March 2005 - Fractint - mailman.xmission.com

FOTD 06-03-05 (Transfer [4])
by Jim Muth 06 Mar '05

06 Mar '05

FOTD -- March 06, 2005 (Rating 4) Fractal visionaries and enthusiasts: Today's image is a sideways view of the valley leading to the period-6 bud on the northeast shoreline of the Mandelbrot set. The orientation of the slice is rotated 75 degrees from the Oblate direction toward the Rectangular direction. A different formula, the multirot-XZ-YW-new formula, was needed to actually calculate a slice of the Julibrot in this particular direction. I gave the image the un-exceptional name "Transfer". The name was inspired by a feeling of energy flowing from top to bottom of the frame, which I felt when I first saw the image. The rather disappointing rating of a 4 was all I could do for the picture. I really did not give the colors the effort they need for a higher rating. Most likely, I lost interest when I saw no great potential in the image. The render time of 1/2 hour on my 8-year-old machine is decidedly slow for such a mediocre fractal. But the download from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> will be noticeably faster. The threatening snow failed to arrive on Saturday. Instead, we saw sunny skies and a high temperature of 41F 5C. The cats enjoyed over two hours lurking in the holly patch, and needed no special treat to keep them happy. Today looks to be a repeat. For me it looks like an average day -- that is unless I find a truly spectacular fractal, which would make the day special. The next FOTD will appear in 24 hours. Until then, take care, and the next fractal will (hopefully) be better. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Transfer { ; time=0:29:31.67--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new center-mag=-0.55744\ 397337778850/-0.00365254194306321/134.1987/0.0193 params=90/75/2/0/0/0/0.375205/0.2201383 float=y maxiter=15000 inside=bof61 logmap=37 periodicity=10 colors=000MeqOecSeaUeXXeTZePbeMeeHgeDieAnn6nw4nz0n\ z0nz0nz0nz0nz0nz0nz0nz4kzAbqHUhMMYTEOX0Me0Ml0Mq0Qq\ 0Tq0Yq0_q0cq0eq0jq0lq0qq0sq0wq0zq0zq0zq0zq0zq0zq1z\ q1zq5zqAzqEzqHzqMzqQwqUsqXqqizcezebze`zeZzeXzeUzhS\ zhQzhOzhMzhJzjHzjEzjAzj7zj5wj3ul1ul0sl0ql0nl0ln0jn\ 0hn0en0cn0cn0eq0eq0eq0eq0eq0eq0hq0hq0hq0hq0hq0hq0h\ q0jq0jq0jq0jq0jq0jq0jq0lq0lq0lq0lq0lq0lq0lq0sq5zqJ\ zqUzqezqnzqnzqnzqnzqnzqnzqnzqnzqnzqnzqnzqnznnzlnzj\ izhgzeezcbwc`uaZs_XqXUnVSlTQjROhRQfTQeTSeTScVUcVUc\ VXcXXaXZaXZa_`__`__b_ab_aeYaeYagYcgYciVciVekVekTen\ ThnThnThnQjnQjnQgnQdmKakAZi4Wg0Te0Rc0Pa0N_0LY0JW0H\ U0FS0DQ0BO09M07K05I03G21E60C80AF08N06S14Y42c60f60a\ 80YA0SA0PD0MF0HF0HH0FK0FK0FM0DP0DP0DR0AT0AT08V08X0\ 8X06_06a06a0A_0H_0M_0Q_0V_0_X0_X1_X3_X5_X5_X7_VA_V\ A_VC_VE_VE_VC_RA_PA_K7_H5_F5_A3_83_41_10_00_00_00_\ 00_00_00_00_00_00_0H_qJ_l } 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 PARAMETER FILE=========================================

1 0

FOTD 05-03-05 (Oblate Miniature [6])
by Jim Muth 05 Mar '05

05 Mar '05

FOTD -- March 05, 2005 (Rating 6) Fractal visionaries and enthusiasts: The Mandelbrot set is filled with miniature versions of itself. All these miniature M-sets are of the same basic shape, though some are distorted to a certain degree. It is the different surroundings of the miniatures that create most of the interest. The Julia sets of the miniature Mandelbrot sets are filled with miniature Julia sets, but these Julia sets, as well as their surroundings are all alike, so there is no great reason to explore them. But then there are what I call Oblate miniatures. The word miniatures is not quite correct, for, unlike Mandelbrot and Julia miniatures, the holes that appear in the Oblate slices of the Julibrot bear little resemblance to the shape of their parent fractals, and in fact often are unpredictable and unexpected. Today's image shows an Oblate miniature associated with a point near where the negative stem of the M-set joins the main body of the set itself. (This explains the name "Oblate Miniature".) Oblate miniatures can be of almost any shape except the familiar Mandelbrot shape. They frequently have perfectly straight edges, something that is never seen in either Mandelbrot or Julia miniatures. At other times, as in today's image, they resemble miniature Julia sets. When they do resemble Julia miniatures, these miniatures are not all alike. They will vary throughout the parent fractal. Finding Oblate miniatures is made more challenging by the fact that the parent fractals are sometimes stretched to a large degree, and must be unstretched and sometimes skewed before any sense can be made of the scene. Today's image needed only a small amount of stretching, though considerable skewing was required to bring it to an undistorted shape. The object it pictures is more like a 'Siegel Disk' Julia miniature than anything else. It has no open center, though the stuff filling the center is of extremely high iteration, and slows the calculation to nearly an hour. The rating of a 6 includes the mathematical interest. The artistic rating is closer to a 5. The slow rendering may be avoided by downloading the finished image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Friday was a little warmer here at Fractal Central, but 39F 4C is still not balmy, and the fractal cats demand balmy, so extra tuna was needed to keep the complaints at a minimum. Today is starting with some sun, but I see possible snow mentioned for later today. It looks like another questionable day for the duo. In my department the situation appears settled. The commercial work is about caught up and the fractals are coming along on schedule. The next FOTD will appear in 24 hours. Until then, take care, and look to the light. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Oblate_Miniature { ; time=0:54:21.47--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip passes=1 center-mag=+0.00001661999961360/+0.000003\ 43572018929/1.324138e+010/1.1184/-22.9825910406299\ 059/5.63619786054203864 params=0/90/2/0/1.401863/0\ /-1.401863/0 float=y maxiter=250000 inside=255 logmap=332 symmetry=none periodicity=10 colors=000ptzpszprzpqzppzpozpnzpmzplzpkypjypiwphwp\ gupfupetpdtrcrrbrtapt`pu_nuZmwYkwXhyWfyVdzUbzTZzSY\ zRWzQUzPQzOOzNMzMKzLHzKFzJDzIBzHDzGFzFHwEIuDKrCMpD\ OmHQkMShQUfUWbZYZbZYh`UkbSpdOtfMyhIziHzkDzmBzm9zi9\ zh9zf9zd9zb9z`9zZ9zW9yU9wS9uQ9tO9rM9pK9nI9mF9kD9iB\ Bh9Df7Fd5Hb3I`7KZ0MY0OW0QU0SS0UQ0WO0YM0ZK0YI0WI0SM\ 0QQ0MU0KU0IU0HQ0FM0DI7BHF9DK79S55Y33d00i00p00u00y0\ 0z00z00y00w07u0Bt0Fr0Ip0Mn0Km0Ik0Ii0Hh0Ff0Fd0Db0D`\ 3BZ39Y59W57U55S75Q73O93M90KB0KB0MD0MD0MF0OF0OF0OI0\ UK5YO9`QFfSIiWOmYSr`Yub`ydfzhizinznyzkrzhkzdfz`ZzY\ SzUMzQFzO5zM9zKBzIDzHFzFHzDIzBKz9Oz7Qz5Sz3Uz0Wz0Yz\ 0Zz0bz0dz0fz0hz0iz0kz0mz0mz0nz0pz0pz0rz0rz0tz0tz3u\ z5uz7wzBwzDyzHyzIzzKzyOzwQzuUzuWztYzr`zpbzndznbzm`\ zkZyiYuhWtfUpdSnbQk`Qi`OfZMbYK`WIYUHWSFSQDQOBMMBKM\ FMOIOQMQQQQSSSSWUUZUUbWWdYWhYYkZYn`Zr``tb`wdbzdbzf\ dzhdzhfzifzkhzkhzkhzkhzkh } 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 PARAMETER FILE=========================================

1 0

Re: FOTD -- March 03, 2005 (Rating 5)
by Vortex Swirling 05 Mar '05

05 Mar '05

No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.0.308 / Virus Database: 266.6.0 - Release Date: 3/2/2005

2 1

Re: FOTD -- March 03, 2005 (Rating 5)
by Vortex Swirling 04 Mar '05

04 Mar '05

I wasn't getting anything like that. Did you mean to change the p4 parameter? Anyway, now I see what you mean I no longer need to struggle. Messing around with the parameters I was getting all sorts of odd ball shapes like rectangles and such. Just pure blocks of color, nothing else. Intersting in and of itself. -- No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.0.308 / Virus Database: 266.6.0 - Release Date: 3/2/2005 -- No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.0.308 / Virus Database: 266.6.0 - Release Date: 3/2/2005

1 0

Re: FOTD -- March 03, 2005 (Rating 5)
by Jim Muth 04 Mar '05

04 Mar '05

At 11:15 AM 3/4/05 -0500, Vortex S. wrote: >I'm getting a big oval. I have no idea what might be wrong. But the path to the Julia set that I described is a convoluted one. The easiest and by far the fastest way is to calculate the Julia set directly from the 'Julia' formula and apply the 'believe' color map. I have already done this and included the parameter file. START PARAMETER FILE============================= Believe_Julia_set { ; time=0:02:23.03--SF5 on a P200 reset=2004 type=julia passes=1 center-mag=0/0/0.8503401 params=-0.7499/0.01360067933 float=y maxiter=500000 bailout=9 inside=0 symmetry=origin periodicity=10 sound=off colors=000PLAPM8PN7PO6PP5OQ5OR4OS3NT0OU3OV5PW7PYAP\ _CQaEQcGQfJRhLRjNRlQSnSSpUUqUTrVSrWRrWRqXQpXPoYOoZ\ OoZNp_Mp_Mq`LqaKqaJrbJrbIrcHsdHsdGteFteEtfEugDugCu\ hCvhBviAwj9wj9wk8xk7xl7xl9wmAvmBunCtnDtnEsoGroHqpI\ qpJppKoqLnqMnqOmrPlrQksRjsSjsTitVhtWguXguYfuZev_dv\ acx`dv`du`et`er`fq`fp`go`gm`hl`hkbhieihcwVcwAbjdbk\ cakbbla`l_`lZ_mY_mW_nV_nU_oT_oR_pQ_pP_qO_qM`qL`rKa\ rIasHbsGbtFctDcuCduBduAct9ct9bt9bs9bs8as8ar8ar8`r8\ `r7`q7_q7_q7_p7Zp6Zp6Yp6Yo6Yo6Xo5Xn5Xn5Wn5Wn5Xm4Ym\ 4_m4_l4`l3al3bk3ck3ck3ck2cj2cj2cj2ci2ci1ci1ci1ch1c\ h1ch0cg0cg0cg0cg0be3bd5ac8abA`aC__FYZHWYJUXMSWOQUQ\ OTTMSVKRXJU_JWbJYeJ_jJanIcsJcsKctLcsMcsNcsOcrPcrQc\ pRcpScoTcnTcmUcmVckWZkXUiYPhZOg_Pe`PdaPbbQbcQbcQad\ QaeRafR`gR`hS_iS_jS_kSZlTZmTYnTYnT_oUapUcqUerUgsUi\ tUkuUmvUowTqwTswTuwTwwTxwTywQzvNzvKzuGzuDztAzt7zs4\ zu0zt1zs1zr1zq1zp1zo1zo2z } END PARAMETER FILE============================= >How do you set the symmetry inside fractint (without >altering the par)? Bring up the command line by striking the 'g' key, and enter the command 'symmetry=origin' >Is setting the Logmap to 0 the same as setting the Log >Palette to 0? Yes. Jim M.

1 0

Fractint Midi Files
by Harry Bissell Jr 04 Mar '05

04 Mar '05

Someone had a utility to output Fractint sound files as MIDI data at one time ? Does anyone have any information about this ??? TIA H^) harry

1 0

FOTD 04-03-05 (Point of Contact [4])
by Jim Muth 04 Mar '05

04 Mar '05

FOTD -- March 04, 2005 (Rating 4) Fractal visionaries and enthusiasts: Today's image is something entirely different. It is a slice, cut in a different direction, of the same abstract four- dimensional figure that gives us the well-known Mandelbrot set and the infinite variety of Julia sets. But it resembles neither the Mandelbrot set nor a Julia set. The orientation of the slice is very near but not exactly the Oblate direction. It has in fact been rotated 0.008 degree of arc toward the Julia direction. When one is exploring the Julibrot, a tiny rotation can sometimes make a big difference. If the 0.008 value of real(p1) is changed as much as one degree, the entire image will collapse into a mere horizontal line. The location of the center of the slice is near the tip of the negative stem of the M-set, but removed 1.3 units from the tip, along the real(z) axis. The image, which has been stretched horizontally by a factor of almost 1300, features both a hyperbola and a point of contact. Since I have many hyperbolae in my fractal collection, I named the image "Point of Contact". For some reason, the idea of today's image seems to exceed the quality of the image itself, and I could give it a rating of only a 4. But there can be no disappointment, for the render time is so fast that the image will be finished before disappointment can set in. Rendering may be dispensed with entirely by downloading the already-rendered image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With a temperature that never rose above freezing and brisk winds from the north, Thursday was an indoor day for the fractal cats, who took their pleasure watching birds from the comfort of their window shelf. The usual treat of tuna kept them happy. Today is starting sunny and quite cold, but the wind has died and it is due to turn warmer this afternoon. The fractal cats should be more tolerant of these conditions. It looks like an average day coming up for me, which means do what needs to be done, then move on to fractal land. The next glorious fractal will appear in 24 hours. Until then, take care, and don't get scammed. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Point_of_Contact { ; time=0:00:20.76--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip center-mag=-1.29966327214381100/+0.000037418181458\ 39/11605/1281.9 params=0.008/90/2/0/0/0/-2/0 passes=1 float=y maxiter=95 inside=0 outside=tdis logmap=28 periodicity=10 colors=000D00E00F00G00H00I00J00K00L00M00N00O00P00Q\ 40R20S10T4FU6FV8HWAIXCJYEKZGK_IK`LIaNHcPGdRKfTPfWU\ hZZhccghhfmmerrdwwczzhzzmzzmzzrzwwzrzzmzzhzzczzczz\ czzczzczzczzczzczzczzczzczzczzczzczzc000000000000J\ aXLcVNdTPeQRfOThMViJXjHZkFXlHVmITnJRoKPoLNpMMqOKrP\ IrQGsREtSCuTBuUFnZIgbM`gPUkTNpWGtVJrUMqTOpTRoSTnRW\ mQZlQ`kPcjOeiNhhNkgMmfLpeLrdKtjKvoJxtJyyLzuNzrOzoQ\ zkSzhTzeVzbXzZYzW_zTazQbzMdzJfzGgzD2Bj5Ei7Gh9IgCLg\ ENfGPeJSeLUdNWcQZcS`bUbaWda__YbVUeRQhMNkIJnDFq9Cp8\ Bp8Ao89o78o77n76n75n64m63m62m62aGgeKiiNjlQkpTmtWnw\ Zou_ns_nr`np`nn`nmankanjanhbnfbnecnccnacn`dnZdnYdn\ Zcm_bl`ak`aja`ib_hcZgcZfdYeeXdeXcbYa`Z_YZZW_XT_WR`\ UOaSMaRJbPHbOOWMUPK`JJfCHl6Gl9IlCKlFMlIOlLPlORlRTl\ UVlXXlZYfaQacJWeCRg5QcMQ_aQWqPVmOViNUeMUaLTYKTTJSP\ ISLHRHGRDFQ9EQ5DQ1FR3N9UN8XO7`O7cO6gO5jO5mP7lQ8lRA\ kSBkTDjUEjUGjVHiWJiXKhYMh } 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 PARAMETER FILE=========================================

1 0

FOTD 24-02-05 (Close but no Cigar [8])
by Vortex Swirling 04 Mar '05

04 Mar '05

Done. It was taking a while to do the central spiral area. As soon as I learned to resume the fractal from the partial gif I was able to get it to go to completion. The final time (using the Tab screen) it says it took a total of 1:35 (h:m) to do it. But I wasn't paying attention, if that was the total time or the time from where I resumed. This was on a P4 2.53 under XP. -- No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.0.308 / Virus Database: 266.6.0 - Release Date: 3/2/2005 -- No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.0.308 / Virus Database: 266.6.0 - Release Date: 3/2/2005

1 0

Re: FOTD 27-02-05 (Tessellation-II [10+])
by Vortex Swirling 04 Mar '05

04 Mar '05

I generated the two fractals to compare them to see exactly why I liked the first one. I didn't want it to be simply because I saw that one first. I liked the part of the first one because of the rainbow colors in the lower half. But if I rotate the color pallete on the second one I can come up with some very pleasing variations on that one too. I finally decided its because, on the first one, the top part looks like trees. There must be something pleasing about tree like fractals, they get the higher ratings and higher numbers of url hits. In one explanation of StarTrek I read it was explained that the drive was able to create extremely high levels of magnetism. Like on the surface of an ethernet cable, space is warped a bit, in ST they were able to warp space big time around those two funny things that look like rockets. Gene Roddenbery originally made those look like chemical rockets. I saw him back in 1976 at an ST convention and he admitted that originally they didn't even try to explain how it was done and made them look like something believable for the time. Anyway, the idea (that they seem to have applied as a patch) is that since space is infinitely malleable, and that they had enough energy (cough... cough...) to warp a bubble of space around the Entreprise, that bubble could move FTL because space is allowed to do that. But what would make it move? Well, thats part of the function of the two funny things (ok, now they call them "nacelles"). Part of them is built with material that doesn't warp along with space so they can ride on the "wake" that is produced between normal space and the warp space bubble. Got that? I like the method they came up with in Gateway, by Frederik Pohl. In that story they discover a stash of space ships in a cave beneath the surface of Venus but they don't know how they work. They do know that when they turn them on they go away at FTL speed. Some of the return, others don't. You get to ride one based on a lottery system. But I don't want to ruin the story for all you that haven't read it. Shall I tell you how they worked when they found out? Its a rather interesting idea, not possible, at present, but an interesting concept. -- No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.0.308 / Virus Database: 266.6.0 - Release Date: 3/2/2005 -- No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.0.308 / Virus Database: 266.6.0 - Release Date: 3/2/2005

1 0

FOTD 03-03-05 (Believe It Or Not [5])
by Jim Muth 03 Mar '05

03 Mar '05

FOTD -- March 03, 2005 (Rating 5) Fractal visionaries and enthusiasts: The next paragraph has nothing to do with fractals. The really interesting stuff starts in the third paragraph. My day started with a bang when I checked my e-mailbox and found that I had won three lotteries which I had never entered, and that there were four floating bank accounts totalling over 50- million dollars that people wanted to transfer into my pathetic account. There was also a letter from a large well-known national bank, with which I have no account, informing me that their computer had crashed and they needed me to re-enter my account information. (Don't they keep a data backup?) I also saw that ebay has scrambled my account information, and Earth- link has lost my credit-card information etc. etc. etc. With so many 'phishing' scams out there, it is hard to believe that anyone would fall for such obvious deception. But I suppose public stupidity knows no bounds. In my wonder years, when I was just discovering the world and was hugely fascinated with science, I never missed the daily 'Believe It Or Not' cartoon. (For a while, I took the odd facts that appeared in the cartoon as absolute truth, but I gradually came to realize that the claims were intended more as entertain- ment than as proven facts, and some claims were quite a bit exaggerated.) I named today's image "Believe It Or Not" because it is difficult to believe that the delicate, wispy arches and solid horizontal beams are a part of the very familiar Seahorse Valley, yet it is a fact, and in today's case, most definitely a true unexaggerated one. What happened to the valley is that I have sliced it in an unfam- iliar direction -- the Oblate direction. In the image we are seeing the valley as it appears when the three-dimensional (real(c),imag(c),real(z)) slice of the four-dimensional Julibrot is rotated 90 degrees around the Y-axis, with the eastern edge of Seahorse Valley acting as the axis of rotation, and the resulting image is stretched 400,000 times in the vertical direction. The horizontal breaks in the purplish background are actually the Mandelbrot buds on the eastern shoreline of Seahorse Valley, which have been stretched horizontally to infinity. The greenish foreground elements are lower iteration features whose points have escaped before they had a chance to settle into the familiar Mandelbrot shapes. The Mandelbrot view of the scene can be viewed by going to the 'z' screen and changing the imag(p1) parameter to zero, and then going directly to the 'F6' screen and changing the X-magnifica- tion factor to 1. The symmetry must then be reset to 'none'. Since the resulting image will be very slow, it is best to render it in a thumbnail size. The Julia view of the scene can be viewed by going to the 'z' screen and changing the real(p1) parameter to 90 and the imag(p4) parameter to 0.01360067933, then, on the 'F6' screen, changing the X-magnification factor to 1 and the magnitude to 0.85. The symmetry should be set to 'origin' and the logmap should be reset to zero for fastest and best results. The Julia set is actually quite striking. I was undecided on the proper (IMO) rating for today's image, and finally settled on a rating of 5, which is average in every respect of the word. The bad part of all this is that, even with Y-axis symmetry, the image takes 3-1/2 hours to render. But salvation is at hand on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The image has been sent ahead and should already be posted. Cold winds, snow-covered ground, and a freezing temperature kept the dynamic duo indoors on Wednesday. They took their confinement bravely however, and I rewarded them with an extra big serving of tuna. Today is starting cold and windy again, only slightly less harsh than yesterday. Can the duo be brave two days in a row? For me, the commercial work is minimal, which means lots of time for fractals, and maybe some philosophy. Regardless of what happens, the next FOTD will appear in 24 hours. Until then, take care, and what will we do when we eventually run out of fractals? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Believe_It_Or_Not { ; time=3:29:45.98--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip passes=1 center-mag=0/+0.01360067933683444/551139.\ 1/4.153e-005 params=0/90/2/0/0/0/-0.7499/0 float=y maxiter=500000 inside=0 logmap=1489 periodicity=10 colors=000cuAPZ8PY7PW6PU5OS5OQ4OO3NK0ON3OP5PR7PTAP\ VCQXEQZGQaJRcLReNRgQSiSSkUUlUTmVSmWRnWRnXQnXPoYOoZ\ OoZNp_Mp_Mq`LqaKqaJrbJrbIrcHsdHsdGteFteEtfEugDugCu\ hCvhBviAwj9wj9wk8xk7xl7xl9wmAvmBunCtnDtnEsoGroHqpI\ qpJppKoqLnqMnqOmrPlrQksRjsSjsTitVhtWguXguYfuZev_dv\ acx`dv`du`et`er`fq`fp`go`gm`hl`hkbhieihcwVcwAbjdbk\ cakbbla`l_`lZ_mY_mW_nV_nU_oT_oR_pQ_pP_qO_qM`qL`rKa\ rIasHbsGbtFctDcuCduBduAct9ct9bt9bs9bs8as8ar8ar8`r8\ `r7`q7_q7_q7_p7Zp6Zp6Yp6Yo6Yo6Xo5Xn5Xn5Wn5Wn5Xm4Ym\ 4_m4_l4`l3al3bk3ck3ck3ck2cj2cj2cj2ci2ci1ci1ci1ch1c\ h1ch0cg0cg0cg0cg0be3bd5ac8abA`aC__FYZHWYJUXMSWOQUQ\ OTTMSVKRXJU_JWbJYeJ_jJanIcsJcsKctLcsMcsNcsOcrPcrQc\ pRcpScoTcnTcmUcmVckWZkXUiYPhZOg_Pe`PdaPbbQbcQbcQad\ QaeRafR`gR`hS_iS_jS_kSZlTZmTYnTYnTYoUXpUXqUXrVWsVW\ tVVuVVvWzwWzxWzybzxZzxWzwTzwQzvNzvKzuGzuDztAzt7zs4\ zu0zt1zs1zr1zq1zp1zo1zo2z symmetry=yaxis } 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 PARAMETER FILE=========================================

1 0