sz`Rz`QzaPzaPzbOzbNzcMzcNzdOzePzeQzfRzfSzgTzgUz\ hUziUziUzjUzjUzkUzkUzlUzmUzlUzmUzmUzmUzmUzmUzmUzmU\ zmUzmUzmUzmUzmUzmUzmUzmUz } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-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 PARAMETER FILE=========================================

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FOTD 23-11-07 (Forever Nameless [No Rating])
by Jim Muth 22 Nov '07

22 Nov '07

FOTD -- November 23, 2007 (No Rating) Fractal visionaries and enthusiasts: Today's image is a scene in West Valley of the Z^(3.001)+C Mandeloid, which is entirely different from East Valley. Unfortunately, this difference is totally invisible in today's image, which could just as easily have been found in West Valley of the much-simpler Z^3+C Mandeloid. I named today's image "Forever Nameless", which is kind of a paradox, since I will never know for sure whether the image actually has a name. Of course, the image is not rated. I could never rate a fractal that I found with my eyes almost closed. The only thing saving the image from the waste-basket is its calculation time of only 22 seconds, which is faster than the speed of light in water. And if even this is too slow, the finished image will soon be posted for instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A sunny and warm morning was interrupted by a midday shower, followed by a sunny but breezy and cooler afternoon here at Fractal Central on Thursday. The temperature reached 66F 19C just before the shower arrived. I was too busy eating to take too much notice of the weather, while the fractal cats were too busy begging treats from the table to care about it. The next FOTD will be better planned and will arrive in just about 24 hours. Until then, take care, and seek until you find. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Forever_Nameless { ; time=0:00:22.11-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot4 center-mag=-0.397860578\ 06555000/-0.00251690882813523/6.89109e+007/1/-97.5\ /-1.58e-005 params=0/0/0/0/0/0/0/0/3.001/0 float=y maxiter=1800 inside=0 logmap=99 periodicity=10 colors=000UKcUKdUKeUKfUKgUKhUKiUKjUKkULlTMmSNnROoQ\ PpPQqMRqJRsGRuDQxERxFRxGSwHSvITuJTtKUsLUrMVqNVpOWo\ PWnQWmOXnNYoMZoLZpK_nJ`jH`gI`fK`cP_aUZZ_YVdXRhWNlU\ JnSFoPKnMPlJUhJZcKcZMeUNgPOiKQgCTdIVdOY`U_Q_aIdbAh\ b3ib5ib7ja9jaBj`Dk`Fk`Gk_Il_KlZMlZOmYQmYSmYTobVqgW\ rlYtqZuu_pvdkvifvmavrXvvTnfQgRN`CLYEJWGIUHGRJFPLDN\ MCLOAIQ8GR7ET5BV49W27Y15Z6D`AKaERcJZdNefRlgVshUncT\ j_SeWRaSQYOQTKPPGOLCNG8MC4M80NA2NC3NE4OG5OI6OK7OM8\ POAPQBPSCQUDQWEQYFQ_GPYIPXJPWKPVMPUNPTOPRQPQRPPSPO\ UPNVPMWRJVSHVTFVVDVWBVX9VZ7V_5V`3Va1Vc2Xd3Ze4`g5bh\ 6ci7ej7gl8im9knAlpBnqCprDrsDslCnfCi`BdVB_PAVJAQDAL\ 9TO6kQ3lR0lS2kT3kT4jT5jT6jU7iU8iU9iUAhUBhVChVEgVFg\ VGgWHfWIfWJfWKeWLeXMeXNdXOdXPdXTeUWfRZfPagMdgKhhHk\ iEniCqj9tj7ri9phAngClgDjfEheGfdHddIbcKFVa`bLZaMXaO\ V`PT_QRZSPZTNYULXWJWXHWYFV_DU`avg_tfZrfXqfWoeUmeTl\ eRjdQidPgdNecMdcKbciE2gF4 } frm:SliceJulibrot4 {; 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=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 22-11-07 (A Fractured Valley [8.5])
by Jim Muth 21 Nov '07

21 Nov '07

FOTD -- November 22, 2007 (Rating 8.5) Fractal visionaries and enthusiasts: Today's striking image needed no special hand-written formula to create it. The built-in manzpower formula did the job all by itself. The parent fractal is the Z^(5.001)+C Mandeloid, which on the surface looks exactly like the Z^5+C Mandeloid. But this surface similarity is deceiving, as the valley on the negative X-axis is entirely different. Today's scene lies quite deep in the debris lining the edge of this valley, which resembles a wedge more than a fractal valley. I named the image "A Fractured Valley". One look at the image will explain the name. The rating of 8-1/2 includes a half- point bonus for my coloring work, which really is the better part of the image. The calculation time of just under 4 minutes is well within reason for such a worthy image. And if unreason prevails, the finished GIF image will soon be posted to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Wednesday began chilly, damp and dreary here at Fractal Central, but a warm front passed at noon and the afternoon turned most pleasant. The sky cleared and the temperature shot up from 43F 6C to 64F 18C. The fractal cats approved of the improved condi- tions and eagerly watched the squirrels that came out to gather last-minute nuts in the yard. My day was routine, but tomorrow is Thanksgiving Day in the U.S., and F.L. says there is a special dinner in the works. Regardless, the next FOTD will appear in 24 hours. Until next time, take care, and don't give up the fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Fractured_Valley { ; time=0:03:52.39-SF5 on P4-2000 reset=2004 type=manzpower passes=1 center-mag=-0.5\ 354169829881127/-0.00042766186970615/7.515239e+011\ /1/-127.5/-0.03 params=0/0/5.001/0 float=y inside=0 maxiter=3600 logmap=472 periodicity=10 mathtolerance=0.05/1 colors=000UWAVM8WD7_M6cV6gc5kl5mu5huUctcZs_UqOSoVQ\ jaVehZan`clbekdgifhhhjgjlelndnocl`LkN3kV5kb7ki9ekC\ _lFUmIOoLIpOCqQGddJTrd_zhewljtpoqstndnZRhKDc5K_7QX\ 8WT9aQAhNCnJDtGEzDFrHJjLMbPQWSTOWXG__8cc1ffC`bMWZW\ RWeMSoHPhXRblSW`aQPkKEtPHpTKmXMj`PfdSchU`lXXp_UtaR\ u_SuYTuWUvUVvSWvQXwOYwMZwK_xI`xGaxEbyCcyAdy8erJ`kU\ WlzwhxwjuwflsfhkYaVXcWVeWUgXTiYRiYQjZPjZNk_Mk_Ll`K\ l`NjbQicThdVgfYeg`dhbcjebkh`lj_nmZopYprXqnamj`gg_b\ dZXaYSZXMWXHXYIXZJX_KX`LY`LYaMYbNYcOYdPZdPZeQZfRZg\ SZgSHS_0Cg7AcE8`L6XS4UZ2Qd1Na2M_2LY2KW2JT2JR2IP2HN\ 2GL2GN5FP7ER9ETBDVDCXFCZHB`JAbLAdN9eP9`MVSYdByV_wm\ MdedDScGRbIQaLP`OO_QN_TNZWzYYLX`KWcJVeIUhHUjHVfIVc\ JV`KVYLVVMVSNVPNWMOWJPWGQWDRWASWKTWPT8UpCZnFclJhjM\ mhQrgTveXzc_zacz`fzZjzXmzVpzUozXnz_mzalzdkzgkzimzh\ nzhozhnzjmzllzmkzokzphzkezgczc`zZZzVWzRUzMRzIPzE`z\ MmzUyzatzbozbjzbfzb5zRTzC } END PARAMETER FILE=========================================

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FOTD 21-11-07 (Zoom Out to Windmills [No Rating])
by Jim Muth 21 Nov '07

21 Nov '07

FOTD -- November 21, 2007 (No Rating) Fractal visionaries and enthusiasts: Today's FOTD is a simple outzoom from yesterday's image. I had to post it because I think it is somewhat of an improvement over yesterday's version. Of course, there is no way I could rate a near-repeat, so I let it go un-rated. When I did the outzoom, the image reminded me of a whole wind- mill farm, thus the rather cryptic name "Zoom Out to Windmills" The calculation time of 1-1/2 minutes is quite fast considering the maxiter of the image and how much of it consists of 'inside' stuff. Yes, a good part of today's image, as well as most of yesterday's, is made of 'bof60' inside fill. To see just how much, change the inside option to 'numb'. Now a word about the missing characters in some of my parameter files. I think this happens when I cannot connect to Mindspring and must post the FOTD through AOL, which appears to send email in html format. And there is a bigger problem. The philofrac- tal list rejects html format. This explains the missing philo- fractal postings. Finally, if the finished image is unavailable on the FOTD web site, give Paul a chance to render and post the image, and try again later. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Continued dull, dreary, damp and chilly weather prevailed here at Fractal Central all day Tuesday. The rain ended at daybreak, but then a fog set in, which covered the area for the rest of the day. Due to the dampness, the near-normal temperature of 41F 5C seemed much colder. The fractal cats must have agreed, for they hugged the radiators most of the day. My day was average, with nothing of unusual importance to make it memorable. The next in the unending line of FOTD images will be posted in 24 hours. Until then, take care, and, (SQOTD), no one has ever seen an atom, so how do we know they exist? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= ZoomOutToWindmills { ; time=0:01:24.08-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot4 center-mag=0/0/2.423648 params=90/90/90/90/-1.222743994189852/2.3436721194\ 31135e-006/0/0/4.003/0 maxiter=2500 inside=bof60 float=y symmetry=origin periodicity=10 sound=off colors=000W_aYY_VVXTTWRRUPPSNNQKLNIIKGFHECEA9AGAMK\ ATSOGXRJaTNfWQkZUp`Xuc`zecvddrdencfjcgfbhbbiZajVaj\ ZXbbTWfPPjLIlMLnNOoOQqPTsQVtRYvS_xTbyUdvLZsDTq5OpB\ LoGJoMHnREmXCmaAkZBjWCiUDhRDfPEeMFdKFcHGbEH`CI_9IZ\ 7JY4KX2KVGRTTYRedQrji8icAbZBXiNQkKKlMEiQFpQGvUGuYH\ tbIugIzlJzpJzlIyiIufHtbHt_HsXGrTGqQFpNFpKFlLJhMNdM\ Q`NUXNXUO`QOcMPgIPjEQnBQqzPnzSkzVizXgy_exbcwdaug_t\ jXslVqoTprRotPmwNlzLkzJmxLnuMorNpoPqkQrhRseStbUu_V\ vWWwTYxQZyN_zK`zIayGayEbyCbxAcx8cx6dy2ex4dw5dw6cv7\ cv8cu9buAbtBbsDasEarF`rG`qH`qI_pJ_nCWpK_rRcsZfuejw\ mnzuswwwwwwzzzzzzzzzwwwwwwwsowofwndwmcwmawl`xk`wl_\ wl_wm_vm_vm_vn_un_uo_uo_ljtuo_ztGzsFzsEzsDzrCzrBzr\ Azr9zq8zq8zq7zp6zp5zp4zp3zo2zo1zo0zq0zo0zm2zk4zi6z\ g8zeBzcDzaFz_HzYJzWLzUOzSQzQSzOUwMWtKYqI`nGbkEdhCf\ eAhb8j_EgYKdYPaZVZZ_WZeT_kQ_oN_oK_oHXoKVoNToQRoTPo\ WNoZLoaJodMocOocQobSnbUka } frm:SliceJulibrot4 {; 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=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD November 21, 2007 (Zoom Out to Windmills [No Rating])
by JimMuth＠aol.com 20 Nov '07

20 Nov '07

1 0

Fractint version 20.4 patch 7
by Jonathan Osuch 20 Nov '07

20 Nov '07

Folks, Fractint (and Xfractint and Winfract) version 20.4 patch 7 is now available on the developer's web sites: www.fractint.org or www.fractint.net What's new: Added feature to write the base map name to the first line of the file when a map file is saved and the only change has been a rotation of the palette. The base map name is then read in and used as the current map name when the new map file is restored. The recordcolors=comment command line option has been modified to not create a comment line in PARs. Two colors= entries are now created with the first one in the format colors=(a)fname.map and the second in the format colors=000<24>0n0...010. When a PAR entry is read, the first colors= sets the map name, and the second colors= effectively rotates the colors. Updated the Xfractint Makefile to install using sudo instead of as root. Jonathan

4 6

FOTD 19-11-07 (All Broken Up [5.5])
by Jim Muth 20 Nov '07

20 Nov '07

FOTD -- November 19, 2007 (Rating 5.5) Fractal visionaries and enthusiasts: Today we forget the user-created formulas and return to one of the formulas hard-coded into Fractint. The formula in question is type=manzpower. I brought up this formula because I started wondering about the Z^(4.003)+C Mandeloid. Another Mandeloid, the one created by the formula Z^(2.003)+C, has a very interesting area just east of a large broken minibrot on its main spike, which has broken into infinitely divided fractal railroad tracks. I wondered if the corresponding area of the Z^(4.003)+C Mandeloid is equally interesting. Well, the area is not quite as interesting as it is in the Z^(2.003)+C Mandeloid, but it still holds several interesting and quite similar features. Once again, the main spike is infinitely divided, especially in the area around the eastern edge of the large minibrot. But, as today's image shows, the features break apart in a different manner. A good part of today's image consists of 'inside' stuff made visible by the 'bof60' inside fill and colored by none other than myself. But even the coloring cannot make a work of art out of a casual fractal created with near-zero inspiration, so I could rate the image no higher than a 5-1/2, which is just the tiniest bit above the long-term average. The name "All Broken Up" describes the scene, which certainly has come apart into enough pieces. Unfortunately, the calcula- tion time is a rather slow 9 minutes even on the fast machine. And on the old machine the image would take nearly an hour to complete. The best way to avoid this delay is to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and see the finished image there. This same area in the Z^(2.003)+C Mandeloid has very curious rectangles in its Julia sets. I must check soon to see if the Z^(4.003)+C Mandeloid has something similar, perhaps octagons. Light to moderate snow fell all day Sunday here at Fractal Central, though a steady temperature of 34F +1C confined the accumulation to the grassy areas. The fractal cats watched the flakes falling past the window for an hour or so, then decided it was too chilly there, and settled next to a warm radiator. My day was on the slow side. I have every hope that tomorrow will be the same. The next FOTD will be posted in 24 hours. Until then, take care, and a brief glance through a book about quantum chromodynamics (or quantum anything) will reveal that the world appears to be made of numbers. At least this is what the high priests of science would appear to be saying. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= All_Broken-Up { ; time=0:09:05.80-SF5 on P4-2000 reset=2004 type=manzpower center-mag=-1.2227439940\ 46724/-0.000002343682231/8.062602e+008/1/61.75/\ 2.86744777859559985e-007 params=0/0/4.003/0 float=y maxiter=5000 inside=bof60 periodicity=10 colors=000RhzTcvQ_rOXmMUhKScIQZFOVDMRBKM9HI7EGDHDI\ KGNMKSPNXRRaUUfXYkZ`paducgqbhmbiiajeaka`lY`mU_nQ_n\ UVfYR_aNTeJMgKPiLSjMUlNXnOZoPaqQcsRftShqJbnBXl3Sk9\ PjENjKLiPIhVGh_EfXFeUGdSHcPHaNI`KJ_IJZFKYCLWAMV7MU\ 5NT2OS0OQEVORaMchLpnd6mZ8fU9`dLUfIOgKIdOJkOKqSKpWL\ o`MpeMnjNsnNrjMqgMpdLo`LoYLnVKmRKlOJkLJkIJgJNcKR_K\ UWLYSL`PMdLMgHNkDNn9Or6OuzNrxQowTmvVktYis`grbepeco\ h`njZlmXkpVjrThuRgxPfzNhvPisQjpRkmTliUmfVncWo`YpYZ\ qU_rRasObtLcuIduGetEetCftAfs8gs6gs4ht0is2hr3hr4gq5\ gq6gp7fp8fo9fnBenCemDdmEdlFdlGckHciA_kIcmPgnXjpcnr\ krtswsrusqtsqrspqsoosonsnmrmkrmjrlhrkgrkerjdsidrjc\ rjcrkcqkcqkcqlcplcpmcpmcghxpmczrKyqJxqIwqHwpGvpFup\ EtpDtoCsoCroBrnAqn9pn8on7om6nm5mm4no1mm4lk6ki8jgAi\ eChcFgaHf_JeYLdWNcUPbSSaQU`OW_MYZK_YIaXGdWEfVChUAj\ T8lS6nTCkTIhTNeUTbUY_UcXViUVnRVtOVyLSzOQzROwUMxXKx\ _IxbGxeExhHugJrgLofNlfPie } END PARAMETER FILE=========================================

4 3

FOTD 20-11-07 (Julia Broken Up [6])
by Jim Muth 19 Nov '07

19 Nov '07

FOTD -- November 20, 2007 (Rating 6) Fractal visionaries and enthusiasts: Today's image is named "Julia Broken Up" because it is the Julia set of the center of yesterday's 'All Broken Up' image. As such, it shares many of the features of that image, as well as virtually the same color palette, but at the same time it brings enough new aspects to make it worth being chosen as the FOTD for November 20. With nothing really totally new to offer, the image could hardly be rated much above a 6, and in fact, this is what I rated it. Perhaps the most interesting thing about the image is yet to come. I could have created the image more directly with the type=julzpower formula, but I used the SliceJulibrot4 formula instead. I did this because I am curious as to the appearance of this area of the Z^(4.003)+C Julibrot when sliced in the four remaining mutually perpendicular planes of the four-dimensional space in which it lies. I will check these other orientations sometime tomorrow, and if I find anything of unusual interest, I will include it as tomorrow's FOTD. The calculation time of 4-1/2 minutes is thankfully brief. Even briefer is a visit to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the finished GIF image there. Very unpleasant weather prevailed here at Fractal Central on Monday. Not only was it cloudy and just above freezing all day, but the melting slush made walking a major effort. The fractal cats passed the day keeping warm. My day was just busy enough to keep my mind off the miserable conditions. The next FOTD will appear in 24 hours. Until then, take care, and search for the real reality. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Julia_Broken-Up { ; time=0:04:25.07-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot4 center-mag=0/0/18.8653/\ 1/22.5/0 params=90/90/90/90/-1.222743994189852/2.3\ 43672119431135e-006/0/0/4.003/0 float=y maxiter=2500 inside=bof60 periodicity=10 colors=000RuzThvQdrO_mMWhKTcIQZFOVDMRBKM9HI7EGDHDI\ KGNMKSPNXRRaUUfXYkZ`paducgqbhmbiiajeaka`lY`mU_nQ_n\ UVfYR_aNTeJMgKPiLSjMUlNXnOZoPaqQcsRftShqJbnBXl3Sk9\ PjENjKLiPIhVGh_EfXFeUGdSHcPHaNI`KJ_IJZFKYCLWAMV7MU\ 5NT2OS0OQEVORaMchLpnd6mZ8fU9`dLUfIOgKIdOJkOKqSKpWL\ o`MpeMujNznNvjMtgMpdLo`LoYLnVKmRKlOJkLJkIJgJNcKR_K\ UWLYSL`PMdLMgHNkDNn9Or6OuzNrxQowTmvVktYis`grbepeco\ h`njZlmXkpVjrThuRgxPfzNhvPisQjpRkmTliUmfVncWo`YpYZ\ qU_rRasObtLcuIduGetEetCftAfs8gs6gs4ht0is2hr3hr4gq5\ gq6gp7fp8fo9fnBenCemDdmEdlFdlGckHciA_kIcmPgnXjpcnr\ krzswzruzqtwqrwpqvootonsnmrmkrmjrlhrkgrkerjdsidrjc\ rjcrkcqkcqkcqlcplcpmcpmcghxpmczrKyqJxqIwqHwpGvpFup\ EtpDtoCsoCroBrnAqn9pn8on7om6nm5mm4no1mm4lk6ki8jgAi\ eChcFgaHf_JeYLdWNcUPbSSaQU`OW_MYZK_YIaXGdWEfVChUAj\ T8lS6nTCkTIhTNeUTbUY_UcXViUVmRVmOVmLSmOQmROmUMmXKm\ _ImbGmeEmhHmgJmgLmfNlfPie } frm:SliceJulibrot4 {; 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=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 18-11-07 (Zexpi Minibrot [4])
by Jim Muth 17 Nov '07

17 Nov '07

FOTD -- November 18, 2007 (Rating 4) Fractal visionaries and enthusiasts: I had one of those days Saturday where I just couldn't find a worthwhile fractal no matter how far I looked. I finally settled for the image that appears as today's FOTD, but even though it appears as an FOTD, I could honestly rate it no better than a 4. The image takes us on a trip to the Zexpi fractal, which is what I named the fractal with an exponent of Z equal to PI. We check the fractal as it appears 4 levels up the logarithmic ladder, where it resembles a comical little clown with his head facing southwest. Today's scene is located on the sole of the clown's left foot. The only thing not totally ordinary about the image is the fact that a good part of it consists of 'inside' stuff made visible by the 'fmod' inside fill. I named the image "Zexpi Minibrot", which is simply its descrip- tion. The calculation time of just under 3 minutes stretches to around 14 minutes on the 200mhz machine -- hardly a bargain. But relief is waiting on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is posted for instant viewing. A cold, cloudy day threateneing rain or snow made no one happy here at Fractal Central on Saturday. The fractal cats spent the day on their shelf by the window, bravely enduring the unpleas- ant conditions. My day was average -- enough said. The next FOTD will appear in 24 hours. Until then, take care, and how many Mandelbrot sets exist at this moment? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Zexpi_Minibrot { ; time=0:02:40.43-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=floor center-mag=+0.17206725258491350/+0.675860279367873\ 30/33541.71/1/-57.5/-1.49841909713e-010 inside=fmod params=3.14159265358979/0/4/0 float=y maxiter=1800 proximity=0.09 logmap=yes periodicity=10 colors=000000000000000000000000000000000000deYbhYa\ kY`mYg8Gj9DlABoB9qC7sD5rC7qC9pBAoBCnAEmAFl9Hl9Ik9K\ j8Mi8Nh7PC6Ff6Se6Ue6VM2WL3UK3SJ4QI4PH5NG5LF6KE6ID7\ GC7EB8DA8B9998987CI6FS6Ia5Lk5Ot7Rq8Ur9XsAlkBriCxgF\ rbHmYJhTLbONYJPTER_tTSDVSDA_tYSC_SCaSBA_tAbuAevefI\ enMeuPgrOioOklOmjOogOqdOrbOrYKrTGrPCrK8rF4rB0pD3oE\ 5nG7mH9kJBjKDiMFhNIgPKeQMdSOcTQbVSaWU`TV_QV_OWZLXZ\ IXYFYYDYbIXgMWlRVqVVo`PmfKklFirAhx5fu7er8co9blA`iB\ _fDYcEX`FVYGUVHSSJRPKPMLDOFGMIJJLMHOPFQTDTWBWZ8Za6\ ad4dg2gj0ie4ha7hXAhTDgOGgKJgGMgILeJLcKKaLK`NJZOJXP\ IWQIUSHSTHRUGPVGNXFMYFKZEI_EHaIJcMKePLgTNiWOk_PmcR\ ofSqjTrmUpkRniPlgNkeLicJgaHe_EdYCbWA`U8ZS6YR4kKLyE\ `qzTmvUirVeoWakWZhXVdYRaYNYZKV_GR_CO`8Ka5Ha6F`7E`8\ D`9B`AA`B9`C7`D6`E5`F3`G2`H1`H0`K4aN7bQAbTDcWGdZJd\ aMedPecQgbRhaSiaTj`Uk_Vl_VmZWnYXoYYpXZqW_rW_sR`mNa\ hJbbFcYBdS7eNTOCgEMv4Wt7X } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-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 PARAMETER FILE=========================================

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xfractint again
by John Wilson 17 Nov '07

17 Nov '07

O.K. Stone Soupers! What's the status of xfractint, please? I'm lost. One of Paul's links is for an "Xfractint 20.4.4" which takes me to a fractint.org page. This page references: a) Scott Boyd's obsolete page and "xfrac20.2.04-bin.tar.gz"... a compiled package. and b) the developers ftp site, where I see "Xfractint 20.04p06.tar.gz", and "xfradev.tar.gz". Meanwhile I find, in the Ubuntu Linux distribution, an xfractint 20.4.00-1. At this time I have 20.4.00-1 installed and running. I'd be reasonably happy with this, in spite of the loss of colour cycling and some strange key assignments, if I could find, or simulate, an sstools.ini file. I am told that my initial colour problem was caused "because Xfractint can't find the sstools.ini file or the default map file". I'm not surprised that Xfractint can't find the sstools.ini file... neither can I! I don't believe that the packages I've tried include such an animal. If I manually navigate to a par which includes the colors, all is well. Beyond that I'm "sstools-less". I am also told that "the latest developer's version installs the sstools.ini file in /usr/share/xfractint and the map, par, frm, ... files in the applicable subdirectories". Well, sstools isn't there, and please don't tell this newbie that files are in "the applicable subdirectories". :-) Does xfractint really use an sstools.ini file? Does Linux recognize .ini files in "the applicable directory"? I know, I know... I should compile source packages, but I can't - yet. I need the spoonfeeding which is provided by a package manager. Help! John W. (who has also changed his ISP).

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FOTD 17-11-07 (Forty-Ninth Radical [6.5])
by Jim Muth 16 Nov '07

16 Nov '07

FOTD -- November 17, 2007 (Rating 6.5) Fractal visionaries and enthusiasts: Today's image, which is named "Forty-Ninth Radical", takes us once again to the Mandelbrot set. The name has no connection to the Forty-Ninth Parallel that separates Canada from the U.S. It refers instead to the tiny radical with a periodicity of 49 on the south shore of East Valley of the M-set. A radical refers to all the stuff, such as filaments and sub-bays, associated with a particular bud of a particular periodicity. I think Mr. Mandelbrot himself created the name. Today's image is located deep in the star associated with the 49th radical. Virtually the entire effect of the image is due to the coloring, so I had no choice to reward myself an extra half-point for the color work, making the image worth a grand total of 6-1/2. The prominent octagon with rounded corners that surrounds the minibrot in the image appears to be somewhat askew. Actually, it is perfectly straight. All the crookedness is a true part of the Mandelbrot set at this point. The calculation time of a lightning-fast 15 seconds is true on the fast 2000mhz machine. On the slow 200mhz unit the same image takes over 5 minutes to finish. One would assume that a machine 10 times as fast would calculate a fractal in 1/10 of the time, but my machine does it in 1/20 of the time, at least with the type=mandel and type=julia fractals. Curiously, with type=formula images, where I do most of my fractal work, the fast machine finishes in only 1/5 of the time. All this confusion about calculation time can only detract from the worth of the image, so why not view the finished product on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and end the day with fractal satisfaction. Cloudy and blustery weather with near freezing temperatures prevailed all day Friday here at Fractal Central. A few insig- nificant flurries of snow simply added to the interest. The fractal cats must have been annoyed by the conditions, for they got into a tussle when Cassie took Nico's favorite spot in the window and he had to bat her out of the way. An hour later however they had made up and were washing each other's ears. My day was busy enough to keep boredom at bay, but not too busy for relaxation. The next FOTD will appear in 24 hours. Until then, take care, and things are not always as they seem. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= FortyNinth_Radical { ; time=0:00:15.09-SF5 on P4-2000 reset=2004 type=mandel center-mag=+0.2540484531638\ 9070/-0.00041135003772769/3.848895e+010/1/-124.5/\ -2.25460584006437204e-005 params=0/0 float=y maxiter=50000 inside=0 logmap=-6510 periodicity=10 colors=000obaobaobaobasi`rh`qf`pe`obanbamaal_akZaj\ XaiWahVacXb_YbVZbR_bM`bIbbDcb9db4eb1fb7i_EkYJmWQoT\ WrRatPgvMnxKszICL3DN6EP8FRBFTDGVGHXIHZLI`PJbUJdZKf\ cLhgLjmMmrMowMmzMcyMUxMKkWCcaLUe0TzfLwcLuaLq_LoXLk\ ULiRLfNLdKLbHLXINSMPNPRXQt_WzbZze`zgczjfxmhypkzrmz\ ocqlUiiK`fBTeMSeWSdeRdoRWjWNe_E`d5WhM_qbczxUYtRXqO\ XnLWkJWhGVeDVbBVCcbKedSffZggfiinjkuklgehU_dHU`LcqO\ `jQYdSWYUTSWQMYOF_L9aJ3eP9iVFm`KqfQulWxq`luJax2`n2\ `e2_X2_O2ZF2Z62TkCYhSSgUNfWIeXMg_PhaTjdWkf_mibnkYh\ lTbmOXnJRoEMpbTsz_vvapscjkcicciXchPchIchYuHSqFNmDH\ iBCe96a71Y61`A1bE1dH8bJE`LK_NQYPWXRaVTgUV3BAALDHVF\ OcHVmJavL_rNYnPWkRUgSScUQ`W9XP9RO9MNBPSDRWFU_HWcJY\ hL`lNbpOdtGav9_x2Yy7TvCOtHJrMEpQ9nPHlPPjPXiOcgOkfO\ sdOzcotLmsMkrMiqMgpMeoNcnNamN_lN`nPaoUbpZbrccshdtm\ durbvvawz`xz`yz_zzZzzZzzYzzYzzZzzZzzZzzZzzXzzVzzUz\ zVzzSzzQzzNzzezzlzzszzyzz } END PARAMETER FILE=========================================

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FOTD 16-11-07 (A Seahorse Named Epsilon [6.5])
by Jim Muth 15 Nov '07

15 Nov '07

FOTD -- November 16, 2007 (Rating 6.5) Fractal visionaries and enthusiasts: It turns out we're still in the Zexpe fractal today, or at least one of the Zexpe fractals, since there are an infinity of them. And we're also still at the fourth level of the logarithmic ladder. Today we check the main-bay side of the southwest branch of what corresponds to Seahorse Valley of the parent fractal, where we find today's strangely realistic scene. I named the image "A Seahorse Named Epsilon" because it lies in a parent whose generating formula is Z^(e)+C. A rated it at a modest 6-1/2, one-half point of which is due to my coloring. The calculation time of 2-1/3 minutes is reasonable. It is equally reasonable to view the image by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it has already been calculated and posted. Heavy rain fell all night Wednesday here at Fractal Central. By the time it ended at 11am Thursday, 3.6 inches or around 90mm of rain had fallen. The rest of Thursday was cloudy and blustery, with a temperature of 45F 7C. A few puddles appeared in the new fractal cellar during the downpour, but nothing like the several inches that used to flood into the old fractal basement during heavy rain. The fractal cats slept through it all. My day was adequate. Hopefully, tomorrow will be the same. The next FOTD will appear in 24 hours at this same internet spot. Until then, take care, and if I could, I would go back to the year 1900 and spread the news that fractals were coming. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Seahorse Named_E { ; time=0:02:20.66-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=floor center-mag=+0.5129196182676702/-0.567400274301192/\ 1.208445e+010/1/37.4997739850628022/0.000251376\ 462945825108 params=2.71828182845905/0/4/0 float=y maxiter=4800 inside=0 logmap=228 periodicity=10 colors=000cRm_PjWNjSMkKRdIT_LTVIOcGT6EP7bhoBYoCSTJ\ WUFRIISwy`X`TK5gV9XJGpQEeJDWDbQJWPGPODINA9uaAlUBcM\ CVEZOQRNJJMDl`9_W8OR7v7mfCZRHLsSudQdQOOI0vv_MZTEgb\ t_YgSUWKQJlPu_OdONOF58EA7DE7CI72jB7Y99hm6qR9aHgJPN\ OE2T4S3vTFwTQwU`xUkxZ`jz_XzRJuK5mFBgA0a50Y00T00P00\ 5bx9UYaBGTFDKJAa0cV6VPBNIHFixoAJ0BK2BL4CM6A4IB9FBD\ CCI9d7_VCQLHG2bg7UP1UZ_BmuwqimeZdUNVIVOHxhW8baAUMh\ umYiZNYLAyPBeG671t8YhCRYFKNJDekrWbbMUNKXoGRTFpOEeI\ DWCaXIVUFPRCIO9SmbMcSHVHNq8Ha7gIsXKbMLNV1GmO`cNTVN\ MLMEbwXGaiEUQUeUUaUCWICRCFI4EJ5DK6CL7GEmFGbEISDKH1\ zpedP826A97BG7A05BB6E9nDGTwhsg`bSTNPIzIKzoozW`zEZz\ DSz9YzTEzOGzKIzGKzBozCezCWzGvzEizDKzH6zFAzEEzDIz6v\ zW9zMGzNZzKVzHSzEPz53z8AzAGzPjzLzZIzQFzGIzrLzvGzX1\ zbVzZOzPIzG6zs9zVQzH1zA7z8YzkzzlzzSzzHzzCzzizzizz7\ zz7zzSzzMzzHzzCzzAzz8zzYzzKzzvzzvzzXzzazztzzczzNzz\ VzzQzzLzzGzzBzzUzzIzzvzzX } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-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 PARAMETER FILE=========================================

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FOTD 15-11-07 (The Fractal Origin [7])
by Jim Muth 14 Nov '07

14 Nov '07

FOTD -- November 15, 2007 (Rating 7) Fractal visionaries and enthusiasts: It is claimed that it all began with a big bang, and we are told that speculation about what happened before the big bang is as meaningless as speculating about what lies north of the north pole. In both cases it is less than nothing. If this is so, then we have finally found a spacetime where fractals or even their potential does not exist. But even if there is no such thing as before the big bang, this makes nothing an idea that does exist. After all, we hear it said that the energy of the vacuum caused the inflation of the big bang, and if a vacuum, which is nothing, (or is it?), can have energy, which is something, then why couldn't fractals exist 'before' the big bang, when nothing did indeed exist? It's a puzzle that requires a new type of thinking and also a new definition of the word 'nothing'. But today's image most certainly is not nothing. It is a scene lying in the same Zexpe fractal that gave us yesterday's image. Today, we travel to the tip of one of the main stems of the parent, where we find a routine Zexpe minibrot. To add a bit of interest, I reduced the bailout radius, (imag[p2]), to the point where the entire scene was on the verge of being swallowed up. Then I gave the scene a very brilliant but rather heavenly palette of colors. When I viewed the result, I thought of the moment when when the Creator said, "Let there be light", and I named the glaringly brilliant image "The Fractal origin". The rating of a 7 seems reasonable for such a pastel-pale image. The image is one of the fastest ever, with a total calculation time of 10 seconds on the 2000mhz machine and 38 seconds on the 200mhz unit. The image if very fast, but the most convenient way to see the finished image is to go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view it there. Wednesday dawned sunny here at Fractal Central, but the sun did not last long. Heavy clouds arrived before noon, and the rest of the day was heavily overcast, threatening the rain, which finally arrived after dark. The fractal cats were more concerned with falling leaves than the potential for falling rain however. My day was notably un-notable. The next FOTD will appear here in 24 hours. Until then, take care, and where would we be if the big bang had never happened? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Fractal_Origin { ; time=0:00:10.12-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=floor center-mag=+0.9853342206082071/-1.122216812523160/\ 2.144398e+008/1/-92.5/8.51735598085545664e-007 params=2.71828182845905/0/4/-97.7695 float=y maxiter=3000 inside=255 logmap=19 periodicity=10 colors=000LJWLN_LRcKWeKZiK`lK`oPaoUboYcoQdrbinuspr\ opelvbgr_drXbk_gfalgcpkuupzuprzymrqimiirfjwcjz`kzY\ kzWazQcxKewFgu9is4kq6mp8ooAqnCsmEulGwkIzjKziVzkezm\ pzo`zqMzs7zwBzwFzwJzwNzwRzwUzwXzw_zutzsszprziqzfpI\ mzNmzRmzVmzXmz_mz_mz`mz`mzamzamzamzcmzdmzemzgmzhmz\ imz_mzSmzWmz_mzcmzjmznmzrmzLmzMmzMmzMmzMmzXmzfmzem\ zcmzdmzQmzwmzpmzjmzAwzQwz8wzJwzUwz5wzEwzNwzWwzCwzK\ wzRwzYwzlwzhwzNwzWwzjwzhwzgwzewz`wzawzbwzcwzWwzZwz\ `wzbwzzwztwzowziwzawzbwzcwzdwzawzowzAwzQwzbwz0wzEw\ zSwzYwz8wzPwzqwzlwzhwzKwzQwzVwzQwzIwzQwzYwzVwzZwza\ wzrwznwzkwzgwz6wzswzowzkwzgwzdwzdwz3wzGwzTwzOwzgwz\ 6wzIwzUwz5wz2wzzwzuwzowziwzEwzNwzWwz7wzGwzOwzXwzOw\ zUwz_wz0wzBwzLwzVwzhwzHwzPwzXwz5wzNwz`wzawzbwzcwz9\ wzHwzPwzXwz7wzSwzZwzVwzYwz_wzbwzswzowzkwzgwz`wzbwz\ cwzAwzQwzawzcwzNwzTwzZwzIwzlwzVwzZwzawzewzhwzkwzew\ z`wzWwzRwzLwzGwzBwz6wzzzz } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-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 PARAMETER FILE=========================================

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FOTD 14-11-07 (Zexpe at Large [7.5])
by Jim Muth 13 Nov '07

13 Nov '07

FOTD -- November 14, 2007 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image lies in the Z^(EPSILON)+C Mandeloid, sometimes known as the Zexpe fractal. But today, instead of concentrating on the ground level, we examine the Zexpe at a height 4 levels up the logarithmic ladder, where it is shaped roughly like a Mandelbrot set rotated so that its west side is facing south- east. Today's scene is located in a tiny valley in a bud on the northeast shore of the main bay of this parent fractal. Only my modesty prevents me from admitting that most of the effect of the image is due to my coloring efforts. The extra half-point in the rating of 7-1/2 recognizes this effort. The name "Zexpe at Large" can mean whatever the individual fractal viewer wants it to. The magnitude of the image is 2*(10^13), large enough to make the mathtolerance entry necessary in the included parameter file. The calculation time of under 2 minutes on the fast machine would stretch to about 7 minutes on the slow unit. But even this small bit of time may be saved by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. Tuesday dawned rainy here at Fractal Central, but the rain ended by 8:00am, leaving behind heavy clouds and a light fog. Then, just before noon, a breeze sprang up, clearing the clouds and fog almost by magic. The afternoon was sunny and quite mild, with a high temperature of 61F 16C. The fractal cats observed all this with passing interest. The squirrels foraging in the back yard were far more interesting to the cats. My day was fairly busy, though still well under control. The next FOTD will appear in 24 hours, give or take a few. Until then, take care of your fractals, for perhaps they are mere delusions that are common to many people. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Zexpe_at_Large { ; time=0:01:54.52-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=floor passes=1 center-mag=+0.77754390860285990/+0.036243793086052\ 48/2.00498e+013/1/-46.7/0 params=2.71828182845905/\ 0/4/0 float=y maxiter=1700 inside=0 logmap=156 periodicity=10 sound=off mathtolerance=0.05/1 colors=000ND9Q89T49X6D`8Gc9JgBMkDPnESrGVuHYcf8Y`AS\ VCNPEHKFCEH68J13KWGDzS6kcBXnGJyLBcV4IcQMVkQNjVMjZM\ ibLigLhkKhoKhsKilLifMj_MjUNkOOkHOlBPzzzzzzzmzvhzrc\ zmZviUrbPmWKiPDeI6eDIeEKiFMmFNpFOrFPtFQvFSxDUzBQdA\ TX8WO7ZG5a84c0CX6KQCSJI_DNYCPXBQWBSVATU9VT9WYDWaGW\ fJWjNWoQWsTWrX`r`eqciqgnpkspnwfbqYRlPFfG4aHDYHMUGV\ RITPKRNLPLNOJQMHSKFVIDXHBYIEYIHYJJYJMYKPZKRaJWeJ_h\ JclJgoIksIovIsyIwsJtmKqhLnbMkXNhSOeMPbHQ_ONWUKT`HP\ fEMlCJjJQhPWfVadahbgn`mtSmhKmXPh`TddY`haWlfSpjOtcS\ nXWiQ_cJcZCgUMbSVYQdTOmONlLOmQWnUboZipbpqfwbhiPjWB\ kJMgTWdbeal_ZjUWhOUfIUdCUb7U`EUcLUeRUhYUjcUmjUopUq\ VUaAUMKUHTUDaU8jU4_V6QW8GXA6YBDZDJ_FQ`GWbIabKhcLnc\ NtcOscQscRscTscUpcQmcMjcJhcFecBbc8_c4Yc1`cBbeLdgUf\ ichklgmigoggqdgsbdu_`wXYyUUzRRzOOzLKzIHzFDzCAz96z6\ 3z3wzjozdhzZ`zTczVfzXezXdzYdzYczYczZbzZbzZ`zTZzNYz\ HUzORzVNzaKz_9z9Cz9Gz9Jz9 } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-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 PARAMETER FILE=========================================

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FOTD 13-11-07 (A Hairy Situation [7])
by Jim Muth 12 Nov '07

12 Nov '07

FOTD -- November 13, 2007 (Rating 7) Fractal visionaries and enthusiasts: Today's scene returns us to the mother of all fractals, the Mandelbrot set, where we check a rather difficult area at the limit of a small side-bud of a radical on the northwest shore line of the large period-2 bud. This area is a difficult place in which to work because of its extreme iteration count, which in today's image is 1,750,000, demanding a logmap setting of minus 146,000. The magnitude of almost 6*(10^12) makes the mathtolerance entry necessary. If the calculation flipped to arbitrary precision math, the rendering would drag on for a day or more. The name "A Hairy Situation" came about when I noticed how closely the curving filaments resemble hairs. The rating of a 7 is all I could do for just another trip into the not-so-deep depths of the Mandelbrot set. I did put some extra work into the coloring, but not enough to figure in the rating. The calculation time of 9 minutes is reasonable. But this time is true only on my fast 2000mhz machine however. On the slow old 200mhz unit, the parameter file would take over 2-1/2 hours to finish. Since some fractalists still run Fractint on older computers, I have sent the image on ahead to Paul at the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it may be viewed almost instantly. A cloudy, dreary, drizzly day here at Fractal Central on Monday brought pleasure to no one, not even to the F.C. cats. The temperature of 48F 9C was too warm to be cold and too cold to be warm. The ground was wet all day, though the total rain never amounted to even a single millimeter. The fractal cats showed their disgust by sulking at each other. My involvement with work left little time to be concerned with the weather. Luckily, the work went well. The next fractal image will be posted in 24 hours. Until then, take care, and what is the greatest number of fractals that might possibly exist? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Hairy_Situation { ; time=0:09:08.57-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.1719\ 9191062237200/+0.24288823917726240/5.826131e+012/1 params=0/0 float=y maxiter=1750000 inside=0 logmap=-145837 periodicity=10 mathtolerance=0.05/1 colors=000AuzAuzAuzAuzAuzAuzAuzAuzAuzAuzAuzAuzAuzA\ uzAuzAuzAuzAuzAuzAuzAuzAuzBuzCuzBuzBuzBuzBuzBuzBtz\ BszBpyBmxBkwBhtBfqCcnDakEZhFWeGUbHS_IQXJOUKMRLJOMG\ LNFKODKQDKSCKUCKWBKZBKXCKVDLTFNRFPPGQOGUNHZMGcLGhP\ NmSUrW`vZfzbmzetzwzzzzzwvzetzdqzcozbmyajx`hw_gvZfu\ YdtXcsWbrV`qZ_pcZohYom_nm`nmbnmcnmenmfmmhmmimmkmml\ mmnlmolmqlmrlmtlmulmwgmybmzYzzZzzczzJzzczzZRpHUkGY\ fFa`FeWEzREzSDzTDzUCzUCmVBmWBmXAmXAmYAmZ9m_9m_8m`8\ ma7mb7mb7mc6md6me5me5mf4mg4mh4mi7mj9mkCmkEmkHmkJmk\ MkkOikRgkTekVckYak__kbYkdWkgUkiSklPknKkqFksAkuDksH\ krLkqPkpTkoXkn`kmaknakobkobkpckqckqdkrdlsenseptfsu\ fvuaylYzdUzXPzOLzGHz8LzAOzCRzDVzFYzG`zIczJgzLjzMmz\ OpzPmzRkzTizUfzWdzYbzZ`z`YzbWzcUzeSzgPzhNzjLzlJzmG\ zoEzqCzrAzt7zv5zw3zy1zz3zw5zu7zr8zpAznCzkEziFzgHzd\ JzbKz`MzYOzWQzTRzRTzPVzMXzKYzI_zFazDbzBdzAezAgzALz\ IGzHCzG8zF4zE6zF8zF9zFBzF } END PARAMETER FILE=========================================

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FOTD 12-11-07 (Ordinary Diversion [6])
by Jim Muth 11 Nov '07

11 Nov '07

FOTD -- November 12, 2007 (Rating 6) Fractal visionaries and enthusiasts: There is not much to be said about today's image, which is pretty much a standard scene deep on a filament in the eastern suburbs of the large minibrot on the main spike of the Mandelbrot set. I named the image "Ordinary Diversion" because fractals in general are a great diversion from the problems of life, while today's fractal, at least, is notably ordinary. After I chose the name, I pondered the rating for all of 25 seconds before giving the image a rating of a 6, which is a little above average, though a rating of 5-1/2 might have been more appropriate. The calculation time of 4-1/2 minutes is reasonable considering that the magnitude is well into the range of arbitrary precision math. The most convenient way to see the image, as always, is to go online to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and enjoy the already-calculated image there. Sunday featured sunny skies and somewhat chilly temperatures here at Fractal Central. The fractal cats approved of the high of 45F 7C . . . from the inside of the window, that is, while I approved of the peaceful day. With any luck at all, tomorrow will again be calm. The next FOTD will appear in 24 hours. Until then, take care, and try to dream of the fourth dimension. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Ordinary_Diversion { ; time=0:04:37.70-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.7399\ 006224257385013878/0.01216601517013797332455/3.676\ 873e+018/1/-92.5/1.45072149e-012 params=0/0 float=y maxiter=1550 inside=0 logmap=202 periodicity=10 colors=000Q5IP5JO5KN5LM5MH5NC5OG6PL6RQ6TV7__7ed7li\ 7rgMgf`YeoOdzEavH_oJYfLVWNTOPMHRJBJG5CIA5kGJzU0eHi\ 0CP0GP0KQSNRVRSXUTbRKhNBqT8c`nnjozzoRAKONXLOfIdlFi\ rCqr9us8qo7ik6_f6R`5KW4DS47K5BI5FM6IO6MR7QT7TU8XU8\ _U8XJ8U88S0BY0Eb1Gg2Jl4Lq5Mo5Nn5Ol5Ok5Pj5Qh5Rg5Rf5\ hT7yG8xKAxNBwQCwTDvWEvZFvaGmbCdc8Wc4Nd0Ed0Cf0Ah09i\ 07k06l09h1Ce2Eb2H_3KX4MU4PR5RO5OR3LT2IW1FY0C`0Ab0O\ OI`9aZOfYakXopWzulTnhVgeX`bZU_`NXbGUd9Rf2Og0Xg0eg0\ mg0RwmXvfbu`htVnsPtrJzqDsfCmWBgLA`RCVXEObFIhHBnJ5s\ K8qLBpMEoMHnNKmNNlOQkOOiLMhIKgFIeCGd9Ec6Cb4AE0HG2O\ I5UJ8`LAgNDmOGtQJzRLpPOfORYNTOLWEKZ5J`OLYeNVwPSZF_\ A6gJ7gS7g`8gh8ggGifNjfVleameiodppdwqdlbdbPdSAdI0id\ hddb`dXXdRTdLIXP7QSPYMfeHwmCxoBxqAys9yu8yw7zx6zy5z\ z4xz9vzEtzJrzOpzTnzYlzaezV_zPUzJxzbnzWezQXzJVz_SzS\ QzKez2`z5Xz8SzBhznbzdYzWTzMWz03zIKzZMzRNzK_zAWzBSz\ Cjz1bz5Vz9tz0cz5WzPWz0jzR } END PARAMETER FILE=========================================

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FOTD 11-11-07 (Evaporated Fantasy [No Rating])
by Jim Muth 10 Nov '07

10 Nov '07

FOTD -- November 11, 2007 (No Rating) Fractal visionaries and enthusiasts: I named today's image "Evaporated Fantasy" because it is an evaporated image and a rather fantastic one at that. Of course, fractals are fantastic by nature. At least, I have never seen one walking down the street. The parent of today's image subtracts 1.7 parts of Z^(0.75) from 1.7 parts of Z^(-1.25), then adds straight C. This parent resembles a large circular bay filled with curious debris dotted with mandel-buds and valleys. Today's scene is located in a blunt valley in this debris. Yes, I have noticed that the formula contains a positive exponent of Z, and only fractals with all negative exponents are supposed to 'evaporate' when the bailout radius is raised to one-googol, but apparently today's fractal has not heard this, and evaporates quite effectively. After trying unsuccessfully to find a satisfactory rating for the image, I decided not to rate it at all. But it's a rather pleasant image, well worth the minute or so required to run the included parameter file. And even running the file may be avoided by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. Cold dark clouds prevailed here at Fractal Central on Saturday. With the temperature hovering around 41F 5C, and a chilly wind blowing, the fractal cats sought the warmest places they could find, while I sought the day's fractal. The next FOTD is due in 24 hours. Until then, take care, and perhaps fractals would never have existed if we had never started creating them. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Evaporated_Fantasy { ; time=0:01:11.86-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident center-mag=+1.321509355350085/-4.114202335613342/\ 6.889624e+008/1/-127.5/-0.000493473542789300834 params=1.7/-1.25/-1.7/0.75/0/1e+100/0/0 float=y maxiter=1600 inside=bof61 periodicity=10 colors=000gwzB55QBHcHTqNdtHjvCox6tz1zvAssImpRgmZaj\ gWgoROQe41tF5kQ9c`DWkHOvLGDTBERLFPUFNbGLkGJtFNbEQL\ DT3h1ea8WVEMOKCHQ2IO7INCJLHJKMJIRKHWKF`KEeJIdIMVHQ\ QHULGYGFaBFd6KfDOgJThQXjWakbelhWY`MKTD6LQFWbOfoWph\ ZlaaiWdfPgcIj`ClYDmVDnTEoQEoOFWGFC87CR8CS9BT9BT9CP\ 9DM9EJ9FG9GD9HA9H7CJ8EL8HM8JO9MP9OR9RLXTUAWH`YXAVf\ SSoiRmfXMdQjaQi_QgXPfVPdSPcQOmNO`LN_INYGNXDMVBMU8M\ T6LV9KXChUFr_IIaLHbOGdRGeTKhPzjLQlHzoEzqAzs6zu3zu3\ zv4zw4Nw4zx5Fy5zy5Gw7zv8Mu9ztASrBzqCYpDzoFcnGzlHik\ IzjJoiKzhLmkKzmKzzKzrKUtKzvKJzJKxKLvLMtMNrNOpNPnOP\ lPQjQRhRSfRTdSUbTV`Upb3VZU5TwAVsEXoIZkM`gQbcRcbUc_\ WcYYcV_cTbcRdcOfcMhcKjcHzcFocDqcAsc8yq8uc6qQ5mC4lF\ 6lH8lJ9lMBlODlQEkTGkVHkXJk_LkaMkcOmgOkePjdPicQhbQf\ aRe_RdZScYSaXT`WT_UUZTUXSVWRVVQWCUuUPWlLUkL6lK9lJB\ mIDmIFnHHnGJoGLoFNoEPpERpDTqCVqCXrBZrA`rAbbRUNgL8z\ B7xD7vF7tH7rI7pKkeyjkyhqz } 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 10-11-07 (Incomprehensible [No Rating])
by Jim Muth 10 Nov '07

10 Nov '07

FOTD -- November 10, 2007 (No Rating) Fractal visionaries and enthusiasts: Today's FOTD is late because I had no chance to finish it on time. But here it is in all its hasty glory -- a scene picturing a 'minibrot' in the 'East Valley' of the Z^(1.7)+C Mandeloid as it appears 44 levels up the logarithmic ladder. Since it took me only 2 minutes to find the image, I could give it no rating. The name "Incomprehensible" describes my impression of the world of fractals. The calculation time of 1-1/3 minutes will cause no impatience. And as always, the finished image is available on the FOTD web site. But due to the lateness of this posting, give Paul a chance to render and post the image before visiting the site, which may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy clouds, light rain and chilly temperatures made Friday one of the more unpleasant days here at Fractal Central. The fractal cats were so put off by the conditions that they didn't even bother to look for the pigeons that sometimes peck for food on the sidewalk. (BTW, what food do pigeons find on pavements that is nourishing enough to keep them so healthy?) My day was unexpectedly busy, but tomorrow will be slower. The next FOTD will appear in only 12 hours. Until then, take care, and when time ends, will fractals still exist? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Incomprehensible { ; time=0:01:21.47-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=floor center-mag=+0.127824723136437/+0.1574929171029857/\ 1.557655e+007/1/2.5/0 params=1.7/0/44/0 float=y maxiter=2000 inside=0 logmap=152 periodicity=10 colors=000gKbhKfhKeiKdiKdjKcjKcjKbjKbjKakKakK`lH`l\ D_m9_lAajAbhBcgBdeCecCgaDh`DiZEjXEkWElVFjUFhUGfTGe\ TGcSHaRH_RIZQIXQIVPJTOJSOKQNKONKMMLLLLJLMHKMFKMEJN\ FIOGHPHGQIGQJFRKESLDTMDTNCUOBVPAWQAWR9XS8YT7YUAXVF\ WZKUbPTaUU`ZW_cYZh_YlaXmcWoeVqgUsjTulSwnRxpRvqTuqU\ sqVrqWqqXorYnrZlr_kr`jrahscgsdesedsfcsgath`uiZujYu\ kXulWsmVqnUpnTnoTloSkpRipQgqQfqVj0Zh5ag9dfDgeHkdLn\ cPqbTtaXs`Xr`Xr_Xq_Xp_XpZXoZXoYXnYXmYXmXXlXXlWXkWX\ jWXjVXiVXiUXhUXgUXgTXfTXfTXgSXhRXiQXkPWlOWmNWnMWoL\ WfMXZMXRMXJMXBMX3MX6NU9NSCNQFNOINLLNJONHROFUODXOA_\ O8bO6eO4gO2dNAaMHZLOWLVTKaQJhNIoKIvLJsMKpNLnOMkPNh\ QNfPOgPOgPPhPPhPQiPQiPRjPRjPSkPSkPSkSbfUlaWvXSpVPj\ TMdSJZQGTPDNNAHL7BK45I10H62IA4JF6KJ8LNAMSCNWEO_GPc\ IQgKRkFQoBQsFSuJTwNUxRWyUXzWYzYZz_XzaVzcUzeSzgQziP\ vkNrmLmoKhqIcsHZuKWwNUxQRyTOzWMzZJzaGzdEzgBzj8zm6z\ p3zs1zv6ztAzrFzpJznNzlPzg } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-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 PARAMETER FILE=========================================

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FOTD 09-11-07 (Child of the Ages [8])
by Jim Muth 08 Nov '07

08 Nov '07

FOTD -- November 09, 2007 (Rating 8) Fractal visionaries and enthusiasts: Today's FOTD is from the same Z^(1.75)+C parent fractal as yesterday's. But today, instead of checking the chaos up north, we check the inside shore of the north branch of the valley enclosing the large period-2 bud on the east side of the large main bay of the parent. Once I reached the spot, it was not too difficult to find one of the minibrots that inhabit the area, and color it appropriately. The rating of an 8 shows that I am well satisfied with the final result. The name "Child of the Ages" is simply a phrase that came to mind while I was checking to see whether the scene is located on the parent or child side of its valley. It is on the child side. The sight of the image is worth its calculation time of 6-3/4 minutes. But absolute worth is a subjective thing, so for more convenience, the finished image is posted for instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Cloudy skies and a temperature of 39F 4C, along with flurries of leaves, made Thursday feel quite like autumn here at Fractal Central. The fractal cats were more concerned with the pigeons than with the autumn leaves. My day was busy but under control. The next FOTD will appear in 24 hours. Until then, take care, and are fractals good, evil, both, or neither? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Child_of_the_Ages { ; time=0:06:47.33-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=floor center-mag=+0.75351497361/+0.06981942344/108600.6/\ 1/-42.5/-3.34186859e-010 params=1.75/0/11/0 float=y maxiter=25000 inside=0 logmap=557 periodicity=10 colors=000__`MMaEMe7Mi1Mm0Mq0Os1Ok1Nc3MW3LO5KG7J77\ J08J08J0AJ0AJ0CL0EP0GS0IV0KY0K`0Mc1Of7PiASlGUnKUnO\ xqczxszquzkxzgxuazmWzgSz_MzSGzKCzC7z51z00z00z00z01\ z01x03u03s05o05m07k07i08k08m08m0Ao0Aq0AqGEW_IAsM0z\ P0za8zmkzxzzszzquuogquUmoGgk3cg0_c0MCG_0sUaImz0oz0\ oz0zz3qzAqzGqzMszUsz_szeszkqqkockmOkkAki0kg0ke0kS0\ cG0W50O00G00800C30GC0IM0MY0Pg0Sq0Wz0_z0au1ge1mS1qC\ 1x01z01z01z00z00x00uz0qm0ma0dU3Z30S50a70Y80U0zi1zg\ 1zg1he3zr3xc3sc3mc5ga5ca5Q_5Y_7U_7PY7MY8IY8EW8CW88\ UA5zA1wPWSKYPCUO5eK0gI0fE0xC0qA0cUEPmYCzo0zq5zqAzq\ GzsMxsSosYiseaumWuuOuzIuzCmzAgzAazAUzAOzAIzAAx85x8\ 0x80s80s80s80mG0kM0gU0c_0_e3ca7ecCgeGkgMkiPokWsm_u\ oczqizsmzuszxxzzzzzzzzzzzzzzmzzazzezzizzmzzqzzuzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzz_zzWzzUzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzIzzCzz7zz7zz8zz8zz8zz8z\ z8zz8zz8zz8zz8zzezz_zzUzz } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-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 PARAMETER FILE=========================================

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FOTD 08-11-07 (A Riot of Colors [7.5])
by Jim Muth 08 Nov '07

08 Nov '07

FOTD -- November 08, 2007 (Rating 7.5) Fractal visionaries and enthusiasts: The name of today's image, "A Riot of Colors", says it all. It is perhaps the most colorful FOTD image of all time, helped in no small degree by myself. The parent fractal is the Z^(1.75)+C Mandeloid as it appears 11 levels up the complex logarithmic ladder, which could perhaps be more accurately described as a hyper-helix. As a matter of interest, the formula for calculat- ing the complex natural logarithm is: (1/2)ln(x^2+y^2)+i(atan(y/x)+2kPI) The logarithmic ladder, or hyper-helix, exists because k can be given any value from minus to plus infinity. Today we are at step +11 of the infinite ladder, where the parent appears as a single large oval bay with, strangely enough, two large period-2 buds, one on its east side, the other more irregular one on its northwest side. A large area of chaos extends north from the irregular bud, and today's scene lies just east of a larger minibrot lying near the northern tip of this area of chaos. The image is far too gaudy to earn a superior rating, but it is well worth a 7 plus the 1/2 point I gave myself for the little extra work I did on the color palette. The calculation time of 3-1/4 minutes is perhaps a bit slow for the total image, but the colors alone will assure that those who take the time to run the included parameter file will not be totally disappointed. Iteration frustration may also be avoided by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. Typical late autumn conditions prevailed here at Fractal Central on Wednesday. Brisk northwest winds blew, the sunlight alterna- ted with dark scudding clouds, and the temperature reached only 43F 6C. Snug indoors, the fractal cats spent the day by the heat, warm as toast, while I kept warm fighting with a job that just would not do what the customer wanted. The next FOTD will be posted in 24 hours give or take a few. Until then, take much care, and be at ease with this mysterious world. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Riot_of_Colors { ; time=0:03:18.17-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=floor passes=1 center-mag=-0.30648810766/+1.86666607889/6240791/\ 1/77.5/-9.14082472e-009 params=1.75/0/11/0 float=y maxiter=32000 inside=0 logmap=160 periodicity=10 colors=000zNQmON`QJNQIBSE0SD0U90U80L40E2680G20D009\ 0080340420600900B00D30J90QG0WO4bWBibGnkNvrUzzZzvUz\ rQvnNnkJigGbdDX`9QX6LU3GQ09N04J00G00D00900600B00G0\ 0L00Q00W00`00e00k00p00v00z00n2DbDOQNbEZn3kz0vzz0mz\ 0gz2dz6`z9WzDSzIOzLJzOGzUDzX8zb4ze2zi0zn0zr0zv0vv0\ rv0nv0kv0gv0bv0Zv0Wv0Sv0Ov0Up0Xk0`g0db0zX0kU0nO0rJ\ 0zG0tI0rJ0pJ0nL0zL0mN0kN0iO0gO0eQ0eQ0bO2`O4ZO8XNBW\ NEUNISLLQLOOLUNJXLJ`JzdIggGZkEZnDLfIBYN4ZN0QS0NY0P\ b0QzxNztJzpGzmDzi9zd6zZ3zU0tO0nL0iO0eS0`W3WZ6Sb9Nd\ DJdGGeIDeL9eN4gQ2gS0iW0iX0i`0kb0ke0mg0mk0mm0pg0rb0\ vX0xS0zN0zI0zD0z86z3Ez0Nz0Wz0dz0mz8vzGzzQzz`zzizzt\ zzzzzvzznzzgzz`zzUzzNzzOzzdzzvzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-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 PARAMETER FILE=========================================

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FOTD -- 08-11-07 (A Riot of Colors [7.5])
by JimMuth＠aol.com 07 Nov '07

07 Nov '07

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FOTD 07-11-07 (Forever Fractured [6])
by Jim Muth 06 Nov '07

06 Nov '07

FOTD -- November 07, 2007 (Rating 6) Fractal visionaries and enthusiasts: Today's image takes us into the parent fractal created when Z^(-1.1) is mixed with Z^(-2.2) and (1/C) is added. This somewhat oversized parent fractal consists of 3 large, nearly circular bays, with a large area of apparent chaos on the west side. There are also 2 fragmentary mandibles like those of a fire ant. It's not a very promising start, but I never give up on a fractal unless it is totally hopeless. The first thing I noticed was that the large area of chaos is filled with objects pretending to be minibrots, and that some of these are rather interesting. I decided to check just west of the largest 'minibrot', in an area consisting mostly of fractal sand, with occasional larger stones thrown in. I expected to find little of interest, but when I applied a very broad color palette I found that there is a subtle pattern hidden in the chaos. Once I emphasized this pattern, I found a previously invisible, symmetrical arrangement of elements that indicates the presence of either a dry valley or a real minibrot. Luckily, it turned out to be a minibrot, and that minibrot lies at the center of today's image. The minibrot is surrounded by a pattern equally as subtle as the pattern of the overall area. And it also needs to be emphasized by fine tuning the colors. Unfortunately, I seem to have gone a bit too far with the colors, resulting in a texture too rough and muddy to make a great image. But the rating of a 6 that I gave the image is fair enough. I named the image "Forever Fractured" because of the excessively rough texture of the image. The calculation time of 2-1/2 minutes will not be too much of a burden, but an even faster way to see the image is to view it on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Tuesday was a bit chilly around the edges, but a fine autumn day nevertheless here at Fractal Central, with a temperature of 50F 10C. The fractal cats, (designated so by me), were on their best behavior most all day. The only slip was when Cassie took her sharpened claws to the arm of my favorite chair. Other than this, my day went as good as could be expected. Only the day's fractal fell a bit short. But the next FOTD will be posted here in 24 hours, and who knows, it may be the best of all time. Until then, take care, and if the outer world is as real as the Mandelbrot set, then what's going on? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Forever_Fractured { ; time=0:02:30.61-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip inside=0 center-mag=-2.453051913790731/+0.0431330890981556/\ 8.35236e+009/1/145/0 float=y params=1/-1.1/1/-2.2/\ 0/0/0/0 maxiter=3200 logmap=256 periodicity=10 colors=0000000000000000000000000000000000000000000\ 00000000z0zz0zz0zx0zs0zp0zk0vh0rd0ma0hX0cV0cQ0cO0c\ K0cH0cE0wB0w70w50w00w00c30Z50U90TB0OG0KH0GM0BQ07T0\ 3X00_00d00e00k00p00zw0zw0zw0zw0zw0zw0zw0zw0zz0zz0z\ zzzzzzzzzzzzz0zz0zz0zs0zh0za0zV0zO0zH0zB0z50z00z00\ z00n00n00a00a00a00d00d00d00d00p00p00z00z00z00z00z0\ 0z00z90zG0zO0zO0zV0za0ze0xh0sn0ns0hx0dz0_z0_z0az0a\ v0ds0dn0dk0ee0ed2h_3hX5hT7kQ7kM9kKBnGEnEGp9Hp7Kp3M\ s2Ms0Ov0Qv0Tv0Vx0Xx0_x0_s0ap0an0dk0de0dd0ea0e_3hV5\ hT7hQBkOEkKGnHHnGMnEOp9Qp7Tp5Xs3_s0av0ev0hv0kx0nx0\ sz0vz0xz0zz0zz0zz9zzKzzVzzezzszzszzszzszzszzszzszz\ szzszz0zz0zz0zv0zn0ze0ze0zd0za0z_0z_0zX9zVKzTVzTez\ QszOzzMzzMzzKzzHzxGzxGzxEzvBzvBzs9zv7zx5zz5zz3zz2z\ z0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz2zz5zz7zz9\ zzBzzEzzGzzKzzMzzOzzQzzTzzVzz_zzazzdzzezzhzznzzkzz\ hzzezzdzzazz_zz_zzXzzzzzz } 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 06-11-07 (Caught in an Orbit [7.5])
by Jim Muth 05 Nov '07

05 Nov '07

FOTD -- November 06, 2007 (Rating 7.5) Fractal visionaries and enthusiasts: ALERT -- TODAY'S FORMULA IS A NEW ONE! SAVE IT! Monday evening I reached the point where I could no longer endure the flawed MandelbrotBC2 formula, with its ground level at +3.14159... so I added PI to the fifth line of the BC2 formula and named the tweaked version MandelbrotBC3. Today's image was created with the BC2 formula and converted to the BC3 formula, which explains the odd value for real(p2). (The value was 89 in the BC2 version; the value in the BC3 version is 89 minus PI.) In addition, I generalized the function. Today's fractal was created by the expression Z^(1.09)+C, which is so close to being linear that one could hardly expect it to produce an interesting fractal. But we are dealing here with fractals, and fractals, even those of such a low order, do not always behave in a predictable manner, especially when they are calculated 85.8584... levels up the logarithmic ladder. At this height, the parent fractal of today's image resembles a torpedo. Not surprisingly, the minibrot in today's image also resembles a torpedo, or perhaps a rocket ship that has landed on a lost planet circling the red-dwarf star Wolf-359. I named today's image "Caught in an Orbit" for a reason I have long since forgotten. The rating of a 7-1/2 includes the extra work I put into the coloring and also minor task of writing the new formula. The calculation time of 2-1/2 minutes is slightly slow, but the image is worth it, and relief from iteration pains is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the pre-rendered image is posted for instant viewing. Monday turned out better than expected here at Fractal Central. The skies were sunny, the wind was light, and the temperature reached 57F 14C. The fractal cats checked the pigeon situation, then spent most of the afternoon on their shelf in the sun. Rain moved in after dark, but by then it had already been a fine day. My day was close to average, the way every day should be. The next FOTD will appear in 24 hours. Until then, take care, and how many visionaries does it take to see an actual fractal? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Caught_In_An_Orbit { ; time=0:02:35.44-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 center-mag=-1.8897526870\ 35/+16.753530446161/2324853/1/-170/0 params=1.09/0\ /85.858407346/3500 float=y function=floor maxiter=36000 inside=255 logmap=135 periodicity=10 colors=000YSCVRAXR9WRAWRAVRBVQBVQBUPCUPCTODTNDTNDS\ MESNESNERNFRMFQLGQLGQKGPKHPJHPJHNIGLHFKGFIFEGDEFBD\ D9CB9CA8B87B66A5693591580683B96G99L9CO9FSAHSAK_ANb\ AQfBTjBWnBYqBhzCZnCZmCZlC_kC_jC_iC_hD_gD`fD`eD`dD`\ cDabDaaDa`Ea_EaZEbYEbXEbWEbVEbUE`TG_SHZRIYRJXQKVPL\ UOMTONSNORMPPLQOLRNKSMJTLIUJIVIHWHGXGFYFFZHH_IJ`JK\ aKMbLNcNPeOQgPSiQTkRVmTWoUYqVZsW`uXawZcx_dy`fzagzb\ izcjzahy`fxZdwYbtX`qVZnUXkTVhRTeQRbPP_NNXMLULJPJHK\ IFFHDBFB9E96D84H79L7DP7IT7MX7Q`6Ve6Zk6cq6gw6kt8jq9\ inBhlCglDfkFejGdiHdiJchKbgLafN`eO_eQZdRZcSYbUXbVWa\ WV`YU_ZT__TY`UXaUWbVVcVTdVSeWRfWQgWOgXNhXMiXLjYJkY\ IlYHmZGnZFnZHk`JiaLgbNecPbdR`eSZfUZgW_hY`i_ajabkcc\ lddmfenhfojgplhqnirojsmkpllnkmkzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzmmz } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-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 PARAMETER FILE=========================================

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FOTD 05-11-07 (Spectral Encounter [7])
by Jim Muth 04 Nov '07

04 Nov '07

FOTD -- November 05, 2007 (Rating 7) Fractal visionaries and enthusiasts: Today's image is named "Spectral Encounter". I named it when I pondered the fact that the image is not really there. It is an evaporated image, a ghost if you will, made manifest by the 'bof61' inside fill. Since ghosts are not supposed to be real, I could give the image a rating no higher than a 7, but it's actually a rather pleasant diversion, whose only drawback is the slow calculation time of 15-1/2 minutes on my fast P4-2000 machine and almost 1-1/2 hours on the slow old P200. The image itself is indescribable, vaguely resembling some exotic tropical jungle. There is a midget at the center, but it lies far beyond the resolution limit. In fact, the resolution is already starting to break down in the actual image. The 'mathtolerance' entry is necessary to assure that the parameter file renders at the correct magnitude of 3.66*10^12. The generating expression combines various negative portions of Z^(-1.1) and Z^(-11.1) then adds (1/C). Before it is evaporated the resulting parent fractal is an immensely oversized thing consisting mostly of rings and requiring several outzooms to fit completely onto the screen. Today's scene lies in the East Valley area of a large minibrot not too far southeast of the origin. The frustrating wait for the parameter file to finish may be avoided by stopping by the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the already finished image there. A few too many clouds and a temperature a few degrees too chilly made Sunday only an average day here at Fractal Central. The fractal cats were not bothered by the temperature of 52F 11C, but those pesky pigeons pecking on the sidewalk annoyed them no end. Finally however the pigeons flew away and the cats settled down for their afternoon naps. My day was as good as could reasonably be expected. The next FOTD image and discussion will be posted at this same internet spot in about 24 hours. Until then, take care, and where will the universe be a google years from now? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Spectral_Encounter { ; time=0:15:31.59-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+7.365065632339196/-7.058195106026997/\ 3.660111e+012/1.0009/162.8253108182/0.065113202793 params=-5/-1.1/-11/-11.1/0/1e+100/0/0 float=y maxiter=6000 inside=bof61 logmap=1274 periodicity=10 mathtolerance=0.05/1 colors=000aKWbOUZSRVWOR_LNcIJgGFeDBcA7`74_58X9BVDE\ TGHRVKPNNN`RKVUIYXGa_EdbCheAkcEmbHn`Ko_NpYQqXUsVXt\ U_uSbvRewA63D95GB6IE7KG8NJ9QLBSOCUQDXSE_VFaXHc_Ifa\ JidKkfLnhMogNpfOqfPpePoeQodRndRmcSmbTmbUmaUnaVn`Wm\ `WjZTgXRdVPaTPZRPWPPTNPQLPNJNKJLHIJFIKEIKCIKBIKAIK\ EJKHKKKKKNLKQLKTMKWMHZNEaNBdO8gO5_QKTSYMUkFWyJ`kMe\ ZPjMSo9Ss5XdT`RpbQodQofQogQniQnkQnmQmnPmpPmrPltPlu\ PlwPkyPkzPkyQhxQfwQdvQbuR_tRYsRWsRUrSRqSPpSNoSLnTI\ mTGlTElTCiUEgUGeUIcUK`ULZUNXUPVVRTVTQVUOVWMVYKV_IV\ `NTZSQXXNVaKTfIS`HRVGQPGPJFODEN7EM4aW2xe5ph8ijBblE\ WnJ`lOekTjiYnhdVJbTHjREjSCfSAbN8XJ6TF4JF2IF0IJ6INC\ JRIJVOJYUI`_IcdM``QZYUWUYURaRNePKiMKrPKzUPvGGnELhC\ QbAVX8_F9`H9aJAaLAbNBcPBcQCdSCeUDeWDfYEg_EgaFhbFhc\ FgcGedHcdIbeI`eJ_fKYfKXeK_MUQWUZeUgnUpiUkeUfaUaYUX\ UUTQUOMUJIUEEU9AZ5Dc5Fh5Im5mr5mv5mz5mz5mz5mz5mz5az\ 5cz5fz5hz5kz5mz5iz7RzKQzM } 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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Re: xfractint
by jackoftradez＠comcast.net 04 Nov '07

04 Nov '07

. Hey keep this thread going! I just bought a new Alienware system, have setup multi partitions, and am now trying to drink up the nerve to install Ubuntu as a dual boot without hosing the original XP OS. My goal is to learn linux well enuf so I never need MS again - I do not, nor will ever have, vista. Obviously, one of the first things I will do with it is Xfractint. I played around with it a little a few years ago on Mandrake 8.1 but I was not impressed, maybe its better now ... .

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FOTD 04-11-07 (Rusted Blues [6])
by Jim Muth 03 Nov '07

03 Nov '07

FOTD -- November 04, 2007 (Rating 6) Fractal visionaries and enthusiasts: Today's fractal is an understudy, which comes from the FOTD boneyard. I had to dig there because I spent most of the day in the outdoors. But just because an image was created several months ago does not mean it has no value. In fact, today's 3-month-old evaporated fractal is a rather pleasant scene in the parent fractal that results when 11 parts of Z^(-11.1) are subtracted from Z^(-1.1), and it rates a 6. I named the image "Rusted Blues" because of its downbeat mood, dominated by deep blues and dull rusts. The calculation consumes all of 56 seconds on the fast machine and 5 minutes on the slow one. The image may also be seen on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Thin morning clouds cleared away to a beautiful afternoon with a temperature of 54F 12C here at Fractal Central on Saturday. It was such a fine day that Fractal Lady and I could not resist taking the day off to enjoy the great outdoors. After being left alone all day, the fractal cats were sulky when we returned, but a generous serving of tuna soon restored their good spirits. The next FOTD, hopefully a new one, will appear right here in 24 hours. Until then, take care, and be present at all times and places. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Rusted_Blues { ; time=0:00:56.91-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+1.07119400116945200/+0.000053380183571\ 27/949037.1/1/150/-1.04674938655041627e-006 params=1/-1.1/-11/-11.1/0/1e+100/0/0 float=y maxiter=500 inside=bof61 logmap=20 periodicity=10 colors=000SK0FG0IE0KD0NB0QA0X80S50H0IcM0R9Z3DV6Gc8\ JgANdCKpEKvGKiIRqMSiQSrUTqSWpQYpOZmNamLbmJemIfmGim\ EjmDlmKnmQpmWrmasmhumnvmtxmzxmwsmtmmqhmnbmkYmhSmeN\ mbIx_EyYHuWJrVLoTNlRPhQReOTbMV_LXXJZTH`QGbNEdKDfHH\ bGL_GPWFTTFXPE_MEcIDgFDkBCo8Cr5CeFETPGGZI4gKE_JNSI\ WLHdDGm6Fn8Gn9GnBHnCHnDIoFIoGJoHJoJKoKKpMLpNLpOMpQ\ MpRNpSNlTMiULfVLbWK_XKXYJUZJQ_IN`HKaHGbGDcGAdF7dFA\ bGDaGG`GJZHMYHOXHRVIUUIXTI_RJbQJdPJ`OKXOLUOMQOMNON\ JNOGNPCNP9NQ5NR2NR7MQBLQFKQJKQOJQSIQWHP_HPdGPhFPlE\ PpEPkDRfDSaCTXCUSBVNBWIAXEAYRGgbMpaLn`Km_JlZIjYIiX\ HhWGfVFeUFdTEbSDaRC`RC_UGbWJeZMh`QjcTmeWpgZriTjkNc\ mHXoBQp5Jm8LjBNgDPeGQbJS_LUYOVVRXSTZPW`NZaK`cHceFe\ fM`dSWbYS`cNZiJXoEVuAUsCXrEZqG`pIboKdmMflOhkQjjSli\ TnkYkmahofeqjbso_usXwwUsuSotRlrPhqOepManLZmJVkISjG\ OiFLgDHfCEdAAc97b8CciHdhLehPfgTggXhf`ifdjfhkellepm\ dtndxodunesneqmeomelmejle } 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 03-11-07 (Eyes of Taurus [5.5])
by Jim Muth 02 Nov '07

02 Nov '07

FOTD -- November 03, 2007 (Rating 5.5) Fractal visionaries and enthusiasts: In the mail today I received the holiday offering from a popular- ized science book club I belong to. Most of the books offered were of the typical 'learn string theory in a day' variety. But on the back page of the advertising magazine I saw an offer for a $199.00 book titled "The New Encyclopedia of Unbelief", which when ordered for the special club member's price of $124.99 will come wrapped in holiday gift wrapping. It seems to me like some kind of macabre joke, giving someone a book about Atheism for Christmas. It is probably no accident that the book is published by a well-known skeptical organiza- tion that exposes phony psychics and generally debunks claims of the paranormal. Their real agenda is the promotion of Atheistic Rationalism. Hmmmm . . . I wonder if hard-core skeptics believe in the reality of fractals. Anyway, it doesn't matter what skeptics believe, since I am a true-believing born-again believer in fractal reality -- at least a true believer in the reality of pictures of fractals. And to prove my point, I have included the parameter file of a fractal that was created by the formula Z^(1.5)+C. To create the parent fractal I turned to the MandelbrotBC1 formula, which is a more versatile version of the MandelbrotBC2 formula. To add extra interest, I calculated the formula with the function set to 'cotan', rather than the hard-coded 'floor' function of the MandelbrotBC2 formula. The result is a totally different fractal. This new fractal is little more than a shapeless bay surrounded by filaments and chaos. Today's scene is located in a small, narrow, pinched-off valley on the northwest shore line of the shapeless bay. I named the image "Eyes of Taurus" because of the multitude of bulls-eyes scattered throughout the scene. The little minibrot just to the upper right of center adds a point of interest. But despite all this, I could not bring myself to rate the scene any better than a 5.5, and a half-point of this is due to the extra effort I put into the coloring. At least not too much time will be spent calculating the image. The included parameter file runs in 5 minutes. And for those who do not calculate, the finished image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Only a slight nip in the air kept Friday from reaching total perfection here at Fractal Central. The cloudless skies and high temperature of 55F 13C made any outdoor activity except swimming a pleasure. The fractal cats voiced their agreement as they asked for their tuna. Other than the book offer, my day passed with nothing worth mentioning taking place. The next FOTD will be posted in more or less 24 hours. Until then, take care, and be where it's at. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Eyes_of_Taurus { ; time=0:05:19.89-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=cotan passes=1 center-mag=-0.308369929869/+0.572186118653/1002987\ /1/37.5/-5.421888982e-008 params=1.5/0/10/0 float=y maxiter=4000 inside=0 logmap=333 periodicity=10 colors=000iVgpQhlVhh_hddh`ihXnhSymTrhUkcUdZVYUJKFP\ OLVRQ_UWeX`k`epckvfpziuxhrvhotgmqgjofgmfekebhe_fdY\ ddVbcS_cQYbNWbKUbIXZEmWaiaKfg2i`5lV7oOArICtCEsEDsF\ CsHBsIArK9rL8rM7rO6qP5qR4qS3qT2G70gVcbSZZQUVOQRMLN\ JGJHCFF7BD27B08I5qV`kSWfPR`NNWKIQHDLF9FC4A90OmqMil\ LfgJccI_ZGXVFUQDQMCNHAKD9G87D46A0sfjj`abVTUPLMJCDD\ 3z_otXinUchRYbOTYLNSIHMFCGC6A909su8oq8lm8ih7ec7bZ7\ _U7XP6TK6QH6ND6K95G65D25A0_mRXiOUeLSbJPZGNWDKSBHO8\ FL5CH3AE07A05DE5B7O91zs6vn4pi3jd2d_1ZV0TQ0NL0HG0BB\ 0rJUnIRkHPhGNdFKaHIZMGVRDSWBP`9Le6Ij4Fo2Bt08y0PxKN\ pILkGKfEIaCKXAPS8UO6ZO4cP2hK0mG0rB0oL2iMHkRFnWCp`A\ reCtjFvgKxcPzdUzjZzlcynhxpmwrqvoutlusiurguqdupaunZ\ umWulTukQujNulNujMuiLuhLufKueKudJucJuaIu`Iu_HuZHuZ\ IuhXurkuhou_suRwuEzuGzuIzuKyuMxuNwuP`uR`uT`uV`uW`u\ Y`u_`ua`uc`uL`uVjudfuceuceubduxXum`ubduYmuVjuShuPe\ uMcuJauN`uR_uVZuYYuaXueWu } 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 PARAMETER FILE=========================================

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xfractint-3
by John Wilson 02 Nov '07

02 Nov '07

Hey! Riko Voipio's xfractint version 20.4.00-1 is up and running in my Ubuntu computer. Don't know what I was doing wrong in my earlier attempts... might be as simple as which screen I had the focus on. Anyway I have only one problem left, (other than cleanup of my manual installation). My colours are all in the blue and green end of the spectrum. Got to investigate that, otherwise all looks good. John W.

2 1

Xfractint_2
by John Wilson 02 Nov '07

02 Nov '07

Well, well, well. As I mine through the innards of Ubuntu Gutsy, I find that the Synaptic Package Manager supports xfractint version 20.4.00-1, maintained by Riku Voipio in Finland. I installed this through the Manager with partial success. Upon activation, the initial scrolling screen appears in my Terminal and F1 starts up the "help" screens. However, the following screen remains black and any further commands return me to the prompt. My first, abortive, attempt to install xfractint was a manual installation of Scott Boyd's xfrac-binary-20.2.04.gz executable. As far as I know, this is still buried in the innards of my machine and I've no idea of how to clean it all up! (This is something which baffles me about Linux... how to manage an application for which the files are strewn around the four corners of the file system.) The package manager will look after removing Riko Voipio's xfractint for me. Scott Boyd's xfractint page mentions that "Xfractint was updated to Fractint 20.2.04 by Tim Wegner, Jonathan Osuch, and others." So where does Riko Voipio's xfractint version 20.4.00-1 come from? Puzzled JohnW.

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FOTD 02-11-07 (Ambiguous Blobs [7.5])
by Jim Muth 01 Nov '07

01 Nov '07

FOTD -- November 02, 2007 (Rating 7.5) Fractal visionaries and enthusiasts: To begin today's venture into fractal land, I mixed 1.5 parts of (1/Z) with straight Z and added (1/C). The combination produced a hyperbola with the open end facing west. On the surface, the edges of this hyperbola appear smooth and featureless, but a closer examination reveals that the edges consist of the typical Mandelbrot buds and their radicals. Today's scene is located in a kind of elephant trunk in the narrow band of Mandel stuff on the northern side of the parent hyperbola. It is rather surprising that the midget in today's image has an East Valley appearance, since the area in which it lies bears no resemblance at all to a valley. When I saw the four flat disks that appear to stand out in front of the rest of the scene, I named the image "Ambiguous Blobs". And since I did put a bit of extra effort into the coloring, I decided to reward myself with an extra half-point rating. The rating of 7-1/2 equals a little more than only an average amount above the FOTD average. The calculation time of 3-1/2 minutes is within reason for the rational fractalist. Those who are not rationalists may view the finished image without effort by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Thursday, the day on which we honor all the saints, began with heavy clouds here at Fractal Central. But at noon the dark clouds quickly moved out, leading to a very pleasant autumn afternoon, with brilliant sun on the colorful trees and small fluffy clouds in the background, while the temperature reached 61F 16C. The fractal cats, not even being close to sainthood, found their share of mischief. For me, the day was busy enough to prevent boredom and still leave time for the day's FOTD. In all probability, tomorrow will be the same. Until next time, take care, and save the best for last. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Ambiguous_Blobs { ; time=0:03:37.06-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=-2.031365658088821/+1.969163472099974/\ 1.90048e+009/1/142/-1.34e-006 params=1/1/1.5/-1/0/\ 0/0/0 float=y maxiter=7200 inside=0 periodicity=10 colors=000oyEmxFkwFiuGgsGeqHcoHamH_kIYiIWgIUeITcIS\ aJS_JSYJSXJTWJTVJUUKUTKVSKVRKVQKWPKWOLXNLXMLYLLYKL\ XKNYJLZIK_IJ_HH`HGaGFbFEbFCcEBdEAeD9eC7fC6gB5gB4eD\ 6dE7cG9bHAaIC`KDZMEYOGXQHWRJVSKUTMSUNRVOQWQPXROYTN\ ZUL_VK`XJaYIc_He`GgbEicDjdCkfBlgAni9pj5pn8qkAqiCqg\ FqeHqcJq`LqZOqXQqVSqTUqRSoPRmOQkMPjLOhKNfILdHKcGJa\ EI_DHYBGXAEV9DT7CR6BQ5AO39M24M08L1BL2FL3IL3ML4PL5T\ L6WL6ZL7bL8eL9iL9lLApLBsLCwMAvLCuLDtLFfC7`HBWNERSI\ LXLGbPAgS5lW0qZ1oX2mV2kT3iR3gP4eN5cL5aJ6_H6ZGLhRZr\ aYqbYqbYpcYpcYpdXodXoeXneXnfXnfWmgWmgWlhWlhWlhXjjX\ hkXglXemYdnYboYapY_qYYrZXsZVtZUuZSvZRw`SsaTocTldUh\ fUdgVaiWYjWUlXRmXNoYJpYGh_IaaJVbLOdMHeNMgSQhXUiaZj\ fbkkflo`emV_kPTiKNgRP_YRSdTLkVDqW6cODQHJDAPLIMTQJU\ RJUSJVUJVWJWYJX_JZaJacLdeKggJhUIWUGQNFKGED6DF9CGBC\ HDCJGDKIDLKEMMFOPHPRHQTISWITYIU_HVaHXdGYfGZhF`kFam\ EboEcqDetDfvCgxChyClzDpzE } 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=========================================

4 3

Xfractint
by John Wilson 01 Nov '07

01 Nov '07

I wonder if anyone on the list has installed Xfractint in Ubuntu? I've just abandoned Microsoft, and my Media Centre machine is now totally dedicated to Ubuntu 7.4, (Gutsy Gibbon). Very much a Linux newbie, I've downloaded Xfractint and tried to install it and run it in Terminal. It doesn't... yet! I just get a very transient message that Xfractint can't find something... a .HLP file is what it looks like, although why that should influence anything I can't say! I installed in my Desktop and maybe this is the problem? Help! John W.

1 0

Re: Misk
by jackoftradez＠comcast.net 01 Nov '07

01 Nov '07

. Someone asked, so... The fractint PAR for the buddhabrot is: Buddhabrot { reset=2004 type=mandelcloud passes=1 center-mag=-0.300522/-4.44089e-016/0.8079007/1/-90/-1.23373533611470521e-014 params=751 float=y maxiter=751 fillcolor=0 inside=0 outside=summ sound=off colors=200A84<20>oiPqjQslR<3>zsW<25>CB6A95874653442220000400<23>o00q00s00<3>z00<25>C00A00800<3>000<2>554776998BBACCB<18>\ iihjjillk<3>ssr<25>BBA998776<2>221000011<24>0bn0cp0er<3>0ky<25>09B089067<2>021000210<2>863 } The colors were saved out as a map, and referenced in sstools.ini. Thus it is simpler: Buddhabrot_ { reset=2004 type=mandelcloud passes=1 center-mag=-0.300522/-4.44089e-016/0.8079007/1/-90/-1.23373533611470521e-014 params=751 float=y maxiter=751 fillcolor=0 inside=0 outside=summ sound=off } A BASIC script prints out the whole thing as a literal string, but the params and maxiter numbers are variables; a simple loop varies them from 2->751 and prints out all the PAR entries to one file, along with a BAT file which runs fractint and references the entries sequentially. XFRACTINT? I tried it a few years ago when I was investigating linux. It didn't seem to be as fast or as versatile as DOS fractint so I shelved it. I'm still waiting for 64 bit Fractint ... In the mean time, I've finally got ultrafractal to read some of my fractint pars, like for the universe sequences, but I have to hack them up a bit. Maybe I can re-render the U3 viddie in 32 bit color if I can get it right. But I don't know if current systems can be run 24/7/365; they are not as robust as older systems and tend to overheat. I can fix that, but the rendering time should be much quicker since a windows app can take advantage of the full proc capabilities and 32 bit memory addressing, but they actually render slower than fractint. Don't know why that is ... JoTz .

5 5

FOTD 01-11-07 (Terraces Without End [6])
by Jim Muth 31 Oct '07

31 Oct '07

FOTD -- November 01, 2007 (Rating 6) Fractal visionaries and enthusiasts: Today's image returns us to the sqrt(2) Mandeloid as it appears sqrt(2) levels up the complex logarithmic ladder, where it resembles a limbless torso. Today's image is located in a rudimentary East Valley in the southeast part of the largest bay. Since I feel I am overdoing these low-order fractional images, I could rate today's effort no higher than a 6. I named it "Terraces Without End" because of the terraced effect created by rendering the image with the outside set to 'tdis'. The somewhat excessive calculation time of almost 12 minutes on the fast machine and one hour on the slow unit is due to the unusually large maxiter of 150,000. To save time, I have sent the finished image on ahead to Paul at the FOTD web site, where it may be viewed without needing to run the parameter file. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Near perfect weather here at Fractal Central on Halloween kept the streets filled with assorted T-or-T ghosts and goblins, while the fractal cats kept themselves busy watching and chatter- ing at the local pigeons. My day was neutral, which is all I can say about it. The next FOTD is due in 24 hours. With any luck, it will actually appear at that time. Until then, take care, and did fractals have a special creation or did they just happen? And what's the dif- ference? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= TerracesWithoutEnd { ; time=0:11:58.04-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 center-mag=+0.1349853617\ 9728480/-0.00172600004154470/737862.7/1/-102.5/\ 8.45140832317e-011 params=1.4142/0/1.4142/0 float=y maxiter=150000 inside=0 outside=tdis periodicity=10 colors=000mePqgSthUsdTr`TrYTqUTpQTpNTpR_pVepZlparg\ Ym_ViSSdKO`CLW4ISDGTLFUTEV`DWhCXjJYlQYnWYobZqhZsoZ\ tuZngShVMbIG`IIZIKXILhINcIOZIQTHMNGHIFDFD8MIHSPQYW\ Yccfhfhmjkrnmsjjshhsffsddtbbt_`tXZtVXuSVmPTcMRUJPK\ GNPDLUAJZ8Hc9JhAKmALrBMvBNzCOvCPrDQmDRhEScETZFUoFV\ oGWoGXkFYhFZdF_aE`ZE`VEaSDbODcLDdIDdJH`KLYKOVLSSLW\ PMZMNbJNfGOiDOmAPq7Pt4Qu7RuAzvDzvGzrJzmLzwOzxRzxUz\ yXzy_zyazwZzvXztVOsTLqRJpPGnaEmLBkJ9jHChGFfGIdFLbF\ O`ERZEUXDXVD_TCbRCePBhNBkLAnJAqH9tF9fENUE_GDl3DyJU\ vYjslfpmflnfiof0pfcqw`rwYsvVtvSuuPuuMihcYXcNLcMOcL\ QcLSmKVmKXmJZmJamISmIemHhmHjmGlmGKmDfwBfw9fw7fw5fw\ 3fw3fw3fw3fw3fw3pw3pw3pw3pw3pw3pw3zw3zw3zw5zw6zw7z\ w8zw9zwAzqBzqCzqDzrEzrFzrGzrKzpNzoRznUzmYzl`zkdzjg\ zikzhnzgrzfuzefzjTznFzs1zw5zvzzuzztzzszzrzzqzzpzzo\ zznzzmzzlzzkzzjzzizzizzjzzkzzkzzlzzlzzmzzmzznzznzz\ ozzozznzz8zzBzzEzzGzzJzzM } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100, p=real(p2)+PI q=2*PI*floor(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 PARAMETER FILE=========================================

1 0

FOTD 31-10-07 (Blue Sea Shells [7.5])
by Jim Muth 30 Oct '07

30 Oct '07

FOTD -- October 31, 2007 (Rating 7.5) Fractal visionaries and enthusiasts: Recently, I have had occasional trouble getting connected to Mindspring, which is why some recent FOTD's have been posted through my AOL account. Unfortunately, the philofractal list does not accept postings in the AOL format, which is why the philofractal posting might be later than usual. Hopefully, I can solve the access problem by switching to another Mindspring (Earthlink) access number. We'll see how it goes. Today's fractal goes very well indeed. One glance at the image shows why I named it "Blue Sea Shells". It could easily be a glimpse of a fantastic under-water garden. To reward myself for the small amount of extra effort I put into the coloring, I added an extra half point to the rating of a 7. The parent fractal sprawls far beyond the edges of the default opening screen, but the central feature is a string of bays which together resemble a large ant with a long mandible. Today's scene is located about halfway to the tip of this mandible. The calculation time of just over 2 minutes should be no problem. But if the unexpected happens and calculation becomes problema- tic, the image may also be seen by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> After a foggy start, Tuesday turned out to be a great day here at Fractal Central. The temperature of 63F 17C, clear skies and light winds pleased the fractal cats, who finally took notice of the pigeons taking up residence under the eaves of the house next door. With two such alert cats on patrol, those birds had better start pecking for food on some other sidewalk. My day was notably calm, and if all goes as planned, tomorrow will be the same. The next FOTD will be posted 24 hours from now. Until then, take care, and things may not be as they seem. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Blue_Sea_Shells { ; time=0:02:06.28-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=+1.197786011751566/+0.3097971774991937/\ 2.526904e+007/1/-105/2.91469709041286551e-006 params=-5/-1.5/-2/-2.7/0/0/0/0 float=y maxiter=5000 inside=0 outside=tdis periodicity=10 colors=000_M__IZ_GXmESzEOzEIzEEzGCzGCzGCzGCzGCzICz\ ICzI9zI9zI9zI9zK9zK9zK9xK9uK7sK7rM7pM7oM7mM7lM7jM7\ hO4gO4eO4cO4bO4_Q4ZQ4VQ0UQ0SQ0QQ0OS0MS0KS0IS0GS0ES\ 0CU09U07U04U00U00U00V40V90VC0VG4VI4VM4XQ4XS4XV7XX7\ Y_7Yc7Ze9Zh9Zj9Zm9Zp9ZrCZuCZwC_zC_zE_zE_zEZzE_zGoz\ EkzEhzEezEczE`zEYzEWzEUxERwENxEMsCNlCKiCEhCCgC9fC7\ eC4dC0cC0UC0SC0QC00E00G00I00K00M07O09Q0ES0IS0KU0OV\ 0QX0UZ0X_0Zb0bc0ec0ge0jg0mh0oj0rl0sm0wo0zo0zp0zr0z\ s0zu0zw0zx0zz0zx0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0\ zz0zz0zz0zz0zz0zz0zz0zz0zz0xz0wz0uz0uz0sz0rz0pz0pz\ 0oz0mz0lz0lz7hzCezGbzKZzOXzSUzVQzZMzbKzhGzkCzn7zp0\ zs4zr4zs4zs4zj4zj4zh4zg7zg7ze7ze7zc7zb7zb7z_9zZ9zZ\ 9zX9zX9zV9zU9zUCzSCzQCzQCzOCzOCzMCzKEzKEzIEzGEzGEz\ EEzEEzIGzKIzMIzOKzQKzUMzVMzXOzZOx_QucSseSrgUphUojV\ lmVjmXhmXgmZem_bm__mbZmbXmcVhcSheQheOhgMhhKhhGhjEh\ jCil9jl7km4lmXmgXmeZmcZmb } 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=========================================

1 0

Map comparisons for duplicates
by David M Fisher 30 Oct '07

30 Oct '07

I am putting this on the general listing in case there are others interested whom I do not know about, but this is directed specifically to Jonathan Osuch. There is a problem with map files. They work fine for coloring, and in all ways intended. The problem is in comparing for duplication. Two identical maps as far as color values and sequence goes will not show as duplicate if one of the maps has been cycled and then saved. Would it be possible to have fractint list the map file used in the par even if the par is saved with colors? This would provide a reference by name to the map used in the par. Or could fractint somehow place a stop bit (sync place holder) in the map files so they could be aligned in the editor with a key entry? The best solution would be a program which first would enter place holders within the map file so that all maps would be uniform, then run a comparison for sequence of RGB values regardless of place. In other words, if the only difference between two, or more, map files was the linear order of the same values, it would show as a duplicate. I wonder how many map files on people's drives are actually duplicates, with the only difference being sequence? Just a thought. David M Fisher sunfish(a)intercom.net

5 5

FOTD 30-10-07 (Square-Root Picnic [No Rating])
by Jim Muth 30 Oct '07

30 Oct '07

FOTD -- October 30, 2007 (No Rating) Fractal visionaries and enthusiasts: Today's image takes us once again to one of the infinity of fractals created by the formula Z^sqrt(2)+C, this time to the fractal that appears 1.4142 levels up the logarithmic ladder, a fractal that resembles a limbless torso with a head attached -- a perfect parent fractal for the day before Halloween. The scene is located in the chaos on the eastern side of the head. The image shows a small minibrot and its surrounding pattern. As must always be the case in fractals where the power of Z is fractional, the features in the image are broken and scrambled. But the broken features make a rough kind of symmetrical pattern around the midget, which is barely striking enough to raise the image to FOTD status. I can give no logical reason for the name "Square-Root Picnic". Since I have done so many of these scrambled fractals with exponents of Z between 1 and 2, and achieved only a modicum of success, I could not give the image an honest rating, but it is still worth a look. The calculation time of 7 minutes is slightly slow for such a less-than-splendid image. To save time and frustration, I recommend going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. After a foggy and frosty start, Monday turned quite pleasant here at Fractal Central, with sunny skies, light winds, and a high temperature of 55F 18C. The fractal cats were more con- cerned with something in the hallway than with the weather. They must still remember the mouse that popped out of the hole in the floor by the radiator last year around this time. When no mouse appeared on Monday, I comforted the disappointed duo with a treat of tuna and cheddar cheese. The next FOTD will appear in 24 hours. Until then, take care, and don't get caught up in a non-local fractal field pattern. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Square-Root_Picnic { ; time=0:07:06.50-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 center-mag=-0.1110651380\ 7892870/+1.444879230159444/5.566726e+010/1/-52.5/\ 0.0361740551652163 params=1.4142/0/1.4142/0 float=y maxiter=3000 inside=0 logmap=848 periodicity=10 colors=000cAqcApcApcAncAmcAkcFkhKjmPhrUgvZgzcfzhdz\ mgzrdztczvaxt`vqZtpYsnXpkVnjTkgSjfRhdPfaOd`MaYL`XJ\ ZVIXSHVRFSOERMCOJBMI9LH8IE6HC5E93C82B6183062030020\ 0100200300500600800900B00C00E00F00H00I00J00L10M10O\ 10P10R11S11T11V21X21Y22Z22`22a22c33e33g33i33k33m35\ o35q55s55t56u56v56w56x28y36z56z65z85z95zB3zC3zE3zF\ 2zH2zH2zI1zJ1zL1zM0zO0zP0zR0yS0xT0wT0vV0uX0tY0tZ0t\ `0ta0tc0td0tf0xd0tf0pg0mg0hh0fh1aj3Yj5Vk8Rm9OpCJqE\ FtHCvI8xL3xO5zM6zM8zM9xMBwMCvMEtMFsMHqMIsMJvMJxMLz\ MMzMOzMPzMRzMSzMTzMVyMXxMYwMZvRYuOYqMYmJYkIYiHYgEY\ eCYc9Ya8Y_6YY3YW2YU0YS0XQ0YO0YM0ZK0ZgzZqz`zz`zz`zz\ awzamzaczca0ca0c`0d`0d`0dZ0fZ0fY0zY0zg0zn0zn0zg0zV\ 0zT0zT0zS0vS0nR0gR0`R0TP0FPgFOgFOgFMgFMgFMgFLgc9zc\ AzcEzcIzcMzcQzcUzcYzcazcezcizzmzzozzqzzszzuzzwzzyz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzwzzxzzzzzzzzzzzzzzz\ zzzzzzxzzwzzwzzvzztzztzzs } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100, p=real(p2)+PI q=2*PI*floor(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 PARAMETER FILE=========================================

1 0

(no subject)
by JimMuth＠aol.com 29 Oct '07

29 Oct '07

1 0

Re: MAPS etc
by jackoftradez＠comcast.net 28 Oct '07

28 Oct '07

. Here is another MAP problem while we are on the subject. You have a fantastic fractal image but the colors not so good. You have THOUSANDS of map files accumulated over the years. How render this image with all the maps so to choose the best one? You can do manually with the "G" key, but thats tedious and takes forever. I was able to write a VB script that will RENDER and save the image from its parameters for any number of maps, you just have to type in the names of all the maps at the start and let it rip. An improvement, but still not ideal. So how about a way to load the GIF, change to a different map, and save. And do this in auto-batch mode for all the maps in the directory? I envision some kind of for-in-next loop to do it, but sofar unable to make it work. Any idears?? .

1 0

CORRECTED FOTD 29-10-07 (Sparkling Splendor [8])
by Jim Muth 28 Oct '07

28 Oct '07

FOTD -- October 29, 2007 (Rating 8) Fractal visionaries and enthusiasts: Today's visit to fractal land takes us to the country created when 5 negative parts of Z^(-2) are mixed with 1 negative part of Z^(-10) and (1/C) is added. This parent fractal consists of 3 nearly circular large bays, with many smaller more irregular bays attached. Today's scene is located on the edge of a blunt valley in the westernmost irregular bay. I named the image "Sparkling Splendor". The minibrot at the center appears to be sparkling alone in a world of lurking dark- blue shapes. The entire scene impresses me as being well above FOTD average, which accounts for the rating of an exceptional 8. The included parameter file takes 3-1/2 minutes to finish on the fast machine and 17 minutes on the slow unit. It can be viewed much faster by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and checking it there. Brisk autumn conditions arrived here at Fractal Central on Sun- day, with north winds, sullen-looking clouds, and a temperature of 50F 10C. The fractal cats spent most of the day snuggled amidst the stuffed animals in the spare room, while I spent the day trying to do as little as possible. The next FOTD will appear in 24 hours. Until then, take care, and if matter is an image created in the mind by a pattern of frozen energy, then energy is the realest reality, mind is less real, and matter is the least real. Anyway, regardless of the real reality, I don't mind if it doesn't matter. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Sparkling_Splendor { ; time=0:03:31.79-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-1.130804843380894/+0.1056974133879144/\ 2.492825e+010/1/-120/-0.00231352616010034595 params=-5/-2/-1/-10/0/-51/0/0 float=y maxiter=3000 inside=0 outside=real logmap=320 periodicity=10 colors=000J0PJ0QJ0RJ0SJ0TJ0UJ0VJ0WJ0XJ0YK0ZM0_O0`P\ 1aP2bN1bK3bI4bH5aG6`F7_D9ZCAYBBXACW9DV7EUBEU4EV4EW\ 4FW6FV9FWCFXFFYIFZKF_LE_LE_ND_OD_PC_QC_RB_SB_JB_cB\ _TB_RA_PA_NA_LA_JA_J9_J9_J9ZJ9YJ9YJ9YJ8UJ7QxgNwgOw\ gQvgRufStfUtfVseWreYqcZqa_q__sY_uWZwUYxSXyQVzPUyPT\ xORwNQuMPtLNsLMrKLpJJoIInHHmHFkGEjFDiEBhDAgD9fLEeS\ JdZOcfTbmYatbazf`ze`yd`xc`wc_vb_uaPOIWUMb_QidUpjYw\ pazudzwbzy`zzZzzXzzVzzTzzSyzRwwQuuQrrPpoOnlNljNjgM\ gdLeaKc_KaXJ_UIXRHVPHTMGRJFQDDPHFOLGOOHNSINVKMZLMa\ MLeNLhPKlQKoRJsSJvTLrVNoWPlXQiYSeZUb_W_`XXaZTc`Qdb\ NecKfeGglDzlAzl9zdBbZFWSIQTIPUIPUIOVIOWINWINXIMXIM\ YILZILZIK_IK_IK`LKaNKaPKbRKbTKcVKdXKd_KeaKecKfeKgg\ KgiKhkKjnGhmKflNekQcjTaiW`hZZhaYgdWfgUejTdmRcpQdsR\ fmRhgRjbRkXRlSRmMSn7RoHRpQQr_LtgQvhVxiZzjczkhzllzm\ qznvzpuzotznsznrzmqzlizsqzlyzezz_zzTzzMzzFzz8zzAzz\ BzzCzzEzzFzzGzzIzzJzzKyzM } 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=========================================

1 0

FOTD 29-10-07 (Sparkling Splendor [8])
by Jim Muth 28 Oct '07

28 Oct '07

FOTD -- October 29, 2007 (Rating 8) Fractal visionaries and enthusiasts: Today's visit to fractal land takes us to the country created when 5 negative parts of Z^(-2) are mixed with 1 negative part of Z^(-10) and (1/C) is added. This parent fractal consists of 3 nearly circular large bays, with many smaller more irregular bays attached. Today's scene is located on the edge of a blunt valley in the westernmost irregular bay. I named the image "Sparkling Splendor". The minibrot at the center appears to be sparkling alone in a world of lurking dark- blue shapes. The entire scene impresses me as being well above FOTD average, which accounts for the rating of an exceptional 8. The included parameter file takes 3-1/2 minutes to finish on the fast machine and 17 minutes on the slow unit. It can be viewed much faster by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and checking it there. Brisk autumn conditions arrived here at Fractal Central on Sun- day, with north winds, sullen-looking clouds, and a temperature of 50F 10C. The fractal cats spent most of the day snuggled amidst the stuffed animals in the spare room, while I spent the day trying to do as little as possible. The next FOTD will appear in 24 hours. Until then, take care, and if matter is an image created in the mind by a pattern of frozen energy, then energy is the realest reality, mind is less real, and matter is the least real. Anyway, regardless of the real reality, I don't mind if it doesn't matter. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Sparkling_Splendor { ; time=0:03:31.79-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=reci passes=1 center-mag=-1.130804843380894/+0.1056974133879144/\ 2.492825e+010/1/-120/-0.00231352616010034595 params=-5/-2/-1/-10/0/-51/0/0 float=y maxiter=3000 inside=0 outside=real logmap=320 periodicity=10 colors=000J0PJ0QJ0RJ0SJ0TJ0UJ0VJ0WJ0XJ0YK0ZM0_O0`P\ 1aP2bN1bK3bI4bH5aG6`F7_D9ZCAYBBXACW9DV7EUBEU4EV4EW\ 4FW6FV9FWCFXFFYIFZKF_LE_LE_ND_OD_PC_QC_RB_SB_JB_cB\ _TB_RA_PA_NA_LA_JA_J9_J9_J9ZJ9YJ9YJ9YJ8UJ7QxgNwgOw\ gQvgRufStfUtfVseWreYqcZqa_q__sY_uWZwUYxSXyQVzPUyPT\ xORwNQuMPtLNsLMrKLpJJoIInHHmHFkGEjFDiEBhDAgD9fLEeS\ JdZOcfTbmYatbazf`ze`yd`xc`wc_vb_uaPOIWUMb_QidUpjYw\ pazudzwbzy`zzZzzXzzVzzTzzSyzRwwQuuQrrPpoOnlNljNjgM\ gdLeaKc_KaXJ_UIXRHVPHTMGRJFQDDPHFOLGOOHNSINVKMZLMa\ MLeNLhPKlQKoRJsSJvTLrVNoWPlXQiYSeZUb_W_`XXaZTc`Qdb\ NecKfeGglDzlAzl9zdBbZFWSIQTIPUIPUIOVIOWINWINXIMXIM\ YILZILZIK_IK_IK`LKaNKaPKbRKbTKcVKdXKd_KeaKecKfeKgg\ KgiKhkKjnGhmKflNekQcjTaiW`hZZhaYgdWfgUejTdmRcpQdsR\ fmRhgRjbRkXRlSRmMSn7RoHRpQQr_LtgQvhVxiZzjczkhzllzm\ qznvzpuzotznsznrzmqzlizsqzlyzezz_zzTzzMzzFzz8zzAzz\ BzzCzzEzzFzzGzzIzzJzzKyzM } 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 28-10-07 (Seahorses go Deep [7])
by Jim Muth 27 Oct '07

27 Oct '07

FOTD -- October 28, 2007 (Rating 7) Fractal visionaries and enthusiasts: I found today's scene in the Mandelbrot set almost automatically. It lies in the Seahorse Valley area of a larger minibrot located near the tip of the long filament extending from the large period-3 north bud of the large minibrot on the main spike of the M-set. With that much said, I must tell that I named the image "Seahorses go Deep". I did this in recognition of its location deep in the Seahorse Valley of a larger minibrot. When all the naming was said and done, I rated the day's fractal work at a 7. It's really not such a bad image, perhaps a bit too busy for perfection, but considering that its magnitude is well into the range of arbitrary precision math, its calculation time of 8-1/2 minutes is really quite reasonable. But 8-1/2 minutes is still 8-1/2 minutes. Luckily, relief for possible fractal impatience is at hand. The finished image is or soon will be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Actually, the only thing seahorsey about the image is its name. At this extreme magnitude, all minibrots begin to look the same, with circular rings after rings surrounding the midgets and obscuring most of the other detail. But the circular nature of the features in today's image can easily be escaped. Outzooming to the surface of the M-set will reveal some quite attractive and non-circular patterns on the way. Saturday began with rain here at Fractal Central, but by noon the clouds moved out, leading to a mostly sunny afternoon with a temperature of 66F 19C. The fractal cats, Nicholas and Cassandra, (Nico and Cassie), enjoyed the returning sunshine to the utmost. Fractal Lady and I took the afternoon off for a short trip to a nearby forest, which had been refreshed by the rain. The next FOTD will appear in 24 hours. It might even be a great one, but there is no guarantee. It could just as easily be a loser. Until then, take care, and as Halloween approaches, don't be spooked by a specter. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorses_go_Deep { ; time=0:08:26.74-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.7688842240831\ 541913994/0.0574770069313667297793/4.44274e+017/1/\ -142.425445748274058/0.000213803 params=0/0 float=y maxiter=5000 inside=0 logmap=476 periodicity=10 colors=000GR28OITRBJO79H3P4eG2K81AXrdGRKBSO8LI5EC2\ 76AmN6XF3G7LOBFI8AC5562gDjM6NArH6_BzU5z4Nm2Fk17cJ1\ _C0060IH8DC6984442e`NLIBcN3_OJdXFhdCll9zsFszK_nOLc\ S7TVPZMedEvj6_V8DG9M`tGReBIS59EfMdSERE7Dv1wsUzJ`zJ\ qz7tz5ai3PV1CFNEEHAAB77533K42K31K21B10Eem9SX4EGHKM\ BDE567Ab76Q43D2zbRjTKVJDF962_i1INJ4m92PeirVYdLNRAB\ DzhQzCDzmFzUdzcMQCEDU7ZJtQEeH9S84E8cNzzF2D7qloROQn\ wgahXPUMCFB2lE1_A1O70C3BSFmO_se7`S4IE2B64OH8C84CLR\ 6ADI4oD3b92Q41DzsHveUnWccEmP6mG4c82UGm3AQ25D19rq6_\ _3IIMKlyeHzc8SM5EB23cz26z14V02FZeTccLHLE8A7pm3QP1a\ 5DP38C142mc1PKUX2FG1WldGOKZOmOITGCJ869QscDSKnKuYDa\ H6JIoaCYP6HC1wI0U9a5ES3AJ27913p`2bU1QU1DU0zUmVAPrB\ g_7TI3E5to2SQPNqzz_zzIzzCzz8zz4zzgzzTzzEzzzzzVzz6z\ z4zz3zz1zztzzeQzSDzEmzOPzCEzH7z80zg0zX0zM0zBUzqSz0\ Iz09z0oz1bz0Qz0Dz00zf0zLqzoGzoAzY5zHNzOFzG7z8Bz08z\ 05z02z0qzE_z9Iz4Mzw_z1vzS } END PARAMETER FILE=========================================

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FOTD 27-10-07 (Unexpectedly There [8.5])
by Jim Muth 26 Oct '07

26 Oct '07

FOTD -- October 27, 2007 (Rating 8.5) Fractal visionaries and enthusiasts: Let's have a little philosophical Halloween diversion before we get to the fractal discussion. Halloween is but four days away and everyone is thinking of ghostly things. In keeping with the spirit of the season, I was stopped on the street this morning by a reporter from the local newspaper and asked if I believe in ghosts. Apparently they were taking a poll of the local population. Since I had no time to spare, my answer was simply 'no'. But the facts are not so simple. Ghosts do exist! One thing for certain is that people do see ghosts. Legends of people being visited by ghosts exist in every culture. The question should have been, 'what do you think ghosts are?' Then I could have given the two most obvious answers: 1 -- A ghost is the surviving spirit of a dead person. 2 -- A ghost is an internally-generated mental image projected outward into the real world. Neither answer is totally satisfactory, since both answers raise more questions than they answer. The first answer raises the question of the existence and nature of surviving spirits, while the second answer questions the nature of both mental images and the external world. And the claim that a ghost is a mental image induced by the presence of a surviving spirit brings everything into question. IMO, it all comes down to the age-old problem about the nature of reality. If we could ever answer this question, (which I doubt), most of the other haunting questions would likely be answered at the same time. And speaking of ghosts, I was really spooked by today's image, which lies in the parent fractal that is created when 0.8 negative parts of Z^(-8.8) are combined with 5 negative parts of Z^(-1.8) and (1/C) is added. This parent consists of two large circular bays surrounded by many smaller irregular bays and minibrots. Today's scene is located on the shoreline of one of the large circular bays, in an area that at first appears to be totally non-critical, and where a pure minibrot would be the last thing expected. But not being put off by the apparently impossible, I checked the hopeless area anyway, and much to my surprise, I found a well-hidden minibrot. This minibrot lies nearly invisible at the center of today's image. The image was rendered in an unusual manner, with both the inside and outside parts set to 'fmod'. To see which parts are 'inside' and 'outside', reset the inside option to 'numb' and the outside option to 'iter'. The name of today's image, "Unexpectedly There", is a simple statement about the scene. The rating of 8-1/2 rewards me 1/2 point for the extra effort I put into smoothing the colors. The calculation time of 10-1/3 minutes may be cut by a minute or two by setting the passes to 'g'. But doing this misses some of the finer parts of the spirals. The all-around best way to see the image is to view it in finished form on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy clouds, steady rain, and chilly temperatures made the Friday weather unpleasant here at Fractal Central. The fractal cats seemed to agree, for they spent a good part of the day snuggled in the warmest places they could find. My day was busy enough that I had little chance to complain about the inclement weather. The next FOTD will be posted in 24 hours. Until then, take care, and the next time you see a ghost, say to it: 'what are you and what do you want?' Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Unexpectedly_There { ; time=0:10:19.52-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=t center-mag=+0.723105839047/-0.510872744279/4126147\ /1/-62.5/8.37e-006 params=-0.8/-8.8/-5/-1.8/0/0/0/0 float=y maxiter=5000 inside=fmod proximity=0.8 outside=fmod periodicity=10 colors=000cnjdnifnggnfinejndlncmnbonaqsdpn`piXodTo\ _PnVLnQHmLDmG9mB5iC9fCCcCF_CJXCMUCPQCTNCWKCZHCaGF`\ FI`EK`DN_DP_CS_BU_AXZ9_Z9aZ8dY7fY6iY6kY8oY9sYBy`Av\ YAtWArUApRAnPAlNAjKAhIAfGBdHBcICbICaJD`KD_KEZLEXMF\ WMFVNGUNGTOHSPHRPHQQIORINRJMSJLTKKTKJULIULGVMFWMEW\ MFXMGYMHYMIZMJZMK_ML`MMaMNbMOcMPdMQeKReJSeITeGUfFV\ gDWhCXiAYj9Zj9Zj8Zo8_o8_o8`o8ar8bs7cn7dp7er7du7ew7\ gz7gw7ht7jq7jn7ll7ni7nf5odApcFpaKq_PrYUsXZsWcrWhrV\ kqVnqVqpUtpUuoUvoTwoTwnSwmSwlSwkRwjRwiRvhQwgQwfPve\ PtdPrcOqbOpaOn`Nl_NkZMjYMhXMgWLeVLdULbTM`SN_SOYRPX\ RPVQQTPRSOSQNSPMROLQOKPOJOOINOHMNGLMFKLEKKDKJCKHBK\ GAKF9KF8KG7KH6KH5KI4KJ3KK2KL1KK0KK0KK0KK0KK0KJ0MJ0\ OJ0QJ0SJ0UJ0WL0YN0ZO0ZQ0_R0aT1cU2eW2iX3kZ3m_3oa3qb\ 3sd3ue3wg3zi2yh3xg4wf5ud6sc7qb8oa9m_AkZBiYCgWDeVEc\ UFaTG_RHYQHXPHWNHVMHULHTKHSIHQHIOGKMFLKKNGOPDSRHWT\ L_VPcWTcXXcY`cZdc_hc`gcag } 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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Re: Extraction of .map from displayed image
by jackoftradez＠comcast.net 26 Oct '07

26 Oct '07

. Invoke fractint then load the gif. Hit "E" key and you will see a pallette box. Then hit "S" and give it a filename. You will save the exact map from the image, not cycled. Then hit ESC to lose the pallette box. To compare maps, use the "FC" command in DOS (it is also available in the WinXP command shell), which shouldnt be a problem unless you are commandlinephobic. Here is what it does: Compares two files or sets of files and displays the differences between them FC [/A] [/C] [/L] [/LBn] [/N] [/OFF[LINE]] [/T] [/U] [/W] [/nnnn] [drive1:][path1]filename1 [drive2:][path2]filename2 FC /B [drive1:][path1]filename1 [drive2:][path2]filename2 /A Displays only first and last lines for each set of differences. /B Performs a binary comparison. /C Disregards the case of letters. /L Compares files as ASCII text. /LBn Sets the maximum consecutive mismatches to the specified number of lines. /N Displays the line numbers on an ASCII comparison. /OFF[LINE] Do not skip files with offline attribute set. /T Does not expand tabs to spaces. /U Compare files as UNICODE text files. /W Compresses white space (tabs and spaces) for comparison. /nnnn Specifies the number of consecutive lines that must match after a mismatch. [drive1:][path1]filename1 Specifies the first file or set of files to compare. [drive2:][path2]filename2 Specifies the second file or set of files to compare. There are also a number of file compare utilities out there.... .

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Extraction of .map from displayed image
by David M Fisher 26 Oct '07

26 Oct '07

Need information as to how to get the .map information from a displayed .gif WITHOUT going to color cycling and entering <s>. If that can not be accomplished, is there any way to compare .map files to eliminate duplicates? I have a program which compares .map files and lists dups, but if the .map is cycled, then saved, and compared it doesn't list a duplicate since the first RGB entry is different due to the rotation. What I am looking for is a comparision for duplication regardless of the placement of the RGB values as long as they are in the identical sequence between .map files. I have multimap.exe, which is fine for comparision if the .map has not been cycled. I have a .gif for which I am trying to find the .map. I did, from a screen display, cycle the colors; then entered <s>, saved to an entered file name. Exited fractint, found the saved file and ran multimap.exe to find the .map in my .map directory. No duplicate found, although I know it is there. I then did a test: Took a known.map file, cycled it, saved as above and did a multimap comparision. No duplicate was found, and it is my guess that the cycling rotated the RGB order so that a linear comparision, while correct, is not accurate. Am I pissing into the wind? Or is there a solution somewhere? Any help will be greatly appreciated. Even negative responses. David M Fisher sunfish(a)intercom.net

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Re: FOTD 23-10-07 (The Wheel of Eternity [6.5]) (Paul N. Lee)
by jackoftradez＠comcast.net 26 Oct '07

26 Oct '07

. Jim Muth wrote (and P.N.L. commented): > > When working with fractals, one can > know either a little about a lot or > a lot about a little. I have made > the latter choice. > As with P.N.L., I lean towards the former in life, thus my handle Jack Of (many) Trades, but as such, condemned to be a Master of nothing. With fractals, I am like Muth, specializing at and very good at one small aspect (animations), but not very good at other things like finding good images or color maps. Live free or war. JoTz .

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FOTD 26-10-07 (The Vanishing Point [6])
by Jim Muth 25 Oct '07

25 Oct '07

FOTD -- October 26, 2007 (Rating 6) Fractal visionaries and enthusiasts: With the number of video cameras, cell phone cameras, etc. now in circulation, why has no one yet produced a clear photograph of an alien space craft? I want to believe, but I have nothing to believe in, other than fractals, that is. And I'm not even sure I believe fractals are real. For today's fractal adventure I mixed Z^(0.996) with Z^(-0.996), added straight C and cut the escape radius to 90. To me, the resulting parent fractal resembles an alien flying saucer lying on its side. Some might see Bozo the Clown or maybe Popeye the sailor, but whatever one sees, the whole fractal is on the verge of evaporating, which is the reason for the name "The Vanishing Point". In fact, I had to reduce the bailout to 90 to keep the part of the parent where today's image is located from slipping into the imaginary fractal world. My efforts were rewarded with an FOTD that rates a 6. It could have been better, but it also could have been worse, so I can't complain. Today's image is located on the north shore of the parent fractal, at the point where the bud-filled chaotic shore ends and the smooth shoreline begins. I added extra interest by rendering the scene with the inside set to 'fmod' and the outside set to 'summ'. The calculation time of 8 minutes is slightly slow, but still well within reason for an image that has never before been seen and never again will be seen. And an even faster way to see the image is to go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the image in finished form there. The Thursday weather proved un-notable here at Fractal Central of central Pennsylvania. The high temperature of 61F 16C was fair enough, the partly cloudy skies were fair enough, and the mild wind from the east was fair enough. The fractal cats agreed as they kept a sharp eye on the pigeons roosting under the eaves of the house next door. I had a rather busy day working on a menu for a local restaurant. But the work went smoothly and the task was completed with ample time remaining for the day's fractal. The next fractal will be posted in 24 hours, more or less. Until then, take care, and it would be great if aliens from other worlds actually were flying around the earth in their alien space craft. Maybe they could teach us a thing or two about fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_VanishingPoint { ; time=0:07:59.95-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.7429016609182963/+0.5321247063450321\ /6.34773e+008/1/42.5/-6.18e-005 params=1/0.966/1/\ -0.966/0/-10/0/0 float=y maxiter=12000 inside=fmod proximity=0.1 outside=summ periodicity=10 colors=0008V_8V_8UZ8UZ8TZ8TY8SY8SY8RX8RX8QX9QW9PW9\ PW9OV9OV9NV9NU9MU9MU9LT9LT9KT9JS9JS9IS9IR9HR9HR9GQ\ 9GQ9FQAFPAEPAEPADOADOACOACNABNABNAAMAAMA9MA9LA8LA8\ LA7KA7KA6KA6JA5J72E93HA5JC7LD9NFBPGERIGTJIVLKXMMZO\ O`PRcRTeSVgUXiVZkXamYco_eq`gsbiuelxckzbkzajz_jzZjz\ YizWizVizUhzShzRhzQgzPgzNfzMfzLfzJezIezHezFdzEdzDd\ zBczAcz9bz8bz6bz5az4az2ay1`x0`w0`v0_u0_t0as0_r0Zq0\ Yp0Wo0Vm0Uk0Si0Rg0QetXYtcWthUtuTtuStuStmSteSt_SpTS\ gVSYWSOXSHZSJ_SM`SObSQcSTdSVfSXgSZhSajSckSelSjsThp\ SgmSekSdhSbfSacS`aSZZSYXSWUSVSSUPSSNSRKSPISOFSNDSO\ DRPDRPDROEQOFQNFPNGPMGOMHOMHNLINLIMKJMKJMJKLJKLJLK\ ILKIMJHMJHNIGNIGOHGOHFPHFPGEQGEQFDRFDREDSECSDCUDBV\ CBXCBYCC_DD`DEaEFcEGdFHdFIdGJbGKaHL`HM_INYIOXJPXJQ\ WKRVKSTKTTLUTLVSMWTMXTNYTNYTOZTO_TP`TP`TQaTQbTRdUR\ eVRfWSgXSiYTjZTk_Um_Un_Vo_Vq`Wr`Wt`Xu`Xw`Yx`Yy_Zx`\ Yw`YwaYvaYuaYubY8X`8W`8W_ } 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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Re: FOTD for 10/24/07
by Paul N. Lee 25 Oct '07

25 Oct '07

Brian Prentice wrote: > > Here is a detail from the parent fractal discussed by Jim today: > http://linuxenvy.com/bprentice/Fractals/Set%2012/BP_12_84b.jpg > A nice render. Thanks for sending a link to see it. Sincerely, P.N.L. ------------------------------------------------- http://home.att.net/~Paul.N.Lee/PNL_Fractals.html http://www.Nahee.com/Fractals/

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FOTD 25-10-07 (Over a Blue Horizon [6])
by Jim Muth 24 Oct '07

24 Oct '07

FOTD -- October 25, 2007 (Rating 6) Fractal visionaries and enthusiasts: The formula behind today's image subtracts Z^4 from Z and adds straight C. This mixture produces a Mandelbrot-like figure rotated 180 degrees with two sizable extra bays sprouting like butterfly wings from its butt end. Today's scene is located on the south shore of the new valley separating these two extra bays. Most of the interest was achieved by rendering the image with the outside set to 'tdis' and the inside set to'fmod' with the default proximity factor of 0.01 in effect. The mathtolerance entry was necessary to assure that the image calculates at the correct magnitude. I named the image "Over a Blue Horizon" because the greenish elements in the foreground appear to be floating over a hazy, more distant, bluish background. Then I bestowed a rating of 6 on the whole works. I could see no real reason to give a higher rating. The included parameter file finishes in 5 minutes on the fast machine and 22 minutes on the slow one. The time required to go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the image already finished there is even shorter. Heavy overcast, with a chilly temperature around 55F 13C, light rain and a raw wind from the north made Wednesday an unpleasant day here at Fractal Central. The cats of the fractal variety needed a bit of extra petting to keep their spirits up. My day was boringly average, a situation that I actually found quite pleasant. The next FOTD will appear in about 24 hours. Until then, take care, and if everything is an illusion, then nothing, whatever nothing is, is having an illusion? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Over_a_BlueHorizon { ; time=0:05:03.90-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.02240988266139494/-0.000848508846262\ 04/2.054005e+012/1/97.5/3.878382e-005 params=-1/4/\ 1/1/0/0/0/0 float=y maxiter=600 inside=fmod outside=tdis periodicity=10 mathtolerance=0.05/1 colors=000UXAUTAUPAURAUTAUVAUXAUZAU`AUbAUdAUfAUhAU\ jAUlAUnAUmAUgAUdAPaAPbAPZAKVAFSA5PA0KA5PAAVAK_AUeA\ UkAcpAciAccAFfzJ`zNVzMTzMSzMQzMPzMOzMMzMLzMKzMIzMH\ zMGzQNzUUzY`zagzeizikzmkzqkzmpzjpzfuzcuz`yzXwzUvzR\ tzNrzKpzHozDmzAkz7jzAgzCezEczG`zIZzKXzMVzOSzQQzSOz\ UMzVIzVEzVAzTIzRPzPWzObzMizKpzJwzOuzTsz0zz1zz6yzBx\ zFwzKszPpzUnzaczhczJJzLOzNSzPXzR`zTdzVizXmzNDzcFzb\ Rz`Yz_dzZkzPjzUnzpmzlmzhmzdmz`mzXZzYbzYezYhzYkzYnz\ 7BzLXz5szPkzRlzSmzTnzUnzVozWpzXqzO`zNdzQgzSjzUlzWo\ z0vz4tzEszOczgFzfPzfTzfSzgRzfPzfNzjJzmEznLzlSziYzh\ `zf_zaYzXUzSKzOBzQKzSTzU`za`zWiz0Ez4Jz8OzDTzHYzLbz\ QgzUlzh_z5QzAUzEYzIazMezQizUmzFczJfzNizRlzVozRpzTp\ zUnzWpzXnzKpzNpzQpzTrzWozWpzXqzEwz0Az4Gz8LzDRzHWzL\ azQfzUlzMmzPnzSozVpz0GzATzMezdwzbuzatz_szZrzNzzTuz\ 0zzOPzTczYQzYVzY_zYczYhzYmzEkzHlzKmzNnzQozTpzWqzeW\ zeWzeWzfWzfWzfWzfVzfUzfTz } 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 24-10-07 (Nevermore Land [5.5])
by Jim Muth 23 Oct '07

23 Oct '07

FOTD -- October 24, 2007 (Rating 5.5) Fractal visionaries and enthusiasts: The parent fractal of today's image, which was created by combining Z with Z^(-0.5) and adding C, resembles a fractal bullet. Today's scene is located on the north shore of the bullet, where some very tiny mandel-buds are located. I named the image "Nevermore Land" because after finding what lies there, it is unlikely that I'll ever go there again. I could rate the image itself at only a 5. My semi-expert color- ing efforts added the extra half-point. Today's fractal image shows an abstract land of fractals -- a land created by numbers and populated by the horde of similar figures that fill the frame. Not surprisingly, as we dive deeper into the image, these figures are repeated at ever smaller sizes without end, all the way to infinitesimal infin- ity. That's the way fractals are. An overwhelmingly prominent, blazing white minibrot sits at the center of today's scene, looking strangely out of place, almost as though it were dropped there by some higher power. It has little symmetry to betray its existence, and almost no basin of attraction around it. Other smaller minibrots are scattered throughout the scene, all of them similar to the one in today's image. The parameter file at the end of this discussion takes just over 5 minutes to complete on the fireball P4-2000mhz machine. On the droopy old P-200mhz snowball unit it takes about 1/2 hour. On the FOTD web site the image has already been calculated and posted for maximum enjoyment. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy clouds and occasional rain spoiled the day Tuesday here at Fractal Central. The temperature of 72F 22C, however, was quite pleasant. The fractal cats, who dislike rain, spent the day watching the humans do their work. My work was finished earlier than expected, which gave me a chance to find today's parent fractal. The next fractal will be posted in 24 hours. Until then, take care, and numbers describe the universe so well because we created them intentionally to do just that. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Nevermore_Land { ; time=0:05:11.42-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-1.0890400699647/+0.07599607053382/\ 7288.355/1/-35/1.85112133954667968e-011 params=1/1/1/-0.05/0/0/0/0 float=y maxiter=6000 inside=255 logmap=128 periodicity=10 colors=000aAp_8nY8nW8lU7lS7jQ5jO5hM5hK3fI3fG1dE1dC\ 0bA0b80_70_50Y30Y10W00X10X10X10V30V30U30U30T50T50T\ 50U70T70U70T70TC0QG3OK7OOAMTEMXIK_MKdQIiXIn_GrdGvg\ EzlEzpCztCzxAzz8zzMzzXzzezzpzzzvzzrzzmzpmzemzXmzMm\ zCmzAmzAizAezCazCYzCUzCQzCMzCIzCEzCAzC6zC3zC0zC0zC\ 0zC0zA0zC0vC0rC0nE0iI0eM0aQ0YV1VX5Q_8MbCIeGEiIAlK7\ nM3pO0nO0lM0jK0iI0jG0kE0lE0mE0nE0mE0lE0kE0kE0kE0kG\ 0kG0kG0kG0kG0kG0kG0kG0kG0kG0kG0kG0kG0kG0kI0lI0mK0n\ K0oM0pM0pO0pO0pQ0pQ0pQ0pT0pT0pT0pV0pV0pV0pV0pV0pV0\ pV0qV0rV0sV0tX0uX5vYAwYFxZKy_Kz`LzaNzdKzdMzaMzaNza\ KzaJzaIzaJz_Iz_Jz_Jz_Lz_Lz_NzYNzYPzYPzYRzYRzYQzXSz\ XRzXRzXSzXSzXRzVUzVTzVTzVVzVVzVVzTXzTXzTXzTYzTYzTY\ zQ_zQ_zO_zMazKazIazGdzEdzCdzAez8ez7ez5ez3ez1ez0ez0\ ez0ez0ez0ez0ez0ez0ez0ez0ez0ez0ez0ez0ez0ez0ez0gz0iz\ 0lz0nz0pz0rz0tz0vz0xz0zz0zz0zz0zz0zz0zz0zz0zz0zz0z\ z0zz0zz0zz0zz0zz0zz0zzzzz } 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 23-10-07 (The Wheel of Eternity [6.5])
by Jim Muth 23 Oct '07

23 Oct '07

FOTD -- October 23, 2007 (Rating 6.5) Fractal visionaries and enthusiasts: Today's image is named "The Wheel of Eternity". I was in a kind of mystical mood when I searched for a name, and this is what I came up with. And why not get mystical with fractals? After all, almost anything seems to be considered true by someone some- where in today's world, where those who have actually experi- enced the preternatural know that it does exist, and skeptics, who are solidly grounded in physical reality, know that it does not. Since I have yet to decide whether fractals are real, un- real, or somewhere in between, I have no comment at this time on the preternatural. (I might have a comment in the not-too- distant future however.) One thing in-between is today's image. Though it is worth about a 6, I actually rated it at a 6.5. The extra half-point is to reward myself for the minimum of extra effort I put into the coloring. I am sometimes asked why I post so many images of Minibrots. The answer is that this is the infinitesimal part of the infinite world of fractals that I have chosen to concentrate on, and learn as much as possible about. When working with fractals, one can know either a little about a lot or a lot about a little. I have made the latter choice. The parent fractal was created when I subtracted Z^(1.1) from 10 parts of Z^(-1.1) and then added C, while increasing the escape radius to 625. This parent fractal lies totally off the default screen, making a couple outzooms necessary before it comes into view. It consists of a distorted Mandeloid, shaped somewhat like a dumbbell, with a period-2 bud larger than its main bay, and a smaller, half-obscured Mandeloid some distance southwest. Today's scene is located in what appears to be a kind of East Valley of this smaller Mandeloid. With its calculation time of 1-1/4 minutes, today's image is blessedly fast. But the minor chore of setting up and running the included parameter file is still there. This minor task may be avoided however by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the completed image there. With partly cloudy skies and a temperature of 73F 23C, Monday was rather pleasant here at Fractal Central. The fractal cats must have agreed, for they spent a good part of the day sleeping. My day was average busy. If all goes well, tomorrow will be a repeat. The next FOTD will appear in 24 hours. Until then, take care, and beware. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= TheWheelOfEternity { ; time=0:01:16.85-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-6.964125413119925/+5.786985493853145/\ 2.118189e+009/1/-103/0.0131289825157970344 params=-1/1.1/10/-1.1/0/525/0/0 float=y maxiter=1600 inside=0 logmap=112 periodicity=10 colors=000KISNLWRO_VSbZVfaYjeamidqlgtmhuniuoivpjvq\ kwrkwrnxspxtsyuryvwzwxzzzzjkzYgzLczN_zPXmRUdTRYVOH\ WL8cH4jD1pOGvYVzgzzdiu`fzYcuVXvSUsPRpLPoIMmFJkCGj9\ Di6Aj38g6Bd9EaBHZEKVHNSJQOMTKPWGRZCUa8Xd5ZgNdTciEz\ n0zo3zp5zq7zq9zrBzsDqtGqtIquKpvMpwOpwQkrPfnObjOYfN\ UbMPZMLVLGRKCNKASH8XE7aB5f83k52p26n4Am5Ek6Ij7Lh8Pg\ ATeBXdC`bDcaEfYFiVFlSFoOGrLGuIGxFGvKFtPEsUDqZCocCn\ hBlmAjr9iv9RrV8op8opzzzUIQdHaR76nHmmLklPjkThkXgkQd\ kKakEZk8XeJT`TPVcLQmIJiYDemCZfCS_CLTBEMB7FB18C4IC6\ RD8_DBhEDqEFzPPw_Zuimujhskdqk`olWmmSkqJnmOjiSfeWba\ `ZYdVOoGUhSS`oZacwXXdaTMfP4jL9dNEcOJePOgQTiRYkSbmT\ goU_pRTqOLrLEsI3tF7uGBvHFwHJxINyJRzJVzKVzQYzK_zKaz\ PczUezZkzcpzhuzmzzrezvLzzqzz1zz4zz6zz8zzBzzDzzFzz9\ zz4zz8zzBzzFzzIzzNzzSzzXzzazzpzzezz2zz4zz5zz7zz6zz\ 8zz9zzAzzBzzCzzEzzFzzGzzIzzJzzKzzPzzTzzYzzazzezz_z\ zUzzPzzJzzEzzJzzNzzCzzGzz } 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 21-10-07 (A Lot of Nothing [6.5])
by Jim Muth 21 Oct '07

21 Oct '07

FOTD -- October 21, 2007 (Rating 6.5) Fractal visionaries and enthusiasts: After a run of images that take sizable portions of an hour to calculate, today's rather dark and gloomy but sizzling-fast image finishes in 13 seconds. The image is a scene in the parent fractal that comes about when 0.3 part of Z^2 is subtracted from 0.3 part of Z^(-3) and straight C is added. This parent fractal is an oversized thing that vaguely suggests a Mandelbrot set that has been rotated 180 degrees and filled with fascinating intricacies. Today's scene in located in the part of the parent fractal which might be the remnants of the large minibrot on the negative X-axis. I named the image "A Lot of Nothing" for no logical reason at all. There certainly is a lot of something in the image -- an infinity of it. In fact, there is enough stuff in the hidden depths of today's image to give every fractalist on earth a different infinity to explore from now through eternity. After I named the image, I rated it at a 6-1/2. Once again I rewarded myself for the extra effort I put into the coloring. The calculation time of 13-2/3 seconds is as fast as lightning. Even the worn-out old P200 machine finishes the calculation in under 1 minute. But the most convenient way of all to view the image is to go to the FOTD web site and view it in finished form there. The FOTD web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Saturday turned out to be a near perfect day here at Fractal Central, with a deep blue sky set off by puffy white clouds, and a temperature of 68F 20C. The fractal cats must have found the day pleasant also, for they spent a good part of it stretched in the sun streaming through the south window. My day was un-notable, the way I wish all days would be. The next FOTD fractal will be ready in 24 hours. Until then, take care, and be on the watch for that elusive something known as the ultimate reality. It might be a fractal! Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Lot_of_Nothing { ; time=0:00:13.65-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident center-mag=+5.065449254256304/-1.226811093382541/\ 6.289509e+009/1/101.747334433732746/-0.00792485\ 470680458215 params=0.3/-3/-0.3/2/0/0/0/0 float=y maxiter=400 inside=0 logmap=29 periodicity=10 colors=000A9kAAiABgACeBDc8E`6FX7ET7DP7BL7ACFBDNCEU\ DF`EGlFHsGUzUczimzzzL8k95tCPBHgFmzJQzN0zRZzVbYZw_b\ w`fd_WZ_LQTMIMNAFO28O0`K5XQAUVER_JOdNLzT_zYwzSwzMe\ zHbzKXzMSzONzRIzTDzV8zX3zT7zPBzMEzIIzFLzLRYRWdWala\ fsWdnQbiK_cEmZ7mT7mF6m08mABmKEmUDbUCbTAaS9aS7`R6`Q\ 4_P9_SE_VJ_YOZ`TZcYZfcYieaegeaiiYlmUnqQpuMszHpqNmg\ UiZ`fPgcGn_6u_Eq_Nl_Wg_db_mY9miDrNBpJ9mE7kA5h53e0R\ g6njDnhHneLnbQn_UnXZnUbmRgfTeZWcRYaK`_CbY4eWObMg_C\ faHecNdeScgYbicakh`mnZptZoqYnnYlkXkhXieWhbVfZWgTYi\ N_kHamBZmBVmARm9osoelcWdRMXFCP2CV3C`4Cf6Cl7Cr9CgLD\ XYEMjFBwuh7viTwjotgnqcmn`lkXkhUjeQibMgFm7HmDKmKMmR\ PmYSmcUcjXhq_nxchuhbqlXmqRjuLfzEbmzb_zcNzd9zeKzhWz\ kgznszqhznXzkMzhAzdyzJqzShzayz2vzBrzKozTkzagzkkzap\ zSuzIzz7zzXyzvyzryznyzjxzfxzbxzZwzUizSVzPHzM2zJjze\ hzgfzjdzmazp_zsYzvVzy_zyezxjzxpzwtzsyznozVdzBjzBqz\ CnzDjzEgzFczG`zHXzITzKTzK } 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 22-10-07 (The Lost Minibrot [No Rating])
by Jim Muth 21 Oct '07

21 Oct '07

FOTD -- October 22, 2007 (No Rating) Fractal visionaries and enthusiasts: Today's image is named "The Lost Minibrot". I gave it this name for a good reason -- I lost the parameter data when I saved the image in the wrong format. The image, which I did not rate but which would be worth an 8, can be seen only by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> All I can say about today's image is that it was probably crea- ted with either the MandAutoCritInZ formula or the MandelbrotBC2 formula. I'll try to track it down when I get a chance, but success is very unlikely. Sunday turned out totally perfect here at Fractal Central. The cloudless sky and temperature of 73F 23C was perfect for almost anything except farming. The fractal cats agreed as they basked on their window shelf in the warm sun. My day was pretty good. It would have been better if I had not lost the parameters of today's image, but the image itself survived even though it will probably never be further explored. The next FOTD will appear, along with its parameters, in just 24 hours. Until then, take care, and what is it all about? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com NO PARAMETERS AVAILABLE===================================

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Fractint meets Scientific American (not the first time...?)
by Tony Hanmer 21 Oct '07

21 Oct '07

Thanks to an online survey in which I participated some time ago, Scientific American online has invited me to be a member in its new online community, which is quite exciting. I'm listed as Anthony Hanmer, and my blog there is called SubCreator. My first series of posts will reissue the letter I wrote to the Fractint list in early September 2004, dealing with "Tiles of the regular reptiles for all dimensions above 1". Most of the work for that letter comes from experiments in Fractint; in the new posts I add illustrations and some minor polishing. It can be found, in multiple parts starting with the first part now, at http://science-community.sciam.com/index.jspa Anthony Hanmer Tbilisi, Republic of Georgia My photo/graphic blog: www.geosynchronicity.blogspot.com

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FOTD -- October 20, 2007 (Maximum Distortion [7.5])
by JimMuth＠aol.com 21 Oct '07

21 Oct '07

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[Fractint] Re: FOTD -- October 18, 2007 (Rating 8) Minibrot revealed
by jackoftradez＠comcast.net 20 Oct '07

20 Oct '07

. Jim Muth say: ""I have not done the calculation, but I suppose that at the scale of today's image, the entire Mandelbrot set would occupy a significant part of the visible universe"" I did these calculations years ago, around the turn of the century. The observable universe spans 10-20 Billion light years, depending on your source of info. Assuming a 19 inch monitor display, a fractal magnification of about E+27 puts you there. Thus your image at E+37 is not ten times the size of the universe, it is ten orders of magnitude bigger, that's ten billion times the size of the universe. Hard to fathom, but numbers don't lie. I actually have a simple DOS program on my site that does this calculation. Stay Amazed! JoTz .

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FOTD 21-10-07 (A Lot of Nothing [6.5]) FOTD -- October 21, 2007 (Rating 6.5)
by JimMuth＠aol.com 20 Oct '07

20 Oct '07

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FOTD 19-10-07 (X Is Where It's At [7.5])
by Jim Muth 18 Oct '07

18 Oct '07

FOTD -- October 19, 2007 (Rating 7.5) Fractal visionaries and enthusiasts: Greetings once again from Fractal Central, located in glorious central Pennsylvania. Today's image takes us to the parent fractal that is created when 5 negative parts of Z^(-1.5) are combined with 1 negative part of Z^(-5) and (1/C) is added. For extra interest the escape radius is reduced to 40 and the scene is rendered with the outside set to 'tdis'. This parent fractal is a string of 3 north-south aligned, nearly circular bays. Today's scene is located not too deep in one of the western valleys between the bays. I named the image "X Is Where It's At" because of the prominent 'X'-shaped figure around the central minibrot. This 'X' is almost entirely a result of the coloring, so I decided to reward myself by adding an extra 1/2 point to the 7 that I rated the image. In contrast to the images of the past few days, which had a calculation time of hours, today's image finishes in a mere 50 seconds. And it is even more convenient to go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the already-finished image posted there. Another summer-like day here at Fractal Central was spoiled on Thursday by too many clouds. But despite the clouds, the temper- ature reached 77F 25C, bringing out the shirt sleeves and shorts in the area. Not needing clothes, the fractal cats spent the day stretched in the window, waiting for the sun. Unfortunately they got only a few minutes of sunshine for their effort, and extra tuna was needed to ease their disappointment. My day was busy but under control. The next FOTD will appear in 24 hours. Until then, take care, and with Halloween coming, isn't it a good thing that all those crazy supernatural things that make the day so much fun are not real . . . . . . or . . . I wonder . . . no, it couldn't be? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= X_Is_Where_It's_At { ; time=0:00:49.97-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=-0.047579342015/-1.341910586642/3793/1/\ -164/-8e-012 params=-5/-1.5/-1/-5/0/-60/0/0 float=y maxiter=1600 inside=0 outside=tdis periodicity=10 colors=000uuM0SZ0QZ2M_AI`IFaQBbY8cFEX0JR1OK5SD9W7C\ Z9E`AGbBJdCLfDNhFQjGSlHUnIWpJiMLdLI`LGXKETKCPJALJ8\ HI6DI49H25H01H07K0DN2JQ4PT6VW8_YAY_JWaRUh_TwzLmzDc\ zQPWaFHm92gGBaNJXURXPMXKHXFCZA8Z5A`6Fc7Kf9PhBUiDZj\ CajCajFbjIbjLbjObiQbgRbeQccPc`NdXLdTJdRHcNEcLCbzz`\ tpZofUoZPpTKoTInWHp_FrbEseDkgCciCXkBPmBHoB9qA2sA1q\ A5oFFmJOkNTiQXgS`eUecXiaZmZ`qYbbWZPXVAYR0YN0ZS0_V1\ `Z3`a4ae6bh7blGWdPPYXJReCKm6Dl5Kl4Ql3Xk2bk1ik0o4lU\ 6kY8ka9jeBjiDimEiqFhjFgdFfZFeTFdMFcGFbAFa4EX7DTACP\ DBKGAGJ9CLBEMDGMEHMGJNILNJMNGJMEHLCFK9CJ7AI58H36H0\ 7H07H0CJ0GK0KL0ON0SO0XP0aQ0fS0kT0pU0tV0oT1kR6gPAcN\ FZLJWJOTISQGYMEfJCkHArS8zU7qPChBHc0M`0R_0WU0_P0WK0\ SF1O54K88GBBCEF8HI4KM0NP0QS0SR0UQ2VQ6XPAZPE_OIaOMc\ NQdNUfMYgMZfLXfLSfLNfLIeKDeK8eK3eK0eK0eYPekr`hpXfn\ TdlOajK_hGYgEXeCXdAWc9Wb7V`5V_4UZ2UY0TX0TV0SU0ST0R\ S0RR6EEJ11RbUL`VFYWAWX4UY } 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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Type "Circle" and variations thereof
by Gerald K. Dobiasovsky 17 Oct '07

17 Oct '07

Hi, Just a small diversion... Please keep in mind the parameters chosen are only meant to be used as a starting pattern (monitor resolution was 1024x768), not to create any artistic images per se - that's what you'll have to accomplish yourself :-) So...zoom out!!! Regards, Gerald START PARAMETER FILE================================================= My_Circle {;Own implementation of Fractint type "Circle" ; reset=2004 type=formula formulafile=archiv.frm formulaname=Circle passes=1 corners=-2/2/-1.5/1.5 params=100/0 float=y maxiter=2 decomp=256 colors=(a)chroma.map } Hyperbola {;Same principle as in "Circle", for hyperbola x^2 - y^2 ; reset=2004 type=formula formulafile=archiv.frm formulaname=Hyperbola passes=1 corners=-2/2/-1.5/1.5 params=100/0 float=y maxiter=2 decomp=256 colors=(a)chroma.map } Parabola {;Same principle as in "Circle", for parabola x^2 - y ; reset=2004 type=formula formulafile=archiv.frm formulaname=Parabola passes=1 center-mag=0/0/0.6666667 params=300/0 float=y maxiter=2 decomp=256 colors=(a)chroma.map } frm:Circle {;Own implementation of Fractint type "Circle" ;decomp=256 ;------------------ ;p1r: Magnification ;------------------ z = |pixel|*real(p1): z = exp(flip(z-floor(z))*2*pi) z != z } frm:Hyperbola {;Same principle as in "Circle", for hyperbola x^2 - y^2 ;decomp=256 ;--------------------- ;p1r: Magnification ;--------------------- z = real(sqr(pixel))*real(p1): z = exp(flip(z-floor(z))*2*pi) z != z } frm:Parabola {;Same principle as in "Circle", for parabola x^2 - y ;decomp=256 ;-------------------- ;p1r: Magnification ;-------------------- z = (sqr(real(pixel))-imag(pixel))*real(p1): z = exp(flip(z-floor(z))*2*pi) z != z } END PARAMETER FILE===================================================

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FOTD 18-10-07 (The Minibrot Revealed [8])
by Jim Muth 17 Oct '07

17 Oct '07

FOTD -- October 18, 2007 (Rating 8) Fractal visionaries and enthusiasts: Yesterday's image showed part of the pattern surrounding an infinitesimal minibrot in the East Valley area of the large minibrot at -1.75 on the negative X-axis of the Mandelbrot set. Today's image takes us all the way down to this tiny minibrot. The depth of today's scene is truly amazing. At the scale of today's image, yesterday's scene would be enlarged to many times the size of the solar system, while at the scale of yesterday's image the entire Mandelbrot set would also be enlarged to many times the size of the solar system. I have not done the cal- culation, but I suppose that at the scale of today's image, the entire Mandelbrot set would occupy a significant part of the visible universe. I named the image "The Minibrot Revealed". Since the name says it all, no further explanation is necessary. The minibrot is actually quite an impressive one, revealing as it does the tendency of all minibrots at such a magnitude to be surrounded by a large number of concentric, circular, but well ornamented rings. The image is well worth the rating of an 8 that I bestowed on it. The drawback is the extreme slowness of the image, which takes almost 2 hours to complete on the fractal fireball and would take around 10 hours on the old cold snowball. But salvation is at hand in the form of the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the image will shortly be posted, if it is not already posted. Only a bit too much haze and a few too many clouds kept Wednes- day from being absolutely perfect here at Fractal Central. The high temperature of 75F 24C was certainly perfect enough. The fractal cats must have agreed, for they spent most of the day watching the pigeons roosting and cooing on the roof of the house next door. I might say my day was almost perfect also, but before I could make such a claim, I would have to know just what an absolutely perfect day would be like. So far, I have never had a day when nothing at all went wrong, so I guess I'll be satisfied saying my day Wednesday was rather good. The next FOTD will appear in 24 hours give or take a few. Until then, take care, and be at peace with the powers that be. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= TheMinibrotReveald { ; time=1:52:37.82-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.7465\ 2317861165630378879937150792993485941/0/\ 2.106321e+037 params=0/0 float=y maxiter=50000 bailout=4 inside=0 symmetry=xaxis periodicity=10 colors=000zzzxxzwvztuwqstnpqkkmhhhacdZ_XXZUUYRQXQN\ VNLULISIGRGDQDAOCDQDGREIRELSGMSGPUHRVHUVIXXIYXJ`YJ\ cYLeZMh_Mi_NlaNnaPqbPtdQvdQxeRzeRzfTzfTvhPliLciHUj\ DLz9Cz52z10m00i11e44a56Z79V9CRCGQ6EOJDOPCOXANb9Ne7\ Ni6Nn9MqCKtEJwHIzJIzMHzNFzQEzTDzWDzYBz`Azc9zd9zeAz\ eBxgDwgEtgEshFphHniIliIkiJhkKgkMdkMclN`lOZmQXmQWmR\ TnSRnUPqVMnUNlUPiUPgUQdSQaSRZSRXSTWSTTRUQRWNRWLRXI\ QXGQYDQYAQZ9QZ9NZAKZAIZAE`AB`C9`C6aC3aC1aD0cD0cD0c\ 00Y60`D0cJ0dQ0gX0ic0ki0mp0pw0qz0tz0vz0tz6tzEtzNtzU\ sLHUNHTPIRRIRUIQXIPYIP`INcIMzB0zcMzHPYFRWETTDWQBYN\ AZL9aI7dG6eD5h43cA5iH6pN7wU9zZ9zaDzdHvgKniOilScnXX\ q_QtdLmiHhnDct9aq7an7`l7`i7Zf7Zd7Za7YZ7YX7XU7XR7WO\ 7WM7WJ7UH7UE7RB7Q97N67M37L27P6CR9GUBJXEMZHQ`JUaMYc\ Q`dSdeVhgYlh_nibskewlhzzRCzSEzSGzSHzUIzUJzULwVMvVN\ tVPsXQqXRpXTzUenXUdZJTa9Id0Le0Mf0Nf0Qh0Rh0Ti1Uj1Xj\ 1Yl1Zl1am1zzzzzzzzzzzzzzz } END PARAMETER FILE=========================================

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FOTD 17-10-07 (East to the Sixth [7])
by Jim Muth 16 Oct '07

16 Oct '07

FOTD -- October 17, 2007 (Rating 7) Fractal visionaries and enthusiasts: Today's image is named "East to the Sixth". I gave it this name because it is a scene in the East Valley of a minibrot in the East Valley of a minibrot in the East Valley of a minibrot in the East Valley of a minibrot in the East Valley of a minibrot in the East Valley of the large minibrot on the main spike of the Mandelbrot set. With all those minibrots lined up above today's scene, it's little wonder that some unusual things have appeared in what should be an everyday scene in a typical East Valley. Actually, the high magnitude of today's scene, which has been rotated 89.99 degrees, (There's a bug that prevents a full 90-degree rotation.), reaches nowhere near the magnitude of the unseen minibrot at the center, which is about 10,000,000,000 times as great. But there is quite a fine minibrot down there, which will likely make the FOTD in a day or so. I decided to rate today's FOTD image at a 7. Maybe the central minibrot itself, when it finally appears, will rate an 8. With a calculation time of over one hour on the fireball and five hours on the snowball, today's fractal almost demands a visit to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> for an immediate viewing. Tuesday's temperature reached 68F 20C here at Fractal Central, but increased clouds kept it from being another perfect day. The fractal cats must have agreed. They spent a good part of the day working the hall carpet loose. My day was peaceful enough. With any luck, tomorrow will be the same. The next FOTD will appear in 24 hours. Until then, take care. And with video cameras so common, why has no one yet produced a clear photograph of an alien space craft? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= East_to_the_Sixth { ; time=1:05:35.85-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.7465231786116563037887993715079/0/\ 3.389166e+027/1/89.99/0 params=0/0 float=y maxiter=100000 bailout=4 inside=0 symmetry=xaxis periodicity=10 colors=000_TZgTUbXaY_hTcoPfvNjjLrZJzNIwBKtDLqENpGO\ mHPjJRiKSgMUeNVdPWbQY`SZ_T`YVaWWdgcbVX_JQaIRbIRcIS\ dISeISgIThITiITjIUpIUvIUzGTzcTzmSzcSvCRqBRk9Qe8Qd7\ Pc6Pb5Ob4Oc5Qc6Sc7Uc7Vc8Xc9ZcA`cAccBhcCmcDrcDvcEzc\ FzcGzfFxcGt`GoYGjWGfTGaQGXOGULGQIGMGGJDGFAGB8G87JC\ 6LG5OJ4QN3TQ2VU1YX0_`0ac5XeATfFPgKLhPHiUDjZ9kc5lg1\ mh7nhCoiHpiMqjRrjWsj`tkeukjvlowltxlyxembarMZbIWOEX\ 16T9APGEPGCMNHJULG_PDfTAmX9wc8s`8oZ7kX7gU6cS6_Q5WN\ 5SL4OJ4KG3GE0CA3DC5EE7EFAFHCGIEGKHHLJINKJOLIOLHOMG\ OMFONEONDONCOOBOOAOP9OP8OQ0GP8OPGWPOcPWkXjwTfuPcsL\ _rHXpDTo9Qm7Fz5Nl3VZmim2bLEeIQgGaiDzw8zsAzoBzkCzeE\ zaFWWGRSIMOJEGMGILIKKKMKLOJNQJPSIQUISWHUYGW_GXaFZc\ F`eEagEWiGQkIKmJEoL8qN3sO7oPAlPEiQHeQLbRO_RRWSVTSY\ QTaMTdJUgGUiPZjWblcfmjkoqopxszyszzrzzrwwqruqmrpjop\ jmoijohgogengcnfame`mdZldXlcWkbUkaSkaRj`Pj_NiZMiZK\ hYIhXHgWFgng5mf6AVoJUiRUd } END PARAMETER FILE=========================================

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FOTD 16-10-07 (Hyper-Dry Valley [6])
by Jim Muth 15 Oct '07

15 Oct '07

FOTD -- October 16, 2007 (Rating 6) Fractal visionaries and enthusiasts: Today's curious image is another venture into the fractal that results when 0.2 parts of Z^3 are subtracted from Z^2 before C is added. This fractal appears as a Mandelbrot set rotated 180 degrees, with an extra spike extending from its East Valley, which of course is on its west side. But today we ignore this extra spike and check the more conven- tional spike extending eastward from the Mandeloid's nose. There is a very prominent minibrot on this spike, which appears to be two partially merged minibrots. Today's image is located rather deep in the northern branch of what at first appears to be a Seahorse-type valley, but actually is an entirely new type of valley. I named the image "Hyper-Dry Valley" because despite the promis- ing appearance of the chaotic yet symmetrical 'object', I could find no minibrot at the center. The minibrot might be there, but the resolution failed before I reached it. Despite the disappointment, I rated the image at a 6. The fractal object, if indeed it *is* an object, has such a real appearance that I could do no less. I'll leave it to the philo- sophers to argue the actual reality of fractal objects such as the Mandelbrot set. But one thing that cannot to be argued is the calculation time of the image, which is a rather slow 10-3/4 minutes on the fractal fireball, and just over one hour on the fractal snowball. The finished image has been sent ahead to Paul at the FOTD web site, and by the time you read this, it should be already posted and ready for instant viewing. <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Very fine weather prevailed here at Fractal Central on Monday, with sunny skies and a temperature of 68F 20C. The fractal cats enjoyed the sun from their shelf in the window. My day was as average as the fractal. I expect another average day tomorrow, but hopefully the fractal will be better. The next FOTD will appear in 24 hours. Until then, take care, and everyone has some degree of faith in something. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Hyper-Dry_Valley { ; time=0:10:44.72-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident center-mag=+1.589436551517345/+0.0185571325367402/\ 7.396629e+011 params=1/2/-0.2/3/0/0/0/0 float=y maxiter=10000 inside=255 periodicity=10 colors=000nVbmUflUikTlDVOB_O9dO7iN6gb5er3cz3cz3cq4\ dh9ZgFTfLNeRHdXBbbHahN_oUYePSWKMLEGLHHLKILNJLQKLTL\ LXNNYPPZRR_TUaWWbYYc_`ebaf_bgXchUdjRekOflLgnIjaOmO\ UqA`hGW_MRRSMIZHOcLUhQ_mVer_kwdrzilyhftg`pfVkdPgcJ\ bbDZa6U_B_eGekLlrIjmEggBda7bX4_R0XL9TNJOPTJSaEUk9W\ u4Zp6Wk9SeCP`FLWIIQLEOW_LgunJElNGjRIgVKe_NccP`gRZk\ TWpWZ`YaL`cJYfHViFSlDPoBMr9Ju7Gx4DxJNxYXxlfxzqrznk\ zkdzhZzdSzaLzZEzVKx`RugYsmdptknzrkzjguabhTYWQSeNLo\ KFyH8zGEzFKyEQtCWnBaiAgc8mYAgcCaiEahHagJ`fM`eP_dR_\ cUZbXZ`ZZ_aYZcYYfXXiXWkWVnWUqVSqVSpWSpWToXToXUnYUm\ YUmZVlZVl_Wk_Wj`XhZWeXVcVU`STZQRWOQULPRJOPHNMELNEQ\ ODSPDUQCURCUSBUTAUUAUV9RX8DTIJOSOJaTEkY9ucCqeGmgJi\ iNdkQ`mUXnXSo`OpcKqgFtdFqaFnYFkVFhSFeOFbLFdHFaEFZB\ FW7FT4FQ0GNBKLNOJYSHiWFu`Du`Gt_JsZNrYQqYTpXXoW_H00\ K00N00Q00T00W00Z00a50eA0iF0mK0qP0tU0wZ0yc0vh0sm0oh\ 0lc0hZ0eU0bW0`X0YY0WZ0T_0 } 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 15-10-07 (In a Blue Mood [6])
by Jim Muth 14 Oct '07

14 Oct '07

FOTD -- October 15, 2007 (Rating 6) Fractal visionaries and enthusiasts: Today's discussion will be unusually brief. The reason is simple -- I was in an unusually lazy mood all day. Today's image is a scene in the fractal that results when Z^3 is mixed with straight Z and straight C is added. The resulting parent fractal appears as a Mandelbrot set rotated so that its normally west-facing nose faces south and its eastern butt faces north. It has spikes extending straight out from both its nose and butt, and these spikes are littered with interesting bits and pieces of fractal debris. Today's scene is located in a small bit of chaos that lies on the spike extending south from the parent fractal's nose. I named the image "In a Blue Mood" because I'm in kind of a blue mood after the brief return to the place that served as Fractal Central for so many years and the aging cats who were the frac- tal cats even longer. After not very much thought, I rated today's image at a 6. And most of that rating comes from the (IMO) expert coloring. The calculation time of 2-1/3 minutes is well within reason. Even more reasonable is a trip to view the image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Another perfect day prevailed here at Fractal Central on Sunday, as F.L. and I recovered from the trip back to Old Fractal Cen- tral on Saturday to see the old fractal cats Thomas and Tippy, who are still hanging in there after almost 18 years. They are now kept quite happy by my sister, who still serves their tuna treats every evening. Curiously, the old and the new fractal cats have never met, and probably never will. Tippy fights all strange cats first and asks questions later. The next FOTD will appear in 24 hours. Until then, take care, and what came first -- the fractal or the numbers? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= In_a_Blue_Mood { ; time=0:02:21.12-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident center-mag=-0.00127303306054411/-1.076075627545789\ 00/3.21923e+009/1/92.5/-9.10166470642626013e-007 params=1/1/1/3/0/0/0/0 float=y maxiter=1600 inside=0 logmap=439 periodicity=10 colors=000J6aK8bLAcMCdNEeOGfPJgQNhRRiSVjTZkUblVemW\ coXbrV`uQ_wLZxGYyBXz7Wv9WrAWmBVkDVhEVeFVbHV_IVXJVU\ LVKMV9NY6QbBUiGcpLjwQcrPUmOKhOBcNC_NEXMGTLHPLJLKKH\ KMDJNAJQBKTBKVBKYBK`CKbCKeCKhCKwDKzUKzUKzUKwCMiCNe\ BPaBQYASUATQAVM9WI9YE8ZA8`68a5Ab5Bc5Dd4Ee4Gf4Hg3Jh\ 3Ki3Mj2Nk2Pl2Qm1Sn1To1Vp1WqIVVYU8WTAVTBUTCTTESTFQT\ GPTIOTJNTKMTLKrGJsHHtHFuI5QS6SR6TR7UQ7VQ7XQ8YP8ZP8\ _O9aO9bO9cNAdNAeNAgMBhMBiLBjLClLCmKCnKDoJDqJDrJEsI\ EtI7W28Y49_59a6Ac7Ae9BgABiBjKSiJQiIOeMMbPL_SKXWJUZ\ IRaGOeFLhEIkDFnCEjDEgDEdEEaEEYFEVFDSGDPGDLHDIHDFID\ CIO8QY5Yg2eh5fi7gjAhkCilFimHjnKkoMloOliNmcNnYNoSNp\ MMqGMrAMs4MtAKsFJrLHqQGpVEoYDo`BncAmf8li7kz6rzXzza\ zG3Q13S35U47Z69c7BhJCmVChfDcqDZpJaoOdnUgmZjmcmjakg\ `id_gbZe_XcXWaUV_SUZSUZRVYRVYRWYRWXQXXQXXQYWQYWPZW\ PZVP_VP_VFaIOcVOhUOmUOrUNvTNzTNzTNzSMzSMzSMzSMzRLz\ RLzRLzQLzQKzQKzPQz5azImzV } 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 14-10-07 (Mysterious Hexabrot [No Rating])
by Jim Muth 14 Oct '07

14 Oct '07

FOTD -- October 14, 2007 (No Rating) Fractal visionaries and enthusiasts: Today's quickie fractal was found with so little effort that I could hardly give it a rating. Before I entered the parameters I knew that the parent fractal would be a Mandelbrot set rotated 180 degrees, with a prominent spike extending from its East Valley as well as from its west end. And I knew that a strange little Mandeloid would lie on this extra spike. This strange little Mandeloid has a string of 5 extra bays ex- tending from its west end, and curiously, the largest of these bays lie farthest from the main body of the Mandeloid. Today's scene lies rather deep in the southern branch of the valley sepa- rating the fourth and fifth bays, which are the two largest. I named today's image "Mysterious Hexabrot" because the pattern around the minibrot consists unexpectedly of 6 lobes rather than the usual 4. I am finding this particular oddity more and more often in my travels through the fractal backwoods. I have no idea what it means, though I imagine that some mathematical genius somewhere on earth has already answered the question. The only thing not super quick about the image is its calcula- tion time of just under 4 minutes on the nuclear P4-2000mhz machine. The tired old P200 unit, which is still in fractal service, would take about 25 minutes to do the job. Taking all this time into consideration, I recommend viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> But because of the unusual post time of this FOTD, I would give Paul a couple hours to calculate the image and post it on the web site. Brilliant sun and autumnal temperatures in the 50's F, or around 13C, prevailed at Fractal Central on Saturday, making it a most pleasant day to be outdoors. While F.L. and I were outdoors, the fractal cats were having an equally pleasant day indoors. But they still demanded an extra treat when we returned in the evening. The next FOTD will appear on schedule in 12 hours or so. Until then, take care, and we will never solve all the myst- eries of existence until we discover them. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= MysteriousHexabrot { ; time=0:03:55.08-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident center-mag=-1.9597975605951/-0.0184877289191/4.841\ 299e+008/1/-45/0.00032688 params=1/2/-0.2/3/0/0/0/0 float=y maxiter=10000 inside=0 periodicity=10 colors=000Q`C2ttLwxczzuzzpyxkvrgtlbqeZo_UlUPiNLgHG\ dBCb5B_CAYIAWO9UV9S`8Qf8OlARnBUoDWpEZqF`rHcsIftKhu\ LkvMmwOpxPsyRuzSxzTzzUtwVmrWhmWciX`dYZ_ZWVZTR_RM`P\ H_MDZIBWJEQOGOSJQXLR`NTeQUiSWnUXrXZwZ_z`YybWwdUvfS\ thRsjPqlNpnLnpKmrIktGjvEhxDgyKeomLkhPicThZXgU`fZNS\ XQUWTWVVYTY_S_aRbcxUKsWNoXQjZTf_Vb`YYb`UccfUuY_mMv\ cE6zGCxIItKOpMUlO_h4ChFRfLZuM`qNanObkPch6n`9laCkbF\ icIhcLfdOeekkvmpjiniflhbjg_igWgfTeekupepm`ljVhgvXI\ mZOQEkNEqJLlFShBYdBVaBS_BPYBMWBJUBGSBDQDJRFORHTRJZ\ RLcRNiROoRTuVXzZbsahlcneetZgzTiW`X2hKSdcbm`_kaYjbW\ hcUgdSeeut5xOzsRwnTtiWqdYn_`kVbhMQRNTUOVWOYZP_`Qbc\ X2_`feZeeXeeWeeUdeTdeRde2as6bq9boDcmGckKdiDq9HpAKp\ BOpBRpQ9AS9BU9CW9DY9E_9Fa9Gc9HeCLfFOfISfLWgOZgRbhU\ fhWihTkgRlgPmgMngKogIqgFrgDsgBtg9ugCrdFobIl_LiYNgW\ TcTY_RbXPhTMmQKrMIwJGaMEGODKRJNTPQVVQWTQWSQXQQXPQY\ OQYMQYLQZKQZIQ_HQ_GQ`EQ`D } 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 13-10-07 (Slightly Skewed [No Rating])
by Jim Muth 12 Oct '07

12 Oct '07

FOTD -- October 13, 2007 (No Rating) Fractal visionaries and enthusiasts: Tomorrow I'm making a short trip back to Old Fractal Central, and the preparations kept me busy most of today. As a result, I had to cut short the fractal search and look where success was guaranteed. After a couple minutes, I found a fractal scene of FOTD quality in the Mandelbrot set. Today's image is another quickie from the large minibrot on the main spike of the Mandelbrot set. This time we delve quite deep into the north branch of the Seahorse Valley of this minibrot, where we investigate a filament extending from a bud on the east side of the valley. I named the image "Slightly Skewed" for a very good reason. The scene has been intentionally skewed 3 degrees. I did this to straighten the pattern around the minibrot, which actually appears a bit skewed in its natural state. Of course, such an easily achieved image can not be fairly rated. So I gave it no rating. But the calculation time of 42 seconds will try the patience of no one. As always, the best way to see the image is to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view it there. A far more pleasant though still chilly day prevailed here at Fractal Central on Friday. Despite generous sunshine the temperature reached only 57F 14C, which really had the squirrels searching for nuts. The fractal cats spent most of the day at the back window, keeping watch on the back yard, where the squirrels were most active. I kept active enough without searching for nuts. I still have a few things to pack for the trip back to Old Fractal Central on Saturday, but it's only for 1/2 day, so I won't need to do to much. I expect to be back here at New Fractal Central in time to post the FOTD for October 14 only an hour or two late. Check back then to see if I make it. Until next time, take care, and I thought I had lost my mind, but I found it behind the bookcase. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Slightly_Skewed { ; time=0:03:08.94-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.7685293035675\ /+0.0000964321759/8.20597e+009/1/-27.5/3 params=0/0 float=y maxiter=500000 bailout=36 inside=0 periodicity=10 colors=000L_fL`eMadMbcMcbQLVPNWPOWPPXPQXORXOSYOTYO\ UZOVZNWZNX_NY_NZ`M_`M``MaaMbaJaTKbWLcZMd8McAMcCMcE\ MvGzzIzzKvzMvsOvoQvjSviUvhWvgYvfRueTrdVpeYmeZieZgd\ YebVc_RaXN_UJZRFYPBYO7VPBURETTHSUKRWNQYQPZTO`WNbZL\ LQMMRMNSMOSMPTMQTMRUMSUMSVMTVVJXSJYPJYMJZJJZGJ_DJ_\ AJ`7J`5J`9IYDHWHGULFSPEPTDNXCL`BJdAGh9El8Co7AnCEnG\ ImKLmOPlSTlWWk__kcblIflIfG1EH0BI48J3AK17L09M0BN0DO\ 5IPBGLCPMDRIETKFVPGXOHZLI`GJbCKd8Lf4Mh0Nj4Ph8RgBSf\ FUeIWdMXcQZbT``Xa__cZceYgfXjhWnjVqkUnjVliVjhVhhVfg\ WdfWafW_eWYdWWcXUcXSbXPaXNaXL`YJ_YHZYFZYCYYAXZ8XZ6\ WZ4VZ2VZ9YYF`YMcYSeYYhXdkXjnXppXmnWkmWhkWfjWchWagW\ ZfWXdWUcVSaVP`VN_VKYVIXVFVVDUVBTVCRTCPRCNPDLODJMDH\ KDGJBHNAHQ8IT7IW6JZ4Ja3Kd2Kg3Ne4Pc5Rb6T`7WZ8YY9_WA\ aUBdTCfRDhPvjOvqMvvKsvJnvHivG_nIQhJMaKNWLORMNMNMKO\ IHQEFL0006EM01M00H007000DswFnwGiwIgwJgwLhwIBtJCrJD\ qJJpJKoKQnKRlKUkKWjLYiLZh } END PARAMETER FILE=========================================

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FOTD 12-10-07 (Depth Without Limit [7.5])
by Jim Muth 11 Oct '07

11 Oct '07

FOTD -- October 12, 2007 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image is a very deep zoom into one of the side filaments radiating from the minibrot in yesterday's image, which I found in the eastern part of the basin of attraction of the large minibrot on the negative X-axis of the Mandelbrot set. There is another similar minibrot at the center of today's image, but it is so small that it occupies only one pixel. At the scale of yesterday's image, the entire Mandelbrot set would be about the size of our solar system. At the scale of today's image, it would probably be near the size of the entire visible universe. And this is only the beginning. No wonder I named the image "Depth Without Limit". Unable to decide on a rating of 7 or 8, I rated today's image at a 7-1/2. Since the magnitude is well beyond the limit of fast double-precision math, the image is a rather slow one, finishing in 19 minutes on the fast machine and in about 1-3/4 hours on the slow unit. But relief for boredom is at hand, for I have sent the finished image on ahead to Paul at the FOTD web site, so by the time this discussion hits the internet, the finished image should already be posted, ready for viewing at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The impossibly perfect weather came to an end on Thursday here at Fractal Central when it rained all day and the temperature never rose above 54F 12C. The fractal cats ignored the rain, busying themselves instead by chasing each other up and down the hallway. A fight nearly broke out when Cassie leaped from the side-by-side and landed right in front of Nicholas, but luckily, Nicholas, a true gentleman cat, refused to strike a lady. My day was rather busy. The next FOTD is due to be posted in 24 hours. Until then, take care, and some fractals are only half- infinite, but that doesn't make them any less. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= DepthWithoutLimit { ; time=0:19:00.97-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.74878254143695351379988935110856/0.0\ 13714274845087793359918872878676/2.395274e+028/1/\ 22.5/3.43884642983738331e-013 params=0/0 float=y maxiter=5000 inside=0 periodicity=10 colors=000QhBQgDQgFQgHQzJQzLQzNQzPQgRQzTQgVQgXQgZQ\ g`QgbnfWag`tk`pjamjajibgibdzbahcZhcWgdTgd`RAZTEYVH\ XXKWYNV_QUaTTbWSdZRfaPPTQQUQRVQSVQTWQUWQVXQWXQWYQX\ YZN_WN`TN`QNaNNaKNbHNbENcBNc9NcDM`HLZLKXPJVTISXHQ`\ GOdFMhEJlDHpCFsBDrGHrKLqOOqSSpWWp_ZocbogepMipMiK5H\ L4EM8BN7DO5AP4CQ3ER2GS9LTFJPGSQHUMIWOJYQK_SLaPMcKN\ eGOgCPi8Qk4Rm8TkCVjFWiJYhM_gQ`fUbeXdc`ebcgagi`kj_n\ lZrnYuoXrnYpmYnlYllYjkZhjZejZciZahZ_g_Yg_Wf_Te_Re_\ Pd`Nc`Lb`Jb`Ga`E`aC`aA_a8Za6ZaDa`Jd`Qg`Wi`al_ho_nr\ _tt_qrZoqZloZjnZglZekZbjZ`hZYgYWeYTdYRcYOaYM`YJZYH\ YYFXYGVWGTUGRSHPRHNPHLNHKMFLQELTCMWBMZANa8Nd7Og6Oj\ 7Rh8Tf9VeAXcB_aCa`DcZEeXFhWGjUHlSznRzuPzzNwzMrzKmz\ JcrLUlMQeNR_OSVPRQQQORMLTIJO000AIP05P13K20A300HwzJ\ rzKmzMkzNkzPlzMFwNGuNHtNNsNOrOUqOVoOYnO_mPalPbkPci\ PdhQegQffQgeUPYTRZTSZTT_TU_SV_SW`SX`SYaSZaR_aR`bRa\ bRbcQccQdcQedQfdNeWOfZPga } END PARAMETER FILE=========================================

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FOTD 11-10-07 (Faster than Light [No Rating])
by Jim Muth 10 Oct '07

10 Oct '07

FOTD -- October 11, 2007 (No Rating) Fractal visionaries and enthusiasts: How could I give a fair rating to just another fractal image in the Mandelbrot set? I couldn't. So I let today's image go un-rated. But it's really a rather attractive scene from the eastern environs of the large minibrot on the negative spike. And with its virtually non-existent calculation time of 1-1/2 seconds, it is well worth a glance. In fact, on my fast machine it finishes before the video mode switches. This exceptional calculation speed inspired the name "Faster than Light". Of course, it's impossible for any information- bearing signal to reach a velocity greater than the universal speed limit of light, but fractals are strange things, and I wonder if this limit applies to them. Interesting things might result if it were possible for fractals to exceed the velocity of light. For example, they might go backward in time, and we could see a finished image today that we would not discover until tomorrow. Could fractals possibly go faster than light? Well, fractals are made of numbers, and numbers are human thought processes expressed in symbolic form. We don't know exactly what thought is, but one thing is certain. Thought is not limited by the speed of light. We can imagine ourselves standing on Mars and mentally be there instantly. So maybe fractals in some way actually can move faster than light. But if they can, it is a total mystery what this ability means to us. With its calculation time of 1-1/2 seconds, today's image is one of the rare ones that calculate in less time than it takes to view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> But viewing the image on the web site still saves the hassle of setting up and running the included parameter file. The weather on Wednesday was much more seasonal here at Fractal Central. The high temperature of 75F 24C was still warmer than it should be in mid-October, but far more reasonable than the 91F 33C of the past few days. The indoor fractal cats were more interested in watching the outdoor squirrels gather nuts than in the cooler weather. In my department, the commercial work was wrapped up early, leaving a rather relaxing day. The next FOTD will appear in 24 hours. Until then, take care, and if you take enough care, good things of a fractal nature will eventually come your way. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Faster_than_Light { ; time=0:00:01.37-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.7487825414369\ 3600/+0.01371427484506131/2.048604e+013/1/-80/0 params=0/0 float=y maxiter=1000 inside=0 logmap=195 periodicity=10 mathtolerance=0.05/1 colors=000X4GX4IX6KX8MXAOXCQWESVFWUHWRJYOLWLNZIPaG\ QcFScFUcEWcGYcI_cKacMccOecQgdSieUkfWmgYoh_piaqjcqk\ eqlgqmiqnkrpmqqoprpnsqmtmjsmjsmgrheqharc`pZXoXXnUU\ jRQgPQeMOcKKaIK_GHYDHWBGU9DS6AR40Q20P00O6UzCUzHUzI\ UzIbzIszErrAqj7pc3oW0nP2mN4mM6lL8lKAkJBkIDjHFjGHiF\ JiEKhDMhCOgBQgASf9Tf8Rd7Pb7Oa7M_7LZ7JX7IW7GU7ES7DR\ 7BP7AO78M77L75J74I77K99MABNBDPCFRDHSEFPHDMKCJNAGQ9\ ET7BW68Z45a33cz5bz6bz7bz9azAazBazCazGVzKOzOIzSBzW5\ zY9dZCa`F_aIXcLUdOSfRPgUMiXKj_NhXPgTSeQUdMXbJSbvTa\ sTapUamUajVagVadWaaWa_XaXXaUYaRYaOZaLZaIBwEEuFGsFI\ qFKoFMmFPkGRiGTgGVeGXcGUjKVhJWgJWfIXeIYdHYcHZbGs4F\ mDGhLGcUG_MVZOTZPSZQRZSQZTOZUNZWMZXLZYJZ_IZ`HJlQLm\ PMnONoNPpMQqLRrLTsKUtJVuIXvHYwG8xHByGEzGHzGJzGMzGP\ zGRzGUzGXzGZzMczLhzLmzKrzKvzJzzJzzIzzIzzHzzHzzGzzH\ zzGzzGzzGzzGzzGzzGzzGzzGzz5zz9zzDzzPzzOzzNzzMzzLzz\ KzzJzzIzzHzzTzzPzzLzzHzzD } END PARAMETER FILE=========================================

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FOTD 10-10-07 (The Inner Thrist [5.5])
by Jim Muth 09 Oct '07

09 Oct '07

FOTD -- October 10, 2007 (Rating 5.5) Fractal visionaries and enthusiasts: The name of today's image has a rather unusual origin. On a church bulletin board two blocks from Fractal Central a notice is posted. It reads: 'Only God can quench our inner thrist'. At first glance, all appears to be in order. But being a proof- reader among other things, I noticed that the word 'thirst' is mis-spelled on the board. It is one of the least apparent mis- spellings I have ever seen. I wonder how many parishioners have noticed it. I included the mis-spelling in the name of today's image just for the fun of it. Another mystery is what the name actually has to do with today's fractal, which is a scene on the inside of its parent fractal, which happens to be the same parent that held yesterday's scene. I'll not try to describe the scene's location other than stating that it lies in a field of fractal debris. Due to the work rush I had no time to do a proper coloring of today's image, but it should not be too hard to improve the colors. This inadequate coloring drops the rating to 5.5, and even this might be a bit excessive. The calculation time runs to just over 1 minute on the current fractal fireball computer. On the old fractal snowball the image would finish in about 7 minutes. But nothing can compare to the instant view of the image that can be enjoyed by those who visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A temperature of 90F 32C and hot sun made it feel very summer- like here at Fractal Central on Tuesday. But the un-autumn weather came to a sudden end at 5pm, when a gusty thunder-shower moved in and dropped the temperature to 72F 22C. The fractal cats never worry about weather, as long as they are comfortably situated indoors, that is. My day was busier than average, though still well under control. The next FOTD is not yet under control, but it will be so when it is posted 24 hours from now. Until then, take care, keep your fractals dry, and never forget that a picture of a fractal is not an actual fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Inner_Thrist { ; time=0:01:17.24-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.48718472497610280/-2.225744956798285\ 00/6151.448/1/120/2.31113136267557806e-009 params=0.2/2/-2/-0.5/0/0/0/0 float=y maxiter=1550 inside=0 outside=tdis logmap=48 periodicity=10 colors=000pAXpBWqBVqBUrCTsCRsDQtDPuDOuENvELwEKwFJx\ FIxFHwEGwEGwEGvEFvEFvEFuEFuEEuEEuEEtEEfFobCpZ9qV6r\ O3vQ3tR3sT3rahQdhPggNigMlgKngJoiLpjNqkOrlQsmStnTup\ VvqWwrYxs_yt`zubzvcF4CHCFIJIKRLLYNMdQOlTPsWQzYTxVW\ vTZtQ`sOVcOPPOONWOMbOLiOKpOJwPNtPRrQVpQZnRblRfjSjh\ SnfTrdTvbTz`RwaQtbPrcOodNmeMjfKhfJegIchH`iGZjFWkEU\ kHTiKSgNReQQcTPaWO`ZNZ`MXcLVfKTiJSlIQoHOrGMuFKwEJl\ HMaKORNQGQS6SUBLaGEhL7pQ1wS5uU9sWCqXGoZJm`NkbQicUh\ eYfg`didbjg`lkZnnXprVquUejZV_cKPh9ElEHfIJaNLXRNSWQ\ N_SIdUDhW8j_GkbNmfVniaohZpgXqgUrfSrePseNtdKucIvcFv\ bDwaAxa8y`5z_3z_1oUAeOJWIRMC_C7gLFcTN`aVXibUrjQzqN\ phRg`VZTZQKbHCf84iE8hJBgOEfTHeZKdcNchQbmTarWaRJqTH\ lVFhWEcYC__BV`9Rb7Nd6Ie4Eg39i15j01i27h4Cg5Hf7Mf8Re\ AWdC`cDebFjbGocGmcFmcEmcDKcDKcCKcBqcBqcArc9rc8rc8r\ c7sc6sc5sc5tc4tc3tc3td4re4qe5pf5og5mg6lh6ki6ji7ij7\ gj7fk8el8dl9cm9an9`nA_oAZ } 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 09-10-07 (A Virtual Vacuum [8.5])
by Jim Muth 08 Oct '07

08 Oct '07

FOTD -- October 09, 2007 (Rating 8.5) Fractal visionaries and enthusiasts: What happens when 2 parts of Z^(-0.5) are subtracted from 0.2 part of Z^2 and straight C is added? The parent fractal of today's image results. More than anything else, this parent resembles a Mandelbrot set that has been killed and flattened on the road. I will not try to describe the resulting mess, which bears only a vague simi- larity to the un-flattened M-set. But I will comment that it has a large 2-lobed bay filled with only the tiniest bits and pieces of 'outside' stuff. Today's scene is located in one of the denser fields of this stuff. The effect of broad radiating bands was achieved by rendering the image with the 'inside' set to 'bof61'. The only 'outside' elements in the image are the four large warm-red ones surround- ing the invisible-but-really-there minibrot at the center, as well as the scattered bits of salt and pepper. The first name I chose for the image was 'Road-Kill Fractal". But this name brings up too many unpleasant images, so I finally chose the name "A Virtual Vacuum". Since so much of the image, which is not evaporated, consists of 'inside' stuff, the image actually is rather empty, though perhaps not quite a true vacuum. I kind of like the intense contrasts in the image. The rating of an 8.5 must therefore be considered totally justified. The calculation time of 49 seconds is thankfully brief. Equally convenient is a trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the image there. Midsummer weather in mid-October is hardly to be expected, but when the temperature reached 91F 33C on Monday here at Fractal Central, along with haze and high humidity, one might have sworn it was mid-July. The fractal cats never noticed the hot weather as they hogged the cool air during the hottest part of the day. I was too busy to complain about the afternoon heat, but when evening came and the work was finished, I started to grumble. Luckily, the unusually spectacular fractal of the day eased my dis-satisfaction. The next FOTD image will be ready, along with its brief discussion, in about 24 hours. Until then, take care, and when a question cannot possibly be answered, the question is sometimes a meaningless one. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Virtual_Vacuum { ; time=0:00:49.62-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+2.37151777147614800/-0.506331567794958\ 40/1.611897e+007/1/32.5/-5.04488026451949123e-005 params=0.2/2/-2/-0.5/0/0/0/0 float=y maxiter=2500 inside=bof61 periodicity=10 mathtolerance=0.05/1 colors=0005Kc5JdCNfIQhOTjUWl`Znfapldrrgt`XhKMX3CI9\ HJEMHKREPVCV_9_d7dh5`b8XXBTRDPLGLFIH9LE4N3CwijYalc\ VnhNozGqs9rxCnpEjhHfaJbUMZMOVFRR7TO0WL7ZID`FJcCQh9\ Wm6Zr4Uv6PzRKvOKrKKmHKhFKcEKZCKUCKPCLRVMWeMgpMlxMr\ zNexL_wJVvHPuFJtDEsBDUUQLXbB_n2ahQLcl4Vh8NdBF`E7YH\ KSDXMAiG6uA3rF6oK8lOAjTDgXFdaHbeJXdPRcULbZGbcL_gQX\ jVUm_RpUNlPJhJFdEB`GGdIKhKOkJUmI_oHepGkrGqsIZ_KHGI\ JEGLCENACP8AR68T46V24W1TKVq9xoFpmLikQaiWVgaOefGcl9\ aq2XjBScKOXSJQ`FJhipD8le1rmRuroxw4ZG5`J6bL6dO7fQ8h\ T9jWAlYBn`BpbAoeAogAoiAok9nn9np9nrTbcSacR_cQZdPYdO\ WdNVeLSeKRfJQfIPfHOgGNgFMgEKhDJhCIh9PY7WO4bE2i41WL\ GTQVQVhN_iOZiPYiQXjRXjSWjTVkUUVdIWiJXnKYsKheQsTWgd\ jceb`fWYgPUhIRiBOj4Ed34Z3Cc5Jh6Rm8Yr9dwAfuKhtUisck\ rmlqwhrrdsn`tjXufTvbPwZOo`NgaM_cMSdUWWaZOibFpe7lb6\ h_5dX5`U4YS4lGNz4emCYaJQQRIEYA2d3Cf4Lg5Ui6cj7ll8um\ 8vhAvdCv_EwWGwRIwNKwJM5Lb } 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 08-10-07 (Zits [7])
by Jim Muth 07 Oct '07

07 Oct '07

FOTD -- October 08, 2007 (Rating 7) Fractal visionaries and enthusiasts: To create today's fractal I mixed 0.000001 part of Z^(-15) with Z^(2), then added (1/C) rather than straight C. The result was another interesting parent fractal with more nooks and crannies than could be explored in a hundred lifetimes. Having only one lifetime, at least under my present name, I will have time to explore only an infinitesimal part of this parent before moving on. Today's image is my go at this particular fractal. This parent is mostly a network of criss-crossing filaments with a few small minibrots scattered about. This filament network shows up quite well with today's color palette when the logmap is turned off and the magnitude set to 0.15. The first thing I checked in the parent fractal was a tiny little blip along the negative X-axis, where, after a rather frustrating search, I found the scene of today's minibrot action. I named the image "Zits" because of its pimply appearance, and also because the word is one of my favorite scrabble words, though all too often the enemy adds a letter 'i' and makes the word 'ziti', to which I then add an 's' and make the word 'zitis'. The rating of a 7 honestly describes how I feel about the image. It's a little better than average, though far from outstanding. And the very brief calculation time of 43 seconds will evoke the impatience of no one. As always, the most convenient way to see the image is to view it on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Perfect weather, with blue skies, hot sun and a temperature of 84F 29C, prevailed here at Fractal Central on Sunday, though with all the perfection we have seen lately, it might be best to call the conditions average. The fractal cats were more con- cerned with the pigeons on the sidewalk than with the weather. I took advantage of the Sunday perfection by doing nothing. Un- fortunately, my idleness will end on Monday, when a sizable job is due in. Unless things get totally out of control, the next FOTD will be posted in 24 hours. Until then, take care, and computers can compute four dimensional objects very well. So why can't we? (It must be a genetic mental block.) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Zits { ; time=0:00:43.32-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-0.55725035034667650/+0.001783147086022\ 90/8.73116e+012/1/95.34/0 params=1/2/1e-006/-15/0/\ 0/0/0 float=y maxiter=425 inside=0 logmap=72 periodicity=10 mathtolerance=0.05/1 colors=0000CL0DN0EQ0EU0DZACcFBhKAmNArPAvQLzM`mIicZ\ rUwzDczFcsIJlJYdMPUOcMPOK`MJRLG4JF0ID0GC0OQ0VY0ad0\ im0pu4xz7zzAzxFxmJuaMrSQoIVl6Yi0af0dJTlPQfTO`YMVaJ\ PfIJzFDzD7zAI_9QS7_L4gD3p61y00z9DzJQvTcrcplmzfxzas\ zXprQlfLiVFdJ9a73Y00V00`04f0Gl6QrCaxJlzPxzVzz`yvdp\ pjgjo`liSodJp_CsV3uP0vL01mu0`m0Of0A`00T00O00F00606\ 00C0070C40P00a00o00z00z00z01z04z06z09z0Cz0Ds3LiCS`\ L_QTdIal7js0sy3lr7dlCYfGS`GPYFMVDJS1sX1v`1xd1yiacv\ zJzvOzgSrTXiF``1dSL`QcXQvSQzPQufAsjCsoDssFsvGrzIrz\ JrzLrzLmzVizcdzl`zuSz`LzIFzG9zG4zF0zF0zD0zD1zJFzPS\ zVcz`VzTOzMFzF6z70z1GzLYzcozvzzzzzzzzzzzzxzyvzvuzs\ rzopzlozipzjpzjrzjrzjszjszjuzjuzjvzjvzjxzjxzjyzjyz\ jvzgszdrzcoz`lzYjzXgzTdzQczP`zMYzJXzITzFQzCPzAFzzP\ zz_zvXzmVzdTzXQrOPzFOz6Mz0SzGXz_`zp_zc_zQ_zDczCfzA\ izAlz9oz7rz7azQMzg7zy1zu0zr0zo0zl0zg6zcFz_PzV_zQgz\ Ozz0uz0mz0fz1_z6Sz9LzDDzG } 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 07-10-07 (Whatever Wherever [6])
by Jim Muth 07 Oct '07

07 Oct '07

FOTD -- October 07, 2007 (Rating 6) Fractal visionaries and enthusiasts: I realize that today's FOTD is late. Nothing unexpected took place; I simply decided to have a day of fun instead of work, and as a result I had no time to find a proper FOTD to post at the usual hour. The formula behind today's image adds 1,000,000,000,000,000 times as much Z^(-99) to Z^2 as the formula that created the past 3 days' images. However, the resulting parent fractal still closely resembles the parent of the past 3 days, the main difference being a modest increase in size. Today's scene is located in the East Valley of the small mini- brot on the positive X-axis. I could probably have found a near identical minibrot at the corresponding location in the parent fractal of the past 3 days. I rated the image at a 6, mostly because the past several images have been rather similar, and there *can* be too much of a good thing. The name "Whatever Wherever" must mean something, but if so, I have totally forgotten its meaning. The calculation time of 9-3/4 minutes is slower than the past several images, but still within reason. The fastest way to see the image is to log into the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view it in finished form there without effort. With sunny skies and a temperature of 84F 29C, Saturday was a perfect day here at Fractal Central, which is why F.L. and I decided to take the day off. The fractal cats never enjoy being left alone for the better part of a day, but they endured their isolation stoically. When we returned, their inconvenience was rewarded by a generous serving of tuna. Thr next FOTD will appear in about 12 hours. Until then, take care, and never stop wondering until nothing remains to wonder about. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Whatever_Wherever { ; time=0:09:49.57-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+7.69228057914474/-0.00057047828859809/\ 1.625207e+012/1/36.3338013283574597/0 maxiter=4700 params=1.1/2/1e-015/-99/0/0/0/0 float=y inside=0 logmap=-800 periodicity=10 mathtolerance=0.05/1 colors=000XPSj_OpXKvUHuq7hnIWlTJic6gn4ao3Xo2So1Np0\ Ip0DpECiSCbfCWtCPrFQpHQnJQlLRjNRiPRcUWZY_TacOehIil\ Dmp8qt8jj8ca8XT8QK8JBAGGBELDBPE9UF6ZH4bI1gJYkGMlDX\ lAPm7Dm4Gn1Jn0Mn3Rf8V_DZSHWLMfDRj6Vn0bX4jF9q0DrAHr\ MLrYPriTrtXadaLPf5AjEKdNTcbecincrxczzcchAHI5IB0UB3\ aB6kB8hBBnBDmDHqFKpHOoJRVLVUMYXQU_UQbXNe`JhcGkgCnj\ 9nfEmbJlZOlVTkRYkNbmKgpHlrFpqKkpOgpSboWZo_UncQ`Yd_\ `bZcaYf`Yi_WkXVlUUmRTnORoLQpIPqFOrCPoEQlGRiIRfKScM\ T`OUYQUVSVSUWPWXMYXK_VMXTNUSORQPOPQLNSILTFKUCIV9HW\ 7LV9OUBRTCUSEYRG`RHcQJfPLjOMmNOpMQsMRrNPqOOqPNpQMo\ QLoRKnSJmTImTHlPIkLIjHJiDJh9Jg5Kf1Kf0Kh1Li5MjANlFN\ cKIVUEMcAEm6Lm4Sc3Zc2eP1lK0sG0VFL6mf8md9mcAmaBm`Dm\ ZEmYFmWGmVImTJmSKnQLoPKpQJqRIrSHsTGtUFuVEvWEwWDxXC\ zYBzZAz_9z`8za7zb7zbEz`LzZSzYZzWezVlzTrzSqzTqzUqzV\ qzWqzXqzYqzZqz_qz`qzaqzarz`rz`rz`rz`sz`sz`sz_sz_tz\ _tz_tz_tz_tz_izbZzeOzhZzW } 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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The FOTD for October 7 will be late
by Jim Muth 06 Oct '07

06 Oct '07

Fractal visionaries and enthusiasts: Due to a situation within my control, the FOTD for October 07 will be posted about 12 hours late. Check back at that time to admire it. The FOTD for October 08 will appear on schedule at the regular time. Jim Muth

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FOTD 06-10-07 (Iteration Essence [8])
by Jim Muth 05 Oct '07

05 Oct '07

FOTD -- October 06, 2007 (Rating 8) Fractal visionaries and enthusiasts: The fractal part of today's discussion will be a bit short. I found a magazine article this afternoon that got my philosophi- cal juices flowing, and I decided to say my piece at the end of today's fractal discussion. Those who are bored by philosophy should stop reading at the FOTD web-site address. Today's image is from the same parent that gave us the past two days images. Today I checked the right edge of the parent circle, not far from the X-axis. After a rather difficult search, I found a tiny, well-hidden minibrot, which appears at the center of today's image. When calculating the fractal, I used only the default coloring method, with the outside set to equal-iteration bands. The entire color effect was achieved with the Fractint <C> coloring screen. After very little pondering, I named the image "Iteration Essence". It makes little sense, but then neither does modern physics. Since I think the image is notably above average, I rated it at an 8. The calculation time is only 44 seconds. Even on a slow old war- horse unit the image finishes in 4 minutes. But the best way of all to enjoy the image is to go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and see it there, already calculated. On the philosophical side, I happened to glance at a copy of 'Scientific American' magazine this afternoon, and found yet another article speculating on how the neurons of the brain produce self-awareness. I merely skimmed the article, but its point appeared to be the same as all the mechanism-of-self- awareness articles I have read. Researchers are still debating how the electrochemical activity of neurons produces consciousness, but there are lots of pretty pictures of brain activity in the article, and some unconvincing hypotheses. Despite the mystery, the researchers claim they are making progress toward a better understanding of the biological and neurological processes involved. When will these 'scientists' get the point? The answer has been staring them in the face for decades. Neurobiology seems stuck in a century-old world view. If something is coming out of some- thing, something must be going in. Even a successfully reproduc- ing species of artificially intelligent computers would need the input of human intelligence to get its ancestors started. The neurons of our brains must have some input, as yet unknown to science, and change it into intelligent self-awareness in much the same manner as the circuits of a television receiver change the incoming encoded electromagnetic energy into the out- put that we see as an intelligent program. How futile it would be to study the activity of the circuitry inside a television receiver for the source of the intelligent program, while being unaware of the electromagnetic input. Enough philosophy. Friday turned out to be another midsummer day in mid-autumn here at Fractal Central, with a temperature of 86F 30C, hot sun and high humidity. The fractal cats again spent the day stretched out under the air-conditioner. My day was satisfactorily busy, the way I wish every day could be. The next FOTD fractal will be posted in 24 hours. Until then, take care, and don't think about thought too much. It's a circular path of pseudo-logic that goes nowhere. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Iteration_Essence { ; time=0:00:44.34-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+4.998518795515808/+0.0006317113811069/\ 2.524967e+009/1/114/0 params=1.1/2/1e-030/-99/0/0/\ 0/0 float=y maxiter=1000 inside=0 logmap=76 periodicity=10 mathtolerance=0.05/1 colors=000u0MK3FyYDuXCqVBlTAhR9dP8_N7WK6SH5ND4JA3F\ 72941420zzhvubrpXnkRjhLfeFba8ZY7VT6RO5NJ4KF4GA3C52\ 8113U0ze52m3zm1RcczWWGOOAGG5z87zZ5zTzmN3LH2EB175`m\ zYhzWczUZzRWzPTpNQcKOUILRGIODGKBDH9AD68A4562234ja3\ gZ3dX3aU3ZS2WQ2TN2QL2NJ1KG1HE1EB1B90870540224sO3mL\ 3hJ2cH2ZF2UD1PA1K8s06u03p32k52f72a91YB1TD1OF0JH0FJ\ 0HM5JO9LRDNTHPWLRYPT`UVbYXeaZge`jiblmdhjeegfbdgZbi\ W_jTXkPVlMSnJPoFNpCKq9Hr6FmBHiFIeKJaOLXTMTXNP`PLeQ\ GiRCnT8rU4vV7sX9pZBm_EjaGgcIddLafNZhPXiOZeO_bNaZNb\ WMdSMePLgLLhIKjEKkBKl8MjAOiBQhDSgETfFUcHVeJWgLWiNX\ kPYmRYoSZqU_rW_sY`t_auaavbYwZ0x2VyWzzTzzQzzMzzJzzG\ zzDzz9zz6zz3zzDzz6zzFzzCzz9zz6zz33zz2zz2zz1zz1zz1z\ z0zz0zzxzzqzzkzzezz_zzUzzOzzIzzCzz6zzMzzazzVzzPzzJ\ zzCzz6zz7zz6zz5zz5zz4zz4zz3zz2zz2zz1zz1zz0zzvzzqzz\ lzzhzzczz_zzVzzRzzMzzIzzDzz9zz4zzfzzbzz_zzXzzUzzRz\ zOzzLzzIzzFzzCzz9zz6zz3zz } 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 05-10-07 (A Fractal Quickie [7])
by Jim Muth 04 Oct '07

04 Oct '07

FOTD -- October 05, 2007 (Rating 7) Fractal visionaries and enthusiasts: I named today's image "A Fractal Quickie" for the obvious reason that it is extremely fast, finishing as it does in a little over an unbelievable 12 seconds. And even on the slow old P200 unit it finishes in under one minute. The rating of a 7 might be a bit liberal, but I really do like the brilliant emerald greens in the elements surrounding the central minibrot. Today's image is actually another venture into the same parent fractal that gave us yesterday's outstanding image. But instead of exploring the small minibrot at the eastern edge of the large outer circle, we examine one of the finely scalloped lines well within the interior of the northern part of the circle. I had almost decided the area is non-critical and given up on it when I spotted the tell-tale bit of perfect symmetry that says a minibrot lurks within. A quick series of in-zooms revealed the scene of today's image. The magnitude is not really great enough to require the mathtolerance entry, but the whole fractal gets quirky without it, so I included it just to be safe. The emerald-green scene may be viewed by running the included parameter file and waiting a few seconds, or by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it already is or shortly will be posted. With a high temperature of 86F 30C and a hot sun, Thursday was most un-October like here at Fractal Central. The fractal cats, Nicholas and Cassie, spent the day stretched under the air conditioner, which I thought had been shut down for the season. In my department, the moderate amount of work was wrapped up for the day without incident. The next in the apparently endless series of FOTD images will be posted in 24 hours. Until then, take care, and the FOTD will come to its end when we run out of fractals -- whenever that may be. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Fractal_Quickie { ; time=0:00:12.08-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=+0.4715639002972046/+2.121705306530676/\ 1.748152e+010/1/176/0.0190632524763709107 inside=0 params=1.1/2/1e-030/-99/0/0/0/0 float=y maxiter=325 logmap=43 periodicity=10 mathtolerance=0.05/1 colors=00064A89AADACIAEMAFRAHVAJ_9Lc8Mf6Oi5Qk4So3j\ s2wvPzzzzwzztzzpzzlzzhzvdzq`zmZzh`vhYrcZmKFhIIcHIZ\ GJUFHSQDW_AZj6at3duAeuGfvNgvTgvZhwciwijwnjsnkonkkn\ kgnlcnl_nlWnlSnmOnmKnmGnnCnn8nn5nnBooGooLppQppVqp_\ qqdrqirrnsrssrr5RX8xaKffWQjg9haBgXCeSDdMFbHGaCH_DJ\ YELXENVFPUGRSGTRHVPIXOIZMJ`LJaOUSQdJToAVz1Xz7YzD_z\ I`zObzTczZezdfzihzoizthzphzmgzjgzffzcfz`ezXezUezRg\ zQhzPjzOkzOlzNnzMozLqzLrzKszJuzIvzIxzHyzGzzGtzLozQ\ jzVez_`zdWziRznMzsHzwTzrdzmozinzenzbnzZnzWnzT_zKMz\ BLzAKz9Iz9kzFkzOkzXlzflzolzxczrWzlOzgGza8zXGzTOzPW\ zMczIkzErzBqzDqzEqzFpzHpzIpzJpzKyzJszNnzQizTczXZz_\ UzbRzaOz`Lz_Jz_GzZDzYAzX8zX7zX7zX9zWCzVFzUIzTLzSOz\ RRzQUzPXzO_zNbzIezDhz9kz4nz0qz1tz2wz2zz3zz3zz4zz4z\ z5zz6zz6zz7zz7zz8zz8zz9zz9zzAzzBzzCzzDzzDzzEzzFzzG\ zzGzzHzzIzzJzzJzzMzzPzzRzzUzzXzzZTzj_zdYzfVziTzkQz\ gNzcLz_IzWGzSLzQPzOLzGDzH } 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 04-10-07 (A Hairy Adventure [8])
by Jim Muth 04 Oct '07

04 Oct '07

FOTD -- October 04, 2007 (Rating 8) Fractal visionaries and enthusiasts: Today's image lies in a very unlikely parent fractal -- the one that results when an infinitesimal 0.000000000000000000000000000001 part of Z^(-99) is combined with 1.1 parts of Z^2 and (1/C) is added. This parent consists of a single giant circle filled with detail of the most unusual kind. A small Mandelbrot set lies on the X-axis at the eastern edge of this circle. Today's scene is located in the East Valley area of this M-set. This parent fractal has the strange property of not appearing unless the mathtolerance=0.05/1 command is entered first. If the parameters are entered without this command, the result is a blank screen. I named the image "A Hairy Adventure". It seems a rather pleasant name. The rating of an 8 indicates that the 2-1/2 minutes spent running the included parameter file will be rewarded by a very attractive image. The small effort of going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there, will also prove rewarding. A near perfect day prevailed weatherwise here at Fractal Central on Wednesday. Unfortunately, the workday was not so perfect. But the work did get finished, and the fractal was good, so I would rate the day a mild success. The fractal cats overturned three wastebaskets in agreement. The next FOTD will appear in 24 hours. Until then, take care, and don't be haunted by a fractal ghost. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Hairy_Adventure { ; time=0:02:34.34-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=+4.555093507304436/+0.0002371242405838/\ 3.660635e+011/1/-177.5/0 params=1.1/2/1e-030/-99/\ 0/0/0/0 float=y maxiter=2500 inside=0 logmap=310 periodicity=10 mathtolerance=0.05/1 colors=000TNj_TdYTfVSiTSkQZgNdcLk_IqWGwSLuQPtOTsNX\ rL`qKepIioGmnFqmDulCcaJMRP5GV6HX6HY6H_6I`7Ib7Ic7Je\ 7Jf8Jh8Ki8Kk8Kl9Ln9Lo9Lq9Lr7Wf5eV3oKFgUR_baTkiQppN\ twKxrLvnLtiMrbMpWKnOLlLLjKLlF8rE9oEBkDCgCEbCFYBHUB\ ISFKQINOLRNOVLRZJUaI`eGfiEjlBnp8qt6tw3wz1tv3qq5pn7\ oi9n`BmWDkTCiQCgNBeKBcIBMbeLdgKfhKgiJijIjkIlmHmnGo\ oGppFrqFsrIniLi`OdSR_JUVAXQ1ZR2_S2`T3aU3cV4dW4eX5f\ X5hY6_KQdLThMVmOXqPZuQ`qPYmOViNTeMQbLOZKLVJIRIGNHD\ KGBHGJFGRCGZAGf8GmKS`VbPfnDqy1mx5jw8gvBduE`uHYtKVs\ NSrQOrTLqWIpZFoaCodBnfBmgBlhBliBkjAjlAhmAgnAeoAcp9\ ar9`s9Zt9Xu9XvEWuIVtMUtQTsUSsYRrbRqfoqmmmrrrwwwzzz\ zzztttmmmoplmplkokjnkhmjfmjelickiajh`jhEmWDoXCnXCl\ XBkXAjXAhX9gX8fX8dX7cX7bX9dWCfVFhUIiTLkSOmRRmQUmPX\ mO_mNbnIemDhm9km4nm0qm1tm2wm2zm3zm3zm4zm4zm5zm6zm6\ zm7zm7zm8zm8zm9zm9zmAzmBzmCzmDzmDzmEzmFzmGzmGzmHzm\ IzmJzmJzmMzmPzmRzmUzmXzmZ } 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 03-10-07 (Fireworks Pinwheel [No Rating])
by Jim Muth 02 Oct '07

02 Oct '07

FOTD -- October 03, 2007 (No Rating) Fractal visionaries and enthusiasts: I could not rate today's image because I consider it a virtual failure. I calculated it with great expectations only to see my hopes vanish when the time came to work on the colors. Regard- less of what arrangement of colors I tried, the image just did not look good. And the other 'outside' coloring options worked no better. I'm not sure what went wrong, but I suspect that the basic fractal forms are simply too chaotic to create the well-defined 'objects' that I prefer in my images. And the tiny bits and pieces scattered throughout the scene add nothing at all to the appearance. Something about the image reminds me of a fireworks pinwheel, so that's what I named it. The parent fractal is the same one that produced yesterday's notably superior image, though in today's image I investigated a different valley of the clover-leaf shaped hole. The calculation time of 4-1/2 minutes is not too bad. Even better is the instant viewing available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Partly cloudy skies and a temperature of 75F 24C made Tuesday rather pleasant here at Fractal Central. The fractal cats took enough of a break from their rowdy behavior to notice the sunny intervals. Then they returned to their mischief. We had to crack down when Nicholas overturned a waste basket and scattered the contents around the room. My day was unexpectedly busy, and I suspect the fractal suffered beacuse of it. But tomorrow will likely be slower, resulting in a better fractal. Check back in 24 hours to see if I keep my word. Until then, take care, and in fractals we see the abstrac- tions known as numbers creating 'real' images. In physics we see the abstractions known as atoms creating 'real' material. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fireworks_Pinwheel { ; time=0:04:32.29-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-1.524292990172/-0.00001027990583/1.116\ 77e+009/1/117.5/0 params=1/2/2/0.75/0/0/0/0 float=y maxiter=2750 inside=0 logmap=463 periodicity=10 colors=2224223222222222222222222222222222222222322\ 422522722722822A22B22D22E22G22G22P2AX2Me5ZoDkwKxxT\ xx_xxZoqZeeXWUXMJWDAWHDTKGRNJNTMMWNKZRHcWGf_EjcBmh\ Aro8vt5xx4xy3xz2xz2xz2xy2xx5xu8xrDxoGxjKweNtaNqWNj\ TNePN_MNUJNPGNKENHBNG8NG5NH4NJ8NJBNJGNHJNGNGER8DU2\ GZ2Ja5MeAPhDTkHWoMZrPavUexZfxaexWexRcxKcxGaxAax5_x\ 2_x2Zx2Zx2ax2cx2fx2hx2jx2mx2ox2rx2tx2vx2xx2xx2xx2x\ x2xv2xr2zmAxeNxY_xQZxIXxAWx8UxATxBRxDPxENxGMxHKxJJ\ xKHxMGxMGxNEwPDvRBtTAtUArW8qX7oZ5m_4ma3kc2je2hf2fh\ 2fj2ek2cm2ao2ve2tf2tf2rf2rf2qh2qh2qh2oh2kh2cj2WM2N\ K2NM2NR2WU2cZ2zc2zj2x`czzzfm2em2em2co2co2ao2ao222t\ 22N22N22t22N22N32N52x73c85NA8NBBNDDNEGNHKNJPJKWEMa\ ANh5Pm2Tt2Ux2Wx2Xx2Zx2_x2o2am2Zm2Xk2Uk2Tk2Pj4Nj7Kh\ AJhDGhGEfJBfMAfP7eT5eW3cZ2ca2ce2af8ahG_jNakWamcaok\ aqtarxatxavxawxaxxaxxaxxaxxaxxaxxaxxaxxaxxaxxaxxax\ xaxxaxx2xx2xx2xx2xx3xx4xx } 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 02-10-07 (East Horse Valley [7])
by Jim Muth 01 Oct '07

01 Oct '07

FOTD -- October 02, 2007 (7) Fractal visionaries and enthusiasts: To create today's image I took Z^2, mixed in 2 parts of Z^(0.75), added straight C and let it rip. The resulting fractal is a Mandelbrot set that is cut off on the southeast side, but has lots of extra action in the northwest quadrant. This extra action involves many additional filaments and holes of various shapes and sizes. Today's scene is located near a larger but still tiny minibrot in an ambiguous valley of a large hole northwest of the main period-2 bud. I call the valley ambiguous because it appears to hold Seahorse as well as East Valley features. I named the image "East Horse Valley to emphasize this ambiguity. When it came time to rate the scene I turned generous. The rating of a 7 seems a bit liberal, but why not reward myself for an acceptable image created on a bad workday. The calculation time of 5 minutes on a 2000mhz fireball is within reason. On a 200mhz snowball the scene takes close to 1/2 hour to complete -- still barely within the bounds of reason. The most reasonable way of all to see the fiery image however is to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view it there. A near perfect day here at Fractal Central on Monday went unno- ticed by the fractal cats, who spent the better part of the day sulking at each other for something only they know about. My day was spent trying to straighten out a job that came in in a state of total confusion. (If a customer doesn't know what he wants, how am I supposed to give it to him?) It took mostly a few lucky guesses to get that job out of the way. The next FOTD will be posted in 24 hours. Until then, take care, and could the popular interest in fractals finally have run its course? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= East_Horse_Valley { ; time=0:04:56.66-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-1.47584661761365700/-0.074900264193136\ 27/5.431817e+012/1/42.578105516759706/0.0023852665\ 8395731006 params=1/2/2/0.75/0/0/0/0 float=y maxiter=1550 inside=0 logmap=550 symmetry=none periodicity=10 mathtolerance=0.05/1 colors=020P1SQ3SR5SS9STBSUDTVGTWITXJTYLTZNT_PT`RTa\ STbTTbTRbXQb`VbgZbncbugbvkbwnbxrbys`ztYzuTzvQzwMzx\ HzyFzzDzzDzzDzzBzzBzzBzzAzzAzzAzz8zz8zz8zz8zz8vz8r\ z4tz2vz0xz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zx0zv0zr6tlD\ ngMjcTdY``VhZRqUKsUGsYDs_9sU5sR3sP2sL2sI2sF2sC2q92\ m62j32g22e22`22Z22Q22F2782KD2GJ2FO2DT2Bb29h27g95mD\ 2qJ2sO2sU2s`2sd2sk2sp2sh2sc5sZDsUMsPVsKbsFlsAts5xj\ 2lT6YBHK0S70d20n20l20l20j20j90hF0hM0fT6f_BdeHdmObt\ TbxZ`xe`xj`xoZxqXxsXrsVgsSYsSRsRGsP7sP2sN2sN2sH2sD\ 2jA2`62T22M22B2S42S02S02S02S02S02S02S02S02S02S02S0\ 6S0BS0HV0NW0SY0Z_0RD0J26Dp0Bp0Ap08p06p04p02p02p02p\ 025022022F22g2Gs8Ws4Om2Gb2BT23J22A22022022OLYRJVVH\ RXFMXFKXDGXBDbBBmA7q83s82s62s42s42s22s22s22s22s2Fs\ 2Is2Ms2Rs2Vs2Ys2bs4es6js8ms8rsCwsGysKzsOzqSzsWzs_y\ sczsczsczsczsczsczsczsczsczsczsczsczsczsczsczsczsc\ zsczsczsczsczsczsczsczscz } 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 01-10-07 (Powers and Dominions [6])
by Jim Muth 30 Sep '07

30 Sep '07

FOTD -- October 01, 2007 (Rating 6) Fractal visionaries and enthusiasts: Today's image is based on the formula Z^(2.005)+(2*Z)+C. This formula produces a parent fractal which, on the surface, resembles the Mandelbrot set, but is entirely different inside. The main spike of this parent is infinitely divided instead of being a single infinitesimally thin filament as is the spike of the M-set. Today's image is located in the debris associated with this divided spike. I named the image "Powers and Dominions". The only reason I can give for the name is that the phrase came to mind when I noticed the heavenly blues surrounding the hellish reds. I am currently reading a book about the traditions of angels in various cultures, and these are two of the traditional nine orders of angels. But there is nothing angelic about the image, which rates only a 6. We have seen similar images simply too many times to rate today's any higher. At least the image is a fast one, finishing in only 1-1/4 minutes on the fast machine and 7 minutes on the slow unit. The pre-calculated image is available for instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The morning fog cleared away by 9am leading to a perfect day here at Fractal Central on Sunday. The fractal cats enjoyed the temperature of 75F 24C, while I enjoyed having nothing to do. The next FOTD will be posted in 24 hours. Until then, take care, and fractals are every bit as real as the angels. Or it could be that angels are as real as fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= PowersAndDominions { ; time=0:01:15.85-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-1.72115541311189900/+0.057607899272470\ 40/6295098/1/-111.5/5.46746958873800537e-006 params=1/2.005/2/1/0/0/0/0 float=y maxiter=1250 inside=0 logmap=125 periodicity=10 colors=000F09G07I07G0AF0DF0GD0JD1MC4PC8QABT9EX9H_7\ Ka7Nd6Qg6Si4Wl3_o3cr1eu1ix0mz0rz0pz3ny6lv9ksChoFfl\ IeiLdfOacQ__TYXXXT_UQaTOdRJgPGjLDmIApG7sD3vA0y90z7\ 0z00z60zP0zU0zZ0zc0yh0vm0sr0px0mw0lu0ir1fo3cj4`g6Y\ d7Xa9T_AQXCOTDLPFMMFJOGGSGFVICZI9VJ7WJ4YL1hL0jM0kM\ 0lO0cM0lO0kO0cP3iP6hP9gQCZQGeQJdSMcSPcSTcTXcT_cVcc\ VgcVkcXocXtaXxcYzhYzm`zmYzmVzmTzmQzmPzmMziLzeIzcGz\ cDzdCzd9zf7yf4xg3wg0vi0ui0tj0sj0rl0rl0rl0oi0mg0lf0\ jd0ic0ga0f`0dY0cX0aV0`T0_S0YQ0XP0VM0TL0SJ0QI0PG0OF\ 0OA0MD0MG0LI0LL3LO7JPCJSGJVLIXPI_SIaXGc`GfdGiiFjmF\ mrFpvDrzDuzCxzDvzDvzDvyDvuDurDumDuiFudFu`FsYFsTFsP\ FsL4z0FsIPdf_QzdLzjFzpAyv4xz0zz0vp4sf9oYDlOJiDOd3S\ a0_Y0X_0V`1T`4Qa7PcCOcFMdIJfMIfPGgTFgXCi_Ajc9jh7km\ 4mr6mv8owAqwEswJuwNwwSxwWyw_zzdzzizzmzzqzzwzzxzzyz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ 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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FOTD 30-09-07 (Deep in the Corner [8])
by Jim Muth 29 Sep '07

29 Sep '07

FOTD -- September 30, 2007 (Rating 8) Fractal visionaries and enthusiasts: Early in my research with the MandelbrotMix series of formulas I found that the expression (Z^2)+(2*Z)+C is simply a more complex way to produce the Mandelbrot set. Not wanting just another Mandelbrot set, I changed the (2*Z) in the expression to (2*(Z^0.999)), which resulted in a parent fractal that is almost but not quite a duplicate of the Mandelbrot set. This parent fractal closely resembles the Z^(2.003)+C figure, though the chaos along the negative X-axis has no symmetry and is less orderly. Today's image is located in a tiny valley on the east side of what once was the large minibrot on the negative spike, in an area that is filled with features that resemble tracks in a railyard. I named the image "Deep in the Corner" because the elements in the upper-right (and lower-left) corners have a far greater iteration value than even the area around the minibrot at the center. I rated the image at an 8 because I think it is worth it. Unfortunately, the calculation time of almost 15 minutes is rather lengthy. But relief for fractal indigestion is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is posted. Perfect weather prevailed once again here at Fractal Central on Saturday, and the fractal cats made the most of it. They spent the better part of the afternoon lounging in the sunlight streaming in the side window. At one time they had some kind of a quarrel going on, but whatever it was about, it ended before I found the cause. My day was peaceful enough. The next FOTD will appear in 24 hours. Until then, take care, and the theory of relativity tells us that time and space are not absolute, but change with the individual observer's relative motion. If they appear dif- ferent to different observers, how then can they be considered objectively real? Perhaps the old song was right, and nothing is real -- not even fractals! (But if so, it's still a lot of fun pretending they are real.) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Deep_in_the_Corner { ; time=0:14:45.35-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-1.74584369496664200/+0.005937502955490\ 11/8.95604e+009/1/102.5/0 params=1/2/2/0.999/0/0/0/0 float=y maxiter=60000 inside=0 logmap=747 periodicity=10 colors=000OB`QEdSHhUKjWHlYMn_Rp`UraYsbauccwcexcgyc\ iyckxcmwcoxcqydszfuzhwzmyzrzzvzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzjYei_\ fibhhdihfkghmfjnfmpeoqdqsdstcuvcwwWujOtZGsM8rAAqFC\ pKEoOGoTInYKmaMlfNljQmkSnkUolWplYql_rmbsmdtnfunhvn\ jwolxonxoineeeW`XMXOCTF3VH4XI4ZK4`L4bN4dO5UQ5UU5iK\ 5kK5U06UA6qK6sK6tK6oO8kHAfFCb8EZ1FX4IV6LT8ORBQPDTN\ FWLIZJK`HMcFPfDRiBTk9Wn7Yq5_sDatLbtTct`euUUUUbwhhk\ aiaVjSOrIHs9Jr8LK8NK8PK8RK8TX8VU8XS8cMHiGQoBYpEWqH\ UqKTrNRrQPsTOzcMtZKUKJudHvgFvjEUFTSERQEPODNNDLYDJJ\ CHICFGBDEBBWBAaCFNDJSENXER`FVeG_jGcoHgbIkkIofXhZSd\ YSiLIZETV7L`04P8AVFGoMMdTaX_Yofctmhyjfxhexedwccwaa\ vZ`vX_uVZuSKcQKcNKcLFcJKcGFcEKcCFrIKsN_sS`sYatbbtg\ ctZdcQeOUfPXgQ_hRbiSejTdkXbl_`mcZnfXojWpmXqlYrlZsl\ _tl`ulavlbwlcxldykezkfzkgzkhzkizkjzkjzkkzjlzjmzjzz\ jzzjzzzzzczzzzzzzrzzzzzzz } 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 29-09-07 (The Edge of Time [9])
by Jim Muth 28 Sep '07

28 Sep '07

FOTD -- September 29, 2007 (Rating 7) Fractal visionaries and enthusiasts: Today's image takes us back one last time to the indescribable parent fractal that has been the source of the FOTD images of the past 3 days. This time we check the East Valley area of a tiny minibrot that butts against the surprisingly sharp edge of a very large debris field. While I searched for a name, I imagined the debris field to be changed from spatial to time-like, which would place the scene of today's action right at the edge of time. The name then was obvious. The rating of a 7 is arbitrary. The colors are a bit dull, yet the picture does appear to have an inner life. The calculation time of 4 minutes on the fast machine or 25 minutes on the slow one is a bit lengthy, but relief is at hand on the FOTD web site, where the finished image is posted for immediate viewing. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Perfect end-of-September weather prevailed here at Fractal Central on Friday, as we were graced with sunny skies and a temperature of 75F 24C. The fractal cats were more interested in a stray cat that has been hanging around for the past several days. Along with the day's fractal, my day was near normal. The next FOTD will appear in 24 hours. Until then, take care, and if fractals are infinitely complex, are they complex enough to have self-awareness? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Edge_of_Time { ; time=0:04:05.63-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-0.12762887425876010/+0.008099229374371\ 24/1.765009e+011/1/-155/0 params=-0.88/1.1/1/-1.1/\ 0/0/0/0 float=y maxiter=2900 inside=0 logmap=444 periodicity=10 mathtolerance=0.05/1 colors=000TRnTVnUSnVWmVUmWYmWWmX_mYYmYamZ_l_bl_al`\ dlaclaflbekchkcgkdikdikekkfkjfmjgmjhojhojipjjqijri\ ksiltiltimvimtilthksgjrfjqeipehodhncgmbflafkaej`di\ _dhZcgYbfYbdXacW`bV`aV_`UZ_TZZSYYRXXRWWQWVPVUOUTNU\ SNTRMSQLSOKRNKQMJQLIPKHOJGOIGNHFMGEMFDLECKDCKCBI99\ JBAIA03H04G04G04G05G05G05F06F06F06F07F07F07E08E08E\ 08E09E09E09D0AD0AD0AD0zzzzzzzzzzzzzzzvzzrzzmzzhzzc\ zzZzzUzzPzzKzzFzzFyzGxzGwzGvzHuzHtzHszIrzIqzIpy1ox\ 2nw2mv2lu3kt3js3js3ir4hq4hp4go4fo5fn5em5dl5dk6ck6b\ j6bi7ah7`g7`f8_f8Ze8Zd8Yc8Xb9Xb9Wa9V`9V_AUZAUZATYB\ SXBSWBRVBQUCQUCPTCOSCORDNQDMQDMPDLOEKNEKMEJMFILFIK\ FHJFGIGGHGFHGEGGEFHDEHCDHCDHBCIABIAAI99KldJjcJibJh\ aJg`zfzzezzdzzczJbXJaWJ`VJ_VJZUJYTJXSJWRMHjLGjLGjL\ GkKFkKFkKFlJElJEmJEmIDmIDnHDnHDzHGzGJzGMzGPzFSzFVz\ KYzP`zUczZczcczhczmczrczyczzczzczzczzczzczzczzczzc\ zzczzczzczzczzczzczzczzcz } 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 28-09-07 (Richest-Field Image [No Rating])
by Jim Muth 27 Sep '07

27 Sep '07

FOTD -- September 28, 2007 (No Rating) Fractal visionaries and enthusiasts: Today's image returns us once again to the same parent fractal that was the source of the past 2 days' images, where we check what I assume is the Seahorse Valley area of a large Mandeloid. The underlying fractal forms in today's image are unusual, but with too little time to color it properly, I feel I have missed the best part. After spending over five minutes trying to decide how to rate the image, I decided not to rate it at all. I named the picture "Richest-Field Image" because the colors are some of the richest and most excessive I have seen in a fractal. But sometimes excessive colors can be a good thing, so take a look. You might like what you find. The calculation time of 3-2/3 minutes can be cut to almost nothing by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. If today's image is not yet posted on the web site, check back in a little while. It soon will be posted. Another too-warm-for-the-season day here at Fractal Central on Thursday ended with a bang at 7pm, when a heavy thunder-storm moved in. The fractal cats took the heavy weather bravely. My day was busier than I would have liked, but still well under control. The next FOTD is due in 24 hours. Until then, take care, and keep waiting for the arrival of the great fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Richest-FieldImage { ; time=0:03:40.66-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+0.01663148684857626/-0.145175362313389\ 20/3.729357e+010/1/-10/0.0019081905682646963 params=-0.88/1.1/1/-1.1/0/0/0/0 float=y maxiter=2200 inside=0 logmap=274 periodicity=10 colors=000dQJdRJcUKbWLaYLa_M`aN_cN_fOZhOYjPYlQXnQW\ pRSwNWrRZmVbiZedbi`flWjoSncOhSLcGHZ5EUAGRFHPJJNOKL\ TMJXNHaOFfQDjRBoT9tU7xV5tW8qXAmYCjYEgZGc_I`_KY`MUa\ PRaRNbTKcVHcXDdZAe`7ebu5Rq7Sn8Tj9UgAVcCW`DWXEXUFYQ\ HZNI_JJ`9QeGK`MFWTASZ5Nd0Jb4K`8KZBLXFLVIMUMMSPNQTN\ OWOM_OGfRLbOPZMTWJXSH`OFdLChHAz84lE8ZJBLPEAXF8UH6R\ J4OL2PN0SPBULM_IWcEfeBoo7om8oi9mdAm`BmTClPDlKEkE9j\ GEhIJgKNfMSeOWhQYiS_jTalVclXemYgm_inajnblndnofpogr\ oitokvvszolwhfta_rVUoOOlHHjABg33f45e56e68e79e8Be8C\ e9EeAFeBHeCIeCKeDLeENeFOeGQe9UdGReMOfSLgYIhcFinAni\ Cjj2heDfaNdXYbTg`PqZOqVOqRNqNNqJMqFmzBZz7Us4FjQDbM\ CXJARG9LD7FA697534766988ABACDCDGEFIFHKHINJKPLLSNNU\ POWQQWORWLTWJUWGWWEXWCT_EQbGNeHKhJLkLOnMRqOUtQXyS_\ zRbzRezRhzRkzQnzQqzQtzQwzPzzPzzPzzPzzPzzRzzTzzVzzW\ zzYzz_zz`zzbzzdzzezzgzzizzjzzlzznzzozz`zzMzz4zz7zz\ AzzCzzFzzHzzKzzMzzMzzLzzK } 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 27-09-07 (Afire with Passion [6-1/2])
by Jim Muth 27 Sep '07

27 Sep '07

FOTD -- September 27, 2007 (Rating 6-1/2) Fractal visionaries and enthusiasts: My apologies for the lateness of today's FOTD image. Sometimes these things just can't be helped. Anyway, here it is, twelve hours late, for all it's worth. Today's image comes from the same indescribable parent fractal as yesterday's image. But today, instead of checking a vague spiral in a semi-chaotic debris field as we did yesterday, we check an almost straight but broken string of debris in the same field. What we find there is a variation on yesterday's image. In yesterday's image the emphasis was on the underlying fractal shapes, while in today's image the colors predominate. The name "Afire with Passion" was inspired by the colors. It has nothing to do with a cheap romance novel, so don't expect any lusty pirates or romantic passion. The passion in today's image is of the totally abstract mathematical variety. It's in the fiery colors, not quite as passionate as a romance novel hero but far more intellectual. After much indecision I rated today's image a 6-1/2. The rating is not so great, but today's image is not the best of all time either. It's still worth a look however, especially with a cal- culation time of only 20 seconds. Unfortunately, due to the lateness, the pre-calculated GIF image will not be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> for 12 hours or so. On Wednesday the temperature reached 91F 33C here at Fractal Central, which is located in central Pennsylvania. Such a temperature at the end of September is almost unheard of, and made it necessary to turn on the cool air. The fractal cats did not worry themselves with heat or cool. They were more inte- rested in the pigeons cooing and cavorting on the roof of the neighboring house. Though today's FOTD is shamefully late, tomorrow's should be ready on time. Look for it to appear at this same place at the usual time. Until then, take care, and has anyone ever made a cheap sci-fi movie about killer fractals? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Afire_with_Passion { ; time=0:00:20.48-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=+0.10583782636012190/-0.520610435295059\ 30/1.312072e+007/1/120/-6.21353841898791837e-006 params=-0.88/1.1/1/-1.1/0/0/0/0 float=y maxiter=1500 inside=0 logmap=47 periodicity=10 colors=000JAAKAAMAAMAAPAAOAARAAQAATAASAAVAAV69Y08Y\ 27`46c67e79k9AlBBsCCsHAtL8vP7wT5zV3zZ2zZDzcAzcAC7f\ 00q5CgANfFY`chWhmRezSQmTIZTGSUFLUGMWHNYHN_IO`IPbJP\ dJQeKRgLRiLSkMTlMTzNczNczJczFhzBcz7PV3OP0NK1LL1JL1\ IL1GL1EM1DM1BM19M18N16N14N13N79UDE_JKfOPlRSiTUfVWc\ YY`_`ZabWddTffQhhOdeRabTZ_VWYXTV_QSaNQcJNeGKgDHjAF\ l7Cn49p17r0Bq0Fq0Jq0Np0Qp0Up0Yo0ao0do0hn0ln0pn0sn6\ erCSvIFzMEvPDrSCnVBjZAfa9bd8Zg7Vk6Rn5Nq4Jt3Fr2Hp2J\ n2Kl2Mj2Nh2Pf2Qd2Sb2U`2VZ2XX2YV2_T2`R2bP2cT7aWB`_G\ ZbKYePWiTVlYToaSsfQvjPynOxkNwiNvgNueNtcNtaNs_NrYNq\ VNpTNpRNoPNnNNmLNlJNlHNnNPoTQqZRrdStjTuoUrpWppYnqZ\ lq`jqbhrcerecsfash_sjYtkWvmUxnbzpkzrtztrzspzsnzslz\ sjzsizsgzseztcztazt_ztYzuWzuUzuSzuQzvOzvMzvKzvBzw2\ zx6zu9zrCzpFzmJzjMzhPzeSzbVz`Sz_Qz_OzZMzZKzZIzYFzY\ DzXBzX9zX7zW5zW3zW7zXAzYDzYGzZJzZNz_Qz`Tz`WzaZzaYz\ _YzZYzYYzXYzW_zXZzTYzQXzN } 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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The FOTD for Sep 27 will be late
by Jim Muth 26 Sep '07

26 Sep '07

Fractal visionaries and enthusiasts: The subject line says it all. Due to unforseen circumstances here at F.C. -- (work) -- the FOTD for Sep 27 will be posted in about 16 hours. Sorry for the disappointment fractal fans. Jim M.

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FOTD 26-09-07 (Ancient Attributes [8-1/2])
by Jim Muth 25 Sep '07

25 Sep '07

FOTD -- September 26, 2007 (Rating 8-1/2) Fractal visionaries and enthusiasts: The expression behind today's image takes Z^(-1.1) and subtracts 0.88 parts of Z^(+1.1) from it before adding (1/C). I will not try to describe the resulting parent fractal, which is filled with indescribable almost-Mandeloid things, but I can at least say with certainty that today's scene is located in a debris field of the parent, and that this debris is organizing itself into a field of loose spirals. Unable to decide whether to rate the image at an 8 or a 9, I finally decided to split the difference and rate it at an 8-1/2, which, considering the accidental 3-dimensional effect, seems reasonable. Much less reasonable is the name I gave the image, "Ancient Attributes". I have totally forgotten why I chose such a name, but in a way the name is appropriate. After all, the midget at the center of today's image has been waiting to be stumbled upon since before the 'big bang' opened the universe. The calculation time of under 2 minutes on the 2000mhz fireball is reasonably reasonable. On the slow P200mhz machine, which served as the FOTD fractal generator for almost 8 years, the image would finish in around 10 minutes. But visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the completed image there is still the simplest way to see the ancient fractal When the autumn temperature reached 88F 31C on Tuesday here at Fractal Central, the weather became a little too perfect. The fractal cats, who are most active in the evenings, slept through most of the un-autumnish heat, not coming to life until the sun was low and it was time for their evening treats. I enjoyed a slow relaxing day, something that is a rarity around F.C. The next FOTD will appear in 24 hours. Until then, take care, and the Mandelbrot set certainly has a true shape, but does it have a true size? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Ancient_Attributes { ; time=0:01:52.04-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-0.359501241348669/-0.458041352586948/\ 1396462/1/-112.5/-1.56219443846195016e-007 float=y params=-0.88/1.1/1/-1.1/0/0/0/0 maxiter=1650 inside=0 logmap=168 periodicity=10 colors=00030E40F66G70H97IA1JC9KD4LFAMG6NICOJ7PLDQM\ 9ROFSP9SQFQS9QTAPV7PX4OY1O_0M`0Ma0Mc0Od0Pf0Qg0Qi1S\ j3Ti4Tg6Vf7Xd9XcAYaC_`D`_F`YGaVIcTJcSLdQMfPOfOPgMQ\ iLSjJTjIVlGXmFYmD_oC`pAapFcoJdoMfoQgoTimYim`jmdlmg\ mmlolpplsplxrlzsjzujzvjzsjzojzigzddy`asY_mTYiPVcSS\ YJPTGMOFLI4ID9F60C009007006006004104403903C01G01J0\ 0L00O00P00S00T00X00_00`00c00d00g00i00l00o00p00s00u\ 00x00y00z00z10z30z40z60z70z70z90zA0zC0zD1zF3zF4zG6\ zI7zJ9zLAzMAzOCzODzPFzQGzSIzTJzVLzVLzTJgrcjpalp`mo\ _poYrmXsmVvmTxlSylQzjPzjOzjOzjPzlQzlQzlSzlTzmVzmXz\ mXzoYzo`zogzoozpvzpzzpzzpzzrzzrzzrzzszzszzszzszzuz\ zuzzuzzuzzvzvvvsvoovglv`gvTcoM`gDXg7Tg3Pg0Mg0Og0Qo\ 0Tv0Xz1_z3az4dz7gz9jzAmzDpzFszGvzJyzLzzMzzPzzQzzSz\ zVzzXzzYzz`zzazzczzdzzYzzQzzJzzCzz4zz0zz0zz0zz0zz4\ zz7zzFzzMzzTzz`zzgzzmzzozzozzpzzpzzrzzrzzszzszzszz\ uzzuzzvzzvzzxzzazzazzazza } 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 25-09-07 (Blooming Iterations [7])
by Jim Muth 24 Sep '07

24 Sep '07

FOTD -- September 25, 2007 (Rating 7) Fractal visionaries and enthusiasts: Today's image is part of a parent that is on the verge of turning inside-out. (To turn the parent fractal inside-out change real(p3) from zero to -0.2) This parent fractal, with its 2 large bays, resembles a figure 8, with lots of added attractions in the form of interesting nooks and crannies to explore. Today's scene is located in an area near the origin that is easier seen than described. This area appears to be fragments of two or more overlapping bits of Mandeloid stuff. In addition to a very critical value of the real(p1) and real(p2) parameters, the imag(p3) parameter, which sets the bailout radius, is also a bit critical. Changing the first two parameters totally loses the scene, while changing the third to a lower value loses the scene also. Raising the third parameter to a higher value works subtle but interesting changes. I named the image "Blooming Iterations". There is no good reason why I gave the image this name except that it sounds strange enough to be the name of a fractal. The rating of a 7 was well earned by the 30 minutes I spent tweaking colors. The calculation time of 1-1/3 minutes on the P4-2000mhz Dell fireball stretches to around 8 minutes on the tired old P200mhz unit. As always, the best and easiest way to see the image is to go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view it there. Another perfect day prevailed here at Fractal Central on Monday. The cloudless skies and temperature of 81F 27C could hardly be improved upon. At least, that's what the fractal cats thought as they stretched out in the sun coming in the side window. My day was neutral -- not busy, not boring, just average. The next FOTD is due to appear right here in 24 hours. Until then, take care, and if fractals are made of numbers and the universe is a fractal, is the universe then made of numbers? Or is it that numbers best describe what the universe *is* made of? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= BloomingIterations { ; time=0:01:23.64-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=+0.17339511997376180/-0.105223649893324\ 40/1529334/1/-90/3.88578058618804789e-016 params=-0.85/1.1/0.85/-1.1/0/-60/0/0 float=y maxiter=1500 inside=0 logmap=162 periodicity=10 colors=050_CfdKzd5qe5qc7leAn_CfcDiWA`cDgT5W`AcQ5TY\ 5aO5SV5WM5OP5SJ5PM5AF5AI50B50E505707TZ2mZ0zZCtbOgd\ ZUfkNqv5oz5uzzczzzz5ozzzvFfsJdqPboT`mWZkaZheXiiVdn\ TflRRzktiRzc8zd0rK0zW0iA0nP5c57iIAU5Eb5I85MQ7O0AR0\ CV0DZ0Fb0J`0Hd0Fh0Dk0Cs0Dm0Fh0Hb0JX0LR5NO8PICRCIT7\ MU0PU0RU0TU0TU0VU0XU0XU0ZU0`U0`W0bW0dW0dW0fW0hW0hW\ 0iW0kW0mW0mY0oY0qY0qY0sY0uY2uY2vY2xY2x_2z_2z_2z_2z\ _5z_5z_5z_5z_5z_5za5za5za7za7za7za7za7ht7or5vn2zm0\ zk0zr0zi0z_AzTMzJXuAho5si5zf5zd5zd5zd5zd5zd5zd5zd5\ zd5xd5ud5sd5qf5if5df5Zf5Tf5Of5If5Cf57h50f50d52b55`\ 57Z58X5AV5CO5AT5EX5Ib5Mf5Pi5Ro5Vs5Zx5bz5fz7hzAkzAo\ zCszDvzDxzLvzRuvYukcs`kqRpqPtsOvuMzuKzvIzvIzxGzxEz\ zCzzAzz0zzAzzKzxTzubzqkzmuzizzfzzbzzZzzXzzVzxVzxTz\ vTzvRzvRztVzt`zrfzrkzrqzrvzrzzrzzrzzrzzrzzrzzrzzrz\ zrzzrzzrzzrzzrzzrzzrzzrzzrzzrzzrzzrzzrzzrzzrzzrzzr\ zzrzzrzzrzzrzzrzzrzzrzzrz } 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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"slope" formulas
by GillesNadeau 24 Sep '07

24 Sep '07

Here examples of the effect 3D which produces these formulas. http://www.mathsong.com/casaraku/pages/021/20040627a.htm

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slope-mj.frm
by GillesNadeau 24 Sep '07

24 Sep '07

Hello all, Here of the versions "slope" of some formulas. In another message I will send parameters. Gilles

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FOTD 24-09-07 (Hither and Yonder [6])
by Jim Muth 23 Sep '07

23 Sep '07

FOTD -- September 24, 2007 (Rating 6) Fractal visionaries and enthusiasts: Today's image was created by subtracting Z^(1.1) from Z^(-1.1) and adding (1/C). The parent fractal is little more than a scattering of fractal debris with many small distorted Mandel- brot sets lying in the debris. Today's scene is located near the tip of an archipelago of debris extending from one of the buds of one of the larger M-sets. I named the image "Hither and Yonder", though I have no idea why I chose such a name. The rating of a 6 seems about right for the image, which IMO is somewhat better than the FOTD average. In the image I tried to give the effect of a Minibrot standing out alone in an otherwise empty universe. The rating of a 6 shows how satisfied I am with my success. The near-effortless calculation time of 48 seconds can be bettered only by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the already calculated image there. With an absolutely cloudless sky and a temperature of 79F 26C, the weather was perfect here at Fractal Central on Sunday. I took advantage of the optimum conditions by spending the day in recovery from the day out on Saturday. The fractal cats spent the day helping me recover. The next in the apparently endless line of FOTD fractals will appear in 24 hours. Until then, take care, and remember to feed your fractals enough iterations to keep them healthy. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Hither_and_Yonder { ; time=0:00:48.55-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-0.116881071509402/-0.4370579950961422/\ 1.584087e+008/1/134.25/-5.55357036247e-005 inside=0 params=-1/1.1/1/-1.1/0/0/0/0 float=y maxiter=700 logmap=99 periodicity=10 mathtolerance=0.05/1 colors=00000F00HAK0zmJroQ0J40L60N75P8AR9FUBKWCUYDZ\ _EbaFfdIjcLlbOmaRk`UndZricvnhzsmzxrzzvzzzzzzfAAjFF\ nPPrQPuUUoTUoSUoSUoRUoRUzczzczzczzczuczzczzczzPYzR\ JzS5zU8zWBzYEQ_HHaK`dIsgGziEzhIzhMwhQshUngYigadge`\ giWSLbaJhjHosFuzEszIpzMnzPkyTixXfw`dwcevafu`ftZgtY\ hsXhrViqUjqSjpRkoQlnOlnNmmLnlKnlJkmIhmHemGbmF_mFXm\ EUnDRnCOnCLnBInAFn9Cn9EkCFhEGfHHcJJaMKZOLXQMUTNRVP\ PYQM_RKbSHdTFfVIcWKaXM_YOYZQV_ST`URaWPcZMd`KebIfdG\ gfDhhBij9jl7ki8lg8ld8mb8m_8nY8nV9oT9oQ9pO9pL9qJ9qH\ 9zGSxJRyMRzPRzRRzURzXRz_RzaRzdQzgQzjQzlQzoQzrQzuQz\ wQzQQzTSzVUzYWz_YzbZzd`zgbzidzlfzngzqizskzvmzxnzyk\ zzizzgzzezzczzazzZzzXzzVzzTzzRzzPzzNzzOzzOzzOzzOzz\ OzzOzzOzzPzzPzzPzzPzzPzzPzzPzzQzzRzzSzzTzzUzzWzzXz\ zYzzZzz_zz`zzazzbzzczzdzzczzczzbzzbzzazzazzazz`zz`\ zz_zz_zz_zzZzzZzzYzzYzzXzzQzzXzzXzzWzzWzzVzzVzzVzz\ UzzUzzTzzTzzSzzSzzSzzRzzR } 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 23-09-07 (Hither and Yonder [6])
by Jim Muth 23 Sep '07

23 Sep '07

FOTD -- September 24, 2007 (Rating 6) Fractal visionaries and enthusiasts: Today's image was created by subtracting Z^(1.1) from Z^(-1.1) and adding (1/C). The parent fractal is little more than a scattering of fractal debris with many small distorted Mandel- brot sets lying in the debris. Today's scene is located near the tip of an archipelago of debris extending from one of the buds of one of the larger M-sets. I named the image "Hither and Yonder", though I have no idea why I chose such a name. The rating of a 6 seems about right for the image, which IMO is somewhat better than the FOTD average. In the image I tried to give the effect of a Minibrot standing out alone in an otherwise empty universe. The rating of a 6 shows how satisfied I am with my success. The near-effortless calculation time of 48 seconds can be bettered only by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the already calculated image there. With an absolutely cloudless sky and a temperature of 79F 26C, the weather was perfect here at Fractal Central on Sunday. I took advantage of the optimum conditions by spending the day in recovery from the day out on Saturday. The fractal cats spent the day helping me recover. The next in the apparently endless line of FOTD fractals will appear in 24 hours. Until then, take care, and remember to feed your fractals enough iterations to keep them healthy. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Hither_and_Yonder { ; time=0:00:48.55-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-0.116881071509402/-0.4370579950961422/\ 1.584087e+008/1/134.25/-5.55357036247e-005 inside=0 params=-1/1.1/1/-1.1/0/0/0/0 float=y maxiter=700 logmap=99 periodicity=10 mathtolerance=0.05/1 colors=00000F00HAK0zmJroQ0J40L60N75P8AR9FUBKWCUYDZ\ _EbaFfdIjcLlbOmaRk`UndZricvnhzsmzxrzzvzzzzzzfAAjFF\ nPPrQPuUUoTUoSUoSUoRUoRUzczzczzczzczuczzczzczzPYzR\ JzS5zU8zWBzYEQ_HHaK`dIsgGziEzhIzhMwhQshUngYigadge`\ giWSLbaJhjHosFuzEszIpzMnzPkyTixXfw`dwcevafu`ftZgtY\ hsXhrViqUjqSjpRkoQlnOlnNmmLnlKnlJkmIhmHemGbmF_mFXm\ EUnDRnCOnCLnBInAFn9Cn9EkCFhEGfHHcJJaMKZOLXQMUTNRVP\ PYQM_RKbSHdTFfVIcWKaXM_YOYZQV_ST`URaWPcZMd`KebIfdG\ gfDhhBij9jl7ki8lg8ld8mb8m_8nY8nV9oT9oQ9pO9pL9qJ9qH\ 9zGSxJRyMRzPRzRRzURzXRz_RzaRzdQzgQzjQzlQzoQzrQzuQz\ wQzQQzTSzVUzYWz_YzbZzd`zgbzidzlfzngzqizskzvmzxnzyk\ zzizzgzzezzczzazzZzzXzzVzzTzzRzzPzzNzzOzzOzzOzzOzz\ OzzOzzOzzPzzPzzPzzPzzPzzPzzPzzQzzRzzSzzTzzUzzWzzXz\ zYzzZzz_zz`zzazzbzzczzdzzczzczzbzzbzzazzazzazz`zz`\ zz_zz_zz_zzZzzZzzYzzYzzXzzQzzXzzXzzWzzWzzVzzVzzVzz\ UzzUzzTzzTzzSzzSzzSzzRzzR } 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 23-09-07 (A Rite of Passage [7])
by Jim Muth 23 Sep '07

23 Sep '07

FOTD -- September 23, 2007 (Rating 7) Fractal visionaries and enthusiasts: To begin, I must apologize for the lateness of the FOTD. But we were out all day Saturday, leaving no time for a proper fractal search. With its rating of a 7, today's fractal turned out unexpectedly well, considering the little time I spent on it. The expression being iterated subtracts 2.3 parts of Z^(-1.75) from 2.3 parts of Z^(-1.25) and adds (1/C). The resulting parent fractal contains twin Mandeloids connected at the hip and surrounded by a large field of chaos. This chaos is filled with many small Mandelbrot sets, with today's scene being located in the East Valley area of one of the two largest sets. The image is potentially quite a good one, maybe an 8 or a 9, but as it is, I was too hasty with the coloring, which tends to the muddy side. Still, it's an interesting fractal, well worth a look. The name is pure whimsy. To take that look, run the included parameter file or view the image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> But because of the lateness of this FOTD, it may be a little while before Paul gets the image posted. So be patient. The weather was quite good here at Fractal Central on Saturday (sunny, 86F 30C), which is why we decided to go out and have fun. The fractal cats slept through most of the day. The next FOTD will arrive at this same spot, on time in around 12 hours. Until then, take care, and please curb your fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Rite_of_Passage { ; time=0:04:59.89-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+2.419082571631869/+1.824668113269568/\ 1.26264e+011/1/115/0 params=2.3/-1.25/-2.3/-1.75/\ 0/0/0/0 float=y maxiter=3400 inside=0 logmap=570 periodicity=10 mathtolerance=0.05/1 colors=0009LYBPWCPVDP`FKeGFkHBpNPkSbgd2yZ1rU1lO0fJ\ 0`E0VF3SG6QH9NICLJFIJIGKLELOBMR9NU6OX4OZ2NX7MVBLTF\ KRJJPOINSHLWGJ_FHdEFhDDlDCpGP_J`KLl4Jm6In7Hn8Go9Fo\ ADpCCqDBqEArF9rG7sI6tJ5tK4uL3uMAoGGjBNe5T`0Ra5Qb9O\ cDNdHMdMKeQJfUHgYGgbFhfDijCjnBjrCipChoCgmCflCekCdi\ CchDbgDaeD`dD_cDZaDY`DY_KSVRMRYHMhBIm6Ec9AIB74D49I\ 6EN7IS8NUAUmBcmCmmEwpFwuGwzHwtIwoJmmKcmLYmMUmNRmOO\ mPLmQImRFmSGmTHmTImTImTJmUKmUKmULmUMmUNmVNNVOPVPQV\ PRVPSRPTOOUMNULMUKLUJKUIJVHIVGHVFGVEFVDSgbK`MPfVfH\ `dKacNabQa`Ta_WaZZbYabWdbVgbUjbgiwejudjscjqbjp`kn_\ klZkjYkiWlgVlzUlc0LD0VMXcVeHocJnaKmMRlKSkJUiHVfVSc\ TTcaKb_KaZYeXcdWjcUkbYdHXKMWKQVKVUkZzVAzXDzZGz_Iza\ LzcOzdQzfT_hWYiYVk`SaPTcRTdSTeUTfVTgWThYTiZTZ`TZaK\ ZbMZbOZbQZbSibqdVmhXimYfrZbv__z`Wzaazu_zrZzpYzmXzk\ WziVzfUzd7zf9zeAzeCzeDzeEzdGzdHzdIzdKzcLzcNzcOzcPz\ bRzbSzbPzrQzoRzmRzk9zU9zP } 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 22-09-07 (Here We Go Again [5])
by Jim Muth 21 Sep '07

21 Sep '07

FOTD -- September 22, 2007 (Rating 5) Fractal visionaries and enthusiasts: "Here we go again", I thought as I struck the 'enter' key to create today's very fast fractal image. How many times have I searched for interesting midgets in the fractals with exponents of Z in the range between 1 and 2? And how many times have I come away only marginally satisfied? Too many times to count! Today's scene lies in the Z^(sqrt(2))+C Mandeloid as it appears 1.4142 turns up the logarithmic hyperspiral ladder, where it is little more than a shapeless bay surrounded by a field of chaos, with one dreary bud attached. The image is located at the edge of the chaos on the west side of the shapeless bay. I named the image "Here We Go Again" because I knew ahead of time from long experience that the result would not be worth the effort. Still, I saw enough in the tortured little minibrot at the center to work a bit on the colors and declare the image the FOTD for today. I could rate the result no higher than a 5, but a 5 is not too bad when the image calculates in a hyper-speedy 14-2/3 seconds. And even the little bit of effort required to load and run the included parameter file may be avoided by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Another near-perfect day prevailed here at Fractal Central on Friday. The morning fog burned off by 10am, leading to a sunny day with a temperature of 84F 29C. The fractal cats enjoyed the weather from the indoors, watching the squirrels gathering nuts. My day was notably normal. The next FOTD will be posted in 24 hours, give or take a few. Until then, take care, and might the secrets of the universe be hidden in the manifested abstractions known as fractals? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Here_We_Go_Again { ; time=0:00:14.65-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 center-mag=-1.20822656/\ +0.69457459/2303/1/-120/0 params=1.4142/0/1.4142/0 float=y maxiter=2000 inside=0 logmap=45 colors=000Q5KSAOUFSWNWYR__Vca_gcdkfinhmrjnvgkyagzS\ cyHZv7R6BU7FZ7Id8Mj8Po8Rm8Th8U`8WV8YO8ZI8ZDAZ9BZ5C\ Z1DW3JU4PS5VP7`N8fL9lJAqeXLbWJ`VHYUFWTDTSBRR9PR7PZ\ FPfMPzTPz_czNmzAmzA_eAcc9Hc8acYvYwkZjaZYSZLIZ8VhFf\ qMrzTisV`mWSfXJcYAcZ2c_7cZCcYHcXMdWRhVWlU`pTetSfrW\ fq_focfnfegadaYccUbcQacM`cIYcUVcdShoPszSrsVrmYrgSf\ WMcKHc8NcFSbMXkSUgUScVPcWNcXKcYIcZFc_Dc`DcYDcVDcSD\ fPDmMDsJDyGAjO7cV4ca9cdDcfHchLcjPclTjnXnpahjfcekZ_\ pcVtcQkcaccmWcyTcrRclPcfMc_KcUIcOGcIFcRFcZElgEwokP\ ulSplUklWflYal_XlaSlcNleJjgRhiYfkedmlcnsaip`dn_clZ\ djYegXgeWicVkaUmYUoUTqQTrNSsJStFSuCLvVEwmMxjTyg_zd\ fzamzZpzerzkozmmznjzphzqfzrAztazu_zvWzqTzlQzhMzczz\ JzzLzzTzz_zzgzznzzuzzozzizzczzYzzVzzTzzQzzOzzMzzNz\ zOzzPzzQzzRzzNzzJzzFzzBzz7zz3zz0zz5zzAzzFzzKzzPzzU\ zzYzzazzezzizzlzzpzzizzczzYzzSzzMzzTzzZzzdzzjzzpzz\ vzzuzztzztzzszzrzzrzz2zz2 } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100, p=real(p2)+PI q=2*PI*floor(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 PARAMETER FILE=========================================

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Re: FOTD for 9/21/07
by Paul N. Lee 21 Sep '07

21 Sep '07

Brian Prentice replied to philofractal: > > Here is a detail from the parent fractal > described by Jim Muth today: > > http://linuxenvy.com/bprentice/Fractals/Set%2012/BP_12_61.jpg > Very colorful, and the 1280x960 size shows a lot of details. Sincerely, P.N.L. ------------------------------------------------- http://home.att.net/~Paul.N.Lee/PNL_Fractals.html http://www.Nahee.com/Fractals/

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FOTD 21-09-07 (Squarely Rooted [5])
by Jim Muth 20 Sep '07

20 Sep '07

FOTD -- September 21, 2007 (Rating 5) Fractal visionaries and enthusiasts: Today's image takes us back to the MandelbrotBC2 formula and the complex logarithmic hyperspiralling ladder. Today however we do not need the ladder, since we explore the Z^(sqrt(2))+C fractal at its ground level. The parent fractal is a most curious Mandeloid, with a triangu- lar period-2 bud as large as the main bay and an unusually long zig-zagging main spike extending far into positive-imaginary territory. Today's scene is located deep in a valley separating the large triangular bud from a large sub-bud on its northern edge. The depth of the scene in the valley makes today's image much slower than the FOTD images of recent days. I named the image "Squarely Rooted" because its exponent is the square root of 2. I rated it at a hum-drum 5 because it is plagued by the excessive chaos that is so typical of fractals with exponents of Z in the range between 1 and 2. The calculation time of 12 minutes on the P4-2000mhz computer would be near one hour on the old P200mhz unit. So why not visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the image effortlessly there. Another typical end-of-summer day prevailed here at Fractal Central on Thursday. The morning fog lifted by 10am, leading to a sunny afternoon with a temperature of 82F 28C. The fractal cats made the most of it by lounging in the sun streaming in the southwest window for most of the afternoon. My day was neutral. The next FOTD will be posted for all it is worth right here in 24 hours. Until then, take care, and remember Fractint in your will. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Squarely_Rooted { ; time=0:12:11.04-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 center-mag=-0.1234698959\ 7/+1.53149499923/3184551/1/90/3.88578058618805e-016 params=1.4142/0/0/-97.25 float=y maxiter=7200 inside=0 logmap=1174 periodicity=10 colors=00060K60K60K70K70J70I80H80I80J80K90L90M90NA\ 0OA0PA0Q90RA0SA0TA0UB1TB2SB3RB4QC5PC6OC7ND8ND9NDAN\ DBNECMEDMEEMFFMFFMFFMFGLHHKIIJKJJLKINLIOMHQNHROGTP\ GUQFWRFXSEZTE_UDaVDbWCdXCeYBgZBh_Aj`Aka9la9la9j_6h\ Y3fW6dU9cSBdQEeOGfMJhKLiKOjLQkMTlNVmOYoQ_pRbqSdrTg\ sUitVlwVquWnsWlqXjoXhmXfkYdiYbhY`fZZdZXbZV`_TZ_RX_\ PV`NU`LS`JQaHOaFMaDKbBIb9Hb7F_6EY6DW5CU5AS49Q48N37\ L35J24H23F12D14E35E47E58E6AF7BF8DF9EFAGGCHGDJGEKGF\ MHGNHHPHIQHJSILTIMVINWIOYJPZJQ`JRaJScOPdTMeXJgaGhe\ DijAkn7ls4lz0mw2nt3oq4pn5qk6rh7se8tbAu_BvXCwUDxREy\ OFzLGzJHzGEpDBgB8Y85Q52K30E73BA6CD9EGCGKFHNIJQLKTO\ MWQO_TPbWRfcSjmUnzWkzXfzZ`z_VzbUzbPZbKRbKJaK9`KB_K\ D_KFZKGYKIYKK_OLbNNbSPbRQdQScQUcPWbOXaOZaN``Ma`Mc_\ LeZKfZKhYJjYJk_Oj`SiaWhc`gddfehfhcikZkmUnpPptBzrKr\ qSjp_bngVmoNcxChwFmwIrwLvwOzwRzwUzwXzvWzvWzuVzuVzt\ UztUzsUzsTzrTzrSzqSzqRzQH } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100, p=real(p2)+PI q=2*PI*floor(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 PARAMETER FILE=========================================

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FOTD 20-09-07 (A Tight Squeeze [6])
by Jim Muth 19 Sep '07

19 Sep '07

FOTD -- September 20, 2007 (Rating 6) Fractal visionaries and enthusiasts: I named today's rather unusual fractal picture "A Tight Squeeze". I gave it this name because the poor little minibrot at the center is being squeezed by an ever-shrinking bailout radius, and is at the point where it is about ready to be swallowed up into the nothingness that awaits all uniterated fractals. The rating of 6 is based largely on the coloring, which I spent some extra time on. Without this hand-designed palette, the image would hardly be worth a second look. The parent fractal is an oversized and very distorted Mandelbrot set, notable for its unusually small buds. Most of this parent fractal lies off the left edge of the default screen. This distorted set is surrounded by clusters of debris, with today's scene located in a bit of debris near the negative X-axis, just to the east of the main bay, but still well within negative real territory. The calculation time of 14 seconds is no mistake. This is the time the image takes to finish on the P4-2000mhz computer. On the worn-out P200 machine it would finish in about 1-1/2 minutes. For maximum convenience, the completed image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it may be instantly viewed and enjoyed. Near perfect conditions continued here at Fractal Central on Wednesday. After the early morning fog cleared off, the warm sun warmed the air to 77F 25C. The fractal cats amused them- selves a good part of the afternoon by watching two chipmunks frolicking in the grass in the back yard. My day was kept active by an unexpected job, which occupied most of the morning, but left the afternoon free for leisure. The FOTD will appear again in 24 hours. Until next time, take care, and then some. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Tight_Squeeze { ; time=0:00:12.46-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=-0.54021836525840720/+0.169188470362415\ 70/1.379919e+013/1/125/0 params=0.7/-3/0.7/2/0/\ -94.1665/0/0 float=y maxiter=300 inside=0 logmap=42 symmetry=none periodicity=10 mathtolerance=0.05/1 colors=000N0FQ0KT0KX0KR0LO0300QA2UC1_GFkJNmNWqQezU\ ozmzzwzzVczVavU_rTYmTWhSUcSSZRSWQSUPSWORXMRZLR_KRa\ JQcIQdGQfFQgEPiDPjCPlBPmGTgKXaVdMP`WTdQMLSOORPQQQS\ PRVOSXOTZNUaMVcLWeKbb7_eE_pKZoKZnKZmKZmKYlKYkKYjKY\ jKXiKXhKXgK_P1ZS4ZV7YYAY_CXbFXeIcYzbZva_ra`n`aj_bf\ _cbZdZYeVYfRXgNbrSaqRapQ`oQ`oP`nP_mO_lOZlNZkNZjMYi\ MYiLXhLXgKs6NoDMkJMgPLcWL_aKdx1cv3bu4bt5as7ar8`q9`\ pA_nC_mDZlEZkFYjHYiIXhJJy1Mu5Pq9SnDVjHqCenHakMZhQW\ eVTbZQ_cNnM_lPYjRWhTVfVTeXSc_QaaO_cNYeLTifUhdUhbUh\ aVh_VhZVhXVhWWgUWgTWgRWgQXgOXgNXgLI7XLEUNKSQQQSWOV\ aM1HaG03J66LB8NHAPMCRSETXGVbILUXNWVOZUPcTQhRRmQTrP\ UvNVzMWzL1z45z68z8Bz9EzBHzCLzEOzGRzHUzJ1zCCzFNzIcz\ 3az8_zCYzGiz`hzZgzYfzXezWdzUczTbzSazR`zQ_zOZzNYzMX\ zLKzeLzcMzaNz`OzZPzYQzWRzVSzTTzRUzQVzOWzNXzLszHpzI\ mzIkzIhzJfzJczJazKZzKdzdbzZ`zUZzPAzFDzGGzHJzHMzIPz\ JSzJVzKGzgIzeJzcazhezihzk } 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 19-09-07 (Test [8])
by Jim Muth 18 Sep '07

18 Sep '07

FOTD -- September 19, 2007 (Rating 8) Fractal visionaries and enthusiasts: Today's splendid image owes its existence to the 'fmod' feature of Fractint, which creates the effect of overlapping bubbles. The parent fractal came about when I combined 100 parts of Z^(-3) with 1/100 part of Z^(2) and added C. With 10,000 times as much Z^(-3) as Z^(2), one would think the resulting fractal would be little more than the 4-pointed Z^(-3) Mandeloid, but actually it is a hugely enlarged Mandelbrot set, with bits of debris in the center of the main bay as well as in every bud. Today's image is located in an elephant trunk in the East Valley area of the parent. At first glance the central midget appears to be a routine one of this area, but a comparison with the same area of the true M-set will reveal that the pattern around the midget has changed. The change was enough to inspire me to a rating of an 8. The name "Test" was a total accident. I forgot to name the image, so I went with the default name of all parameter files created by the program. The calculation time of 1-1/4 minutes would be stretched to around 7 minutes on the slower computer. But regardless of the speed of the parameter file, it is always almost instantaneous to view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Another perfect day (sunny, 73F 23C) went un-noticed here at Fractal Central on Tuesday. Of course, if the day was un- noticed, then how do I know it was perfect? That's a question worth pondering. The fractal cats pondered. They pondered their food dishes, that is. My day was routine in all respects, except for the fractal, which turned out better than I had hoped. The next fractal will appear in 24 hours. Until then, take care, and fractals are the strangest creatures ever. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Test { ; time=0:01:13.97-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+27.7974630212/-0.7662145179/52524.91/1\ /-172.5/0 params=100/-3/0.01/2/0/350000/0/0 float=y maxiter=1550 inside=0 proximity=500 outside=fmod logmap=yes periodicity=10 colors=000wxwvwuuvstuqstorsmqrkpqiopgooenncmmalm_k\ lYkkWjjVijUhiUghTggSfgRefQdePddOcdObcNabM`aL_`KZ`J\ Z_IYZIYYHWYGVXFVWEUVDTVCSUCRTBRSAQS9PR8OR7NQ6OQ5NP\ 6NP6NO6NN6NM6NL6MK7MJ7MI7MH7MG7MF7ME7LC8LB8LA8L98L\ 88L78K69K59K49K39K29K19K09K1AK2AK3AK4AK5AK6AK7AK8A\ K9AKAAKBAKCAKDAKEAKFAKGAKHAKIAKJAKKAKKAKLAKMAKNAKO\ AKPAKQAKRAKSAKTAKUAKVAKWAKXAKYAKZAK_AK`AKaAKbAKcAK\ cAKdAKeAKfAPgAUhAZiAcjAhkAmlArmAvnAzoAzpAyqAyrAysA\ xtAxuAwvAwwAwzFwwAwuBwsBwqBwpBwnBwlBwkBriBmgBhfBcd\ BZbBUaBU_BVYBWWBWVBXTBYRBYQBZOB_MB_LB`JBaHBaGBaGB`\ HC`HC`HD_ID_IEZJEZJFZJFYKGYKGXLHXLHXLIWMIWMJVNJVNK\ VNKUOLUPLTQMTRMTRMURMUSMVSMVTMWTNXTNXTNYVNYWNZXN_Y\ N_YO`ZO`_Oa`Ob`ObaOcbOddNcbObaPa`Q`_R_ZSZYSYXTXWUW\ VVVUWUTWTSXSRYRQZQP_PO_OM`NLaMKbLJcKIdJHdIGeHFfGEg\ FDhEChDBiCAjB9kA8lB5nA7lSsBUtDVtFXtGYtI_tJ`tLbtMct\ OetPftRgtTitUjtWltXmtZot_ } 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 18-09-07 (Up High--Down Low [6])
by Jim Muth 17 Sep '07

17 Sep '07

FOTD -- September 18, 2007 (Rating 6) Fractal visionaries and enthusiasts: Today's image is kind of an oxymoron -- a quadratic minibrot surrounded by a pattern expected only in fractals of a much higher order. Well, the higher order part of the image should not be much of a surprise when the generating expression sub- tracts Z^13 from Z^12, then adds C. The quadratic part is simply the shape of most minibrots in the critical parts of most fractals generated by the MandAutoCritInZ formula. The parent fractal is basically an everyday 12-lobed higher- order Mandeloid with a little more fractal debris scattered close around the perimeter than would normally be expected. Today's image is located close to the negative X-axis, in some of this debris. I named the image "Up High--Down Low". I have forgotten why I chose such an unlikely name, but it sounds just unusual enough to be a name for a FOTD. The rating of a 6 means that the image, with its well-defined patches of strong color, is just a little above the FOTD long-term average. The calculation time of 1-1/2 minutes is true on the fast machine. On the slow unit the calculation would take around 10 minutes to finish. But why worry about running parameter files when the completed image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Near perfect weather prevailed all day Monday here at Fractal Central. A bit of river fog in the early morning cleared out by 9am, leading to a day with brilliant warm sun and a temperature of 68F 20C. Good behavior prevailed among the fractal cats, who are fast becoming the official watch cats of F.C. My day was routine, which means busy enough to prevent recession concerns. The next FOTD will appear in 24 hours. Until then, take care, and are fractals good, evil, neither or both? Or is the question meaningless? And if the question *is* meaningless when applied to fractals, what about when it is applied to the events of the 'real' world? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Up_High--Down_Low { ; time=0:01:35.18-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident inside=0 center-mag=-1.006625002317998/+0.00827883211913072\ /3.746549e+012/1/-54.9/0 params=-1/13/1/12/0/0/0/0 float=y logmap=335 maxiter=1850 logmap=335 periodicity=10 mathtolerance=0.05/1 colors=000ASfFTiNUkUVm`SoXTfTQZPMRLIJ04Bs03m0KzZ9z\ uIUzzDFFMCKUAPa8Ui5Zq3czPrwUmuUrsZvqczohzkmzgrzivz\ lzzqzzvzzzzzzzzzzzzzzzzzzzzzzzzzzzzzKUaUPPcLDmH1lO\ 2lV3la3lh4lo4fgB``IWUPQMWLFbF8iA1oL2qW2rf2sp2tkKjf\ ``bqRdjUfcWhXYiQ_kJamCcn6eeGYXPQPYJoZopYjpXfqWbqVZ\ qVVlohgr`buTYxLTzDIFeOLcTRaYX`bbZghYlnWqtVirZbpaWn\ ePmhRngTogVpfXpf`ihcbigXjjQknJlqDm5B2FO7P_BZkFgcl`\ YzmUpwUfuRArK9mN8hJ7cE5Z84U33P02K59FCFAJMIPSOPNTOJ\ ZOFcNBiM7nM3lP8jSDhVHgYMe`QccVbeZebXh`VjYUmWSpTQrR\ PuONwMMoMLhMLaMLUMKNMKGMK9MK8OM8QO7SP7UR6WS6YU6_VF\ _aO_gX_me_sn_yFP5PMGYJRfGaoDlxAvtGmpLdlRWhWNe`EaWL\ YSSUOZQJeMFTJBZNE_RGjVIkZKlrMwwOxwQywSysfkOa6L_7JZ\ 8GX9EW9KUKQSVWQeaOp`Nk`Mf_La_KXYQ_XWbWaeUchTekSgnP\ ilNkjLmh9o4DqAHsFLuKPwQTyVWz__zVczQhzLmzGrzKvzOzzS\ zzWzz_zzczzgzzizzkzzmzzozzqzzszzuzzozzjzzdzz_zzVzz\ PzzKzzFzzQzz_zzjzztzzCGJA } 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 17-09-07 (Lawbreaker [8])
by Jim Muth 16 Sep '07

16 Sep '07

FOTD -- September 17, 2007 (Rating 8) Fractal visionaries and enthusiasts: Today's fractal is a true lawbreaker, which is what I named it. Everyone knows that the number of elements in the patterns around quadratic minibrots increases in the series 2,4,8... as the midget is approached. So how do we explain the midget at the center of today's image, which is obviously quadratic, but is surrounded by a 3,6,12... series of elements? I will not even try to explain it. I'll leave the explanation to the geniuses of fractal mathematics. To me it's just one of the unexpected things that make fractal exploration so fascinating. The parent fractal is another thin ring of radius 1 centered on the origin. This time to get the ring I combined 0.0003 parts of Z^(1001) with 0.0003 parts of Z^(-999) and added straight C. Today's scene is located in the critical detail where the ring intersects the positive X-axis. The rating of an 8 might seem a bit generous, but I think the mathematical curiosity makes the image worth the rating. The calculation time of 1-3/4 minutes is no problem. Viewing the completed image on the FOTD web site is even less of a problem. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Despite a chill in the air, Sunday was near perfect here at Fractal Central. Blue skies and a temperature of 64F 18C are hard to beat. The fractal cats spent a good part of their day on mouse duty, checking every suspicious little hole where a mouse might get in. I did little but take it easy all day. Why do more? The next FOTD will appear in 24 hours. Until then, take care, and don't be a fractalist who has lost his faith. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Lawbreaker { ; time=0:01:49.08-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+0.99754831985625280/+0.000073916471693\ 98/1.967133e+007/1/165/3.64419725437659103e-006 params=0.0003/1001/0.0003/-999/0/0/0/0 float=y maxiter=1800 inside=0 logmap=143 periodicity=10 colors=000DALFBMFCNFDOFEPFFQGGRHHSIIUOKWUPZcUcmZht\ cmzhrzmvzqzzqzzqzzqzzszzuzzwzzzzzzzzzzzvzzrzvmzriz\ mgzhhzchzaiz_iz_jz_jzZkzZkzZlzZlzYmvYmrYnmXnhXocXo\ ZXpUWpTWqSWqSVrRVrQVsPVsPPvEKy4Iw5Hu6Fs7Eq8Do8Bm9A\ kA8iB7gB6eC4cD3aE2_E3aK4bc4gp5iz5nz6rz6oyBkzFgzJbz\ NVzRRvVPrZUmbYhfXcjVZnUUrTPvSNzUOzVOzWOzXPzYPzZPz_\ Qz`QzbQzcRzdRveRrfSmgShhSfiTekTdlTcmUbnUaoU`pV_qVZ\ rV`oUamUbkTchTdfSedSfaRg_RhYQiVQjTPkRPlOOmMOnKNoIN\ iMOdQPZTPUXQO`RJcRDgS8jS9hQAfPBdNCbMDaLE_JFYIGWGHU\ FITEJRCKPBLN9ML8NK7OI5PG4QE2RC1SB0QE1OG1MJ1LL2JO2H\ Q2GT2EV3CY3A_39b47d45g44i44g64f74e94dA4cC4bD4aF4`G\ 4_I4ZJ4XL4WM4VO4UP4TR4SS4RU4QV4PX4OY6P`8Qc9RdASdBT\ dBUeCVeDWeEXeEYfFZfG_fH`fHagIbgJcgKdgKehLfhMghMhhP\ ieSjbUk_XlXZmUanRcnOfnLinIknFnnCpn9sn6um4on8ioCcpF\ YqJSrMMsQHtTKuSUvRcwPmxOvyNzzLzzKzzJzzIzzGzzFzzEzz\ CzzBzzAzz9zz7zzSzzTzzUzzW } 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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Triternion and ismand parameter
by GillesNadeau 16 Sep '07

16 Sep '07

Hello all, I spent the night to be played with the formulas triternions of Russell Walsmith and the parameter ismand. Here formulas and of the parameters by hoping that that will interest of people on this list. Gilles

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FOTD 16-09-07 (Dry Valley Ambush [4])
by Jim Muth 15 Sep '07

15 Sep '07

FOTD -- September 16, 2007 (Rating 4) Fractal visionaries and enthusiasts: Today's image is named "Dry Valley Ambush". I gave it this name because I was ambushed by it. Dry valleys are symmetrical features that look like they have a midget at their centers, but when the symmetry is enlarged, it dies out in a flat blank area. A flat blank area is what I found when I eagerly dove into the broad double spiral in today's image, fully expecting to find an unusual midget at its center. Due to my disappointment, I rated the image at a lowly 4. I doubt that it is worth much more. But with its clashing bright oranges and dark blues, there is a certain mischievousness about it that merits publication. So I decided to change what should have been an immediate discard into the FOTD for today. The parent fractal resulted when I combined 0.01 part of Z^(-77) with 0.01 part of Z^(79) and added (1/C). This parent is little more than a thin ring of radius 1 centered on the origin, with the fractal stuff lying in the interior of the ring. At first, the entire ring looks promising, but only the parts of the ring that lie on the X-axis are actually in the critical state. Today's scene is located near the point where the ring inter- sects the negative X-axis. Because of the location, I expected more at the center of the spiral in today's image than I found there. But fractals are unpredictable, and one is sometimes un- expectedly surprised or, as in today's case, disappointed. At least, the image is a fast one, finishing in 53 seconds on the fast P4-2000mhz machine. It would take near 5 minutes on the old P200mhz unit. The finished image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A slightly chilly but otherwise near perfect day prevailed here at Fractal Central on Saturday. The fractal cats enjoyed the pigeons scrounging for food on the sidewalk. I enjoyed having the work caught up, even though the day's fractal left something to be desired. The next fractal will appear in 24 hours. Until then, take care, and fill in life's blanks with fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Dry_Valley_Ambush { ; time=0:00:52.79-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-1.00587732385816700/+0.000000760828969\ 08/5965409 params=0.01/-77/-0.01/79/0/0/0/0 float=y maxiter=310 inside=255 logmap=50 periodicity=10 colors=0000AK0AK0AK0AK0AK0AK0AK0AK0AK0AK0AK0AK0AK0\ AJ0AM0AP1AR2AU3AU4AU5AU7AU9AUBAUDAUFAUHAUKAUNAUQAU\ TAUWAUZAUaAUdAUfAUiAUkAUmAUoAUpAUrCUtFSvIPwLNxOLyQ\ KzSJzUIzSGzQFvOErMDmKChIAcG9cI8cL7cO6cS8cWAc_CeaEn\ cGnaHo_IoYJpWJpUFmS8jQ8gO8dM8bK8_I8XG8UF7RG7PG7MI7\ PLAUODZRGaUJcXM`_PYbSVeTShTPfTNdTKbTH`TEZTBXT8VTYT\ TfRTgWZl`cudhsbfraeq_doZcnXamW`kU_jTZiRXgQWfOVeNUf\ ORgOPhONiOKiOIjOGkODlOBlO9mMCnLFnJIoILpGNpFQqDTrCW\ rBYpDZoEZmG_lH_jJ_iK`gM`fNadPacQaaSb`TbZVcYWcXXcTV\ fQUhNTjKRmHQoEPqBOsCQsDSsEUsFVsGXsHZsI`sJasC_o6Yk0\ Xg4`d8caBf_FiXIlUMoSPrPTuMWxKTxRRxYPxcNxjLxpPtnTqm\ Xnk`kjchhgegkbeo_drXcnZ`j_Zf`XcbV_cSWdQTfOPgMLhJIj\ HEkFAlD7mB8qv9psAppBpnCokDoiEofFndGnaHn_IjZJgZJcYK\ `YKYYLUXLRXMOXNKWNHWOEWOAVP7VP4VODUNMTMVSMcRR`PVYO\ _VNcSLhPKlMJqJHuGGyDFwCJvBMuBPsASr9Vq9Yp8`n7dm7gl6\ jj5mi5ph4sg4va7sXAqSDoNGm } 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 15-09-07 (More than Meets an Eye [6])
by Jim Muth 14 Sep '07

14 Sep '07

FOTD -- September 15, 2007 (Rating 6) Fractal visionaries and enthusiasts: Today's image continues the thread of the past several days, as we continue onward and upward to an exponent of 6. The parent fractal is the expected 5-lobed Mandeloid, with today's image located just off the spike of the negative X-axis, very near the point where the spike joins the main body of the parent fractal. I named the image "More than Meets an Eye". In my imagination I see many more things lurking in the depths of the image. Un- fortunately, these are beyond resolution, unless one wishes to shift to arbitrary precision math, which is uselessly slow with the manzpower formula. To prevent the calculation time from jumping from a lightning-fast 105 seconds to an almost unbeliev- ably slow 34 hours, I have included the mathtolerance entry in the parameter file. As for the rating, I decided to stick with a rating of 6. The image is too close to what would be expected to earn more than this. The calculation time of 1-3/4 minutes is fast enough to prevent the stress of boredom, and in addition, the image is available for instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The Friday temperature of 75F 24C was near ideal, but heavy clouds and a threat of rain kept the day from reaching its full potential here at Fractal Central. The fractal cats did reach their full potential for trouble however, when Cassie somehow worked her way behind a loose panel in the bathroom closet and spent the next hour or so exploring the no-man's land between the floor and ceiling. She emerged quite dusty but otherwise satisfied with her adventure. My day was busy enough to keep boredom at bay. Tomorrow is still a question, and there will be the next FOTD fractal to contend with. Until then, take care, and stay alert. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= MoreThanMeetsAnEye { ; time=0:01:45.68-SF5 on P4-2000 reset=2004 type=manzpower passes=1 float=y inside=0 center-mag=-1.10976164061526900/+0.000001168008348\ 63/3.847449e+012/1 params=0/0/6/0 maxiter=10000 logmap=438 periodicity=10 mathtolerance=0.05/1 colors=000A0jA0iA0gA0eA0dA0bA0`A0_A0YA0WA0VA0TA0RA\ 0QA0RA0RA0SA0SA0SB0TC0T71T83U84V85W96X98Y99ZAA_AB`\ ADaBEbBFcBGdCIeCJfCKgDLhDNiDOjEPkEQlESmFTnFUoFVoHW\ mJWlKWkMXjOXiPXhRYgSYfUYdWZcXZbZZa`_`a__c_Zd_Yba_`\ b`_daYecWgdVheTifRkhQliOnjMolLpmJqnIroGspFtpEuqDvq\ CwrBxsAyt9zu8zv7zw6zx5zy2zz5zzAzzFzzKzzPzzUzzZzzcz\ zhzzmzzrzzwzzwzzwzzwzzwzzwzzxzzyzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzvzzmzzczvUzrKvmArh2mc4hZ5cY6_X\ 7WW9UVATVBSUCRTEPSFORGNRHMQJKPKJOLINMHNOFMKELG0FC0\ EI0ERCM_DPcESgEVkFYoK`zfcwcfxcdxUbxKaxJ_xKZxKXyLVy\ LUyMSyPRyUPzhOwUNvPMuLLtLKsKJqKIoJHlJGjIFhIEgHDfHC\ eGBdGAbK9aP8`U7_Z6Zc5Zh4Zm3Zr3`v6az8bzAbzCczEczGdz\ IdzKezMezOezQfzSfzUgzWgzYhz_hzaizcizejzgjzijzkgzie\ zhczg`zfZzdXzcVzbSzaQz`OzZLzYJzXHzWFzVIzULzTOzTRzS\ UzRXzR_zQbzPezPhzOkzNmzNpzLrzKuzIwzHszGozGkzGhzGdz\ G`zGXzGUzGWzKXzN_zo`zn`zl } END PARAMETER FILE=========================================

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FOTD 14-09-07 (Qunitic Conundrum [6])
by Jim Muth 13 Sep '07

13 Sep '07

FOTD -- September 14, 2007 (Rating 6) Fractal visionaries and enthusiasts: The logical step beyond yesterday's quartic minibrot is today's quintic minibrot. To explore the Z^5+C Mandeloid I had to turn to the MandelbrotN formula, which can calculate Mandeloids of any order. Things go a bit slower because the type=formula is not quite as fast as the type=mandel4, but I doubt that anyone will complain about a calculation time of 14 seconds on a fast computer and maybe a minute or two on a slower unit. Though the parent Mandeloid is of order 5, it has only 4 lobes, which is the exponent of Z minus 1. This is true of Mandeloids of all orders. Today's image is located on a small filament extending from a small minibrot near the large northwest bud of the parent. The extreme magnitude of over 6*10^12 requires the mathtolerance entry in the parameter file. I named the image "Quintic Conundrum" though I can see nothing unusually puzzling or punnish about it. The rating of a 6 seems appropriate for an image that required so little effort. The major part of running the included parameter file will be copying it in text format into your Fractint directory and running it as you would any other parameter file. Even this minor task may be eliminated by viewing the completed image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Thursday began with a fog bank hanging overhead, but a warm sun cleared away the mist by 9am and the rest of the day was near perfect, with a temperature of 77F 25C. As is usually the case, the fractal cats paid little attention to the weather, diverting themselves instead with various sorts of mischief, such as over- turning waste baskets and scattering the contents. In my department, the work was mostly finished by mid-afternoon, leaving ample time for the fractal search, not to imply that a major search was necessary to find today's image. The next FOTD will appear in 24 hours. Until then, take care, and before you begin a search for reality, be sure you know what reality looks like. Hint -- it might not be the material universe. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Quintic_Conundrum { ; time=0:00:14.12-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotN center-mag=-0.879513612531\ 7894/+0.584447614384022/6.046e+012/1/-15/0 passes=b params=5/0/0/0/0/0 float=y maxiter=500 inside=255 logmap=58 periodicity=10 mathtolerance=0.05/1 colors=000HFZHFXHFVHFTHERGDPECNCBL9AF6790040000000\ 0zBwz5rz8mw7hr6cm5Zh5Uc4PZ3KU2FP2AK15Fzz3itAZh8N`6\ AT54M3201JzOHuMGpKEkIDfHCbFAYD9TCAOAKJ8UF6cB5m73z3\ 1zO5zJ4zE3z92z41nQziNzeLzaJzYHzTFzPDzLAz_pz`ozanmb\ mcblUckKdjFeiDehCfgBgfAhe9hd8ecAcbB`bDZaEWaGU`HR`J\ P_KM_MKZNIZOMXPPVPSTPVRPYPQ`NQcLQfJQiHQlFRoDRrBRu9\ Rx7Rv8Uu9WsAZrA`pBcoCemDhlDjjEmiFogGrfGtdKqbOn`RkZ\ VhXZeVabTe_RiXPlUNpRLtOKwMHpOEiQCcS9XU7RW4KY2EZ4K_\ 6P`8V`A_aCebEjbGpcIudKzdLzeMzeMzeNzeOzeOzePzePzeQz\ eRzeRzeSzeSzeXzYazRfzKkzDhzCfzBdzAbz9_z9Yz8Wz7Uz6R\ z6Pz5Nz4Lz3Jz3Gz6Ez8CzA9zC7zE5zG8zIBzKEzMHzOKzPNzR\ QzTTzVWzWZzYaz_dzagzbfz_ezYdzVczTbzQazO`zM_zJZzHYz\ EXzCXzARz8Mz6Gz5Bz34z25z1EzPDzNCzzBzzAzz9zz8zz7zz6\ zz5zz4zz3zz2zz1zzkzzhrzezzbzz_zzXzzUzzRzzOzzLzzIzz\ FzzCzz9zz6zz3zz`zzIzzLzzJzzHzzFzzEzzCzzAzz8zz7zz5z\ z3zz1zzgzz_zzTzzMzzEzz000 } frm:MandelbrotN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 13-09-07 (Deep in a Quartic [6])
by Jim Muth 12 Sep '07

12 Sep '07

FOTD -- September 13, 2007 (Rating 6) Fractal visionaries and enthusiasts: After a string of really great images, today's effort returns us to the lowlands. But these are not the Z^2+C lowlands; they are the Z^4+C lowlands, where boring everyday minibrots are much easier to find, but where the good ones lie far deeper. Today's scene lies unusually deep in its parent Mandeloid, and thereby escapes the boredom. But it is this extreme magnitude that makes the mathtolerance=0.05/1 entry necessary. The image is located on a short filament leading from a bud on the north- east shoreline of a large midget on the negative X-axis of its parent. This midget corresponds to the large midget at -1.75 on the main spike of the Mandelbrot set. Perhaps the most striking thing about today's scene does not become visible until two full outzooms are done on it, revealing a most un-quartic pattern, more reminiscent of the classic Mandelbrot set than the Z^4+C Mandeloid. The name "Deep in a Quartic" describes the location of the scene. Compared to the most recent fractal winners, today's image rates only a 6, but it is actually a rather pleasant diversion, well worth the few seconds needed to calculate the parameter file, which uses the passes=b option and the super- fast mandel4 formula. Though the parameter file is a fireball, it is still necessary to set up the parameter file for calculation. This small inconvenience may be avoided however by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. Wednesday was an absolutely perfect late-summer day, with blue skies and a temperature of 73F 23C here at Fractal Central, but due to the heavier-than-expected work, I had no time to take advantage of the conditions. The fractal cats were too busy romping to notice the weather. The climax came when they got into a heated tussle on the stairs and rolled halfway down, cursing each other loudly. After that they took a break to make up. The next FOTD is due in 24 hours. Could it be another 10 or another lemon? Check back then to see. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Deep_in_a_Quartic { ; time=0:00:10.47-SF5 on P4-2000 reset=2004 type=mandel4 passes=b center-mag=-1.219\ 512077076407/+0.00327130420977419/2.715843e+013/1/\ -25/0 params=0/0 float=y maxiter=1200 inside=255 logmap=80 periodicity=10 mathtolerance=0.05/1 colors=000A0KA0MA0OA0QA0SB0UC2WD4YH7`LAcPDfTGiWJka\ RjgZimfhsngyvguuuzzzgIPZHFRG6Y`QcuhWebOQXGBSSDhmEz\ c0mZ4hI7cLB_OEVSHQVLMYOH`RDeYNjcXoiftopyuzxvvwvsvw\ puwmtxjsxgsxdmoTggHb_6ZXCVUHSRMOOSKLXHIaSHMaG7bJGc\ MOdPXeSdXUfOVgMZzLbzKezJizHmpGphFt_EwSKsKPpEUmBZj9\ de7i_4nS2sK0nJ4jO8eSCaXGXWKTWNhfEigDjhCiiBhiBhiBgi\ BfiBfiBeizdizdjzcjzcjzbjzajzajz`jz_jz_jzZkzYkzYkzX\ kzXkzWkzVkzVkzUlzTlvTlrUlmVlhWlcXlZYlUZlP_m7`m7am7\ bm6cm6dm6em6fm6gn6hn6in6jn5kn5ln5mn5nn5on5po5qo4ro\ 4so4to4uo4vo4wo4xo4yn5zn6zn7zn8zn9zn9znAznBznCznDz\ nDznEznFznGznHynHxnIwnJvnKunLtnLsnMrnNqoOpoPooPnpQ\ mpRkpSiqTgqUeqUcrVarW_rXYsYWsYUsZTt_Tt`UtaUuaVubVu\ cWvdWveXveXwfYwgYwhZxiZxi_xh_xh`yh`yhayhayhaygbzgb\ zgczgczgdzgdzfdzfezfezffzffzfgzegzegzehzehzeizeizd\ jzdjzdjzdkzdkzdlzclzcmzcmzcmzcnzcnzbozbozbpzbpzbpz\ bozanzamzbmzblzbmzcmzc000 } END PARAMETER FILE=========================================

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FOTD 12-09-07 (A Hairy Situation [10])
by Jim Muth 11 Sep '07

11 Sep '07

FOTD -- September 12, 2007 (Rating 10) Fractal visionaries and enthusiasts: This is unheard of -- two 10-rated FOTD fractal images in a row, and once again from the prolific parent fractal that has been the source of the FOTD images for over a week. Today's image comes from the tip of a half cut-off ring on the northeast shore of the largest bay of the parent fractal. It is another half-evaporated image, with the inside part brought to life by the inside=atan option. For a reason known only to the powers that be, this option creates the blatantly obvious violet blue ring that fills most of the frame. I named today's FOTD "A Hairy Situation". One glance at the image will reveal the reason for the name. Then I rated it at a top-of-the-scale 10. In my opinion, it's as good as yesterday's half-and-half image, which also rated a 10. The calculation time of 33 seconds or 3 minutes is brief enough to hardly be noticed. And even the minor effort of setting up and running the parameter file may be avoided by going to the FOTD web site, where the finished image is posted for viewing. The FOTD web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The temperature was a reasonable 75F 24C here at Fractal Central on Tuesday, but off-and-on rain kept a damper on things. I was busy enough with commercial work to have no time to complain. The fractal cats did complain however. They complained about the lateness of their daily treat. The next FOTD will appear in 24 hours. Until then, take care, and be kind to your iterated fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Hairy_Situation { ; time=0:00:32.90-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+8.694009672137327/-1.671633724707316/\ 1.982862e+011/1/45/-0.004 maxiter=550 params=-5.5/\ -1.4142/-1.1/-4/0/47055000.0/0/0 float=y inside=atan periodicity=10 mathtolerance=0.05/1 colors=000bkVMkmlTYhV`eXcRSSMQSHOSCMR7KR3JR5FP7BN9\ 7LF0JD6IF8HHBHJDGLGFNIFPLERNDTQDVSCXVBZXB`_AbaAXc9\ Re9Lg9Fi89k84l86gA8cBAZDCVEERGGMHIIJ00HM9MO5NP1OO5\ MN8L0H0L0IKJGJNFIRDHVCGZAFc9Em7zr6zzUzw3zz19z0Az2B\ z4Bv5Ct7Cq8DnAEkCEhDFeFFbGG`IH_KHYLIWNIVOHWNHXMHYL\ HZKH_KFZKG_MH_NH`OI`PI`QJaRJaSKbTKbULbVLcWMcXMcYTa\ WZ_UeYTkWRrUPxTOeNxfPvgQugRshSrhTpiVoiWmjXlkYkkZil\ `hlafmbemccndbneag_VaUOWOHQJBOKCMKDKKEJKEHLFFLGELG\ CLHAMI9MI7MJ5MK4MK6ON7PP9QSARUBSXDUZEVaGWcHXfIYhuB\ DlFKcJRVNXMRcDUiCWgCYe000C_cCaaCc_BeYBgWQ12SA9UJFW\ RLY_S_hYapcvlpsVZf2S`9IVG8ZaWavrcQ_hIimBsGXjqbkQfl\ UemZgncio00rlzzqtzuqzrpponollnijlfhkcgjeUzYcgVbfSb\ ePcdMcbJcaGc`Ed_GeXIfUKbRM_OOVLPQIRLFTHCVC9X76Y34l\ f1ne3od5pd7rc8scAtbCvaDwaFx`Hy`IlYF`VCPS9RVATYBV_C\ XbCZdD`gEaiEcdCd`AgS7iN6jJ4lE3mA1n60oA1oD2pG3pJ4pM\ 5qP6qT6rW7rZ8ra9sdAsgBsjB } 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 11-09-07 (Inferno and Paradise [10!])
by Jim Muth 10 Sep '07

10 Sep '07

FOTD -- September 11, 2007 (Rating 10!) Fractal visionaries and enthusiasts: Is today's image truly worth the top rating of a 10? Well, I am not fully convinced it is, but what's the use of having a rating of a 10 if nothing ever makes it there. The image is yet another one in the same parent fractal that has supplied so many FOTD fractals over the past couple weeks or so. It's rare that such a harmless looking parent fractal turns out to hold so many unsuspected goodies. Today's half-and-half scene is located in a little cut-off ring- world near a large ring at the southeast extremity of the parent fractal. So far so good. But what makes the image a 50-50 one? The secret is the bailout radius. I have tweaked the bailout until the line that divides the all-there part from the half- evaporated part runs directly through the center of the frame. The left side of the image is normal equal-iteration-band stuff; the right side is half-evaporated, with the inside parts filled in by the 'zmag' option. While studying the image for a name, I noticed the hell-heaven contrast, and decided to name it "Inferno and Paradise". The rating of a 10 is based half on the artistic effect and half on the mathematical interest. I leave it to the individual fractal fan to judge if the image is truly worth the rating of an almost impossible to achieve 10. The calculation time of a brief 1-1/4 minutes on the P4-2000mhz machine will make the trip to the great fractal beyond quite a short one. On a P200mhz unit, the trip will take 7 minutes -- slower but more scenic. Another easy way to make the trip is to go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the completed GIF image there. The heat and humidity fell off a bit here at Fractal Central on Monday, but the 82F 28C was still oppressive, especially for those who must work outdoors. The fractal cats do their work indoors, so they do not worry about weather. With a 10-rated fractal, my day was good enough. Tomorrow will likely be much the same. The next FOTD will appear in 24 hours. In the unlikely event that it exceeds today's, I will have to expand the rating scale to 11. Until then, take care, and never abandon all hope, even if you find yourself hopping around on the coals of the inferno. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= InfernoAndParadise { ; time=0:01:14.92-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+11.19123687238325/-16.75458653288057/\ 17818.43/1/-147.5/8.86548195966341268e-010 params=-5.5/-1.4142/-1.1/-4/0/32750200000.0/0/0 float=y maxiter=550 inside=zmag periodicity=10 colors=000rzzLCzH7zE3zI7zMAzPEzTHzXLz_OzYRzWUzUXzS\ _zQbzOezMhzKkzImzLizOfzRczU_zXXz_UzbRzdNzgKzjHzmEz\ pAzs7zv4zx1z2AF6AFAAFEAFIAFMAFQAFUAEYAEaAEeADiBDmC\ DpDDqKIrQKwZKtaKuaKzhKzgKviKugKseKscKsaKr`Kr_JrZGq\ YEqXBqW9pV7pU4pT2pS0oV6oYCo_InbOndTngZmidmljmnohjl\ cfiZcfU_cQW`LTYGPVBLS7IP52z95zD7zH9zLCzPEzTGzXIz`L\ zdNzhPzlSzpUztWzwYzvVzuTztRzsPzsNzrKzqIzpGzoEzoCzn\ 9zm7zl5zk3zk1zmAznIzoRzqZzrgzsozqizpczoYznSzmMzlGz\ kAzj5z`6zPMzE`z3oz5kz6gz8cz9_zBWzCSzDPzCYzBezBgzQ1\ zSAzUJzWRzY_zK9zLAzLBzMCzNDzOEzOEzKHzHKzENzBQzDRzE\ RzFRzGRzHRzISzJSzKSzLSzMSzNTzOTzPTzQTzRTzSTzUVzVWz\ WXzXYzYZz`_zb`zd`zfazibzkbzmcz000qdzlbzh`zdZz`XzXV\ zTUzPSzLQzHOzDMz9Kz5Jz8HzAGzDFzFEzHDzKBzMAzO9zR8zT\ 7zV6zT5zS5zQ4zP4zN3zM3zK2zJ2zO8zTEzPDzMCzIBzFAzCAz\ B9zB9zB8zB8zB7zB7zB7zA6zA6zA5zA5zA4zA4zA4zF8zKBzPE\ zUIzZLzcOzhSzmVzrYzWQzSLz } 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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IFS, L-Systems in Fractint
by Tony Hanmer 10 Sep '07

10 Sep '07

Hi Richard (regarding L-systems & IFS types in Fractint, & their future development), Sorry it's taken me so long to respond. I've been away from the internet a good deal this summer, in the high Caucasus mountains of the Republic of Georgia... I've discovered a programme which seems to be the LS equivalent of Apophysis in 2d or XenoDream in 3d: Context Free Art http://www.contextfreeart.org/ I describe it thus because it allows LS programming plus a lot more non-LS work, and because its language is at least related to LS. Are you aware of it? As far as IFS goes... one difference between Apohysis IFS and that of Fractint is a great feature of the latter about which I have not found any literature, so I might as well claim credit for discovering it unless someone else can correct me. This is that if you start off with a shape like a square filled *solid* with holons, and then simply alter the numbers in the 7th column - those which deal with probability - you end up with fantastic fractal textures instead of the solid fill. (These probability numbers should still sum to 1.) I have done a huge number of explorations of squares in this manner, some with triangles, and also discovered new textures for the Dragon Curve and TwinDragon. I was waiting for the new Fractint version to reveal this, but now seems a better time to point it out, in the context of a plea not to do away with such a possibility. (It doesn't seem to work in Apophysis, or at least works differently; I haven't tried it in XenoDream yet.) I don't understand all of the details of your letter below about IFS, but am eagerly awaiting a demonstration of what it all means. Tony Hanmer On 8/1/07, Richard <legalize(a)xmission.com> wrote: > > I'd appreciate input on you regarding the L-systems stuff I posted to > the list recently. For L-systems I want the code to ultimately > approach the realistic plant rendering capability of Prusinkiewicz's > code. We're a long way off from that, but that's the target. > > For IFS, right now the code only supports probabilistic 2D/3D IFS. I > want to add more IFS types like language restricted IFS. For > rendering, I want to use OpenGL to give interactive manipulation of > the IFS rendering as well as a design interface that's better than > editing transformations coefficients in a text file. I also want to > use "point sprite" rendering for IFS which will give them more "body" > with fewer iterations and still be interactive. I've also thought > about doing a potential rendering technique where rendered iterations > define a charge in space and the rendering draws the potential > resulting from such a charge. Finally, I want to extend the text file > specifications so that you can specify the transformations in a > transform language rather than as just raw coefficients. That way you > could naturally right s(sqrt(2)/2)*r(180)*t(0.5,0.5) to mean "scale > uniformly by sqrt(2)/2, then rotate by 180 degrees about the Z axis, > then translate by (0.5,0.5)". I've come across a very nice recursive > descent parser framework for C++ -- the spirit module in the boost > library -- that will let me make a number of improvements across the > board in fractint, both for formula types and for IFS and L-system > types. > -- > "The Direct3D Graphics Pipeline" -- DirectX 9 draft available for download > <http://www.xmission.com/~legalize/book/download/index.html> > > Legalize Adulthood! <http://blogs.xmission.com/legalize/> >

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FOTD 10-09-07 (The Biggest Bang [8.5])
by Jim Muth 09 Sep '07

09 Sep '07

FOTD -- September 10, 2007 (Rating 8-1/2) Fractal visionaries and enthusiasts: For today's FOTD I decided to see what I could do with the parent fractal that has been the source of the images for the past several days, some of which have been unexpectedly good. To begin, I partially evaporated the parent fractal by raising the bailout radius to 1,000,000,000. Then I tried the different 'outside' options and found that 'mult' works best on the outside parts. Next I found that inside=bof61 works best on the inside stuff. Finally I colored the image with a rather harsh blue and gold palette. The result reminds me of a supernova, which is well enough. But why settle for half-way? Why not go all the way back to the big bang and make it an even bigger bang? I did just this, then I named the image "The Biggest Bang". And with a calculation time of 9-1/2 seconds, it would be hard indeed to get more bang for your buck. I did not want to rate today's image as high as yesterday's, one of the all-time best, yet I consider it above an 8, so I decided on a rating of 8-1/2. While searching for a name, I thought of the theory of inflation, which is the present explanation for the enexpected smoothness of the visible universe, but decided that a big bang was enough. Besides, I need some headroom if an even better cosmic-origin fractal comes along. Actually, no one was there at the real big bang, so anything we decide to say about it must remain an undemonstrated theory, backed by the mathematics of course. Speaking of numbers, as I watch the way we manipulate them until they prove our theories, I sometimes wonder whether the universe is made of numbers. To see the biggest bang take a few seconds to run the included parameter file, or go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the finished GIFimage there. Summer heat and humidity continued Sunday here at Fractal Central. With weakened sun and a temperature of only 86F 30C, it was not as oppressive as Saturday, but it was sultry enough to keep the fractal cats in lazy mode. My day was once again mostly adequate. The next FOTD will appear in 24 hours. Until then, take care, and make peace with your fractal formulas. They might be the root of the cosmos Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Biggest_Bang { ; time=0:00:09.30-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-12.0049/6.10011/0.03622717/1/-120/0 params=-5.5/-1.4142/-1.1/-4/0/1000000000.0/0/0 float=y maxiter=800 inside=bof61 outside=mult periodicity=10 sound=off colors=00000K0EZPM_VT_cZahcZkhWrlTvpiztszzzzvqzs_x\ pKzmIqiGjeEeaDZZBWX9TW7RV6PVENUMLUUKZaObdS_gVXjZVm\ bSpeQsiNvlLxkOsjRnjTiiWehY`h`WgbRfeNfgIejDel9Yg7Qb\ 6IY5BU4DW7EX9GYCHZEJ_HK`JMbMNcOPdRQeTSfWTgYShVSiTS\ jRSkOSkMSlKRmHRnFRnDRoARp8Rq6Rq4KiFDaQ6V`AWWEXRHYM\ LZHO_CS`7V`2TcESePRg_QijNhfKgbLf_MeYNdWOcUPbSQaQR`\ OS_MTZJUYHVXFWWDXVBYU9ZT7ZS5UPBQMHMKMIHSEEYACb69h2\ 7m99oFBpLDqSFsYHtcJuiKvkOrmRnnVjpYgqacsd_thWvkTwoP\ yrLzuIytKytLxtMxtOxtPwtQwtSvtTvtUvtWutXutYtt_tt`tt\ attastbstbstcstcstcstdstdrtertertertfrtfrtgqtgqthq\ uhquhquiquipujpujpujpukpukpulpuloumoumoumoun8S_9S`\ 9S`AT`AT`BTaBUaCUaCUbCUbDVbDVcEVcEVcFWdFWdGWdGWdGX\ eHXeHXeIYfIYfJYfJYgKZgKZgKZhLZhL_hM_hM_iN`iN`iO`jO\ `jOajPakPakQakQblRblRblQcmRblRbkSbkSbjSbjTaiTahUah\ UagUagVafV`eW`eW`dW`dX`cX_bY_bY_aY_aZ_`Z___Z__ZZ_Z\ Z`ZY`ZXaYXaYWaYWbYVbYUcYU } 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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Re: FOTD 09-09-07 (The Layered Look [9])
by jackoftradez＠comcast.net 09 Sep '07

09 Sep '07

. yeah - way cool. I like layered fractals, like alot of the "mix" formulas posted by russ walsmith and others. but ... yes - work on the colors some more <g> .

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FOTD 09-09-07 (The Layered Look [9])
by Jim Muth 09 Sep '07

09 Sep '07

FOTD -- September 09, 2007 (Rating 9) Fractal visionaries and enthusiasts: Yesterday's sorrowful image left me unsatisfied, so I atoned for it by finding today's image, which I feel kind of makes up for the failure of yesterday's image. I generally do not care for those trendy fractals that come in layers, such as those created by the fans of fractal-generating programs X and XX. Such images remind me too much of a photogra- phic double exposure. But today's FOTD most definitely has two layers. The difference is that the layers of today's FOTD are an actual part of a single fractal, and are created in a single pass, not piled on individually by a creative fractal artist. The generating formula and parent fractal are the same ones that brought about the past several days' images. Today's scene lies on a minor side-shoot of the immense ring that makes up most of the parent. I named the image "The Layered Look" because of the effect of two separate layers, which in a way actually exist. I rated it at a 9 because I think it's worth it. And if I had had more time to work on the colors, I might have been able to rate it at least a 9.5. The layers were achieved by partially evaporating the 'outside' part of the image by raising the bailout radius to 1,950,000,000 and coloring the newly revealed 'inside' parts with the 'zmag' option, which is responsible for the straight diagonal bands. The calculation time of 2-1/2 minutes on the fireball P4-2000mhz unit would be increased to near 15 minutes on the slower P200mhz machine. But the trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the completed image may be viewed instantly, can be done in under a minute, if all goes well. Lots of heat and humidity prevailed here at Fractal Central on Saturday. The high temperature of 90F 32C felt more like the middle of July than early September. Showers threatened in the afternoon, but passed well south. The fractal cats seemed not to notice the weather, spending their time instead looking for mischief. My day was adequate. All I can hope for is that tomorrow be the same. The next FOTD will appear in 24 hours. Until then, take care, and enjoy the world. It's a big bang of a fractal show. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Layered_Look { ; time=0:02:33.46-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-13.48658364309034/-4.135779398727093/\ 8.047622e+009/1/-177.500087240412142/0.000269112669 params=-5.5/-1.4142/-1.1/-4/0/1950000000/0/0 float=y maxiter=550 inside=zmag periodicity=10 colors=00000AKA0CakCciBegBgeQ1cSAcUJcWRcY_a_hgapmv\ lzsVhf2a`9SVGIZaeavzcQihIsmBzGXtqbuQfvUewZgxciy00m\ zzzuzzuvzrszooyllxijvfhucgt`esYcqVbpSboPcnMclJckGc\ jEdiGefIfcKbcL_cMVcMQcNLcOHcQCcP7cN3cqnBrkDqhFqfHr\ dIscKtbMveAwaPzhAy`AwYPlVMPSJRVKTYLV`MXdMZfP`hUafZ\ bcccZhdUmePrfKwgFwhAwi5wj6wk9wmDwnHwoLwqPwqTwrWwrZ\ wrawsdwsgwsjwbkwMkwlTghVj00AbZp_`sXavWWtUQrTKpSFnO\ JkLNhIReFUbCY_9aX6dVzlfuigpfhkcig`jbYkYVlTSmPPnLah\ HmbJl`Kk_MjZNjYOiWQhVRgUSgT`bWhZYpV`xRbuUdsWeqZfo`\ gmbhkeiigjfikdllbnm`pnZsoXupVwqXvnYulZti`tgasdbrbc\ r`dnbdkcdgddded`fdYgdUhdRieOkeKlcnN`lOYjPVhQTgQQeR\ NcSKaTH_UFZUG_WH_XH`YI`ZI`_Ja`JaaKbbKbcLbdLceMcfMc\ gTaeZ_ceYbkW`rUZxTYeNzfPzgQzgRzhSzhTziVyiWwjXvkYuk\ Zsl`rlapmbomcmndlnekg_daUYWORQJLOKMMKNKKOJKOHLPFLQ\ ELQCLRAMS9MS7MT5MU4MU6OX7PZ9QaARcBSfDUhEVkGWmHXpIY\ ruBNlFUcJ`VNfMRmDUsCWcCYo } 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 08-09-07 (Missing the Mark [3])
by Jim Muth 07 Sep '07

07 Sep '07

FOTD -- September 08, 2007 (Rating 3) Fractal visionaries and enthusiasts: Today's image is a big disappointment. When I found it, I had great hopes for a third stellar image. What I ended up with was a boring image the likes of which has been seen countless times before. Somewhere along the line I missed the mark, which is what I named the image. The parent fractal is the same one that supplied the very fine images of the past two days. I once again found the FOTD in the semi-chaos near the northern end of the chain of large bays, but today's image bears no relation to the previous two days' images. In an effort to bring some life to a fractal corpse, I rendered the image whth the outside set to 'real', not that it made much of an improvement. Before deciding on 'real', I tried the other 'outside' options as well as the 'evaporated' inside options. But these were not even up to the outside=real version I used. I was generous when I rated the image at a lowly 3, and consider- ing its calculation time of 9 minutes on the fast machine and just under an hour on the slow unit, the image cannot be seen as any kind of a bargain. But hey, it's still a fractal, and fractals are what it's all about. And best of all, the finished image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it may be viewed at leisure and without effort. With a temperature of 90F 32C, haze and high humidity, and other annoyances, Friday was far from perfect here at Fractal Central. The cats slept through most of it, while I was annoyed by an irate customer who sent an e-mail claiming I had sent a job in the wrong format. I replied that the format I sent is what the supervisor at the customer's print shop said he needed. An hour later I got an e-mail telling me to ignore the first e-mail. We had none of these irritating formatting problems years ago when I worked with a knife and cement on a light table, a job which actually took a bit of skill. Maybe it's getting close to the time to hang 'em up and concentrate on finding fractals while the rest of mankind reduces itself to a universal plasma of mediocrity for the sake of a bit more convenience. The next FOTD will be ready in 24 hours, glorious or not. Until then, take care, and when you have taken total care, go out and have some fun. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Missing_the_Mark { ; time=0:09:04.53-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-0.57722364191193430/-0.692880201307236\ 80/4726027/1/-30.5/2.6479593885631e-008 logmap=-830 params=-5.5/-1.4142/-1.1/-4/0/0/0/0 float=y maxiter=7500 inside=0 outside=real periodicity=10 colors=000UIUUIUUIUUIUUIUUIUUIUUIUUIUUJUUIVUIXUHYU\ GZTG`RFaOEcMDdKDfHCgFBiDBjAAl89m69n7Cm8Fm9IlALlBOk\ CRkCTjDWjEZiFaiGdhHghHihO__UQS`GJf6BjKDmXFqjHtwInp\ Dij8dd3caAbZHaWOaUUkOOuIJoOPjUVdZ`_dfUilPorKtxJstJ\ sqIsnIrjHrgHrdGr`GqYFqVFqREpOEpLDpHDpECoBCo7Bo4Bo1\ Dm4Fk6Hj9JhBLgENeGPdJRbLTaOV_QXZTZXV`WYbU_dTbfRdhQ\ gjOikNkkQhkSekUbkW_kYYk`VkbSkdPkfMkhKicNh_QfWTeRVd\ NYbJ`aEb_AeZ6hY2jKMo6et9bqB_oEYmGVkJSiLQgONeQKcTIa\ VF_YCY_AWcBRgBNjCInEEqG9uI5xK1wM4wO7wQAvSDvUGvWJuY\ Mu_PuaSucVneThgSbiQXjPRkNLlMFmK9mJ3mI6mJ8mKBmLDmMG\ mNImOLmPNmQQmRSnSVoTXpU_qVarWdsXftYiuZkv_nw`pxarya\ mzehzhczk_zn`zk`zgazdbzaczZczVdzSezPfzMfzJhzPizVkz\ `lzfnzlozrpzxpzupzrpzopzmpzjpzgpzepzbpz_pzXpzVpzSp\ zPpzNlzOizOfzOczO`zOYzOVzOXzNZzN`zNbzNdzNfzNhzNjzN\ lzNnzNpzNrzNtzNvzNwzN`z`FznGzmHzlHzkIzjJziJzhKzgKz\ fLzeMzdMzcNzbNzbvzFwzFxzG } 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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Re: New Formulas
by jackoftradez＠comcast.net 07 Sep '07

07 Sep '07

. A new Russ Walsmith formula, a 3D thing. I'm not sure if he posted them here or not. Loox like a 3D Mandel(something) spinning around in a swirling 3D matrix, like a subatomic particle in quark-soup (runaway imagination -EZ2 do that with fractals). In color, not grayscale. MPEG, 640x480, 60 seconds, 48 Meg: http://www.fractal-animation.net/vid/quark640.zip WMV, 320x240, 60 seconds, 5 Meg: http://www.fractal-animation.net/vid/quark320.zip Since the rotation is a full 360*, the start and end image the same. This viddie could be looped forever projected on a wall for example. .

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FOTD 07-09-07 (A New Direction [9])
by Jim Muth 07 Sep '07

07 Sep '07

FOTD -- September 07, 2007 (Rating 9) Fractal visionaries and enthusiasts: With its texture that reminds me of something I cannot quite pin down, and its lively colors, today's image is unusual enough, at least in my opinion, to rate a 9. It is found at the northern extremity of the string of large bays in the same parent fractal that gave us yesterday's image. I named the image "A New Direction" because its unique texture is something I have never before seen in a fractal. Actually, nothing should be surprising when it unexpectedly appears in a fractal, since the universe is basically fractal in nature. Then again, fractals are basically a creation of the way the human mind organizes the abstractions known as complex numbers, and as such they occupy a strange shadowy realm between real and imaginary. If one prefers fractals to be real, he can make a print of one and show a picture of it to the world. If one prefers fractals to be imaginary, he can defy someone to prove they are real by handing him the real Mandelbrot set on a platter. To me, fractals are the patterns, ideas if you will, behind the material stuff the universe is made of, and the material itself is as real as the probability waves (fractals?) that make up the atoms. Since the universe can be no more real than the stuff it is made of, mankind is reduced (or raised) to a minibrot in an infinite fractal. I'll not broach the question of whether a fractal can be self-conscious. But self-conscious or not, today's fractal image calculates in a little over 2 minutes on the fast machine and around 12 minutes on the slow unit. As always, the most convenient way to see the image is to go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view it there in person. Higher humidity and more haze made Thursday's 86F 30C too muggy for comfort here at Fractal Central. But while the outdoor life was a bit oppressive, the fractal cats made the most of the life indoors by stalking some imaginary creature in the kitchen for most of the afternoon. Of course, maybe the creature was not imaginary to them! Except for the day's fractal, which was well above average, the day turned out about average for me. The next FOTD will appear in 24 hours. Until next time, take care, and the world can be considered as real as we want it to be. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_New_Direction { ; time=0:02:10.66-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+1.373253567881444/-0.0353980831225605/\ 4.556682e+010/1/-55.007934721352008/0.1099798828578 params=-5.5/-1.4142/-1.1/-4/0/0/0/0 float=y maxiter=1650 inside=0 logmap=233 periodicity=10 colors=0000QZ0BW0WT0ZQ0UNE00HO0J00NM6QQHTQQWpZsisb\ IRb0HUM2L00RTNWpsZBTCLgn0s0NisVkEOlJZnEKozzz00szvz\ zzzuuyzzztsvsstpqofhljmiUZgQWdLVqHVaCWl8WY3WW0WU0Y\ TsQP2_JjMF8QB`I6CB2F30I00L00P00Q00l_0oZ0zZ0zY0zh0z\ W0zc0zT0wT0sR1sR2lN0UI0CE0FI0IN0LQ0PV0RY0Ua0Wd0ZY0\ `R0dE0g60i00l00n00o00z00z00z00z00z50z90zF0sK0sO0sT\ 0sY0sa0sf0YhL8hnlFQfIUaMZYObTRgjTzNKiJBfI2bH0`B0W6\ 6R2CN0GI0NE0T90Y6siPsdQs_RkWTdRUYNWQIYIEZC9`6TR1kI\ 3iF5hE8fC9fBBd8Ec6Fa5Ha3UV8fOBsIFsCIsGLsKNsOPqRQnV\ RkZTgaUbdW`iYYlZUp`RpaPpbLpdPp`QpYRpTUpQWpLYpIZpF`\ lI`hJ`aL`YN`RP`NQ`GR`CTa8Wa2YZl0Ui0Qf0Lc0Ia0EZ19W2\ 5T31Q50O50Q81Q91RB2RC2RE3TF3TH5VI5WJ6YL6_N8aP8cQIe\ NRgJaiIkkFsmCsoBaqsbssdusdwsfxsfysgzqgznizlkzkkzgl\ zflzbnzanzZozYrzWyzLzzBzz1zz0zz0zz0zz0zz0zz0zz0zz0\ zz1zz2zz2zz3zz5zz5zz9zzCzzHzzJzzPzzRzzWzzZzzbzzfzz\ 0zz5zzFzzPzzZzzgzzdzzazzZ } 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 06-09-07 (Too Much Too Soon [8.5])
by Jim Muth 05 Sep '07

05 Sep '07

FOTD -- September 06, 2007 (Rating 8.5) Fractal visionaries and enthusiasts: Today's evaporated image probably sets a new record for FOTD gaudiness. It lies in the parent fractal that results when 5.5 negative parts of Z^(-1.4142) are combined with 1.1 negative parts of Z^(-4) and (1/C) is added. This parent fractal is almost beyond belief. It is a bloated Mandeloid with several large bays and a smoothly curved main spike that terminates at the center of a ring that is larger than the Mandeloid it springs from. Today's image is found on a side-shoot of the main spike near the point where it ends at the center of the large ring. I named the image "Too Much Too Soon" when I couldn't decide what to make of it. The colors are basically accidental, though I did tweak a few registers to fine tune the palette. The rating of an 8.5 could easily have been a 9 if the colors had been a bit more organized. The calculation time of 75 seconds will offend no one. Even on an 11-year-old P200mhz unit, the calculation will finish in about 7 minutes. But on some over-qualified S.O.T.A. machines calculation can become problematical. In this case, the easiest way to view the image is to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the image is or soon will be posted, and enjoy it there. Wednesday here at Fractal Central was a bit too warm and brought a few too many clouds for absolute perfection, but with a temperature of 84F 29C and low humidity, it was close enough. The fractal cats were occupied watching a squirrel gathering material for its winter nest, and paid no attention to the weather. My day was kept busy designing a logo to print on a tote bag of a health-care organization. Oh well, I guess it's a living. The next FOTD image will appear in all its glory in 24 hours. Until then, take care, and go ahead and do it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Too_Much_Too_Soon { ; time=0:01:15.52-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-14.19486797243935/+3.358196340354399/\ 5.573916e+010/1/97.6365368770451738/-0.015089388127 params=-5.5/-1.4142/-1.1/-4/0/1e+100/0/0 float=y maxiter=550 inside=bof61 logmap=82 periodicity=10 colors=000000C_cCaaCc_BeYBgWQ12SA9UJFWRLY_S_hYapcv\ lpsVZf2S`9IVG8ZaWavrcQ_hIimBsGXjqbkQflUemZgncio00r\ lzzqtzuqzrpponollnijlfhkcgj`eiYcgVbfSbePcdMcbJcaGc\ `Ed_GeXIfUKbRM_OOVLPQIRLFTHCVC9X76Y34lf1ne3od5pd7r\ c8scAtbCvaDwaFx`Hy`IlYF`VCPS9RVATYBV_CXbCZdD`gEaiE\ cdCd`AgS7iN6jJ4lE3mA1n60oA1oD2pG3pJ4pM5qP6qT6rW7rZ\ 8ra9sdAsgBsjBbkVMkmlTYhV`eXcbZf_`iXalWWjUQhTKfSFdO\ JaLNZIRWFUTCYQ9aN6dLzlXuiYpfZkc_g``bYaYVbTScPPdLaZ\ HmTJlRKkQMjPNjOOiMQhLRgKSgJ`bMhZOpVRxRTuUVsWWqZXo`\ YmbZke_ig`fiadlbbnc`pdZseXufVwgXvdYubZt_`tYasVbrTc\ rRdnTdkUdgVddWd`XdYYdUZdR_eOaeKbcnD`lEYjFVhGTgGQeH\ NcIKaJH_KFZKG_MH_NH`OI`PI`QJaRJaSKbTKbULbVLcWMcXMc\ YTaWZ_UeYTkWRrUPxTOeNxfPvgQugRshSrhTpiVoiWmjXlkYkk\ Zil`hlafmbemccndbneag_VaUOWOHQJBOKCMKDKKEJKEHLFFLG\ ELGCLHAMI9MI7MJ5MK4MK6ON7PP9QSARUBSXDUZEVaGWcHXfIY\ huBDlFKcJRVNXMRcDUiCWgCYe } 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 05-09-07 (Replacement Fractal [No Rating])
by Jim Muth 04 Sep '07

04 Sep '07

FOTD -- September 05, 2007 (No Rating) Fractal visionaries and enthusiasts: The formula behind today's image subtracts 1/2 part of Z^2 from 1/2 part of Z^(-2) and adds straight C. This formula creates a parent fractal that consists of a scattering of mis-shapen Mandeloids. Today's scene is located in a valley leading to a minor bud of the largest and most mis-shapen Mandeloid. I named the image "Replacement Fractal" when I finally gave up on the fractal that was intended to be today's FOTD and pulled up today's image, which I had been saving for just such an occasion. If I had named today's image, I might have named it something like "Four Golden Orbs". Rating today's image was out of the question. To begin, it is not really the FOTD for Sep 5; it is a ringer that slipped in when the real image failed to perform as planned. So how could I give it a rating? But with its blue background, brilliant green-yellow orbs, and subtle interior purple, it is not that bad an image, and well worth a look. That look will require a wait of over 1-1/2 minutes while the included parameter file runs to completion. Or things can be made faster and more straightforward by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the scene there. The endless string of perfect days here at Fractal Central is getting to be boring. Totally bored, the fractal cats slept for a good part of Tuesday afternoon. My day was kept busy with enough commercial work to prevent boredom however. The next FOTD will appear in 24 hours. Until then, take care, and don't become entangled in the fractal uncertainty principle. It leads only to paradoxes. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= ReplacementFractal { ; time=0:01:42.80-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident center-mag=+1.101020760806052/-2.11631173658624/\ 329305/1/135/-1.310869424745e-007 params=0.5/-2/-0.5/2/0/0/0/0 float=y maxiter=3200 inside=0 logmap=170 periodicity=10 colors=0007ES8FT9GUAHVBIWCJXDKYELZFM_GN`HOaIPbJQcK\ RdLSeMSfOTgQUhSUiUVjWVkYWl_XmaXmcYleZkgZki_jk_im`h\ oahqagsbfubfwbUxbItdHqeGmfFjgEfhDciD_jCXkBTlAQm9Nn\ 9TmDYlHckLhjPniTsiWrjUqjSpjQokPnkNmkLllJllIklGjmEi\ mChmBgn9fn7fn6dl7cj8bh9afA`dB_bBZ`CYZDXXEVVFUTGTRG\ TOHTLITIJTFKTCTT9ZVA`WBZWDVWGSWIOWKJWNJWPJWRJXTJYU\ JZVI_XI`YIaZIb`IcaHdbHedHfeHgfHhgHifJieKjeMjdNkcOk\ cQlbRlaSmaUm`Vn`Wn_YoZZoZ`pYapXbqXdqWerVfrVhsUisUj\ rWhqXfpYdo_bn``maZlcXkdWjeUigShhQhiOgjMflKemIdnHcp\ FbqDarB`t9_u7Zv5Zw4`x6ax8bxAcxCdxEfyGhyImyKryMvyOz\ zQwzSuzUszWozYpz_rpXvfUwXRwNOwDLw3Jz5Kz7Kz9KzBKzCK\ zELvGLrILmJLhLLcNLZPMURMPSMRUMSWMUYNWZNX`NZbN`dNae\ N_gLYhKWiJUjISlHQmFOnENoDLqCMrBOs9Qt8Sv7Uw6Wx5Yy4_\ z6az7cz9ezAgzBjzDmzEpzFszHvzIzzJzzLzzMzzNzz`zznzzl\ zzkzzjzzizzhzzfzzezzdzzczzbzz`zz_zzZzzYzzXzzVzzUzz\ TzzRzzQzzPzzQzzTzzWzz_zzb } 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 04-09-07 (Scepter Rattling [7])
by Jim Muth 03 Sep '07

03 Sep '07

FOTD -- September 04, 2007 (Rating 7) Fractal visionaries and enthusiasts: Today's fractal image is a stellar scene on the eastern side of the northern branch of Scepter Valley of the Mandelbrot set. I named it "Scepter Rattling" in memory of the old cold-war days, and rated it at a 7 to reward myself for the extra time I spent working on the moody but lively blue coloring. Almost the entire effect of the image is due to the color palette. Trying a new palette will quickly demonstrate this. I would have liked to give the image a higher rating, but it is hard to find a reason to give such a scene in the overworked Mandelbrot set a rating higher than a 7. The calculation time of the included parameter file is a zippy 33 seconds, which will keep the time and effort to a minimum. Running a parameter file and watching the image appear almost by magic is fun, though not the most convenient way to see the image. The most convenient way is to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the finished image there. I put the mathtolerance=0.05/1 entry into the parameter file as a safety precaution. Without this entry the program could flip over into arbitrary precision math, especially at the higher resolutions, which would increase the calculation time by a factor of over 420, to well over 3-1/2 hours, with no noticeable increase in quality. Absolutely perfect weather again prevailed here at Fractal Central on Monday, which, as the first Monday of September, is Labor Day in the USA. Perfect weather is defined as a deep blue cloudless sky, high temperature of 85, gentle wind, and low humidity. Perfection in fractals is more difficult to define, and for fractal cats, it is nearly impossible. My day was not quite perfect, but it was good enough. The next FOTD will be posted in 24 hours. Until then, take care, and keep the fractal faith. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Scepter_Rattling { ; time=0:00:33.72-SF5 on P4-2000 reset=2004 type=mandel passes=1 inside=0 float=y center-mag=-1.24827499159888600/+0.031915703805430\ 75/8.306274e+011/1/44/0 params=0/0 maxiter=60000 logmap=-8575 periodicity=10 mathtolerance=0.05/1 colors=00000T00T00T00T00T00T00T00T00T00T00T00T40T8\ 0TC0TG0TE0VC0XA0ZA0`A0bA0dA0eA0gA0iA0oE0vH0zL0zP0z\ T0zzzzzzzzzzzzzzzzzzzzzzzzzuzzqzzmzzgzzdvz`qzXoxTm\ zPgzLdzH`zCXz8Rz4Nz0Jz0Gz0Gz0Gz0Gz0Eu0Eo0Cg0Cb48V8\ 6PzzzzzvzzsLzqzzmzzkzzg0zezzVzuJzu80z0zz0zz0zz0Hz8\ zzPezPzuNdmLziJCLH00000000000400A00G20J40P80VA0ZE0\ dG0iJ0mL0sN0vG0mAHe2dX0xP6vPEvPLvPTvP`vPz0doAsePzu\ Amz0Vz0Rz0Nz0Jz0Gz0Cz08z04z02z00z00u00k00g00e00d00\ `00X00V00R00P04L0AJ0GG0LE0PX0`m0kz0vx0zs0zo8ziGzdN\ z`XzVdzRkzTmzTmzTmzVmzVozVozVozXozXozXqzZszZuzZvzZ\ xzbzzdzxgzkizXmzJoz4qz0gz0Zz8RzGHzNAzX0zd0zk0zs0zz\ 0zz0zz0zz0zz2zz6zzCzzHzzLzzRzzXzz`zzbzzbzzbzzbzzdz\ zdzzdzzdzzZzzVzzRzzLzzHzzEzz8zz4zz0zz0zz0zz0zz0zz0\ zz0zz0zz2zz6zz8zzCzzGzzHzzLzzNzzRzzTzzXzzZzzdzzizz\ ozzuzzzzzzzzzzzzzzzzzzzzzzzzzzuzzozzizzdzzXzzRzzLz\ zGzzAzz2zz0zz0zz0zz0zz0zz } END PARAMETER FILE=========================================

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FOTD 03-09-07 (Fractal Stand-In [No Rating])
by Jim Muth 02 Sep '07

02 Sep '07

FOTD -- September 03, 2007 (No Rating) Fractal visionaries and enthusiasts: I regret having missed the FOTD for September 02, but sometimes these things are unavoidable. Because today's image was found with so little effort, I could give it no rating, but with its brief calculation time of just over 3 minutes, it is certainly worth a look. I named the image "Fractal Stand-In" because I feel it is standing in for the real FOTD image for September 03, which I was too lazy to get up and search for. There must be far better scenes to be found in the vicinity of today's image, and far better images that could be created from the same scene. The parent fractal came about when I subtracted 5 parts of Z^(1.3) from 5 parts of Z^(1.2) and added straight C. This parent resembles a Mandelbrot set rotated 180 degrees which is starting to split apart at the center of both the east and west ends. Today's scene is located in the chaos surrounding a small bud on the far shoreline of the largest bud. The image shows a minibrot surrounded by a fairly typical pattern of semi-chaos, with rather well-defined filaments zigging off into the unknown. And speaking of the unknown, only the great unknown knows why this particular minibrot is found at this particular location in this particular fractal -- a fact that is true for every part of all fractals. Though the included parameter file is a fast one, the need to do the calculation may be totally avoided by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Absolutely perfect weather conditions prevailed both Saturday and Sunday here at Fractal Central. So on Saturday, F.L. and I went out and took advantage of the situation. We spent Sunday in recovery, which meant a day of solid relaxation, and can be great fun as long as one does not make a habit of it. The fractal cats were a bit cranky at having been left alone all day Saturday, but they regained their carefree spirits as soon as the tuna treat was served. The next FOTD image will appear in 24 hours. Until then, take care, and don't give up. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fractal_Stand-In { ; time=0:03:13.61-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+3.846906537660213/+0.3379029437233428/\ 5122061/1/-112.5/1.32364045017652199e-006 params=-5/1.3/5/1.2/0/0/0/0 float=y maxiter=2400 inside=0 logmap=325 periodicity=10 colors=000TUmRUmPUmNUmLUmJUmHUmFYmEanCfpAjr8ot6sv5\ wv7uu8ttAssBrrDpqEopGnoHmnIkmKjlLjkQjjVjiXkg`kedkc\ dkafkcekdckeblf`lg_lh`mj`nkaolapnaqobrpbsqbtscutcv\ ucwwdxxdyydzzeyyfyxgywgyvhyviyuiytjyskyrlyrlyqmypn\ yonyoTvYVmWXdVYXT_OS`GRYHUVHWTIZQI`OJcLJeJKhGKjEKl\ GHbHEUJBKK8BI8DG8EE8GC8HA8I88K68L48N28O18Pj4Th8UgC\ UeFUdJUbNUaQU_UUZYUX`UWdUVgUWfSXfRXePYeOZdMZdL_cJ`\ cI`bGabFbaDbaCc`Ad`9d`8caDbbIbcNadS`eX`fa_gf_gj_ih\ _jg_ke_md_nb_oa_p__rZ_sX_tW_vU_wT_xR_yQXwUVuXTs_Rq\ cPofMmiKkmIipGgsEfvJeuOdtTdsYcrbcqgbplboj_miYkhWig\ UgfSeeQcdObcM`bKZaIX`GV_ETZCRYAQWEPUIOSMOQQNOUMMYM\ LaLJeLHiKFmJDqJBuIAyIEuMHrQKnUOkYRgaUdeY`i`YmcVpbR\ laOh`Ld_IaZFYYCUX9R_AUaAWcAYeA`hAbjCdlEgnGiqIksKnu\ MpwOryQtwSsuUssWsrYrp_rnarlcqkeqigqgipekpdmpeomeqk\ esieugfvefwbfx`fyZgzXgzVgzSgzQhzOhzMhzKhzIizKjzLjz\ MkzNZzRYzWXz`Xzd`zXczPfzH } 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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Fmod
by Russell Walsmith 31 Aug '07

31 Aug '07

2 1

FOTD 01-09-07 (Warped Perception [No Rating])
by Jim Muth 31 Aug '07

31 Aug '07

FOTD -- September 01, 2007 (No Rating) Fractal visionaries and enthusiasts: Today's image starts off the new month by returning us to the scene of yesterday's image. The only difference is that today's image is sliced in an entirely different direction -- 1/3 of the way from the Parabolic toward the Elliptic orientation. The result is a much distorted and stretched version of the elements that appeared in yesterday's image. The other rotations in hyperspace stretch and twist the image elements in various other ways, but after unstretching and skewing, the underlying effect remains pretty much the same as today's. Therefore, today's FOTD will be my only attempt to see what changes in the image the different orientations can make. Since today's image is not really a new one, and with only a few minor changes, I used the same color palette, I could not give it an actual rating. The name "Warped Perception" indicates that it is only our limited view of the transcendental four-dimensional Julibrot that has changed. The basic formula, Z^2+C, remains the same. The calculation time of 20.20 seconds has nothing to do with vision. It is the time it takes the parameter file to finish running on the speedy P4-2000mhz computer. On the slow old P200 unit, the parameter file will finish in a still-speedy 2 minutes. Of course, the easiest way to see the image, as always, is to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view it there. With deep blue skies, low humidity and a high temperature of 79F 26C, Friday here at Fractal Central was as close to perfection as it is possible to come on this planet. The fractal cats agreed as they searched for mischief, finally finding it by knocking a picture off the wall. My day was not quite as perfect as the weather. An unsatisfied customer spoiled what might have been a near-perfect day. But the problem was quickly solved, and all ended well. The next FOTD will appear in 24 hours. It will be an all new one this time. Until then, take care, and since time and space are mere subjective creations of the mind, why not change our perception of them like we so often do with fractals? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Warped_Perception { ; time=0:00:20.20-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2a mathtolerance=0.05/1 center-mag=+1.832893479e-014/+1.040270804e-014/\ 3.405775e+013/0.1704/166.246022919272576/23.573\ 3773441832462 params=30/90/0/0/-1.999999779397065\ /0/-1.999999779397065/0/2/0 float=y maxiter=1000000 inside=0 outside=tdis symmetry=none periodicity=10 colors=000wfapfZifW9x5PoH7phIlbTiYcbxcdmcebbJncVcQ\ kbViZ_gWVPFYVK``PVrUYnT`jTC4SKaXUdVeJ1dRBcZKQ5LJJP\ JJjU_bUSiXWdZ_`acXRPrbWeGG2MR9S`GYaNO3LWNPzr2zhBzU\ KzzQzzRVTS__TNLRzYSWmS_aTcz7arFblMOK1SQ8WWF_aMzcz`\ czzczbczzczWczzczaczzczWczzczpczzczgczzczWczzczdcz\ zczyczzczvczzczoczzczcczzczgczzczgczzczfczzczbmzcm\ zcmzcmzHmzTmzomzkmzgmzemzrmznczjczfczWczZczamzu2ho\ GbiUY3rGMlNLM`6`KoNziXKWk1Yi8_hFagMFRjSZzK1GRFLYTP\ 1j8BiELhJVgOStVVpUYmU`iTHBHTRN9fvPfgQGHVPL_YPtQcVB\ HYML`XP86095pHFjPOdXYZOt19KuHY8TbJ_v`qndlk`ghXbBGc\ MLcXPsEuoMmkTfg__4McGT_S_WUmtYjj`haIRCQXIXaOWpfYmb\ _k_ahWwBNpMPiXR`6JaGMbPOcYRL9JSLNYWQhoSflTejTdhTHs\ HNoKTlNZiQVzZYsX`lVhGgeU_2ljFjdShZptolpiimcfiYR0FY\ MMwowplliibqpVllUgiTt3NoDPkNQgXSMUp5XuD4tMHjVUaCw1\ MqBVkKtlWkiUUxcXs`ZoYajVjmJgjNehQhHVeUU9j0Hi8PhFXg\ Mi2EWz7cGzd8ZcQWZNi`Ucb`Y } frm:SliceJulibrot2a {; 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|<=sqr(real(p5)) } END PARAMETER FILE=========================================

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FOTD 31-08-07 (Out on a Filament [6])
by Jim Muth 30 Aug '07

30 Aug '07

FOTD -- August 31, 2007 (Rating 6) Fractal visionaries and enthusiasts: Today's image takes us to the tip of the negative spike of the Mandelbrot set, where we examine a tiny minibrot. In fact, it is the most remote minibrot on the spike reachable with conven- tional math. But where is the minibrot? Actually, it is very close. The problem is that we have perturbed the view, and therefore have just missed the minibrot. But we have come close enough to skim through the outer fringes of the pattern around it. To see the actual unperturbed mini- brot simply reset the real and imaginary p2 parameters to zero and shift the view a bit. I have added to the interest by reducing the bailout radius, which is real(p4), to the point where the entire scene is on the verge of being swallowed up entirely. I have added even more interest by rendering the image with the outside set to 'tdis'. I named the image "Out on a Filament", since that is its location. But the rating of a 6 was all I could do for an image that is basically just another trip to the over-viewed negative spike of the Mandelbrot set. The calculation time of a sizzling 39 seconds will try the patience of no one. And the task of calculating the scene may be done away with entirely by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. As I write this, I wonder what this Mandelbrot-set location would look like in some of the odd orientations through the Julibrot. Well, there is one way to find out, and that is to go and look. If I find anything of exceptional interest, it will appear as a future FOTD. The weather was too warm for comfort here at Fractal Central on Thursday, with a high temperature of 90F 32C and quite sticky humidity. In the evening however a light thunder-shower cooled things down a bit. The fractal cats don't worry themselves with outside heat unless there are squirrels to go along with it. If there are no squirrels, a chipmunk or two will do. My day was appropriately busy and tomorrow promises to be the same. The next FOTD is due in 24 hours. Until then, take care, and give particular attention to the questions that appear to have no answers. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Out_on_a_Filament { ; time=0:00:39.39-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotVE-VP passes=1 center-mag=-1.99999977939708600/-0.000000000000023\ 21/2.706509e+013/1/2.47067461084123785/0 params=2/0/1.3e-007/6e-008/0/0/1.9999997799/0 float=y maxiter=3000 inside=0 outside=tdis symmetry=none periodicity=10 mathtolerance=0.05/1 colors=000wfapfZifW9x5PoH7phIlbTiYcbxcdmcebbJncVcQ\ kbViZ_gWVPFYVK``PVrUYnT`jTC4SKaXUdVeJ1dRBcZKQ5LXOP\ JJjU_bUSiXWdZ_`acXRPrmceGG2MR9S`GYaNO3LWNPzr2zhBzU\ KLEQQMRVTS__TNLRSRSWWS_aTcz7arFblMOK1SQ8WWF_aM_Uz`\ Yza`HbcNTeWWfVZfUafz_EzWcz_fzpGzkPzgYzSHzWQNUdzdSz\ oFzy3wwMlvdbuwToqXikzcfzeadgXziShgWdGprf_`dczb8zcH\ BcQHcZNH9wTQgoTzkYigb`eDxrHtnOmjUff`_W5cZI_aVzu2ho\ GbiUY3rGMlNLM`6`KoNziXKWk1Yi8_hFagMFRjSZzK1GRFLYTP\ 1j8BiELhJVgOStVVpUYmU`iTHBHTRN9fvPfgQGHVPL_YPtQcVB\ HYML`XP86095pHFjPOdXYZOt19KuHY8TbJ_v`qndlk`ghXbBGc\ MLcXPsEuoMmkTfg__4McGT_S_WUmtYjj`haIRCQXIXaOWpfYmb\ _k_ahWwBNpMPiXR`6JaGMbPOcYRL9JSLNYWQhoSflTejTdhTHs\ HNoKTlNZiQVzZYsX`lVhGgeU_2ljFjdShZptolpiimcfiYR0FY\ MMwowplliibqpVllUgiTt3NoDPkNQgXSMUp5XuD4tMHjVUaCw1\ MqBVkKtlWkiUUxcXs`ZoYajVjmJgjNehQhHVeUU9j0Hi8PhFXg\ Mi2EWz7cGzd8ZcQWZNi`Ucb`Y } frm:MandelbrotVE-VP {; Jim Muth real(c),imag(c) a=p1, z=p2, c=pixel+p3, b=sqr(real(p4)): z=z^(a)+c, |z| < b } END PARAMETER FILE=========================================

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FOTD 30-08-07 (Sickles galore [7])
by Jim Muth 29 Aug '07

29 Aug '07

FOTD -- August 30, 2007 (Rating 7) Fractal visionaries and enthusiasts: For today's FOTD I went back to the parent fractal that results when 12 parts of Z^(1.02) are subtracted from 12 parts of Z^(0.98) and straight C is added. I have used this fractal as the source of several previous FOTD images. To find today's image I examined the chaos on the northwest shore line of the parent's large central bay. The first thing I found there was a small minibrot. Today's much smaller minibrot is located near the East Valley of this first minibrot. The East Valley location is evident in the shape of the fuzzy greenish area around the central midget. The fragmentary overall appearance, with its sickle-shaped bits and pieces, shows the nature of the parent fractal at this location. I named the image "Sickles Galore" because it is filled with these fractal sickles. I rated it at a 7 to reward myself for the 1/2 hour of extra effort I put into the search as well as the colors. The calculation time of 81 seconds is brief enough to keep every- one happy. Another way to stay happy is to go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the fully-rendered image there. Wednesday was a bit too warm and humid for comfort here at Fractal Central. The temperature of 88F 31C, hot sun and high humidity kept things at a lazy pace. The only excitement came when the fractal cats spotted two pigeons scrounging on the front sidewalk. The cats kept the vicious attacking birds at bay. My day was reasonably busy, but I was quite efficient, and the work was wrapped up by early afternoon, leaving ample time to locate and tweak today's image. The next glorious (IMO) FOTD image will appear in 24 hours. Until then, take care, and the answer may be clear, but what is the question? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Sickles_Galore { ; time=0:01:21.02-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-3.181809015911311/+1.876979770976725/\ 268480.3/1/-85/2.13341735978700431e-007 params=12/0.98/-12/1.02/0/1000/0/0 float=y maxiter=1300 inside=0 logmap=125 periodicity=10 colors=000wxwstrmmmggg`bePZ_ESRIHBLOGPWLScRWkWZr`W\ maTibRecO`dLXdJTeGOfDKgBGmINzOTzUZzWUzYQz_MzaIzcEz\ dAvbCraDm`Eh_FeZGcYHcXIdWJdVKeULeTMfSNfROfMJbIFZEB\ Vm7SzDQzIPzNOzSNzXMzeLzmKzrJzzIzrJzmJmkJcgJUdKJbKI\ `KKZKMWLNULPSLQQLONMKLMKJMKHMKMLKQKKUJQZIPbINfHMkG\ KoFJsEIwEHqFGlFFgFEcGDcGCcGBcHAcH9cHDcIHcJKcKOcLRe\ MVzNYzNXzLWzKWzIVzHVzFUzEUzCTzzTzzSzzSzzUzzW`zX_zZ\ Zz`YzaXHcWJeVLfUMhTOiSPfWQdZQbaR`dRZgRWkSUnSSqTQtT\ OwTHiNAZI4ZDDZLLZSUUZaUfjNmrNtqOpqPlpQhpRdoR`oSXnT\ UnUQmUMmVIlWElXAlX7kZDk`JkbPkdVjf_jhejjkjlqjmvimtg\ nsfnrdoqcooaon`pmZpkYqjWqiVrhTrfSseQsdPscRrdSreTrf\ VrgWrhXriZrj_rk`rlbrmcrndrofrpgrqhrrissississitsit\ sitsiusiusiusiusjvsjvsjvsjwsjwsjwsjxsjysjzsjzskzpl\ znlzkmzinzfnzdozapz_pzXqzVrzSszQtzRuzSvzSwzTxzTyzU\ zzVzzVzzWzzWzzXzzYzzYzzZzzZzz_zz`zz`zzazzazz_zzZzz\ XzzWzzUzzTzzRzzQzzPzzqzzs } 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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[RE][Fractint] Re: Fractint Digest, Vol 54, Issue 9
by Russell Walsmith 29 Aug '07

29 Aug '07

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Re: Fractint Digest, Vol 54, Issue 9
by jackoftradez＠comcast.net 28 Aug '07

28 Aug '07

Keep trying Russ! Good things come to those who persevere. (why not just get a REAL email account and avoid these hassles ...)

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FOTD 29-08-07 (Fractal Apocalypse [6])
by Jim Muth 28 Aug '07

28 Aug '07

FOTD -- August 29, 2007 (Rating 6) Fractal visionaries and enthusiasts: I normally place little faith in written revelation, since I can never be sure who or what wrote the revelation, but in today's case I'll make an exception. In yesterday's discussion I said that the image contains invisible minibrots. Today's image shows one of these, though the minibrot at the center is still so small as to be virtually invisible. Since I am the creator of the fractal worlds I calculate and then explore, I naturally named today's image "Fractal Apocalypse". But I am not totally pleased with what I have revealed today. Something is not quite right with the colors, which are basically the ones that worked reasonably well in yesterday's image. My dis-satisfaction shows in the rating of an only- slightly-above-average 6. Today's scene is located near the center of the large yellow- orangish object located just left of the center in yesterday's image. The exact location is easy to find. The calculation time of 5 minutes on the fast P4-2000mhz unit stretches to near 1/2 hour on the old slow P200mhz machine. But the time spent in calculation is of no consequence when the image is viewed on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it is posted for apocalyptic enjoyment. Tuesday turned out to be near-perfect here at Fractal Central, with blue skies, low humidity, and a temperature of 84F 29C. I hesitate to call it absolutely perfect because different people will have different ideas of perfection. But it was close enough to keep the fractal cats out of mischief. My day was moderately perfect. Hopefully, tomorrow, when the next FOTD will appear, will be more perfect. Until then, take care, and apocalyptic or not, the FOTD will go on indefinitely. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fractal_Apocalypse { ; time=0:05:12.91-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=+0.1144118099837061/-1.646746920022384/\ 2.419792e+010/1/45/0 params=-5/-1.5/-1/-5/0/0/0/0 float=y maxiter=5000 inside=0 periodicity=10 colors=000z0ez0ez0dz0dz0dzPdz0dzUgz0kzYmzCqzauzRvv\ gzsezolzkuzimzgzzelzexzdjzbvzbhz`szZgzZqzXfzVmzVez\ TkzRexRgxPevPevNesNdqLdoLbmLbkJ`gJ`eJZdHZbHX`EYbHX\ ZJXXLXVNYRPZPRYNTZJVYHX`GZZC``Ab`8db4eb2gb0ib0kd0m\ d0od0qd0sd0ve0xe0zg0zg0zi0zi0zk0zk0zm0zm0zo0zo0zL8\ zREzXJz`NxeTvkZsobougkxkizqezvbzzZzzXzzUzzUzzUzzUz\ zZzzczzhyzmzzpyzvzzzzzzzzzxzzuzzqzzozzkz8BUzez9CVx\ ZzIAZsTzJAZeTz_LhuHzfCpz6zm2zz4zz6zz8vzAuzCqzCozEk\ zGizHgzJdzLbzLZzNXzPTzRRxTPxVLvVJvXGuZEu`Asb8dP0sb\ 6zmCzxHzqLziNzbRzVTzNVzGZz8`z2bz4`z4Zx6Zs6Xm6Xg8Vb\ 8VVATPATJARECR8CP2EP0EN0HL0EN0AN08N04N02N00dEzuRzz\ VrzXrzZlz`lzbfzdfze`zg`ziVzkVzmPzoPzqKzsKzuFzxFzvA\ ztAzr5zo5vm0oj0ig0de0Zb0R`0LY0GY0AU02V00T00U00S00R\ 00P00Q00O00N00L00L02J04H08G0AG0CE0GC0HA0JA0N80P60R\ 60TA0TC0TE0TG0TH0TJ0TL0TN0TR0TV0TV0TX0TZ0T`0Tb0Td0\ TX2NR8HLECEJ68P02V00T00`0 } 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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Re: [RE][Fractint] Re: New Formulas
by Russell Walsmith 28 Aug '07

28 Aug '07

1 0

[RE][Fractint] Re: New Formulas
by Russell Walsmith 28 Aug '07

28 Aug '07

2 1

[RE][Fractint] Re: New Formulas
by Russell Walsmith 28 Aug '07

28 Aug '07

1 0

[RE][Fractint] Re: New Formulas
by Russell Walsmith 28 Aug '07

28 Aug '07

1 0

[RE][Fractint] Re: New Formulas
by Russell Walsmith 28 Aug '07

28 Aug '07

1 0

FOTD 28-08-07 (Celebration Rites [7])
by Jim Muth 27 Aug '07

27 Aug '07

FOTD -- August 28, 2007 (Rating 7) Fractal visionaries and enthusiasts: With today's image we leave the Mandelbrot set and examine the fractal that results when 5 negative parts of Z^(-1.5) are combined with 1 negative part of Z^(-5), and (1/C) is added. This parent fractal is a vertically stacked series of bays, with the typical 'fan' extending east along the X-axis. The scene of today's image is in a blunt valley on the southwest edge of the stack of bays. With its gaudy colors and feeling of pop-art, the image reminds me of a festive celebration, so I named it "Celebration Rites". The usual minibrot appears to be missing, but actually the image is filled with minibrots. They are simply too small to be seen. One of these will appear in 24 hours however, at the center of the FOTD for August 29. All things considered, I rated the image at a 7. The calculation time of just over 1 minute is no obstacle to the rapid enjoyment of today's image. And downloading the completed image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> is even more enjoyable. Perfect weather, perfect cats, and little work on Monday -- what more could a dedicated fractalist ask for? . . . . . . Well, he might ask for a better image, but no fractal can possibly achieve perfection. Be that as it may, the next try at perfection will come in 24 hours, when the next FOTD appears. Until then, take care, and stay filled with wonder, even as you wonder about which wonder to wonder about. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Celebration_Rites { ; time=0:01:14.12-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=+0.1144117535417508/-1.646747111980673/\ 2489156/1/87.5/4.68434676464957178e-009 params=-5/-1.5/-1/-5/0/0/0/0 float=y maxiter=1600 inside=0 periodicity=10 colors=000z0emYez0drUdz0dzQdz0dzUgz0kzYmzCqzauzRvv\ gzsezolzkuzimzgzzelzexzdjzbvzbhz`szZgzZqzXfzVmzVez\ TkzRexRgxPevPevNesNdqLdoLbmLbkJ`gJ`eJZdHZbHX`EXbHX\ ZJWXLXVNYRPZPR_NTZJVZHX`GZ`C``Ab`8db4eb2gb0ib0kd0m\ d0od0qd0sd0ve0xe0zg0zg0zi0zi0zk0zk0zm0zm0zo0zo0zL8\ zREzXJz`NxeTvkZsobougkxkizqezvbzzZzzXzzbzzgzzkzzqz\ zuzzzzzzzzzzzzzzzzzzzzzzzzxzzuzzqzzozzkzzgzzezzbzx\ ZzvXzsTzoPzeTzmNzuHzzCzz6zz2zz4zz6zz8vzAuzCqzCozEk\ zGizHgzJdzLbzLZzNXzPTzRRxTPxVLvVJvXGuZEu`Asb8dP0sb\ 6zmCzxHzqLziNzbRzVTzNVzGZz8`z2bz4`z4Zx6Zs6Xm6Xg8Vb\ 8VVATPATJARECR8CP2EP0EN0HL0EN0AN08N04N02N00dE0uR0z\ V0zX0zZ0z`0zb0zd0ze0zg0zi0zk0zm0zo0zq0zs0zu0zx0zv0\ zu0zs0zq0vo0om0ik0di0Zg0Re0Ld0Gb0A`02Z00X00X00V00T\ 00R00R00P00N00L00L02J04H08G0AG0CE0GC0HA0JA0N80P60R\ 60TA0TC0TE0TG0TH0TJ0TL0TN0TR0TVWTV0TXYTZ0T`ZTb0Td_\ TX2Nf`HLECga68P0hb00T0k`0 } 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 27-08-07 (North Shore Action [8])
by Jim Muth 26 Aug '07

26 Aug '07

FOTD -- August 27, 2007 (Rating 8) Fractal visionaries and enthusiasts: Today's image takes us on another visit to the Mandelbrot set. The trip may at first appear dull, but with more time to search, I have found a better scene. I found it rather deep in the 'star' of a small period-22 bud on the northeast shore of the main bay, very near the large period-3 north bud. The image shows a midget with a surprising number of tendrils spiralling from it. I named the image "North Shore Action" because there certainly is action in the image. Then I rated it at an 8. I put enough effort into the coloring to justify the rating. Perhaps the most striking thing about the image is its magnitude of over 6*(10^13), a magnitude usually beyond the range of the fast conventional math routine. But for some reason, today's image holds up even without invoking the much slower but much more accurate arbitrary precision math routine. I have included the 'mathtolerance=0.05/1' entry in the parameter file to assure that the image finishes in seconds rather than hours. I have been concentrating my fractal activities so frequently on the Mandelbrot set recently because of the incredible speed at which the P4-2000mhz unit calculates the type=mandel fractals. The type=julia is just as fast, though I use it far less often. Other fractal types may be as fast also, but if so, I have not yet found them. As an example of lightning speed, today's image finishes in a little over 6 seconds on the P4-2000 machine. On the old P200 it takes 2 minutes -- almost 20 times as long. Today's image is also a good example of the use of negative logmap values. The setting of negative 1556 spreads the color bands more evenly over the entire range of iteration values. A setting of positive 1556 concentrates the colors too narrowly in the bands with the lowest iteration value, and spreads them too broadly in the higher value bands. To see today's image, run the included parameter file or visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the finished image there. Even with mostly cloudy skies, Sunday was a far more pleasant day here at Fractal Central. A temperature of 79F 26C is far easier to live with than one of 97F 36C. The fractal cats must have agreed, for they spent most of the day watching the ongoing TV show beyond the windows. A window is a cat's television. I spent my day recovering from the day before. The next FOTD image will be posted in 24 hours. Until then, take care, and fractals are like sub-atomic particles. They don't become real until they are observed. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= North_Shore_Action { ; time=0:00:06.14-SF5 on P4-2000 reset=2004 type=mandel passes=1 logmap=-1556 center-mag=-0.04410362337750159/+0.652478579761549\ 50/6.29347e+013/1/-25/0 params=0/0 float=y inside=0 maxiter=8500 periodicity=10 mathtolerance=0.05/1 colors=000TKUUKUVKUWKUXKUYKUZKU_KU`KUaKUbKUcKUdKUe\ KVfKWgHYhG_iF`hEZgEXfEWfEUeETdERdEQcEObDMbDLaDJ`DI\ `DG_DFZDDZDCaCGcBKeAOg9Sj8Wl8_n7cp6gs5ku4ow3sy3wu4\ vq5vm5vi6ue6ua7uY7tV8tR9tN9sJAsFAsBBm7Bh3Cc0CZ8NUG\ P0ER3CV6BY89aB8gDCkEGoFJsGNtGRtHUtIYtJatJdtKhuLlvM\ zwMzxNzyOzzOzvQzsSzpTzmVrjXogYge_abaWWaPPaTNUXLUYJ\ UdMgeOgbSgZVfWYeS_cP`bLbaId`EeZBgY7iX4jW8lUBmSFnQI\ oOLpMPqKSrIWsGZtEauCevAhw8lx6oy4rz2qv5qr7qnAqjCpfE\ pbHpZJpVLpROoNQoJSoFVoBXo7Zp8Xp8Wq9Vq9Ur9TrASsARsB\ PtBOtBNuCMuCLvDKvDJvDIwAOx8Ty6Zy4cw8duBesEfrIgpLhn\ OilSjkVkiYlgamedndhobmp`rq_vrbzsezthzukzvmzwizsfzp\ czm_zjXzgUzcRz`NzYKzVHzSEzOAzL7zI4zF1zC4zB7zBAzBCz\ BFzBIzBKzBNzdozxpzvqztrzrrzpszotzmtzkuzivzhvzfwzdx\ zbxzahz_UzYFzWCzY9zZ6z`3za7z_AzZDzYHzXKzWNzURzTUzS\ XzR`zQczOfzNjzMmzLpzKszJfzTVzaZz`bz_ezZizZmzYpzXtz\ WwzWwzWwzWwzWazIIzIozIjzG } END PARAMETER FILE=========================================

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FOTD 26-08-07 (Seahorse Rhapsody [6])
by Jim Muth 25 Aug '07

25 Aug '07

FOTD -- August 26, 2007 (Rating 5) Fractal visionaries and enthusiasts: When one needs an acceptable fractal in a hurry, what better place to search than Seahorse Valley of the Mandelbrot set. And I didn't have to search long to find today's scene, which lies at only a moderate depth on the west side of the valley. A fractal that comes almost automatically, as today's did, can hardly be rated above average, so I gave it a rating of an average 5. I named the image "Seahorse Rhapsody" when the bluish cast of an earlier version reminded me of the 'Rhapsody in Blue'. I have since toned down the blueness, but the name remains. Perhaps the best feature of today's fractal is its very brief calculation time, which is only 24 seconds on the P4-2000. The image would finish in about 3 minutes even on the tired old P200. But why bother at all with calculating parameter files when the image is posted, already rendered, on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With a high temperature of 97F 36C, Saturday was the hottest day in several weeks here at Fractal Central. The fractal cats, whose ancestors lived in northern Africa, where it is even hotter, didn't mind the heat, but they would have liked a few more crickets to play with. My day was kept busy with a trip to State College, but it was still enjoyable. The next FOTD is due in 24 hours. Until then, take care, and I wonder what wonders are yet to be found in Fractaland, wherever it is located. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Rhapsody { ; time=0:00:23.58-SF5 on P4-2000 reset=2004 type=mandel inside=0 center-mag=-0.75031876327625280/+0.014101150134497\ 41/4.194136e+007/1/166.5/1.26107747491430167e-005 params=0/0 float=y maxiter=27500 periodicity=10 colors=600df5ge5jc5ma5p_5sY5vW5yU5zS5zQ5zO5zM5zK5z\ I5zG5zE5xC5tA5n85j65c55_SRZSSYSTXSUWSVVSSUSRTSQSRO\ SQKUPGWOBYN6_N5aN5cN5eN5_N5WN5SN5YN5aN5eN5aN5_N5YN\ 5WN5UN5SN5QN5MN5KN5JO9IPFIQMIRSIRZIS`IS`IS`IS`IS`I\ SbISbISbISbISbISeISeIQeIMeIIeIGeIv5Iv5Iv5Is5Ii5Ib5\ IUFIOQIGbI9nIBgID`IDWIGQIIJKIFQK9YM5eM5nO5tQ5zQ5zT\ 5zT5eO5IKMIIlI9WI5II5BI5GI5LI5QI5VM5_Q5dUCiWEnWIpW\ KqWHqSDqK6nI5jI5fI5bI5ZI5VI5RI5NI5JI5FI7BIB7ID5IG5\ II5JM5MO5ST5WU5aX5e`5lb5pe5wi5zk5zn7zpDzsIztMzpOzk\ OzfOzaOzXQwSQuNQpIQpDSp8Sp5Sp5Sn5Un5Un5Un5Un5Ul5Wl\ 7Wl7Wl9Wl9ZlBZjBZjDZjD`jD`jG`gH`gIbgJbgLbgMbgMeeMe\ eMeeOeeOgeQgcQgcTgcTgcUjcUjcXjaXjaXlaZlaZla`l_`n_b\ n_bn_en_eo_goYgoYgoYioYipYkoWkqWnoWnqWoqWqoWqqUsoU\ soUtoUuoSvoSvoSvoSvoQvoQvoQvoQvoOvoOvoOvoOvoMvoMvo\ MvoMvoMvoOvoOvoOvoOvoOvoOvoQvoQuoQtoQsoQroQqnQpnSo\ lSnlSmjSljSkgSjgWieZh5ag5 } END PARAMETER FILE=========================================

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FOTD 25-08-07 (Happy the Tenth [6])
by Jim Muth 24 Aug '07

24 Aug '07

FOTD -- August 25, 2007 (Rating 6) Fractal visionaries and enthusiasts: Today's image is titled "Happy the Tenth". I gave it this name because the scene is located in the tenth valley on the negative X-axis of the Mandelbrot set. The first valley is the well- known Seahorse Valley; the second valley is the not-quite-as- well-known Scepter Valley. I don't think the valleys beyond this point have been named, but the scene of today's image is in the very remote tenth valley. But I could rate the image no higher than a 6, because in valleys of such a high-order, a certain boring sameness starts to creep in. The image is striking enough, mostly because of its intense colors, but when studying it, I get the urge to say, 'they all look the same out here'. The calculation time of 5-1/2 minutes on the P4-2000mhz would be about 1/2 hour on the P200mhz, a bit slow but not beyond reason. And the most reasonable way of all to see the image is found on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it is posted for instant enjoyment. The heat, haze and humidity returned to Fractal Central with a vengeance on Friday, when the temperature reached a high of 88F 31C under a broiling sun. The fractal cats didn't worry about the broiling sun, but they did find a cricket, which they toyed with for a few minutes before they finished it. My day was average; tomorrow promises to be the same. The next FOTD is due in 24 hours, but if F.L. and I decide to go out, it might be late. Until next time, take care, and do fractals obey the laws of relativity, or the quantum, or both, or neither? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Happy_the_Tenth { ; time=0:05:30.17-SF5 on P4-2000 reset=2004 type=mandel passes=1 inside=0 center-mag=-1.40115451785449/+0.00000013373512227/\ 8.592431e+010/1/-122.525225924817548/0.00050268\ 3258957907497 params=0/0 float=y maxiter=250000 logmap=-28375 periodicity=10 mathtolerance=0.05/1 colors=000E0AG0CG0CI0EJ0EJ0EL0EN0EN0EP2ER4ER6ES8EU\ AEUCEVEGXGGXIGZJG`LG`MGbNGcOGcPGeQGgRGgSGcTGbUG`UG\ XUGVUGUUGSUGPSGNRGLPGINGGLGEJGCIG8GGEEGJCGPAGUEGZI\ GcJGjJGpJIvJIzJ6zJEzNNzSUzVbz`hzcrzhzznzznzzpzznzz\ kzzgzz`xzVnzRez0`z0Xs0Uk0Sc2PX6NSAJNEGIIECLA8R8GXI\ LcRShZXmgUrcSvbRz``zZmzXxzVzzUzzSzzRzzPvzLnzJgzIXz\ GPzEGzC4zA0x80v60u40r60p80n80kA0jA2hC6gEAcEEbGI`GL\ ZIPVJSUJVSLZPLbNNeLPhJPkGRnERrCSuASpCUkEUhGVcGVZIV\ VJXRJXNLXINZCNZ8P`2R`0R`0Sb0Ub0Ub0Ub0Vb4VbAXbGXcLX\ cRZcVZc`Zce`cj`en`esbexbezcezcgzcgzegzegzegzghzghz\ ghzhhzhhzhjzjjzjjzkjzkjzkkzmkzmkzmkznkznkznmzpmzpm\ zrmzrmzrmzrnzsnzsnzsnzunzupzupzvpzvpzxpzxrzxrzzrzz\ rzzrzzszzszzszzszzszzSzzUzzUzzUzzVzzVzzVzzVzzXzzXx\ zXxzXvzZuzZuzZszZrz`pz`pz`nz`mzbmzbkzbjzcjzchzcgzc\ ezeezeczebzebzg`zgZzgXzgXzhVzhUzhUzhSzjRzjPzjPzjNz\ kLzkLzkJzm6z08z28z4Az6Cz8 } END PARAMETER FILE=========================================

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FOTD 24-08-07 (Helixes All Around [9])
by Jim Muth 23 Aug '07

23 Aug '07

FOTD -- August 24, 2007 (Rating 9) Fractal visionaries and enthusiasts: Today's image rates a 9, and most of this rating is based on its coloring. Without the bit of extra effort I put into the color palette, the fractal would be just another picture of a Minibrot rather deep on the sinuous filament of the period-11 sub-bud on the northeast shoreline of the large period-2 bud centered at -1 in the Mandelbrot set, where the Seahorse Valley characteris- tics are just starting to appear. I named the image "Helixes All Around" when I had the impression that the sixteen wavy lines radiating from the bluish pattern around the Midget are actually three-dimensional helixes. The calculation time of 4-3/4 minutes is surprisingly fast for an arbitrary precision image with a magnitude of over 10^20. But even this short wait may be bypassed by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the already-rendered image there. Thursday brought continuing clouds to Fractal Central, but we enjoyed a short interval of sun in the afternoon, which let the temperature rise to a pleasant 79F 26C. The fractal cats spent several hours watching the scene from their window, but I think they were more concerned with the pigeons cooing on the porch roof than with the weather. My day was pleasantly slow; hope- fully tomorrow will be the same. The next FOTD will most likely appear in 24 hours. Until then, take care, and make your peace with a renegade fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Helixes_All_Around { ; time=0:04:43.69-SF5 on P4-2000 reset=2004 type=mandel center-mag=-0.7797023197491\ 136919845708/0.1503396430159217625308027/\ 1.240172e+020/1/-140/0.00387885 params=0/0 float=y maxiter=1400 inside=0 logmap=290 periodicity=10 colors=000VT8XU7ZV6`W6bX5dY4fZ3h_2k`1na0qbGtcDwdAz\ eFzhKzjPznSzpUzrWzuYzw_zzazzczze9eq7co6am4_k3Yi1Vg\ 5Se4Pc4N`3LX3JU3HR2FN2CK1AG18D16A046023023000000Oj\ qHhoAfm8dj7bg7_d6Ya6VZ5TV5QS4OP3MM3JJ2HF2FC1E91260\ 13GDGzcEzcDzcCvcBrcAmZ9hU8cP7ZK6UF5PA4K53F12A01500\ _pzWizSezP`yLVrIQmELhAFc7AZ35UzLZzJWqIUgGRaFPYDMUC\ KRAHN9FJ7CF6AB47735312NE`KCXIBTG9PD8MB7I95E64B4272\ 13Q_DJR9DI6693y32u21q21m21i21e21a11Y11V11R10N10J00\ F00B00700300UzdMjUFVK7FAINFGKDEICDGABE99C88A668546\ 4342121812701601501401300200100EM07B0lX3Zcz`dybeyd\ fyegyg0xi0xj0xlkxn0wo0wqPwsUwtZwscrrhmqmhqhcphZohU\ miPhjKckFZlAUm5Pm8KmBFmDAmG5mI0mJ0nJ0oJ0pKUqKirKzr\ LzsLzsLztHztEzuAzu7zv8zv8zw8zw8zx8zxAzyAzyAzzAzzAz\ zAzzAzzAzzAzzAzzAzzFzzKzzPzzUzzZzzczzhzzmzzrzzvzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } END PARAMETER FILE=========================================

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FOTD 23-08-07 (Main Stem Fantasy [7])
by Jim Muth 22 Aug '07

22 Aug '07

FOTD -- August 23, 2007 (Rating 7) Fractal visionaries and enthusiasts: All the filaments extending from buds of the Mandelbrot set lead to fractal stars. The number of arms in these stars, including the arm leading back to the bud, is equal to the periodicity of the bud. Thus, the large period-3 bud on the north shore of the main bay has a filament that leads to a star with 3 arms. But what of the straight filament extending along the negative X-axis from the most prominent bud of all, the period-2 bud centered at -1? There is indeed a 'star' on this filament. It is centered some- where around -1.54, though I forget the exact location. But it is not seen as a star because it has only 2 arms, and appears as a straight line. Today's image, which has a magnitude of over 10^52, is located in the East Valley area of a much larger but still very tiny midget on the main stem near the center of this invisible abstract star. I named the image "Main Stem Fantasy" and rated it at a 7. I know it's just another deep scene on the spike, but since I kind of like its colors, the rating of a 7 seems about right. Despite the extreme magnitude, the calculation time on the P4-2000mhz computer is a reasonable 15 minutes. On the P200mhz machine it would take about 1-1/2 hours to finish, so to save time, I sent the image on ahead to Paul at the FOTD web site, where it is posted for instant viewing. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The rain ended but the clouds hung tough here at Fractal Central on Wednesday. The high temperature of 70F 16C was close to per- fect however. The fractal cats must have enjoyed the weather, for they were on their best behavior all day. The real work was heavier than I would have liked, but still well within reason. The next FOTD will appear in 24 hours. Until then, take care, and watch for a miracle. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Main_Stem_Fantasy { ; time=0:15:02.86-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.543689012692172695279198313919702019\ 29621015880257135701/0/1.479071e+052 params=0/0 float=y maxiter=3600 bailout=4 inside=0 symmetry=xaxis periodicity=10 colors=000JOEJVBKb7Ki4Jt2Kp1Ll1Mh1Nd1N`0OX0PT0QP0Q\ M0UJ4XG8`ECcBFg8Jj6Nn3Rq1Ut5ev8pqCnlFlgIjbMhYPfTSd\ OVbJZ`Eac9ch5Zm0Uq0Pk0KefR`cZVafP_nKYoJWqHVrGUrGUs\ EUtCzuBzv9zw7zxmzymzymmv7ctA_qDaoGblJcjMegPfeTgbWi\ `ZjYakWdmTgnRjnMpoPmpRkpTiqWgrYer_csbatd_tfYuiWvkU\ vmSwpQxrOxtMusKsrJqqIopHmoGknFimEglDekCcjBaiA_h9Yg\ 8Wf7Ue6Sd5Pa6N_7KX8IV9FT9DQAAOB8LC5JD3HDeRKeRJeSIe\ SHeTGeTGeUFeUFeUEfUDfUDfUCgUCgUBgUAhUAhU9hU9eWEbYK\ `ZOY`PXbQWdRVfSUhTTjUSlVSnWToXUpYWnXYlWZkV`iUbgTce\ SecRgaQkZMh`PeaRbbT_dWXeYUf_RgaOidLjfIkhFljCnm9oo6\ pq3qs9rrErqJspPsoUtnZtmduliuknvjsvjmndhg_c`UZUPTNJ\ OGEJ98E23I44L64O84SA4VC5YE5aG5dI5hI4gK5gL5gN6gO6fQ\ 7fR7fT8fU8eW9eX9eZAib8e_AbXBZVDWSETQFPNHMKIIIKFFL4\ EICDMEBLJDPNFTSHXWI`_JddKhhLlpJplKohLndMmaNmYOlUPk\ QRjPRhNTjLVkJXlHZmF_nDaoCcpAeqAgrAisAktAmuAovAqwDr\ xKryRuzYwzdxzkyzrzzzzzzzz } END PARAMETER FILE=========================================

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Re: FOTD 21-08-07 (East Valley Scene [6])
by Jim Muth 22 Aug '07

22 Aug '07

At 11:49 AM 8/22/07 -0500, you wrote: >On Mon, 2007-08-20 at 19:38 -0400, Jim Muth wrote: > >> Most of the effect is caused by the closeness of the escape >> radius. To see a totally different image go to the 'Z' screen >> and change the bailout to 25. It's too bad that the type=mandel >> formula permits only integer bailout values to be entered. It >> would be interesting to see what happens when the bailout >> actually reaches the scene. > >This can be done with the formula parser. Yes, but the images take about 20 times as long to calculate.

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FOTD 21-08-07 (East Valley Scene [6])
by Jim Muth 22 Aug '07

22 Aug '07

FOTD -- August 21, 2007 (Rating 6) Fractal visionaries and enthusiasts: As can be seen from the coordinates, today's image lies far out near the tip of the straight filament on the negative X-axis of the Mandelbrot set. The scene is actually located deep in the East Valley of a far larger, but still tiny Midget. For this reason I named the image "East Valley Scene". I might have rated the image a 7, but negative-stem images of this sort are among the first things a fractal newcomer finds. Since the area has been so thoroughly explored, I finally settled on a rating of a modest but honorable 6. Even though the image is well within the range of arbitrary precision math, it is unexpectedly fast, finishing in only 3-2/3 minutes on the P4-2000. On the P200 it would take around 20 minutes to finish -- still a speedy time. Most of the effect is caused by the closeness of the escape radius. To see a totally different image go to the 'Z' screen and change the bailout to 25. It's too bad that the type=mandel formula permits only integer bailout values to be entered. It would be interesting to see what happens when the bailout actually reaches the scene. The image has been posted for convenient viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A steady rain made Monday an indoor day here at Fractal Central. The fractal cats made the most of things by chasing each other through the hallway all morning, then aleeping for most of the afternoon. My day was occupied with routine work. The next FOTD fractal image should be posted in about 24 hours. Until then, take care, and wonder what it's all about. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= East_Valley_Scene { ; time=0:03:41.62-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.9999991175871\ 771353513668292373759/0/1.013802e+030 params=0/0 float=y maxiter=2500 inside=0 symmetry=xaxis periodicity=10 colors=0008u0LZ0ZD05ljGX`wJSrNJ5OOwOLQ0I`0E0zzj0ww\ ejjOZwENyGWyJQoPQlJLk6GuA9nEOn80c00e02g05i080B0300\ O06zSlzGZu5NX0OGz0On0WW0cB6zzzzUbDOOLGLU8Ib0EGzNJc\ eXGQg0Xi0L0iOztNS0zb0cuprpLWzXzzNzzDir3SlgNjQIj9E3\ EJE8GO3E`0DSnUZUNeBGzuzzcpuObp8O900J03S06b09piLnWI\ lIGj5DzLzy6i00n30`O0N0zzQ00X02c06JQeUEWb3L0zSBUJL0\ zU0lb0U3gEEUDOID`5BzQzzrzwLyrWzjNrcEQX60Q00XN0cl0l\ j0ui0zg0zg0ri5XjLDlb0nt2bL6Q03eD0tbzztOQip0UZ2JGSc\ OIWW9Oc2Izu0000UB3b285rbyj0rJ000zB0iz00z00g0230eO0\ Q02DQ0OX0Jc0EWyz6el000I00z2cz0Wy0Or0Itizz0Qu0Lp0Gw\ EN2bzDQyOEg`3Q0ZOWlr`UbeBOE0zQ0l`0U0O0DD0U35nXIlNG\ lDEj3DN0zy0`r0Ny60r02UXZbDNX00zZ2uXrz5Q00L0WENBDzi\ zuQlp9UO0pW0e`0We0L000503Q08ltc0zzGUi000E00W05cBce\ 6Wg2Oi0IlD0j63j08N0OU0LZ0Ie0E0SNG9G0lzLJb0zBEUBzz0\ 0zINZE0r`LNNe0Sg0Li0G0DzG66O38W09c0B0GG89EL5DZ0BNn\ zUZpZLbe6O3`NILIX6EBE8U39 } END PARAMETER FILE=========================================

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FOTD 22-08-07 (Short Shrifted [7])
by Jim Muth 21 Aug '07

21 Aug '07

FOTD -- August 22, 2007 (Rating 7) Fractal visionaries and enthusiasts: The most unusual thing about today's scene in the Mandelbrot set is its bailout, which is set at the unusually small value of 2. With this tight an escape radius, quite a few points that would normally remain trapped actually pass beyond the artificially close escape radius and are considered by the program to have escaped. As a result, all parts of the set beyond a radius of 1.4142 from the origin have been cut off. These elements are lost forever, but the parts of the M-set that remain have under- gone a striking change. The equal-iteration bands have become equal-iteration blobs, which give a totally different effect to today's scene deep in the west side of the north branch of Scepter Valley. Because so much of the parent M-set is missing, I have named today's image "Short Shrifted". But I almost chose the name 'The Scepter of Power'. I rated the image at a 7 because of the unusually vivid color palette. There can be no complaints about the calculation time, which at a superluminal 3-2/3 seconds is about as brief a time as will ever be seen in a FOTD image. The time required to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the completed image there is a bit longer, but the extra minute or so will eliminate the hassle of calculation. Steady rain and drizzle, an unseasonably cool temperature of 61F 16C, and a raw east wind kept all but the hardy few indoors here in the Fractal Central area on Tuesday. The fractal cats are hardly among the hardy few, and they have still not forgotten the great time they had chasing the bat that got into the house last week, but I fear they will have no more bats to chase for quite a while, if ever. My day was nominally busy. The next FOTD is scheduled in 24 hours. Most likely it will appear on schedule. Until next time, take care, be fractal friendly and environmentally alert. Fight global warming by rendering fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Short_Shrifted { ; time=0:00:03.41-SF5 on P4-2000 reset=2004 type=mandel passes=1 float=y center-mag=-1.25866275871275700/+0.036890950315646\ 36/7.802864e+010/1/54/0 params=0/0 maxiter=6250 bailout=2 inside=0 logmap=851 periodicity=10 colors=000nmjcc`UUSKKIAK9gEIZBEQ8AHK78K3SIoMEdGAVB\ KK53AxaDrZ4RK2Gob8QJAKF8KD7KB6K95K73K52K31K1tGBhC8\ Y96MK4BK2EV7AN57K33K1NTKFJD7K6diGZcEUYCPSAKN8FK6AB\ 45K25lA4e83_73U62O51K31K20K1NKMBKBp8Ab67Q45DK2n_1g\ q0ai0Va0PV0JN0CK06K0kePdoLYfHRYEKQADK76K3mxXPUG0KN\ 0KH0KB0K5cccihbVUQFKD4kY2WM1KBufTm`PfWL_QITLELKAEK\ 77K3aDSVANPKIJKECK96K4p`yiWqbRiXNaQIVJKNDKF6K7zmSq\ eOhZK_SGRLCIK89K4ukxiakYS_NJOBKCYb7RV5KN4DK26K1I9z\ D6q94d4KTAXAbegtjAaV6JK3JdBCR76K3nria0YP0NC0BN0300\ Mc0I00F00OR0MU0WY0da0si0pa0zU0hN0bF0VM0JR01U00X00b\ 00r00zS0z`0zU2zF1UA1FK000E00C00A0cz0I60K40K2gWOMKC\ L`kFR_AIO5KCNg6HX4BM35K1Mz3B01Mx4mm3Ec2BU27K13K0Hi\ FEaCBUA8N75K52K2nk5zz4zz3zz2zz2zz1zz0zzfzzZzzSzzLw\ zEtz7qzPnzVkzHhzEezCbzA_z8XzzUzzUzzUzzUzzUzzUzzUzz\ UzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUz\ zUzzUzzUzzUzzUzzUzzUzzUzz } END PARAMETER FILE=========================================

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FOTD 20-08-07 (Deep on the Spike [7])
by Jim Muth 19 Aug '07

19 Aug '07

FOTD -- August 20, 2007 (Rating 7) Fractal visionaries and enthusiasts: At first glance, today's image from the good old Mandelbrot set appears to show just another midget in Seahorse Valley. And indeed it is a scene in Seahorse Valley. But why then does it take over 1-1/2 hours to calculate on the fastest P4-2000mhz machine, and over 5 hours on the slow old P-200mhz unit? The obvious reason is its magnitude, which is large enough to require arbitrary precision math. But why then is such a large magnitude needed when the midget appears to be one of a relatively small magnitude? The reason for this is that the Seahorse Valley in which today's scene lies is not the Seahorse Valley of the M-set itself, but the Seahorse Valley of a miniscule midget just beyond the tip of the main stem of the large midget on the main stem of the M-set. Perhaps the most unusual thing in today's image is the way the near total chaos of this general area of the M-set blends into a very smooth overall image. Only the remnant irregularities around the edges betray the true location of the scene. With all this in mind, I named the image "Deep on the Spike". I rated it at a 7, which seems fair enough. But the very slow calculation time of the image could be a real problem, so I strongly recommend visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing it there. I sent the finished image on ahead to Paul several hours ago, so it should be posted by now. A light but steady rain fell most all day Sunday here at Fractal Central. The area needs the rain, so I guess we can't complain. I spent the day indoors, checking old fractal formulas, (spelled formulae by the over-educated), while the fractal cats spent the day like cats usually do -- sleeping and eating. The next FOTD should appear in 24 hours. Until then, take care and vote for a fractal in the next election. It will probably do a better job of running things. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Deep_on_the_Spike { ; time=1:32:57.96-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.7903\ 364338969715554/7.7315068e-13/1.246083e+015/1/30/\ 3.8857805861880479e-016 params=0/0 float=y inside=0 maxiter=45000 bailout=4 logmap=2106 periodicity=10 colors=000M9gK9hH9iF9jD9kILjNXiRhhSddT`aTXZUTVUQSV\ MPVILWEIWBF`LPdUYfVWgWUhXSiXQjYOkZMl_Km_Io`GpaEqbC\ rbAsc8td6ue4ve3uc8ubDtaIt`Mt_RsZWsY`sXdkVhcUlWSpOR\ tSNsWKr_HrbEqfBqj8pm5ph7kc9fZAaUCXPESKFNFHIBIEJTFR\ cFZnF_iK`dPa_UbVYbRbcMgdHkeCpf7uf3yfHqfVifhabe_ZcZ\ VaYR_XNYWJVVFTUBRT7PS3NR0LQ4NS7OTAPVDRWGSYJTZMU`PW\ aSXcVYdYZf``gcaifbjickjdhkeelfbmf`ngYohVpiSqiQrjNs\ kKtlHulFvmCwn9wn7HR9YO8eM8kK7qI7pG7oJAkMAgPAfPAePA\ dOAcNAaMA_LAYKAWJAUIARHAPGANFBKEEIFGGHJDJMBKP9MS7N\ UCPVGRWKTYLU_LUaLUcLUeLUgLTiLSlJSnLQr7RvATuDVuFXtI\ ZtL`tNbsQdsTfrVhrYkr`lqbpqerphtpjvpktmkrklpilnfmld\ mibmg`leYhbWeZUbWR_TPXQNVNKSKINFGMDDI9BE59D37K9CQE\ HVJM_NR`PSaQSbRScSSdTSdUSeWSfXSgYShZSi_Si`Sf_Ud_Wb\ ZY`ZZZY`XYbVXdTXeRWgPWiNVkLWlJ_nHcpFgrDksBoo9sk7ug\ 5wc4x`9yYEzWJzUOzSTzPYzNbzLgzJbzSZz_UzhQzpMzxJzsGz\ nEziBzd8z_YzbWzcTzdRzePzf } END PARAMETER FILE=========================================

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FOTD 19-08-07 (Seahorse Sympathy [No Rating])
by Jim Muth 19 Aug '07

19 Aug '07

FOTD -- August 19, 2007 (No Rating) Fractal visionaries and enthusiasts: When the weather turned out perfect on Saturday, F.L. and I made a spontaneous decision to go out and enjoy the perfection, which we did. By the time we returned to F.C., totally out of energy, it was well after dark, and I was too exhausted to launch into a fractal search. But after a restful night, my fractal energies returned, and today's minor image is the result. In today's image I re-used yesterday's trick, but I did it with Seahorse Valley rather than East Valley. The result is pretty much the same, not worth a rating, but marginally interesting. The result is pleasing enough to be declared FOTD for August 19 however. The name "Seahorse Sympathy" is pure whimsy. And the calcula- tion time of 5 minutes should leave no one in distress. The most convenient way to view the image is to wait for Paul to calculate the image and post it on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and then view the completed image there. Absolutely perfect weather prevailed in the Fractal Central area on Saturday. The fractal cats slept alone through most of it. My day was very active but also enjoyable. The next FOTD will appear in a matter of a few hours. Until then, take care, and be alert. We are surrounded by fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Sympathy { ; time=0:05:21.70-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=ManJul2CPwr passes=t center-mag=0/0/\ 0.87 params=-0.749973/0.01/0.014/0.014/4/0 float=y maxiter=26000 inside=0 periodicity=10 colors=000WAAXAAYAAZAA_AA`AAaAAbAAcAAdAAeAAfA9gA8h\ A7iA6jC8kDAlEBmDCnDDoDDpDEqDErFGsGHtHJuIKvJLwKNxLO\ yNQzORzPSyQUxRVwSVvTVuUVtUUsUUrUUmUThUTdUS_USWURXV\ RYXSZZU_`V`bX`dY`f_`h``ja`lc`nd`pf`rg`ti`vj`wk`vkZ\ slXqlVomTmnRmoPmpNmoLmmPmkSmi_lgfkcfj_fiW_hSTgONfQ\ LeOJdNHcMFbLEaJC`IAdH8gG7jFAiGDiGFiHIhHLhINhIQhJTg\ JVgKYgK_gKaiJbjIdkHelGgmFhnEjoDkpDmrCnsBptAqu9sv8t\ w7vx6wy6tx8qxAoxBlxDjxFgxGexIbxK`xLYxNWxO`pTehXj`a\ oTetLjxEnuGjrIfoKblM_iOWfPScRO`TLYVHVXDSYAhPPxGcvX\ gulkiQXY3J`CObLTdTYfabhjgjrlcskXskQskSjmUaoVTpXKrZ\ Bt_2uY5sX8qWAoUDnTFlSIjQLhPNgOQeMScLVaKX`JZYI`VHaT\ GcQFdOEfLDhICiGBkDBlBPf5aa0__4ZY8YWCWUGVSKUQOSOSRM\ WQK_OIcNGgMEkObcQzXPvVOrTNnRMjPLgOMeNNcMOaLP_LQYKR\ WJSUJTSIUQHUPHMOMFNR7MW0L_4Ja8IcBGeFFgJDiMCkQAmU9o\ X8qYBnYEkYHiYJfZMdZPaZS_ZUX_XU__S_bP_dN`gK`jI`mF`o\ DZoIYoNWoSH1bF2VD3NB4F957 } frm:ManJul2CPwr {; Jim Muth ; Creates and rotates ^2 Hyperbrot Figure ; P1 sets point of rotation, P2 sets angle of rotation ; P3 sets power of C z=c=pixel: z=sqr(z)+p1+(p2*(c^p3)), |z| <= 100 } END PARAMETER FILE=========================================

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Re: New Formulas
by jackoftradez＠comcast.net 19 Aug '07

19 Aug '07

. Animation of the PARs Russ Walsmith WILL post here SOON is posted: http://www.fractal-animation.net/vid/immortal.zip WMV 640x480, 134 sec., 24 Meg (I used the temporal distortion feature implemented in Fractint to jump ahead of the curve <g>) . Stay amazed! JoTz .

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FOTD for Aug 19 coming in about 2 hours
by Jim Muth 19 Aug '07

19 Aug '07

Fractal fans: The FOTD for August 19 is unavoidably late, but it will be posted in about two hours. Sorry for the delay. Jim Muth

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Re: Strange Mandelbrot Thing
by jackoftradez＠comcast.net 18 Aug '07

18 Aug '07

. I may have Jim Muth's Julia rectangle beat. I found a circle - a perfect circle - in the normal Mandelbrot set! I have spent the past month exploring the region on the West needle just foreward of the large minibrot, at e+100 and beyond, looking for a minibrot target for my next Universe video. I could find none. I have known about and explored this area since my earliest days of fractal work, it is very intriguing. There are weird patterns that are found nowhere else in the set, look like alien egg pods or something. But they keep bifurcating and multiplying forever, they never seem to resolve into anything no matter how deep in you go. So I finally found this circle where I thought a minibrot would be. It is not part of the lake (M_set proper) since it is colored. It occurs to me that it may resolve into something, even a minibrot, if a high enough iteration count was used or needed, but I am limited by the fractint max of 2.1e9 iterations. Strangely, this image looks exactly the same at 10^6 and 2.1*10^9 iterations. I have never encountered that before either, maybe there is a software issue responsible? This PAR takes a LONG time to render, I expect few would bother, so I posted the images on my server, only half a MEG download. Anyone have a clue? http://www.fractal-animation.net/special/strange.zip .

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FOTD 18-08-07 (Absolute Insanity [No Rating])
by Jim Muth 17 Aug '07

17 Aug '07

FOTD -- August 18, 2007 (No Rating) Fractal visionaries and enthusiasts: Now and then I like to pull out old forgotten formulas and see what they can do. Today's formula is about 10 years old. It is an early attempt to draw oblique slices through the Julibrot, while checking different powers of C. It is only moderately successful at doing this, but it still can produce some interesting images. Today's image is a scene in East Valley of the Mandeloid created by the formula Z^2+C^8. The slice is oriented very close to, but not exactly in, the Julia direction. The resulting fractal has the outer shape of the East Valley Julia sets but with a very decorative 'star' in the center. I named the image "Absolute Insanity" because it makes so little sense. With no idea of what other images might lie in the formula, I could give today's image no rating, but it is still a rather interesting, if not the most attractive, image of all time. The included parameter file calculates in 4-1/4 minutes on the fast machine. It would take 23 minutes on the P200mhz. To see the image without the need to calculate it, go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view it there. Friday began muggy here at Fractal Central, but turned quite pleasant during the afternoon. The cats gave up waiting for another bat to appear, and resumed their normal activity of making their own trouble. My day was peaceful enough. The next FOTD will appear in 24 hours. Until then, take care, and walk with spirit. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Absolute_Insanity { ; time=0:04:16.72-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=ManJul2CPwr passes=t center-mag=0/0/1.02/1/-90/3.88578058618804789e-016 params=0.2505/2.06e-005/0.015/0/8/0 float=y maxiter=25000 inside=0 periodicity=10 colors=000XGIzKIAMfAMeAMcALbAKaAJ`AI_AHZAGYAFXAFW9\ EV8DU6CW6BZ6Aa68d63feRIfTJgUKhVLiWMjXNkZNl_Om`PnaQ\ obRocRpeSqfTrgUshVtiWukWvlXwmYxnZyo_zscyp_ymWyjSyg\ OydLyaHyZDyW9yT5zO0yQ2xR4wS5vT7uU8tWAsXBrYDqZFp_Go\ `InbJmcLldMkeOjfQigRhiTgjUfkWelXdmZdn_bo`ao`_oaZpa\ XpbWpbUqcTqcRqdQrdPreNreMsfKsfJsgHtgGthEthDuiBuiAu\ j9ujAthAsfArdArcAqaAp_ApYAoXBnVBmTBmRBlQBkOBkMBjKB\ iJChHChFCgDCfCCfACe8Cd6Cd5Bc6Bb6Ab6Aa79a79`78_88_8\ 7Z87Z96Y96X95WA5VA4UA4TB3SB3RB2QC2PC1OC1NC4PB7RBAT\ BCVBFXAIZAL`ANbAQd9Te9Wg9Yh9`i8ck8fl8hm8il7ik7ik7j\ j6ji6ji6kh6kh5kg5lf5lf4le4md4md4mc3nc3nb3na2oa2o`2\ n_1o`2o`3oa3pa4pa4pb5qb6qb6qc7rc7rc8rd9sd9seAseAte\ BtfCtfCufDugDugExfFugErgEohEmhEjiEgiEejEbjE_kEYkEV\ lESlDQmDNmDKnDInDFoDCoDApD7pD4qDZP52qD5oF8nGBlIEkJ\ HiLKhMMfOPePScRVbSY`U`_VcYXeXYhV_kU`nSbqRctPevOfeE\ YP5QR6RS6RU7SV7SMsONwLOzJ } frm:ManJul2CPwr {; Jim Muth ; Creates and rotates ^2 Hyperbrot Figure ; P1 sets point of rotation, P2 sets angle of rotation ; P3 sets power of C z=c=pixel: z=sqr(z)+p1+(p2*(c^p3)), |z| <= 100 } END PARAMETER FILE=========================================

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FOTD 17-08-07 (Hyperspace Figures [6])
by Jim Muth 16 Aug '07

16 Aug '07

FOTD -- August 17, 2007 (Rating 6) Fractal visionaries and enthusiasts: With today's image we once again enter hyperspace, (not that we ever left it). And just what is hyperspace? It is space of a dimension greater than 3. The most familiar hyperspace is of dimension 4, which just happens to be the space in which the Julibrot figure of the formula Z^2+C exists. Where is this hyperspace? In theory it is all around us, touching every point of our familiar 3-D space. We might say it is sideways to our insides. But what does a four-dimensional object look like? To begin, the question is a wrong one, for hyperspace is not a visual experience, it is a mathematical abstraction. But if we were able to visualize a 4-D object, we would see some kind of unimaginable monstrosity with a surface of three dimensions. On the surface of a four-dimensional hyperplanet, we could walk upright in three mutually perpendicu- lar directions, with the sky always remaining straight above us. Many other impossible things become possible in 4-D space. In my opinion, one of the most unusual is something called a double rotation. In 4-D space an object may be subject to two completely independent rotations at the same time. In 3-D space there is nothing corresponding to this curious motion. In 3-D space, a sphere, when illuminated by a point source at infinity, casts a shadow in the shape of a cylinder with a circular cross section. If this cylinder is sliced straight across, the section is a circle. If it is sliced at an angle, the section is an ellipse. If it is sliced along its length, the section is an infinitely long band of constant width with straight and parallel edges. Without going into hyper-detail, one of these straight edges is what appears on the southeast side of the Julia-like feature in today's image. Even though the image resembles a Julia image, it is actually sliced very close to the Oblate orientation. Today's image is a scene in the vicinity of the East Valley of the large midget on the main stem of the Mandelbrot set. I have rated it at a 6. I might have rated it a point higher, but I feel I have done a bit too many of this type of image over the past few years. I named it "Hyperspace Figures", because it is a scene in hyperspace. Unfortunately, with an maxiter of 1,500,000, the image is very slow -- 42 minutes on the P4-2000mhz and over 2 hours on the P200. To avoid fractal frustration, I recommend viewing the image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Perfection once again proved elusive here at Fractal Central on Thursday. There was simply too much heat (90F 32C) and humidity to call the day perfect. The fractal cats seemed unconcerned. They are still waiting for another bat to come out for them to chase. My day was slow but strangely unsettled. The next FOTD will appear in 24 hours, and that's pretty well settled. Until then, take care, and keep checking back for more fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Hyperspace_Figures { ; time=0:41:58.83-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2a passes=1 center-mag=+0.00328020489643859/+0.664356005504111\ 00/2545329/0.2808/-152.728346262165076/-72.8642931\ 627442465 params=2.75/90.11199999999999/0/90/\ -1.749/0/0/0/0/0 float=y maxiter=1500000 inside=0 logmap=46 periodicity=10 colors=000I0GF1HB2I73J54K25L06M07N08O09P0AQ0BR0CS0\ DT0EU0FV0GY0H_0Id0Le0Oi0Rl0Un8XqF_tKbxOezRhzUkzWnz\ Yqz_tzawzczzezzgzzizzmzzqzztzzwzzzzzmzzczzUtzFmzKc\ zQUmXUmdOziOzoOzvOztOzqOzoOvnOqnOllOgiOdgO_gOVeOQd\ gMagI_gF_g9Yg5Xg2Vg0Vg0Tg0Qe0Od0Oa0K_0HY0DX09T05g2\ 3g50g90lF0qI0xO0zT0zX0zQ0zK0zF0z90z30z00z00z02z07z\ 3Bz7HzDMzHQzMXzQazXizaez_az_YzYXzYTzYOvXMqXInXFiVB\ eV9aV5YT2VT0QT0MQ0IQ0FQ0HT0HT0HV0HV0HX0HX0HY0HY0H_\ 0H_0Ha0Ha0Hd0Hd0He0He0Ia2IY3KX5KT7MO9MMBOIDOFFQDHQ\ 9IT5KT3MV0OV0QX0TX0VY0XY0Y_0__0aa0da0_a2da5ga9iaDn\ aHoaKtaOxaTzaXza_zgdzagzXlzVozVtzVxzTzzQzzTzzVzzXz\ zYzz_zzazzdzzezzgzzizzlzznzznzznzznzznzznzznqzngzn\ YznOznFzn5zn0zn0zn0zn0zn0zq0zt0ox0dz0Tz5HzB5zI0zO0\ zX0za0zd0ze0te0lg0dg0Yi0Qi0Il0Dl05n00n00o00o00q00q\ 00a05M0M90Q70V70Y70_50d50g50i50n30q30v30x20z20z20z\ 20z00z00z00z0DqV7laQ7xM9v } frm:SliceJulibrot2a {; 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|<=real(p5+9) } END PARAMETER FILE=========================================

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FOTD 16-08-07 (Key-Lime Pie [6])
by Jim Muth 15 Aug '07

15 Aug '07

FOTD -- August 16, 2007 (Rating 6) Fractal visionaries and enthusiasts: What does one get if he subtracts Z^(1.2) from Z^(0.8)? A parent fractal of course. And where does one search in this parent fractal for an interesting scene? That depends on the explorer's temperament. Being the designated explorer, I searched the northwest outskirts of the parent, where a large midget is located. I checked especially carefully in the East Valley area of this parent, where, concealed deep in a harmless bit of fractal debris, I found today's scene, complete with sub-midget. I worked a bit on the colors, but I couldn't make a prize-winner from so little raw material, so I satisfied myself with a rating of a 6. The name I gave the image, "Key-Lime Pie" has more to do with the green color palette than any resemblance to that Florida treat. The reasonable calculation time of 1-1/2 minutes will make rendering the image from the included parameter file a treat. And those who don't care for sweet treats may view the already- calculated image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The humidity returned to Fractal Central on Wednesday, making the temperature of 86F 30C a little too oppressive for comfort. The fractal cats were worn out after a futile night of chasing a bat around the house. Around 4am I finally located the critter behind a curtain, caught it, wrapped it in a towel and released it outside. The only harm was to my sleep and Fractal Lady's nerves. As for the cats, they had one of their most frustrating nights ever -- all that running and leaping, and no kill. This afternoon they were still hoping for the bat to reappear. Except for the batty start, today was basically normal. The next FOTD will appear in 24 hours. Until then, take care, and stay alert. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Key-Lime_Pie { ; time=0:01:38.02-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident center-mag=-5.8855024505473/+5.685774193055989/\ 5.931129e+007/1/-162.5/-5.9192343081375387e-005 params=-1/1.2/1/0.8/0/525/0/0 float=y maxiter=2000 inside=0 logmap=193 periodicity=10 colors=000BcKBbIB`HBZGBWEBTDBQBBNABK9BH7BE7BB7B87B\ 37B07B77BD7BKABQDBYGBcIBkLBqOBsTBtWBtZIvcQxfYxidyn\ lzqsztxzyzzzzzzyzvtynqxdlvYitQdsH`qAYo1Tn0Ql0zz0tx\ 0dh0Za0aV0YR0YO0ZL0VI0QG0ID0BA0B70Q40dDAtKVzRdzZdz\ ddzldztdztdztdztdztdtldtddtYdtQdtIdtBdt4dt2dt1dh0z\ f0zd0zc0zc0zT7zKLyAZv1nq0zn0qf7h`EZVLOOTGI`7Dh07h0\ 9h09h09h0Ah0Ah0Ah0Ah1Bh1Bh1Bh1Dh1De1DzPDj2Ga2HZ2IW\ 4LT4NQ4ON4RL6TI6VG6YD6ZA7`77c47d27f9DcDHaHL`NQZRWY\ W`WadVfiTkoRqtQvyOzzNzzLzzQxvVtoYoialcdiYidRlaLqZG\ tVAyR4zO0zL0zy12x44v76v96tB7sE9sG9qIAoLBoNBnQDlTEl\ VEfRHaOKYNLTKONHRIGTEDWAAZ49`06c02f01h00c20`90YE0V\ K0RQ0OW0La0If0Gc0I`0KZ0NW0OT0RR0Tc0In09y2070qE0hL2\ `T7T`AKhEDoH6xL0zO0zR0zz0at4AlL0dcHoKny1lz6kzAizEh\ zIfzNdzRczWaz``zdZziYznWzsVzxTzzRzzRzz`zlhzRqz6yz0\ xz0xz9xzKxzVxzfxzsxzzlzscziTzZKzQAzG1z70z00z00z00z\ 00z0az6Zx9VxBQxELxHHxKExL } 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 15-08-07 (The Joker Laughs [Not Rated)
by Jim Muth 14 Aug '07

14 Aug '07

FOTD -- August 15, 2007 (No Rating) Fractal visionaries and enthusiasts: I had to do it. I just couldn't help myself. I had to take a perfectly lovely little midget in the Mandelbrot set and turn it into a parody of itself. Since the image is just for fun, I could not give it a rating, but the parameter file is quite fast, and even if the image brings no enjoyment at all, little effort will be wasted calculating it. The midget is located on a filament in the vicinity of the East Valley of the large midget on the negative stem of the M-set. To see the original midget in its full glory, bring up the 'Z' screen, change real(p1) to 45, imag(p1) to zero, real(p2) to 45, and imag(p2) to zero. Then go directly to the <f6> screen and change the x-magnitude to 1 and the skew angle to zero. Strike the <enter> key twice. You will find that the true midget is really quite attractive, with its ring of 8 parading elephants. Too bad I spoiled it. What I did was picture the midget from an oblique angle in the four-dimensional body of the Julibrot. The stretching and skew- ing was necessary to undo the natural distortion that results when Julibrot elements are sliced at slight angles. I named the image "The Joker Laughs". The Joker has always been one of my favorite villians in the Batman series. And the cal- culation time of under 2 minutes will try no one's patience. As always, the completed image is posted for viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A hazy sky which noticeably dimmed the sunshine kept Tuesday from being another perfect 82F 28C day here at Fractal Central. The fractal cats ignored the weather. They were too busy watch- ing the pigeons scrounging for food on the sidewalk. When the birds flew away, the cats thoughts turned to fun and treats. My day was busier than Monday, but well under control. The next FOTD will appear in 24 hours. Until then, take care, and look for the bright side of dull, drab fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Joker_Laughs { ; time=0:01:56.82-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 center-mag=-0.000000000\ 32727888/-0.00000000015443144/2.437256e+008/1.8621\ /177.600282113802905/56.7502624222490368 params=131/-44/-97/72/-1.7481510383921/0.001201805\ 9621/-1.7481510383921/0.0012018059621 float=y maxiter=15000 inside=0 periodicity=10 colors=000asYlscnpdondgj`dfKabPZZUWUZTPcQKhNFbKAYH\ 5SD5MA6H76B4751705929B4CD6GF8KH9NJBRLDUNFYPGaRIdTK\ hVMkWNmXOoYOqYOsZPt`PubPxePzhQykQymQwnQvlRriRmfRhe\ RcbSZ`SUYSPWTKUTART5OT2MU2JU2HU2FV2CV2AV28VCFQMLMV\ RIdYEncAwi6tlHroSorbmumntjnthotfotcptapt_qtYqsVrsT\ rsRssPssMtsKtsItsGupFumFujEugEvdDvaDvZCvWCvTBwQBwN\ AwKAwH9wF9wQIw_QwiYvjWukUtkSslQrlOqmMpnKpnIooGnoEm\ pClqAkq8jr6jr4kp5kn6kl7kk7ki8kg9kfAkdAlbBlaCl_DlYD\ lXElVFlTGlSGkTGjVFWOlWSiWVeWZbWaZXeWXiSXlPXpLXsIXw\ EXzBUtGRoLOjQLdVJ_ZGVcDPhAKm8FqBJmEMjHPfKScMV_PYXS\ `UVcQYfN_iJblGeoChr9ju6fh8bXAZKCV8EXDDZID`MDbRDdVD\ e_DgdDihDkmDmqDovDpzDqxHqwKqvNruQrtTrsWrrZqo_qm_qk\ _ph_pf_pd_oa_o__oY`nV`nT`nR`mO`mM`mK`mI`iPceVea`gY\ fiVlkTkeRk_PjUOjOMiIKiCJi7Ih9HgAGfBGeCFdDEdEDLmDMl\ CNkBOjAPiAQh8Rg7Sf6Te5Ud4Vc3Vf4Xd4Zb5``Ab_FeYKhWPj\ VUlTZoRcqQhsOmuMrsGwsMzsS } 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 14-08-07 (Attack of Fraczilla [5])
by Jim Muth 13 Aug '07

13 Aug '07

FOTD -- August 14, 2007 (Rating 5) Fractal visionaries and enthusiasts: Today's image rates only a 5, mostly because we've seen several other images like it over the past several days. And I think this is the third time that I have used the same color palette with only slight changes. The parent fractal was created when 12 parts of Z^(1.02) were subtracted from 12 parts of Z^(0.98) and straight C was added. This parent is a Mandeloid rotated 180 degrees. We have seen quite a few of this type of parent recently, which is another reason why today's image rates only a 5. Today's image is located in the East Valley area of a large quadratic Mandelbrot midget in the chaos on the northwest side of the main bay of the parent fractal. I named the image "Attack of Fraczilla", mostly in honor of Godzilla, who is still my favorite rampaging movie monster. I seem to see a bit of a fractal rampage stirring in the image, which inspired the connection to the king of monsters. There is nothing monstrous about the calculation time of 1-1/2 minutes however. Such a brief time makes running the included parameter file almost a pleasure. An equally pleasing experi- ence is to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and see the finished GIF image there. The only greater pleasure I can think of would be to have a fully functional version of Fractint for Windows-XP loaded on my P4-2000mhz machine, with the ability to use arbitrary precision math with type=formula fractals. The Monday weather turned out as near perfect as is ever seen here at Fractal Central. If an increased amount of bad weather is a sign of global warming, we have nothing to worry about here in Pennsylvania. Unfortunately, near perfect means no excite- ment, and a continued lack of excitement would soon turn boring. The fractal cats agreed, stretched, and went to sleep. My day was well under control. Tuesday should be the same. The next FOTD is due to appear on Tuesday evening, around 24 hours from now. Until then, take care, and maybe the trendy overhyped global warming disasters will bypass Fractal Central. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Attack_of_Fraczila { ; time=0:01:32.04-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-3.29679033764589500/+3.314214004580537\ 00/903626.7/1/12.5/6.22053270005196168e-010 params=12/0.98/-12/1.02/0/1000/0/0 float=y maxiter=4000 inside=0 logmap=131 periodicity=10 colors=000B58C69D7AE8BF9CGADHBEICFJDGKEHLFIMGJOILQ\ KNSMPUORWQT`VYcY`f`cicflfinhkpjmrlopkmnimiehc`cYWZ\ SSVMNQGILADG49CZDBlLAvQ9zX9rTDpIGbBJT6M72X00fF4kVA\ sjFs`UsdZkhbpe_scTp`MfZKXWIXUGaSEfPBfN9fK7fI5fF3fD\ 1fB0aE4XH8XKCXNHXPLYSP`VUsYYf`aibeldcseasf_kgYkhXj\ iVsjTjlRjmPjnOioMspKiqIirHinDjkAkg6ld3l`QLaQNbQPcQ\ RcQTdQVeQXfQZfQ_fSVfURfVMfXIfYDf_9f`5ZX8RTBJPEBMHC\ NICOICPICQICQICRICSICTICUICUIFVKIWMKWNNXPPXQSYSUZU\ _ZVd_Xi_Yn`_raavabvbdvbevebvg_viYvkVvmTvkPvjMvhJvg\ GvfDvdAvc7vb4v`1v_0vZ0v_1v`6vaBvbGvcLvdQveVvf_vgdv\ hivhnvgovgovhovhpripnipejqdjqbkq`krZlrXlrVmsTmsRns\ QnsTofvoUvpIvpFvqCvq9vr6vr4vs1vs0vt0vt0vu0vu0vu3vu\ 6vu9vuCvuFvuIvuLvuOvuPvuPvuPvuPvuPvuPvuPvuPvuOvuOv\ uOruNnuNiuNduM_uMVuMQuLLuLKuLNuJPuIRuGTuFVuDXuC_uB\ au9cu8eu6gu5iu4ju5ju6ju7ju8ku9kuAkuAkuBluCluDluElu\ FluFjuHhuIfuJduLbuMauN_uP } 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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FractInt for Windows (beta 4) -- open for testing
by Richard 13 Aug '07

13 Aug '07

Welcome to the FractInt Makeover! For those of you on the fractint list that may not have heard, I've been overhauling the FractInt source base to move it out of the 16-bit DOS world. Things have been progressing nicely and I'm now at a point where I think widespread testing would be helpful. Download and install beta 4 of FractInt for Windows: <http://tinyurl.com/26dvd7> I've just resubscribed to the fractint list so you can send bug reports to me or to the list. If you have any doubt, just send any bugs to me. A memory dump file will be produced upon a crash, but that shouldn't be happening anymore :-). This is what I would call "Phase I" of the overhaul. It is a migration of the existing DOS source base to a 32-bit Windows application. The user interface looks and acts like DOS because it is just a port of the DOS ui. A minimal amount of "Windows-ification" has been done, but you'll notice a lack of normal Windows things like a menu bar, context menu, paying attention to the mouse, dialog boxes, etc. The next phase will be to backfill these changes into the X Window System version to make all these features available to xfractint. Once that is tested, the beta will be over and a new release made. Known Issues There is no sound output support. There is no mouse support. Panning and zooming is by keyboard only. Video modes with pixel dimensions other than 4/3 aspect ratio assume non-square pixels. The images all render fine, but they appear stretched or squashed. The choice of resolutions in fractint.cfg reflect this. With debugflag=10000, error messages are reported for disk video mode when: start fractint, pick any disk video mode (e.g. 320x200), let it render, wait for completion, then go to the <v> screen, change 320 to 32, submit it. Without the debugflag settings, FractInt for Windows will most likely crash. This problem is present in the DOS fractint and not a result of the port. There are a few gaps in functionality associated with fractal types that were computed via assembly language, but these were mostly integer versions of some of the more common fractal types. If you encounter this situation a message will be displayed informing you that you should switch to floating-point for a useful image. -- "The Direct3D Graphics Pipeline" -- DirectX 9 draft available for download <http://www.xmission.com/~legalize/book/download/index.html> Legalize Adulthood! <http://blogs.xmission.com/legalize/>

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FOTD 13-08-07 (Mainstream Fractal [7])
by Jim Muth 12 Aug '07

12 Aug '07

FOTD -- August 13, 2007 (Rating 7) Fractal visionaries and enthusiasts: Today's image uses a bit of fractal trickery to make its point. Instead of the usual blank black inside and outside equal- iteration bands, the image was rendered with the inside set to 'bof61' and the outside set to 'real'. The generating formula subtracts 250 parts of Z^(-0.9) from 250 parts of Z^(-1.1) and adds straight C to create a parent fractal that resembles the Mandelbrot set fairly closely, but has sausage-shaped holes at the end of its filaments. The greatest surprise is the empty triangle that appears where East Valley would normally be found. Today's image is located on the outside the of southern shore line of this triangle. I rated the image at a 7 rather reluctantly. The colors are a bit too busy for maximum effect. The name "Mainstream Fractal" has ho connection at all to the image. It's simply the first thing I could think of. The image is a rather slow one, with a calculation time of over 18 minutes on the fireball P4-2000, and well over one hour on the old P200 machine. But calculation will be no issue for those who view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunday was spoiled here at Fractal Central when the temperature reached a high of 90F 32C. But if the humidity had been higher, it would have been worse. The fractal cats must have agreed, for they seemed totally satisfied with their life of perpetual indoor confinement. My day was spent recovering from Saturday's outing. The next in the near endless series of FOTD fractal images will appear in 24 hours. Until then, take care, and step lightly. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mainstream_Fractal { ; time=0:18:18.07-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+21.44692078468248/-0.000630261989078/\ 1.042898e+009/1/-80/0.0150935738509659703 params=250/-1.1/-250/-0.9/0/0/0/0 float=y maxiter=12000 inside=bof61 outside=real logmap=1274 periodicity=10 mathtolerance=0.05/1 colors=000000WALW9LV8LV7Ld_mcZmaYm`Ym_XmYWmXVmWUmU\ TmTSmSRmQQmPPmOOmMNmLMmKLmJLmXebK1gI2hH2hG2hE2hD2h\ C2hB2h93h83h73h53h43h33h23h65gA7fE9fIBeMDePFdTHcXJ\ c`LbdNbhPakQahUceXdc`e`cfZfgWjhTmiRqjOtkMwlQvkTukW\ tkZskarkdqkgpjjojmnjpmjsljvkjykjxlhxlfxmexmcxnbxn`\ wo_woYwpXwpVwpTwqSwqQvrPvrNvsMvsKvtJvtHvtGusFtrEsq\ EzjzroDqnCpmBomBolAnkAmj9li8kh8kg7jg7if6he5hd5gc4f\ b4ea3ea3b_4_Y5XW6UU7RS8OQ9LOAIMBFKCCID9GE6EF3CG0BH\ 1EK2HM2KP3MR3PT4SW5UY5X`6_b6ad7`c7_c7_c7Zc7hc7tc7S\ c7Cc8Wc8Wc8Vc8Uc8Ub8Tb8Tb8Sb9Rb9Rb9Qb9Qb9Pb9Ob9Ob9\ Nb9NbFK`LIZQGXWDV`BTf9Rk7PjCLjGIiKEiPBhT7hX4h`1iZ3\ zm5jX6jW8kV9z`BlTCzSEzRFzQHzPInOKoNLoMNpLOpKQqJRqI\ TrHUrG0sFXsEAtD_tCKuBbuAUv9ev8cv7hu8mt9ftAusAdrBzr\ CbqDzqDapEzoF_oFznGYmHvmIWlIrlJVkKmjLTjLhiMRhNchNQ\ gOZgPOfQUeQMeRPdSKdSKcRLcQLbPLbOLaNLaMLaLL`KL`JL_J\ L_IL_HLZGLZFLYELYDLXCLXBL } 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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