December 2002 - Fractint - mailman.xmission.com

FOTD 05-12-02 (The Laugh [4])
by Jim Muth 05 Dec '02

05 Dec '02

FOTD -- December 05, 2002 (Rating 4) Fractal visionaries and enthusiasts: Today's image resembles a disembodied grin -- a rictus someone who likes to use fancy words might call it. I simply call it "The Laugh", a name which properly describes the effect the picture creates. Turned upside-down, the image might be called "The Cry", but let's keep things as pleasant as possible. I'll try to be as pleasant as possible about the image, for which I make no excuses and which I can rate no higher than a somewhat inflated 4. But even a 4-rated image is worth the effort when the time required to render it is only 44 seconds. The hole at the center, shaped like a gaping grin, is actually an odd slice of a midget located near the tip of the northern- most filament of the M-set. At the hole's upper shoreline a bit of one of those ubiquitous straight bridges appears. (In the M-set a slice of this bridge appears as a valley that forms a lip of a bud.) The grin is actually part of a four-dimensional hyper-object. In a space of four dimensions, things that seem absurd in three dimensions become everyday facts. Consider rotation. In a space of zero or one dimension, rotation is impossible. In two- dimensional space, rotation takes place around an axis-point, while in three-dimensional space, rotation takes place around an axis-line. The general rule is that in n-dimensional space, a simple rotation takes place around an n-minus-2 axis. But a simple rotation requires only two dimensions. The remain- ing dimensions simply remain fixed while turning in place. In four-dimensional space, this leaves the two-dimensional axis of rotation motionless, its points rotating on themselves. But even while serving as an axis of rotation, this plane may itself rotate. The resulting motion, which is impossible in three dimensions, is known as a double rotation. When subject to a double rotation, every point of a four-dimensional hyper-object except the point where the two axis-planes intersect is in motion. If the two rotations are equal, all points move in a circle. If the rotations are not equal, the points trace out a surface of double revolution, which is shaped like a four-dimen- sional doughnut. This double-rotation motion can perhaps be more fully realized by considering the Mandelbrot set and Julibrot. With the M-set on the screen, which of the Z dimensions is perpendicular to it, real(z) or imag(z)? Of course, they both are. In fact, every line in the Z, or Julia, plane is perpendicular to the M-set. Keeping the M-set undisturbed on the screen, the Julibrot can be rotated around the M-set, so that every line of the Z plane in turn lies in our 3-space and at a right angle to the M-set. Looking at only the screen, one would never know that the Julibrot was rotating. Now, with the Julibrot still rotating, if the M-set on the screen were to begin rotating on the screen around its origin, carrying the rest of the Julibrot with it, the Julibrot would be in a state of double rotation. Do not try to mentally trace out the path the points would take, it is impossible. It is far easier to imagine the fun of rendering today's super- fast image from the attached parameter file. And those not particularly fond of rendering can download the completed image from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> I'll have much more popularized 4-D curiosities in the weeks to come. Wednesday was hazy and cold here at Fractal Central, but the day was made interesting by a late morning apparition of two brilliantly colored sun dogs. The temperature of 26F -3C was far too chilly for the ears of the intrepid duo, who also dislike dogs of any variety. They wisely decided to pass the day stretched by the warmest radiator they could find. Gazing from the F.C. window this morning, I see snow falling at a moderate rate with 6in 15cm already on the ground and the snow expected to continue until evening. The fractal cats will need comforting. Regardless of the weather, the human's work still needs to be done however. And the best way to finish work is to start it. So until tomorrow, take care, and be of good cheer. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Laugh { ; time=0:00:44.70--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=1 center-mag=-0.00000000000001003/-0.000000000000001\ 47/3.099006e+012/1.4001/0.404762088721556723/-20.7\ 50360169932005 params=-73.9/161.5/2/0/-0.207107799\ 5585138/1.122756154909389/-0.2071077995585138/1.12\ 2756154909389 float=y maxiter=12000 inside=0 logmap=79 periodicity=10 colors=000PKAQLARMASNATOAUPAVQAWRAXSAYTAZUA_VA`W6a\ X5bY5bZ5a_4``4`a4_b3Zc3Zd3Ye2Xf2Xg2Wh9ViFUiLTiRTiX\ SibRihQinPitPizSkyUmyWoyYqy`sybuydwyfxyetwdpvcmtbi\ safq`bp__nZWmYTjXTkXWmPZoFaq0ds1cq1bp2ao2`n3_m3_l4\ Zk4Yj5Xi5Wh5Wg4Yh4_i4ai4bj4dk4fk4hl4il9gjDehIcfMbd\ Q`bVZ`ZXZbWXZSRVOMRLHNHCKE7RCBXAEc8Ii7LQBeigqgclf_\ hdXdcT`aPX`MT_IOYEKXBGV7CU38T04Q4GO8RLBbJFmHIxaTpu\ bin_hhXgaVgWSfPPeJNeCKd6Id7Lg8Oj9QlAToBWrCYtD`wDby\ F_wHYuIVsKTrLQpNOnOLlQJkRGiTEgUCfch5qfDhdK_cSRaZI_\ fAZmKTnTNnbInkCnt7nkHkcQiWZfOhdGqa8z_7mZ6gz5Qz4Ez5\ Fz6Fz7Fz7Fz8Fz9FzAFzAFzBFzCFzDFzDFzDDzDCzGDzGDzFGz\ EJzCMzBPzASz8Vz7Yz6`z4cz3fz2iz5dz8_zAVzDQzFLzLRzQW\ zVaz_fzdkzcizbhzbfzaez`cz`bz_`z__zcbzfezihzlkzonzr\ qzutzxwzurzrnzojzleziazfYzcUz`PzYLzVHzSDz_KzgRznYz\ m_zl`zkazjbziczhdzgezfgzehzdizcjzbkzalzamz_lzZlzYl\ zWlzVlzUlzSlzRlzQlzPlzQfz } frm:multirot-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================

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Xfractint, colormap editing
by Natalie 04 Dec '02

04 Dec '02

Hello again, I tried another fractal generating program for Linux, Gnofract4D. It can't compete with Xfractint, although it has some nice features. It has an evolver-mode (9 images), zooms in and out, there are 9 fractal types, some extra parameter functions, but the nicest feature is: the changing of colormaps (it uses Fractint colormaps!), the fractal is not regenerated (as in Xfractint), the colors are changed instantaneously (like in DOS Fractint). It is possible to edit colormaps in The GIMP and use them in Xfractint. The GIMP also has a gradient editor, which has even more editing features, but gradients have to be changed to palettes to be able to use them in Xfractint. The editing is still very tedious, you can't see directly how the colors turn out in the fractal image, Xfractint has to regenerate the fractal and if the result is not what you want, you have to go back to The GIMP and edit the map again. If the fractal takes a long time to generate, it might be days before you've obtained the result you want. Another possibility is to change the colors of the image in The GIMP, but all Xfractint info will be lost. This is not a problem if you just want to have a nice image, it will be a problem when you want to zoom in or manipulate the fractal with the edited colormap in any other way in Xfractint. So... Dear, admirable programmers, would it be possible to add a colormap editor to Xfractint? Please?? >From The GIMP help file: The GIMP is an OSS (Open Source Software) program covered by the GPL License, which gives you the freedom to access and also to change the source code that makes up the program. >From Gnofract4D help file: Gnofract4D is distributed under the Gnu General Public License. Thanks Natalie PS The GIMP is also great for - adding effects to images - making animations with lots of extra features - adding layers, for example a layer with a copyright notice N. -- Stolen tagline: Linux is like a wigwam, no windows, no gates, apache inside. [ Linux Counter: user 230952 machine: 111180 ]

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FOTD 04-12-02 (New View of the M-Set [3])
by Jim Muth 04 Dec '02

04 Dec '02

FOTD -- December 04, 2002 (Rating 3) Fractal visionaries and enthusiasts: When is Seahorse Valley not a valley?...When it's a bridge, of course. Today's image shows a new view of the Mandelbrot set. But when seen from this angle, it is not the M-set. It's an odd slice of the Julibrot, a slice in some unimaginable direction oriented roughly halfway between the Mandelbrot and Julia directions. To picture the orientation of today's view, imagine the M-set on the computer screen, with normally unseen attached parts of the Julibrot extending invisibly in front of and behind the screen. Then imagine the top half of this invisible 3-D part of the Julibrot cut off and the newly-exposed 2-D surface rotated 90 degrees around the X-axis until it fills the screen. Today's image illustrates that slice. The image vaguely resembles the M-set, but it is not the M-set. The main bay is represented, as are the primary bud on the negative stem and the next bud beyond. Farther west, there is a slice of the prominent midget at -1.75, which barely skims that midget's main bay. Only hints of the stem itself are visible. The large period-2 buds that lie at the north and south edges of the main bay of the M-set are nowhere to be found. They are now lying invisibly in the space before and behind the screen, in the position where the slice now on the screen was originally located. Along the eastern edge of the large bay on the screen, which is actually East Valley, a few of the 'elephants' that roam there can barely be discerned, grossly distorted at this strange angle. The most surprising thing about the new slice is what has happened to Seahorse Valley at -0.75 and Scepter Valley at -1.25. They are in the image, but they have turned into the narrow straight rods which I have named bridges. I have colored these bridges a brilliant green for emphasis. These straight rods are not artifacts. The Julibrot is filled with them. They are caused by the fact that, regardless of where iterated points start, if they do not escape first, they will eventually settle into the same orbits as points that start at zero. The immediate implication is that, when its total shape in the Julibrot is considered, a Mandelbrot valley does not come to a sharp point, but rather a sharp knife-edge. But even this idea is incomplete. The Julibrot is four-dimen- sional, and there are many other orientations in which the Mandelbrot valleys appear to come to sharp knife-edges. In the four-dimensional world, these knife-edges stack together edge-point to edge-point, not side-by-side, forming sharp two- dimensional cutting surfaces, such as a 4-D man would use to shave his hyperface. Like so much that can exist only in the world of four dimensions, these sharp 2-D surfaces are impos- sible to visualize, and the complete shape of the Mandelbrot valleys will therefore never be imagined. I named the lightning-fast image "New View of the M-set". The rating of a below-average 3 might be a bit pessimistic, but hopefully the render time of only 11 seconds will make viewing it worth the effort. As always, the pre-rendered GIF image is available on the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Tuesday was cold and sunny, with blustery winds and a temperature of only 23F -5C. Needless to say, the fractal duo turned around and came back inside as soon as their noses felt the outside air. They passed the day sleeping by the radiators, thankful that they have such a cozy place to take shelter in. This morning is even colder, but there is little wind. It's a fine day to tackle some work. Until next time, take care, and don't get taken for a ride by a Seahorse Valley in disguise. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ New_View_of_M-Set { ; time=0:00:11.70--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=t center-mag=-2.10942e-015/0.61004/0.721356/1.2195/-\ 90/3.88578058618804789e-016 params=4.5/22/2/0/0/0/\ -1.25/0.03 float=y maxiter=5000 inside=0 logmap=yes symmetry=none periodicity=10 colors=000GABJAENAHQAJTAMWAPZARaAUdAXhAZkAanBdqCft\ DiwEksHjoKjkNjhQjdTj`WjYZjUajQdjMgjJjjFmjBpj8rj9ok\ 9lk9ik9gk9dl9al9cl9elAgmAimAkmAmmAonAqnAsnAun9wk9y\ i8zg8ze8zc7z`7zZ6zX6zV6zT5zR5zO4zM4zK4zI3zG3zE2zB2\ z92z71z51z31z15zB9zLDzVHzd`zVszMqzNpzOozPmzQlzRkzR\ izShzTgzUezVdzWczWbzX`zY_zZZz_Xz`Wz`VzaTzbSzcRzdQz\ dLzcHzbDzaDzaDzaDza2zP2zO2zOqz2jzKdzafz_gzYhzWizVk\ zTlzRmzPnzOYzYHzfAzbszbszbszaszarz`rz_rz_rzZrzYrzY\ rzXrzWrzWrzVszXrzVrzTrzRqzPqzNqzLpzJpzIpzGozEozCoz\ Anz8nz6oz4nz5nz6nz7nz7nz8nz9mzAmzAmzBmzCmzCmzDlzEl\ zFlzFlzGlzHlzIkzIkzJkzKkzKkzLkzMkzNjzNjzOjzPjzQjzQ\ jzRizSizSizTizUizVizVhzWhzXhzYhzYhzZhz_mzdjzahz_ez\ XczV`zSZzQXzNUzLSzIPzGNzDNzDMzCLzBKzAKzAJz9Iz8Hz7H\ z7Gz6Fz5Fz5UzLjzbgz`ez_czZazYZzXXzWVzVTzUSzURzTRzT\ QzTQzTQzTPzSPzSPzSOzSOzSOzSNzRNzRNzRMzRMzRLzQLzQLz\ QKzQKzQKzQJzPJzPJzPIzPIzP } frm:multirot-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 03-12-02 (Training Oblates [5])
by Jim Muth 03 Dec '02

03 Dec '02

FOTD -- December 03, 2002 (Rating 5) Fractal visionaries and enthusiasts: I am sometimes asked, 'where is the fourth dimension located?' It is not an easy question to answer. The first answer that comes to mind is the intuitive common-sense reply that the fourth dimension does not exist. It cannot exist because our space has only three dimensions, with no room in it for an extra dimension. But science has long since passed beyond the realm of common-sense, and such an answer can no longer be considered the final word. Almost 100 years ago the theory of relativity appeared on the scene, which treats time as a fourth dimension. But taking time as a fourth dimension is not very satisfying. We want an extra spatial dimension, a space in which time would be the fifth dimension. The fact that time is handled differently mathemati- cally is an admission that time is not the new dimension we seek. When studying the world of the very tiny, Physicists sometimes work with what is known as 'Hilbert Space'. This space can have as many dimensions as necessary, but it is more a mathematical abstraction than a physical reality. Hilbert space cannot serve as the extra dimension. In the 1980's the idea of superstrings burst upon the scene. These infinitesimal things are supposed to lead the way to a theory of almost everything. They are assumed to exist in 10 or 11 dimensions, with their vibrations manifesting in our space as the various sub-atomic particles. But the extra dimensions are now so tiny that they lie far beyond the range of observation. And even if a way were found to actually observe the hidden dimensions, we could do nothing more than take a measurement that told us that the dimensions were really there. With our two-dimensional retinas and three-dimensional-trained minds, we could never observe the extra dimensions. Yet four-dimensional objects do exist mathematically. The 4-D Julibrot is really there in math-space, appearing objectively identical to all who study it. With our computers we can slice it in any direction desired and study the slices. We can study the six perpendicular planes and the four perpendicular three- spaces that exist in 4-D space. Yet, despite this ability, we still cannot visualize the fourth dimension nor a 4-D object as simple as a hypercube. The limitation is apparently in our visual apparatus and minds. Living in a universe of perhaps infinite dimensions, we can visually observe only 3 of them. And this limitation assures that regardless of how hard we try, we shall never visualize even one extra spatial dimension. But if the fourth dimension actually did exist, in which direction would it lie? When asked this question, I reply that the way to the fourth dimension is sideways to the insides of solid objects. If a point were to start at the center of a sphere and move perpendi- cularly into the fourth dimension, the point would not move toward any point on the surface of the sphere. It would dis- appear at once from the center of the sphere, and move away from it, remaining at the same distance from all points on the sphere's surface. Of course, to our 3-D-trained minds living in 3-D space, this seems impossible, and in three-space it is impossible, but in four-space it is only one of the many apparently impossible things that can happen. I'll have much more to say about four- dimensional curiosities in the upcoming FOTD's. And before I forget, we do have a fractal. Today's average- rated fractal is a scene in the Oblate direction of the Julibrot created by the formula Z^(-2.5)+Z+C. I have named it "Training Oblates" because of the train of indescribable open areas lined in a straight diagonal line. Once again the straight theme appears in an odd slice. I will explain this curiosity also in a soon-to-appear FOTD. The render time of just under 4 minutes is slightly slow for an average image. Downloading the completed GIF file from the internet at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> will be a bit more convenient. Monday was cloudy and chilly here at F.C. The temperature of 45F 7C was not too extreme, but for some reason the dynamic duo of fractal cats chose to remain indoors by the heat source. Not one to interrupt a good thing, I let them sleep most of the afternoon. Today promises to be sunnier, but also blustery and much colder. It will likely be another indoor day for the intrepid ones. For me it will be another work day, and if I hope to finish, I must begin. Until tomorrow, same time same place, take care, and always look to the fractal side. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Training_Oblates { ; time=0:03:52.72--SF5 on a P200 reset=2002 type=formula formulafile=slices.frm formulaname=OblateMix passes=1 center-mag=0.531869\ /2.53209e-014/14.49969/0.6895/-69.8080439126262604\ /59.5866633049899761 params=1/-2.5/1/1/0/-1 float=y maxiter=2500 inside=0 logmap=6 periodicity=10 colors=000U8QR7PO6OO5NO4MO3LO3ON6RN8UMAXMC_LEbLHeK\ JhKLkJNnJPqJRtRQwYPzdPzlOzsNzzNzmRm`UqcQoeNmgJliGj\ lDhn9gp6er3dp6co9bnBamEalH`kJ_jM_iPZhRYgUXfXXeZWda\ VccVadQ_eMYfIWgEVhAQnPLtcQodVkdZfdcbegYelUepPfuLfy\ HfkNbZT_LZW8dT8eV7gW7iX6kY6mZ5o_5q`5sa4ub4wc3yd3ze\ 2zf2zg2zhIzVYzHlz4hz7ezAbzD_zGXzJUzMRzPOzSLzUJzUIz\ UGzUFzUEzUCzUBzUAzU8zU7zU6zUczO`zMYzKVzISzGQzENzCK\ zAHz8Ez6Cz5Fz6Hz7Jz7Lz8Oz9Qz9SzAUzAXzBZzC`zCbzDdzD\ ezDezDezDezDezDezDezDezDezDezDezDgzHhzKizOjzRlzVmz\ YnzaozdqzhrzkszotzrezmRzhDzcCzcCzdBzdBzdAzeAze9ze9\ zeJzcTzabz`_z_XzZUzYSzXPzXMzWKzVHzUEzTBzT9zS6zR3zQ\ 1zQ7zNCzLIzINzGTzEYzBcz9hz7nz4sz2xz0wz1vz1uz1uz2tz\ 2sz2rz3rz3qz3pz4oz4oz4nz5mz5mz5iz7ez8az9ZzBVzCPzEQ\ zERzETzFUzFVzFUzETzDSzCRzBQzBPzAOz9Nz8Mz8Pz8Rz8Uz8\ Wz8Zz8`z8cz8ez8fzAgzChzEizFjzHkzJlzLmzMnzOozQpzSpz\ TqzSrzRszQszQNzVNzUNzTNzS } frm:OblateMix {; Jim Muth z=real(pixel)+flip(real(p3)), c=flip(imag(pixel))+imag(p3), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2): z=(a*(z^b))+(d*(z^f))+c, |z| <= 100 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 02-12-02 (Fractal Trinity [5])
by Jim Muth 02 Dec '02

02 Dec '02

FOTD -- December 12, 2002 (Rating 5) Fractal visionaries and enthusiasts: Today's image shows an odd slice of a midget that lies in the East Valley area of the prominent midget on the main stem of the M-set. At this angle, the tiny open area at the center of the image cannot be said to be a midget -- Julibrot holes appear as midgets only when they are sliced in the Mandelbrot orientation along a critical plane. The orientation of the entire image is so far removed from both the Julia and Mandelbrot directions that the hole at its center appears as a mere slit. Much of the distortion of the hole is caused by the extreme stretching and skewing that was necessary to remove the inherent distortion from the surrounding pattern. The world of the odd slices of the 4-D Julibrot is unlike the world of the M-sets or the J-sets. In the odd slices, the features twist, turn and stretch in an unpredictable manner, and must be unstretched to make reasonable pictures of them. So the stretching that went into today's image is actually an unstretching -- a stretching in the opposite direction. I named the final result "Fractal Trinity". The brilliant white triangle around the center slit reminds me of a religious symbol that might be used to represent the Divine Trinity. I'm not trying to promote religion, but I have always wondered whether fractals have a far deeper significance than mere candy for the eyes and ears. After all, fractals resemble the quantum world of the very small, in that they both can be properly comprehen- ded only by the math that describes them. And like fractals, the world at the quantum level does not really come into exis- tence until we make a measurement (iterate a formula) and force it to do something that we can comprehend. Despite (or because of) its religious connotations, I could rate today's image no higher than an average 5. These distorted Julibrot slices have a certain feeling of stress about them that does not make for totally enjoyable viewing. The render time of just under 4 minutes is reasonable enough, but a download of the completed image, which may be found at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> is even more reasonable. The sun was strong on Sunday, but the high winds and tempera- tures barely above freezing (33F 0.5C) kept the dynamic cats indoors all day. Their moods were surprisingly pleasant however as they chased the patches of sunlight streaming through the windows. Since they have never figured out which way the sun- light will move, they were only partly successful in keeping themselves in the warm rays. As for me, I know which way the sun will move, but I'm not sure how the day's work will move, so I'd best take some action to see that it moves in the right direction. I'll return in 24 hours, more or less, still in the third dimension but talking about the fourth. Until then, take care, and follow the sun. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Trinity { ; time=0:03:56.62--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=1 center-mag=-0.00000000000111381/-0.000000000000085\ 77/3.48225e+011/0.02201/173.968599844493554/-76.31\ 6192842800163 params=125.45/-71.48/2/0/-1.74910112\ 6619117/0.0003477184884611/-1.749101126619117/0.00\ 03477184884611 float=y maxiter=2500 inside=0 logmap=426 symmetry=none periodicity=10 colors=000ZCBWBDUBFSBGQAIOAJMALKAMN9LQ9LT9KV9PY9U`\ 9Zb9ce9hh9kj9nmItpKrsMppOomPmjRkgTjdUh`WfYYeY_cY`a\ Yb`YdZYeYWa_UYaSVbQRdOOfMKgKHiIDkHAlNDjSGhXJgaMefP\ ckSbpV`uYZz`YnRUbIQR9MF0IKEJORKSXLWYLCYpBZnA_m9_k8\ `j8`i7ag6af5bd5bc4cb3c`2d_2dZHcRVcKibDwb6Xa_V`YT_X\ SZWQYUPYTNXSMWQKVPJVOHUMGTLESKDSJEQMEOPFMSFKUGIXGG\ _HEbHCdIAgI8jJ6mJ5oL7mN9lOBkQCiREhTGgVIfWJdYLcZNb`\ PabQ_cSZeUYfVXkYHh_IeaIbcI_eIXgJUiJSjJPlJMnKJpKGrK\ DtKBuK8jV6_d4Po2FyBKrJPkRUe_ZZgcTohUwlcwnoxqzyszzq\ uxokvnbsmbqlYmj`mjbmjdmjfmjimjkmjmmjominkineimaimX\ ilTilPhlKhkGhkBhj7hj3hj8jfDlbInZNpVSrRXtNavJewGhqM\ klSnfYqactWiwRoyMtmVhacYQkNL`RHRVDHYCI_CJ`CKbBKcBL\ dBMfAMgANiAOj9Ok9Pm9Qn9Qo9Tj9Vf9Xa9_Y9aT9cP9eL8eK8\ gJ8iI8kH8mG8oG7qF7sE7uD7wC7yB7zBOz9cz8sz7pz8mz8kz8\ hz8ez8cz8`z8Yz8Wz8Tz8Qz8Oz8Nz9Mz9NzlOzlQzkRzjTziUz\ hVzhEzAKzKQzUVzc`zmezwazZ } frm:multirot-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================

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xfractint, still more
by Natalie 01 Dec '02

01 Dec '02

Hello again, Yesterday I wrote about the RDS screen that isn't in the main menu, but does pop up after Ctrl-s. It's the same for Starfield and Ant Automaton, they're not in the main menu, but pressing a/Ctrl-a takes you to the parameter screens. It seems that the (in)visibility of the zoombox depends on the colormap. The zoombox is visible with: chroma defaultw firestrm froth6 & froth616 gamma1 & gamma2 glasses1, glasses2, & glasses5 goodega grid headache landscap paintjet topo The zoombox is invisible with: altern default froth3 & froth 316 green grey lyapunov neon royal Is it possible to make the K (up) and J (down) keys in the save parameter screen act like normal character-typing keys? It is quite annoying not being able to type 'Julia'. As soon as you type Shift-j the cursor moves down. The arrow keys work ok (in all menu screens), so the K and J keys aren't needed for navigation. Thanks again Natalie -- Stolen tagline: Linux is like a wigwam, no windows, no gates, apache inside. [ Linux Counter: user 230952 machine: 111180 ]

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FOTD 01-12-02 (Not a Minibrot [5])
by Jim Muth 01 Dec '02

01 Dec '02

FOTD -- December 01, 2002 (Rating 5) Fractal visionaries and enthusiasts: Today's FOTD features the first of the odd slices of various Julibrots, a theme that will continue throughout December. The Julibrot being sliced in today's image is the best known of them all -- the figure produced by the formula Z^2+C. This Julibrot figure is the assemblage of all the Julia sets into a single four-dimensional unit. It is also the assemblage of all the perturbed Mandelbrot sets, though in this case, the slices are cut through the Julibrot in the completely perpendicular direction. The minibrots that I am so fascinated with are actually slices of holes which are like gas bubbles in a four-dimensional swiss cheese. Their appearance depends on the point at which and the direction in which the holes are sliced. When sliced in the Julia direction, these holes will appear as various julia sets, their exact appearance depending on the point at which they are sliced. When sliced in the Mandelbrot direction, they will appear as perturbed Mandelbrot sets. They will appear as perfect midgets only when the slice is taken at a critical point of the generating formula, which in the case of the formula Z^2+C is zero. The question immediately arises, if these holes can be sliced in at least two different directions, why can they not be sliced in other directions, and in fact an infinity of directions? And if other slices are possible, what might these slices look like? Today's image answers that question. The object at the center of the image, which rather resembles an artillery shell, is part of the Z^2+C Julibrot. But it is obviously not a Mandelbrot midget, nor is it a Julia set. It is a slice through a 4-D hole, another slice of which appears in the M-set as a midget in the Seahorse Valley area. The slice in today's image is taken in a direction rotated 30 degrees from the Julia orientation. In this direction, the hole appears as nothing in particular. It can be said to be only a hole in a fractal, but the pattern that appears around both the Mandelbrot midget aspect and the corresponding Julia sets is still there, though it is distorted into a blunt triangular shape. The hole itself has two sides that are perfectly straight and parallel, a thing that is never seen in J-sets or M-sets. And a glance at the <tab> screen will show that the image has been both stretched and skewed. This is a hint of very important features of the Julibrot figure, which I will discuss in future messages. After much indecision, I have named today's image "Not a Minibrot". Since it is clearly *not* a Minibrot, the name is justified. The rating of 5 for an artistically routine but mathematically interesting image is also justified. Those curious few who would like to see the undistorted Mandelbrot midget can find it in the M-set at today's real and imaginary p(3) or p(4) coordinates. With a render time of only 2 minutes, the parameter file may be the best gateway to the world of 4-D. But for convenience, Paul and Scott have posted the image to their web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Saturday here at Fractal Central featured sun, clouds, showers and wind, with a temperature of 48F 9C. In the evening the temperature started dropping like a rock, accompanied by a few flurries of snow. The cats took their outdoor time in the late morning, when it was sunny and mild. This morning is starting sunny again, but it is very cold and windy. The cats will have a less satisfying day. Since it takes little but fractals to satisfy me, my day will also be satisfying. And I shall return in 24 hours with another 4-D fractal and more talk. Until then, take care, and walk with a fractal in your pocket. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Not_a_Minibrot { ; time=0:02:05.84--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=flip/ident passes=1 center-mag=-0.00000000002510085/-0.000000\ 00183999569/1.549816e+008/0.2727/-99.5810541174990\ 504/-33.4839088781078544 params=90/60/2/0/-0.74860\ 53932854075/0.09514208701232971/-0.748605393285407\ 5/0.09514208701232971 float=y maxiter=2400 inside=0 logmap=159 symmetry=none periodicity=10 colors=000SFJSHNSKSSNWSP_SScSVhSXlS_pSbtSdxUhuWlxY\ rxZwx`rubmpdhkecfgZaiT`kSYlRWnQUpPRrOPsNNlLQeKT_IW\ THZMFaGEd9Cg3Bj8AeCAaH9XL9TP9PU8KY8Gb7Bf77g73eDVbI\ c_NjUSoQXmMXvQ_tUZrYXpaWndVmhTklSipQgtPewOdvVevaev\ hevofvvfvzfgrhTiiE`j0Sk4Tg8TcCT`GTXKUUOUQSUMWUJ_VF\ cVCgV8kV5jZ4jb3jf2ii2im1iq0ht0hx0hz0hz0cy0Zs2Um3Pg\ 5La6cZ0e`2fa5gb8hcBidEjeHkfKlhNmiQnjTokWplZqmarnds\ ogkkfdgeXcdQ_cIWbBSa4P`BQcHRfNSiTTlZUodVrjVukUnlUg\ mT`mTUnTNoSGpS9pS2qNCqJLnMMlPMiSMgUNdXNb_N`bOYdOWg\ OTjPRmPPoPOlQNjRMhRLfSLcSKaTJ_TIYUIWUGVREVOCULAUM9\ UP7TS5TV3SY1S`0Sc2Zf4di5jl4go4dr3bu9_xA`xBaxCbxDcx\ EdxFexGfxHgxIhxJixKjxLkxMlxNmxOnxPoxQpxRqxSrxTrxUr\ xVrxWrxXrxYrxZrx_rx`rxarxbrxcrxdrxerxfrxgrxhrxirxj\ rxkrxlrxmrxnrxorxprxqrxrrxsrxtrxurxvrxwrxxrxxrxxrx\ xrxxrxxrxxrxxrxxrxxrxxrxxrxxrxxrxxrxxrxxrxxrxxrxxr\ xxrxxrxxrxxrxxrxxrxxrxxrx } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 30-11-02 (Alieness [7])
by Jim Muth 01 Dec '02

01 Dec '02

FOTD -- November 30, 2002 (Rating 7) Fractal visionaries and enthusiasts: I have named today's image "Alieness". This name could imply that the image vaguely resembles a female alien, or it could imply that the image has a certain alien feeling about it. Actually, it implies none of the above. I have no idea what a female alien might look like, and all fractals have a certain alien feeling. I invented the name because I liked its sound. The parent fractal of yesterday's fly-trap image is also the parent of today's image. It is the same eastward-flying rocket ship, except that the escape radius has been increased to 100, a change that makes a larger difference in today's image than it would have made in yesterday's. Today's midget, with its deep-blue background, amber arms, and tiny points of light, is located near the tip of a filament extending from a second-order bud near the the center of the western shore line of its parent. The overall impression is more of a seasonal decorative scene than anything alien. The small but brilliant points of colored light could almost be a string of ornamental lights strung on a tree, or in this case, a fractal minibrot. The image is above the long-term FOTD average, which earns it a rating of a solid 7. The render time of 3 minutes is just fast enough to make running the attached parameter file a practical way of viewing the scene. And as always, the completed GIF image is posted on the two FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The Mandelbrot midget in today's image is the last midget that I will post until January. This is also the last time I will use the MandelbrotMix4 formula until January. The FOTD's for December will feature fractals that are neither Mandelbrots nor Julias. Instead, the December images will be oddly oriented slices through various four-dimensional Julibrots, with special emphasis on the Z^2+C figure. The discussions will feature much blather about four-dimensional space and the figures therein, a good bit of which might actually be correct. (In fact, it all might be correct.) The Friday weather here at F.C. was cloudy, breezy and cold, with a high temperature of only 38F 3C. The cats, who dislike such conditions, let their displeasure be known by displaying their least pleasant behavioral aspects. A treat of left-over turkey only partly restored their good moods. My good mood will be restored if I can get through today doing as little work as possible. Searching for fractals is play, not work, so the time I spend in 4-D Fractal Land will not count as work. And before you can count to one-million, I'll be back with the first in the December series of four-dimensional fractal images. Until then, take care, and don't get decohered. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Alieness { ; time=0:03:01.30--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-1.24085769379575800/+0.204660108303418\ 70/2.510576e+007/1/-150/-4.74181136522755509e-007 params=0.45/-1.25/0.7/1.25/0/0 float=y maxiter=800 inside=0 logmap=50 periodicity=10 colors=000z6OzEYqLfgRn__xzzzIzzEbzBVz9Nz6Et24p10g0\ 0a00Y20W90TE0QL2NK8IXDEbJBgO6nT2s_0zd0zi0zk2wlEslQ\ pnalnlipxfpznaqwNaz9Jz02z00z00z00z02z08z0Ez0Jw0Ot0\ Tz0Lz4Ez96zE0zVDskQkzbbzpazk_zgYzbYz_XxXVtRVqOTnLR\ kGQgDQd9Oa4NY1NV0JQ2GN6DIB9EE69J26N01Q00V00Y00b00f\ 00i00d00_00V00R00N10I40D809B04E00I00J00N60OB0QI0RN\ 0VR0XY0Yb0_i0bn0ds0fz0gz0iz0gz0fz0dz0bz0ax0_w0Yt0X\ q0nq2nz9nzGpzEqtDqkBs_BtO9tE8w26w06T0ON6QIDRDLT8RV\ 2_X0fY0lY0p_0qa0sb0tb0wd0xf0zg0zg1zi1zk2zl2zlIznVz\ pizqwzqx0zn0zf0zY0zQ0zG0z80z00z00z00z00z00z60zD0zJ\ 0xR0xY1wd2wf8sfDpfGlfLifQfgTbgY_gbYgfVgkRipOisLixI\ izEizDlzEpxEssEwpExkEzgEzbEz_EzVEzREzXBza8zf4zk2zp\ 0zs0zx0zz0zz0zz0zz0xz0pz0fz6YzDazIbzLfzOgzRkzXlz_p\ zbqzftzkwznzzqzztzzxpztdzsTzpIzn6zk0zi0zg0zd0zb0za\ 0zY0zX0zV0zR0zQ0zO0zL0zJ0zI1zELzDdzBxz9zz8zzLkzXfz\ QbzLgzDkzEpzGszIxzJzzLzzN } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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xfractint crash & more questions
by Natalie 01 Dec '02

01 Dec '02

Hello again I ran some old FOTD pars in x fractint, one of them - Spooky_Radicals (November 27, 2000) - caused a crash and a core dump. I removed the line ranges=..., ran the par again, no problems. The resulting image isn't half as nice as the DOS version though. RDS conversion isn't in the main menu, but the Ctrl-s keys do give access to the RDS parameter screen. The RDS image is ok, but as soon as you go back to the parameter screen and change something, the new image becomes messy. The only solution (as far as I know) is to reload the image, press Ctrl-s, try other parameter settings and if the image is not what you want, reload it again, and so on. Not really an xfractint question, but closely related: Is there any chance that OrgForm will be ported to Linux? Thanks, Natalie -- Stolen tagline: Linux is like a wigwam, no windows, no gates, apache inside. [ Linux Counter: user 230952 machine: 111180 ]

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Re: Fractint digest, Vol 1 #316 - 3 msgs
by Marcus Rezende 01 Dec '02

01 Dec '02

The visibility of the zoom box can be achieved pressing the right botton of the mouse and moving it front and backwards. The configuration of the right botton of the mouse must be the "Context Menu/Alternate Select ", thats the names for the Logitech mouse. Try it Marcus Rezende fractint-request(a)mailman.xmission.com wrote: >Send Fractint mailing list submissions to > fractint(a)mailman.xmission.com > >To subscribe or unsubscribe via the World Wide Web, visit > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >or, via email, send a message with subject or body 'help' to > fractint-request(a)mailman.xmission.com > >You can reach the person managing the list at > fractint-admin(a)mailman.xmission.com > >When replying, please edit your Subject line so it is more specific >than "Re: Contents of Fractint digest..." > > >Today's Topics: > > 1. FOTD 29-11-02 (Venus Fly-Trap [7]) (Jim Muth) > 2. xfractint (in)visible zoombox (Natalie) > 3. Re: xfractint crash & more questions (Jonathan Osuch) > >--__--__-- > >Message: 1 >To: fractint(a)mailman.xmission.com >From: Jim Muth <jamth(a)mindspring.com> >Cc: philofractal(a)lists.fractalus.com >Date: Fri, 29 Nov 2002 09:08:50 -0500 >Subject: [Fractint] FOTD 29-11-02 (Venus Fly-Trap [7]) >Reply-To: fractint(a)mailman.xmission.com > > >FOTD -- November 29, 2002 (Rating 7) > >Fractal visionaries and enthusiasts: > >The parent of today's image rather closely resembles a rocket >flying east. The rocket is a large one, requiring several >outzooms to shrink it enough so that it fits onto the screen. >Today's midget is located near the tip of the southern fin of >the rocket, in an area on the verge of fractal evaporation. > >I named the picture "Venus Fly-Trap". I gave it this name when >the eight prominent elements surrounding the midget reminded me >of the fly-catching leaves of a Venus fly-trap plant that I once >kept as a kind of floral 'pet', feeding it assorted insects >until it could eat no more. No flies are visible in today's >image, though I am certain they are there, hiding in the lush >growth of fractal mayhem. > >The iterated expression behind the image adds 0.7 parts of >Z^(1.25) to 0.45 parts of Z^(-1.25), then adds 1/C instead of C. >The escape radius has been reduced from the M-Mix4 default of >100 to 40, though I doubt that the reduction makes more than a >tiny difference in the resulting fractal. > >The rating of 7 continues my current spate of above-average FOTD >images. But I wonder how long the above-average images will >continue, considering that in two days I will begin a month-long >special of odd Julibrot slices and 4-D chatter. > >The 9-minute render time is a bit slow, but the image is worth >the time spent. And as always, the pre-rendered image file is, >or soon will be, available for download from Paul's site at: > > <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> > >and from Scott's site at: > > <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> > >With a temperature of 36F 2C, the weather Thursday here at >Fractal Central was quite chilly, but ample sun and lighter >winds gave the dynamic cats a reasonably comfortable half-hour >in the yard. In the evening a treat of left-over turkey made >them forget any discomfort they might have experienced. > >This morning I find myself with a backlog of work, so I guess >it's time to get busy. The next FOTD will appear in 24 hours. >Until then, take care, and enjoy today's fractal. > > >Jim Muth >jamth(a)mindspring.com >jimmuth(a)aol.com > > >START 20.0 PAR-FORMULA FILE================================ > >Venus_Fly-Trap { ; time=0:09:04.80--SF5 on a P200 > reset=2002 type=formula formulafile=allinone.frm > formulaname=MandelbrotMix4 function=recip passes=1 > center-mag=-0.92194009192680730/-1.760409673682221\ > 00/1.149573e+008/1/62.5/-3.4353342606152637e-006 > params=0.45/-1.25/0.7/1.25/0/-60 float=y > maxiter=1200 inside=0 logmap=77 periodicity=10 > colors=000LN_POaSPcVQeYRg`SiaTkbUjeRgfOagLVhJPiGJj\ > DCkA6k80t`5sbBsdHsfNrhTrjZrldrmikncdoYYoSRpMKpHJlG\ > IhFHeEGaDGZDFVCERBDOACK9CH9DLBDPDDTEDXGD_IDcJDgLDk\ > NDnOFjNHgMIdLK`LLYKNVJOSJaMC_H6YC0UE2OF4NG6MH7LI9K\ > JBJKCJLEIMGHNHGOJFPLEQMDROCSQCTRBRSBPSAOSAMT9KT9JT\ > 8HU8GU7EU7CV6BV69V68VAOTEbSHcVJcYMd`OdcQdePbaO`ZN_\ > WMYTLXQKVNJUJISGHRDGPAFO7EM4DL1CK3BJ5BJ7AI99HB9HD8\ > GF8GH6GH5HH4HH3HHHD`U9sVBrVCqVDpVEoVFnVHnVImVIlVJl\ > VKkVLjVNiVOgVPeVQcVRaVT_VUZVVYVWXVXWLZVMYWMYXMYYNY\ > ZNY_NY`OYaOYbOYcPYdPYePYfQYgQYhQYiRYjRYkRYlSYmSYnS\ > YoTYpTYqTYrUYsUYtUYuVYvVYwVYxZ2yY7zXCzXGzWLzWPzVUz\ > b8zaAzaBz`Dz`Ez_Gz_HzZJzZKzZLzYNzYOzXQzXRzWTzWUzVW\ > zVXzK0zL2zL3zM4zM5zM7zN8zN9zOAzOBzODzPEzPFzQGzQHzQ\ > JzRKzRLzSMzSOzSPzTQzTRzUSzUUzUVzVWzVXzCFzDGzEHzEHz\ > FIzGJzGJzHKzILzILzJMzKNzKNzLOzMPzMPzNQzORzORzPSzQT\ > zQTzRUzSVzSVzTWzIDzF9zD5z } > >frm:MandelbrotMix4 {; Jim Muth >a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), >g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, >k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): >z=k*((a*(z^b))+(d*(z^f)))+c, >|z| < l } > >END 20.0 PAR-FORMULA FILE================================== > > > >--__--__-- > >Message: 2 >From: Natalie <nat(a)latinae.demon.nl> >To: fractint(a)mailman.xmission.com >Subject: [fractint] xfractint (in)visible zoombox >Date: Sat, 30 Nov 2002 01:15:26 +0100 >Reply-To: fractint(a)mailman.xmission.com > > >Hello again, > >After I discovered that the visibility of the zoombox depended on the >colormap used, I tried to find similarities in the maps. I didn't find any. >Then I played around with the default (DOS) map. I changed the color values >in the final triplets (all 0 0 0) and after some trial and error I got a >visible zoombox. The final triplet is now changed to 64 64 64. The trick >didn't work with other maps, and I really don't know why it works for the >default map, but it'll do until the next patch. > > >Natalie >

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