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FOTD 23-10-10 (Star of the Spike [8])
by Jim Muth 22 Oct '10

22 Oct '10

FOTD -- October 23, 2010 (Rating 8) Fractal visionaries and enthusiasts: The 2-second calculation time of today's image is no mistake. The image is a scene in the best-known fractal of all -- the Mandelbrot set. And on my particular fractal dedicated machine, the Mandelbrot set runs at faster-than-light speed. I originally planned on naming the image "Not Quite Dead Yet" to indicate that the M-set is no tired warhorse on its last lap around the track. It is chock full of interesting and lively scenes, not only of minibrots, but of countless other undiscov- ered wonders. But then I decided that such a name was much too downbeat for such an upbeat image. I finally decided on the name "Star of the Spike", which has a far more positive sound and also indicates the location in the M-set. The image rates an 8. I'm not sure how much of that rating is due to my coloring, but I did work on the colors for well over an hour. The scene lies on a filament extending from the Seahorse Valley of a minibrot located on the main spike of the M-set, not far west of the main body of the set. As I said earlier, the calculation time is an incredibly brief 2 seconds. But there is still the hassle of copying this letter into your parameter file in text mode with a .par extension, hoping that no spurious characters get inserted, then running it as you would any other parameter file. This minor inconvenience may be avoided by going to the FOTD web site at: <http://www.Nahee.com/FOTD/> and viewing the finished image there. A mixture of clouds and sun, a brisk wind from the northwest and a temperature around 52F 12C gave Friday a very autumnal feeling here at Fractal Central. The fractal cats enjoyed the sun when it was shining and the house heat when the clouds prevailed. My day was slow enough to put the extra coloring work on the FOTD. FL had a slightly more active day. I think a trip back to Old Fractal Central, 130 miles (200km) south of here, is coming up on Saturday, so do not be surprised if the FOTD for October 24 is late. Until whenever, take care, and wouldn't it be great if humans had designed the laws of the natural world instead of the great unknown? (But could we have done it with- out fighting?) Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Star_of_the_Spike { ; time=0:00:02.11-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.40473711526\ 07/+0.0001010790714/8e+008/1/180 params=0/0 float=y maxiter=5200 inside=0 logmap=538 periodicity=6 colors=0000AL0AM0AN0AO0AP0AQ0AR0AS0AT0AU0AV0AW0AX0\ AY0AZ0A_0A`0Aa0Ab09c08d07e06f07g08h09i0Aj0Bk0Bl0Cm\ 0Dn0Eo0Fp0Gq0Gr0Hs1It2Ju3Kv4Iy5Kv5Ms6Nq6Pn7Ql7Si8T\ g8Vd9Wb9Y_AZYA`VBaTBcQBdOEcQHcSJbUMbVPbXRaZUa`WaaX\ bbXbcXbcXbdXbdYbeYbeYbfYbfYcgZcgZchZchZciZcgZcd_ca\ ZdZYeWXfTWgQVhNUiKUjHUkEUlCUm9Uo6Uq3Us1Ut2Ut3Yt4bu\ 5fu6ju7ov8tv9zz8zvAztBwrCwpDwnEvlGvjHvgIveJvcKvaLu\ _NuYOuWPuTQuRRtPTtNUtLVtJWtHXyA`tFYoJWkOUfSSaXQY`O\ TeMOiKKmILlKLlMMkOMkPYkA_hB`eBbbBc_CeXCfUEgPIhKMiF\ QjAUk6Yk1an9epHhsOluWoxcszevzUWm85cKX1Vx4_t7dq9grC\ ivEmzDrzDqzDovDcmCbaCSVCHRCANJNMQWBkd0zc0qlFejEbiD\ XgDVfCUeCVaAWY9XV7YR6ZN4ZK3T_COoLRkITgGVcEX`C_X9aT\ 7cP5eM3cOCaQK_SSZU_XWgVYoU_wbbskdotfkqkXnpIku4ovOR\ wP2xQ5tI8qAAn3CoBEpIGpPIqXPmTSlNVkGfzzczzazzZzzXzz\ UzzSzzPzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } END PARAMETER FILE=========================================

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<David> 4 variables define a 4D space
by Hal Lane 21 Oct '10

21 Oct '10

David, Jim Muth said, "...the formula Z^2+C consists of two complex numbers which have four variables in all. Four variables define a space of four dimensions." Here's as much of one four-dimension fractal as can be seen. I've projected the 4D fractal object to 3D, then put a string of these 3D projections together into a pseudo-4D .gif animation. A different 3D portion of the 4 dimensional fractal object is shown in each frame in the animation: http://home.earthlink.net/~hallane/hals_fractals_n_photos/ - Hal Lane ######################### # hallane(a)earthlink.net # #########################

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FOTD 22-10-10 (Unknown Landscape [6])
by Jim Muth 21 Oct '10

21 Oct '10

FOTD -- October 22, 2010 (Rating 6) Fractal visionaries and enthusiasts: Today's image takes us back to the 'Patterns in the Mist' image of October 20 -- two days ago. In that discussion I commented that the image had minibrots, but they were not very interest- ing. Since then, I have done further exploring and found that the minibrots are more interesting than I had assumed. I decided that today's image, which shows a minibrot that was hidden in the earlier image, is worth being declared FOTD for October 22. The color palette is basically the same as the one in the earlier image, with only a bit of tweaking to emphasize the hidden patterns. Now, instead of two levels, we have three levels of near-random chaos. The strongly colored highlights are seen to be gathered near the minibrot, with the outlying, more vague features sugges- ting elements of the actual Seahorse Valley location. The rating of a 6 is all I could give today's image, which after all is basically a repeat of the earlier image. The name "Unknown Landscape" is perhaps a bit overdone. The scene does lie in the Seahorse Valley of its parent, so how surprising can it be that the vague patterns resemble the very familiar elements in Seahorse Valley? The calculation time of 3-1/2 minutes is brief enough to make running the included parameter file worth the small effort. The small hassle of setting up and running the parameter file may be avoided by viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> A brisk west wind, showers of leaves, a mixture of sun and clouds, and a temperature of 59F 15C made Thursday a typical mid- autumn day here at Fractal Central in central Pennsylvania. The fractal cats were fascinated by the falling leaves, and spent several hours in their window, trying to decide what was happen- ing outside. My day was normal; FL's was the same. The next FOTD will be posted in 24 hours. Until then, take care, and if everything is an illusion in the mind, as some mystics claim, in what then is the mind only an illusion? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Unknown_Landscape { ; time=0:03:33.36-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-0.74125203921/+0.04311355888/633984/1\ /37.5/0 params=-3/10/0/0 float=y maxiter=7500 inside=0 logmap=207 periodicity=6 colors=000HHHmcUUcmcmAmrnwKpmsomsnmsmmrkmqimpgmoem\ ncmmbmc`mcZmcXmcVmcUmcSmcQmcOmUMmUKmUJmUHmUFmUDmUD\ mUAmUAmUAmUAmUAmUAmUAmUAmUAfUAgUAhUAiUAjUAjUAkUAlU\ AmUAnUBoUBpUCqUDqUDmUEjUEgUEdUE`UEYUEVUESUERUDRUDR\ UCH02H52H61G61G71G70L70L80L80K90K90K90KA0KA0K00OB0\ OB0OC0OC0OD0OD0OD0PE0PF0QF0QG0QG0RH0RI0RI1SJ2SJ2TK\ 3TL4TL5UM5UM6UN7VO7VO8VP9WP9WQAXRBXRCXSCYSDYTEYUEZ\ UFZVGZVGYUHXTIXTJWSKWSLVRLUQMUQNTPOTPPSOQSOQRNRQMS\ QMTPLUPLVOKVNJWNJXMIYMIZLH_LH_JFZIEZHDZFCZEAYD9YB8\ YA7Y95X74X63X52X61W71W81V91V91VA1UB1UC1UD1TD1TE1TF\ 1SG1SG1SH1RI1RJ1QK1QK1QL1PM1PN1PO1OO1OP1OQ1NR1NR1N\ Q3OQ4OQ5OQ6OP7OP8OP9OPAOOBOOCOOEPOFPNGPNHPNIPNJPMK\ PMLPMMPMNPLOPLQQLRQLSQKTQKUQKVQK0QJ0QJ0QJ0QJ0QS0bT\ 0bT0cT0dU0dU0eV0eV0fV0fW0gW0gW0hX0hX0iX0jY0jY0kZ0k\ Z0lZ0l_0m_0m_0n`0n`0oa0p`0o`0o`0o`0o`0n_0n_0n_0nO0\ 8Q0AR0DS0FT0IU0KW0NX0QY0S } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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FOTD 21-10-10 (Man-O-Peace Fractal [5])
by Jim Muth 21 Oct '10

21 Oct '10

FOTD -- October 21, 2010 (Rating 5) Fractal visionaries and enthusiasts: Yes, today's image is late, but here it is in its full glory, better late than never. The image is a scene in the default manowar Mandeloid. I named it "Man-O-Peace Fractal" because I disapprove of violence. With not much going for it, I could give the image a rating of no more than a 5, which indicates an everyday average fractal. The calculation time of 1-1/3 minutes is brief enough to assure that little time will have been wasted if the image lays a rotten egg. The best way to avoid an unwanted omelet is to view the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> After a foggy start, Wednesday turned rather pleasant here at Fractal Central, leading to an afternoon with ample sunshine and a temperature of 63F 17C. The fractal cats, Nicholas and Cassie, spent the afternoon on their shelf in the southwest window, basking in the strong sunlight streaming in. My day was unexpectedly busy, which also explains the lateness of today's FOTD. The next FOTD will be posted in 24 hours, more or less. Until then, take care, and don't get lost in the Z^2+C Julibrot. If you do, you'll never find your way out. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Man-O-PeaceFractal { ; time=0:01:20.14-SF5 on P4-2000 reset=2004 type=manowar center-mag=-0.1384789735/0\ /92456/1/90/0 params=0/0 float=y maxiter=1250 inside=255 logmap=810 colors=000G0OH0PI0QJ0RK0SL0TM0UN0VO0WP0XQ0YR0ZS0_T\ 0`U0aU0bU2cU4dU6eU8fUAgUChUEiUGjUIkUKlTMmSOnRQoQSp\ PUqNWrLYsJ_sK`rLaqMbqNcpOdoPeoQfnRgnShmTilUjlVjkWi\ jWfiVcgU_eTWcSSaQO_OMYMKWKIUIGSGEQFCOEAMC8KB6KA4K9\ 2K82K72K62K52K42K32K66K8AKAEKDIKFMKHQKKUMMYOO`PQbQ\ RcRTdRVeSYfS_gTbhTdiUgjUikVklVijWghXffXdeYbcZaaZ__\ _YZ`YX`XVaWTbWSbYTO_T9`WDaYHb_LbbPcdTdfXdh_biXajV`\ kT_lQYlOXmMWnJVoHUoFRiHPdJN_LKVMIQOGKQDFRBAT95V70W\ A1XD2XG3XJ4XM4XP5YS6YU7YX8Y_8Yb9ZeAZhBZkCZmCZlFXlH\ VlJUkLSkNRkPPjROjTMjVLiXJiZIi`GibFgWGfPGeIGdBGc4GR\ A8FF1X8Mm2en6anAYnDVnHRnLNnOKnPJnQInRInSHnTHnUGnVG\ nWFnXFnYEnZElWNkTWjQdiNmhKueJsbIr`HpYHoWGmTFlQEkOE\ iLDhJCfGBeEBdDEfDGgCJiCLjCOlBQmBToBVpAYrA_sAbu9dv9\ gx9iyMMMKKKIIIHHHFFFUfOPfSKfWFfZAfb5ff0fi3df5cd8bb\ A``C_ZFZXHXVKWSMVQOTORSMTRKWPIYOG`LD_NE_OF_PF_QG_S\ GZTHZUIZVIZXJZYJZZKY_LYaL } END PARAMETER FILE=========================================

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Fmod Minibrot
by Roger Alexander 21 Oct '10

21 Oct '10

Minibrots-if the iteration loop has x^2 + c its got a minibrot! Another pre-calculated nomadic mandelbug at http://maxitersfractalfollies.blogspot.com. Fmod Minibrot { ; fract481.gif ; blank ; calctime 0:17:12.49 ; created Oct 20, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=kerrym.frm formulaname=hermanm_man-cart passes=1 center-mag=+1.10021739445293500/+0.02785688062135686/341530.1/1/-167.500\ 000001965589/7.71297616053434609e-010 params=4/3/1/0/2/0 float=y maxiter=1500 inside=0 proximity=2 outside=fmod logmap=14 colors=00101211312412413523624724825935936A36B37C47D48E48F49F59G5AH5AI5B\ J6BK6CK6CL6DM7DN7EO7EP7FP8FQ8GR8GS9HT9HU9IUAIVAJWAJXBKXBKYBLYCLZCMZCM_DN\ `DN`DOaDOaEPbEPbEQcFQcFRdFReGReGSfGSfHTgHTgHUhIUiIViIVjIWjJWkJXkJXlKYlKY\ mLZnLZnM_oM_oM`oN`pNapOaqObqPbrPcrPcrQdrQdsResRetRftSftSgtTguThuUhuUivVi\ vVjvVjvWkwXkwYlwYlwZmxZmx_nx_nx`ox`oxapyapybqybqycrydryesyeszftzgtzhuzhu\ zivzjvzkwzmwznxzpxzqyzryzuzzuzzuzzryzqyzoxznxzmwzkwzjvzivziuzhuzgtzftzfs\ zesydrycrybqybqyapyapy`ox_ox_nxZnxZmxYmwYlwXlwXkwWkwVjvVjvVivVivUhvUhuTg\ uTguSfuSftRetQesQdsQdrPcrPcrObqObqOapNapN`oN`oM_nM_nMZmLZmLYlLYlKYlKXkJX\ kJWjJWjIViIViIUhHUhHTgHTgGSfGSfFRfFReFQdFQcEPcEPbEObDOaDNaDN`CM_CM_BLZBL\ ZBKYAKYAJXAJWAIV9IU9HU9HT8GS8GR8FR8FQ7EP7EO7DN7DM6CL6CL6BK6BJ5AI5AH59G59\ G48F48E47D37C36B36A35A259248247236135124124113012001000 } frm:hermanm_man-cart { ; Kerry Mitchell 16feb98 ; ; real(p1) = z exponent (use integer >= 2; m=n-1) ; imag(p1) = g exponent (integers) ; p2 = alpha ; real(p3) = critical point selector (>0 for positive root) ; imag(p3) = unused (<0 for negative root) ; use decomp=256 ; zero and infinity bailouts hardcoded to 1e-6, 1e6 ; coloring speed hardcoded to 4 ; c=pixel, iter=1, n=real(p1), m=imag(p1), nfac=2*n-1 maxr=1e6, minr=1/maxr, speed=4*pi/128, alpha=p2 oln=1/log(n), fac=log(0.5*log(maxr)) c2=sqr(c), hypnum=sqr(n)+sqr(m), pn=1 hypden=sqr(n-m), hypfac=hypnum/hypden if (real(p3)<0) pn=-1 end if if (real(c2)>hypfac) pn=-pn end if if (imag(c)<0) pn=-pn end if afac=c*n, bfac=c2*(n-m)+(n+m), cfac=c*n d=sqrt(bfac*bfac-4*afac*cfac) z=(bfac+pn*d)/(2*afac) : g=(z-c)/(1-c*z), z=alpha*z^n*g^m iter=iter+1, r=|z| ; ; orbit trap around 0 ; renormalize iteration count via decomp angle ; set "iteration done" flag (iter=-1) ; if (r<minr) angle=(iter+oln*(fac-log(log(cabs(z)))))*speed z=cos(angle)+flip(sin(angle)) iter=-1 end if ; ; orbit trap around infinity ; renormalize iteration count via decomp angle ; add pi to angle to separate from 0 orbit trap ; set "iteration done" flag (iter=-1) ; if (r>maxr) angle=(iter+oln*(fac-log(log(cabs(z)))))*speed angle=angle+pi z=cos(angle)+flip(sin(angle)) iter=-1 end if iter>0 } Roger Alexander

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Re: [Fractint] What?
by Jim Muth 20 Oct '10

20 Oct '10

At 09:34 PM 10/19/2010 -0400, D Fisher wrote: >I was going through my fractal files and asked myself a >question to which I don't know the answer: Exactly what am >I seeing when I view a fractal? What is the relationship of >the display to the <z> axis? When a Mandelbrot fractal is viewed, the two C axes are displayed on the screen, while the two Z axes are perpendicular to the plane of the screen. This nonsense is possible because the formula Z^2+C consists of two complex numbers which have four variables in all. Four variables define a space of four dimensions. (In the Julia sets, the Z axes are on the screen, while the C axes are perpendicular.) >Is it possible to rotate any >fractal so that any axis becomes any other axis? Or is the >computed display all there is? Is it possible to begin >parsing with different axes? Yes, any Fractal may be rotated through any orientation in the four-dimensional hyperobject called the Julibrot. The SliceJulibrot4 formula that I frequently use does just this. >Basically, imagine a rectangle the ratios of which (x, y, z) >are 2:4:1 (of any magnitude). Where on, or in, this >rectangle is the position of the fractal? And if it were >observed from the smallest axis (z), what would it look >like? The Mandelbrot set cuts a two-dimensional slice through the center of the Julibrot, though it does not cut the Julibrot apart. The perturbed M-sets cut other slices in the same orientation, though not through the center. The Julia sets cut slices through the same Julibrot in an absolutely perpendicular orientation. When a Mandelbrot set is viewed from the other 2 axes, nothing of the M-set remains but a single point, but we now see new stuff surrounding the point that we call a Julia set. >This has me baffled, and is mind game that is generating a >lot of heat. >Any answer would be appreciated, but especially one I could >understand. >Thx > >David M fisher This is the situation as I see it. Lots of luck understanding it. After 20 years, I'm still not sure I actually understand it. Jim M.

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Patch Level 10
by Roger Alexander 19 Oct '10

19 Oct '10

Posted at http://maxitersfractalfollies.blogspot.com a minibrot ,gif and anti-aliased jpg versions, of the classic Mandelbrot generated with the just released patch level 10 for Fractint 20.04. No problems so far running the new executable under DOSBox in Vista. Fractint 20.04 Patch 10 { ; Fractint 20 04 Patch 10 just released ; fract480.gif ; calctime 0:03:04.88 ; created Oct 19, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=mandel center-mag=+0.41523553474131090/-0.33178413843968140/1.117565e+008/1/90/\ 3.88578058618804789e-016 params=0/0 float=y maxiter=12000 inside=0 logmap=500 colors=000202303505606808A0AB0BD0DE0EG0GI0IJ0JL0LM0MO0OQ0QR0RT0TU0UW0WY0\ YZ0Z`0``0`a0ab0bc0cd0dd0de0ef0fg0gh0hh0hi0ij0jk0kl0lm0mm0mn0no0op0pq0qq0\ qr0rs0st0tu0uu0uv0vw0wx0xy0yz0zy0yw0wv0vt0ts0sq0qp0pn0nm0mk0ki0ih0hf0fe0\ ec0cb0b`0`_0_Y0YW0WV0VT0TS0SQ0QP0PN0NM0MK0KJ0JH0HF0FE0EC0CB0B90980860650\ 530310100100200300500600700800A00B00C00D00F00G00H00I00K00L00M00O00P00Q00\ R00T00U00V00W00Y00Z00_00`00b00c00a12b25c48d5Ae6Df8Gg9JhBLiCOjDRkFUlGWnIZ\ oJapKdqMfrNisPltQouRqvTtwUwxWzzVwyTswRovPktNgsLdqJ`pHXnFTmDPkBMj9Ih7Eg5A\ e36d00b00a00_00Z00X00W00U00S00R00P00O00M00L00J00H00G00E00D00B00900800600\ 5003001100300600900B00E00H00J00M00M00O00Q00S00U00X00Z00a00d00g10k10n10r1\ 0v10z21z21z43z65z87zA9zDBzFDzHFzJHzLJzOLzQNzSPzURzWTzZVzXUzVSzTQzROzPMzM\ KzKIzIGzGEzECzBAz98z76z54z32z00v00o00g00Z00O00D00100100 } Roger Alexander

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What?
by David M Fisher 19 Oct '10

19 Oct '10

I was going through my fractal files and asked myself a question to which I don't know the answer: Exactly what am I seeing when I view a fractal? What is the relationship of the display to the <z> axis? Is it possible to rotate any fractal so that any axis becomes any other axis? Or is the computed display all there is? Is it possible to begin parsing with different axes? Basically, imagine a rectangle the ratios of which (x, y, z) are 2:4:1 (of any magnitude). Where on, or in, this rectangle is the position of the fractal? And if it were observed from the smallest axis (z), what would it look like? This has me baffled, and is mind game that is generating a lot of heat. Any answer would be appreciated, but especially one I could understand. Thx David M fisher

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Re: [Fractint] Fractint version 20.04 patch 10 is now available
by Roger Alexander 19 Oct '10

19 Oct '10

Jonathan Osuch wrote: Fractint version 20.04 patch 10 is now available on the developer's web site So far no problems running it under DOSBox in Vista. Roger Alexander

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FOTD 20-10-10 (Patterns in the Mist [5])
by Jim Muth 19 Oct '10

19 Oct '10

FOTD -- October 20, 2010 (Rating 5) Fractal visionaries and enthusiasts: Today's image rates only a 5, but this is for its artistic aspect, which I admit is not too great. It's mathematical aspect is far more interesting however. While casually rotating the colors of today's scene, and ready to move on to a more promising image, I caught a fleeting glimpse of an unsuspected pattern buried in the chaos that fills the screen. I bit of tweaking revealed that I was not mistaken. The pattern definitely is there -- unlike anything I have seen before. But it takes special coloring to reveal the underground pattern, which is nearly invisible with normal random coloring. The parent fractal consists of a circle with a trapezoidal shape nearly filling it and a large distorted Mandeloid inside the trapezoid. Most of the distortion in the Mandeloid lies in the higher-order buds, which are elongated to ridiculous lengths. Today's scene lies in the northern branch of Seahorse Valley of the Mandeloid. The image is filled with both minibrots and disappointing dry valleys that look like they hold minibrots but go flat before a minibrot appears. I have already checked a few minibrots and found them to be disappointing. This does not mean that no great minibrots lie in the depths, but it is not a good way to start searching. The name "Patterns in the Mist" refers back to the original scene before I began work on the colors, when the dark under- ground pattern was virtually invisible. The calculation time of 2-1/2 minutes will pass in a flash, especially for those who have something else to do while waiting. Those with idle time may avoid impatience by viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> Tuesday turned out really not too bad here at Fractal Central. The morning fog cleared off by 10am, leading to a sunny day with light winds and a temperature of 63F 17C. For some reason, the fractal cats were active unusually early, and settled into their afternoon naps well before noon. My day was rather busy but satisfying. FL was also busy. The next FOTD will be posted in 24 hours. Until then, take care, and the supernatural does not exist, that is unless we are talking about what the human brain is supposed to do. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= PatternsInTheMist { ; time=0:02:31.61-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip center-mag=-0.741183021/+0.043160417/3242/1/\ -12.5/0 params=-3/10/0/0 float=y maxiter=7500 inside=0 logmap=68 periodicity=6 colors=000PPPmcUUcmcmAmrnwKpmsomsnmsmmrkmqimpgmoem\ ncmmbmm`mmZmmXmmVmmUmmSmmQmmOmmMmmKmmJmmHmmFmmDmmD\ mmAmmAmmAmmAmmAmmAmmAmmAmmAfmAgmAhmAimAjmAjmAkmAlm\ AmmAnmBomBpmCqmDqmDmmEjmEgmEdmE`mEYmEVmESmERmDRmDR\ mCH02H52H61G61G71G70L70L80L80K90K90K90KA0KA0K00OB0\ OB0OC0OC0OD0OD0OD0PE0PF0QF0QG0QG0RH0RI0RI1SJ2SJ2TK\ 3TL4TL5UM5UM6UN7VO7VO8VP9WP9WQAXRBXRCXSCYSDYTEYUEZ\ UFZVGZVGYUHXTIXTJWSKWSLVRLUQMUQNTPOTPPSOQSOQRNRQMS\ QMTPLUPLVOKVNJWNJXMIYMIZLH_LH_JFZIEZHDZFCZEAYD9YB8\ YA7Y95X74X63X52X61W71W81V91V91VA1UB1UC1UD1TD1TE1TF\ 1SG1SG1SH1RI1RJ1QK1QK1QL1PM1PN1PO1OO1OP1OQ1NR1NR1N\ Q3OQ4OQ5OQ6OP7OP8OP9OPAOOBOOCOOEPOFPNGPNHPNIPNJPMK\ PMLPMMPMNPLOPLQQLRQLSQKTQKUQKVQK0QJ0QJ0QJ0QJ0QS0bT\ 0bT0cT0dU0dU0eV0eV0fV0fW0gW0gW0hX0hX0iX0jY0jY0kZ0k\ Z0lZ0l_0m_0m_0n`0n`0oa0p`0o`0o`0o`0o`0n_0n_0n_0nO0\ 8Q0AR0DS0FT0IU0KW0NX0QY0S } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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