Too sad! -david ----- Original Message ----- From: <fractint-request@mailman.xmission.com> To: <fractint@mailman.xmission.com> Sent: Thursday, December 23, 2004 8:52 AM Subject: Fractint Digest, Vol 22, Issue 10
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Today's Topics:
1. FOTD 17-12-04 (Gift Wrappings [6]) (Jim Muth) 2. FOTD 20-12-04 (Fractal Flight [5]) (Jim Muth) 3. FOTD 21-12-04 (Otherworld Fractal [6]) (Jim Muth) 4. FOTD 22-12-04 (Super Something [7]) (Jim Muth) 5. FOTD 23-12-04 (Comb Filter [7]) (Jim Muth)
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Message: 1 Date: Fri, 17 Dec 2004 12:05:03 -0500 From: Jim Muth <jamth@mindspring.com> Subject: [Fractint] FOTD 17-12-04 (Gift Wrappings [6]) To: fractint@mailman.xmission.com Cc: philofractal@lists.fractalus.com Message-ID: <1.5.4.16.20041217120654.2b7fe760@pop.mindspring.com> Content-Type: text/plain; charset="us-ascii"
FOTD -- December 17, 2004 (Rating 6)
Fractal visionaries and enthusiasts:
The work is once again falling behind. This will make it necessary for me to cut today's discussion short. The fractal is a harmless one created by the MandelbrotMix4 formula, which I have not used for several months. By setting the outside to 'real' I was able to create the effect of gift-wrap ribbons, inspiring the name "Gift Wrappings".
The rating of a 6 indicates that I consider the image a little above average. The calculation time of 4 minutes gives an overall worth of 141. The image, for all it is worth, may be seen without the need of running a parameter file by downloading it from the FOTD web site at:
<http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
With a temperature of 46F 8C, Thursday afternoon was mild enough for the cats to enjoy an hour in the yard. When they decided to come in, they found the tuna waiting. All in all, it was a pleasant day for the dynamic duo. Today promises to be even milder, giving hopes of another pleasant day.
For me the work is starting to pile up again, which will make it necessary to miss a couple FOTD's, so until Monday the 20th, take care, and be happy when things go right.
Jim Muth jamth@mindspring.com jimmuth@aol.com
START PARAMETER FILE=======================================
Gift_Wrappings { ; time=0:04:15.79--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.86475218508526370/+1.147793265057561\ 00/1.340255e+007/1/-7.5/1.38198046488735571e-005 params=0.1/-1.1/-1.1/1.1/0/0 float=y maxiter=1000 inside=0 outside=real periodicity=10 colors=0001dm4pt7cmARiDGdG4`K7ZNAZRBYVEYYHWaIWdLVg\ NVdLTaLRZKRWKQTKOQIONINKHLHHLEHKBGI8GI5EH2EG0EG0DE\ 0DD0DDarY`mTZjOZgKYdHYaDWZ8WW4VT1VQ0TN0TK0WH0YG0`E\ 0aD0dB0eA1g82j74l57o48p1At0Bu0Ew0Gz0Hz0Iz0Lz0Nz0Oz\ 0Qz0Rz0Qz0Oz0Nz0Nz0Lz0Kz0Kz0Iz0Hz0Gz0Gz0Ez0Dz0Dz0B\ z0Az0AtDdaZzYWzTTzOQxKNwHKuHItHIpHHmIHkIHiIImINnHT\ oGYpGYzKVoNLdRBVW2Ka0Ae00j00oK0t30xO0zT0zX1zT4zP5z\ O8zVBz`DzeGzlHzrKzxLxwOxuRxtVwrYwpZwoaumdulgujiuil\ uipugutexteztdztdzrazrZzrWurVprRlpOgpNcpKZpHVpEQpD\ LoAHo7Do58o24o00o00m10m20m40m50m81mA1mB2mD4lE4lH5l\ I7lK7lL8lNAlQAlRBjTDjVDjWEjZGj`GjaHjcIjdIdQZZBzV0z\ W0zY0zY0zZ0zZ0z`0z`0za0za0zc0zc0zd0zd0ze0ze0zg0zg0\ zi0zi0zj0zj0zl0zl0zj0zi0zg0zg0ze0zd0zd0zc0za1z`2z`\ 4zZ5zY8zYAzWBzVDzVEzRGzQHzNIzLKzKLzIKtHKoGKlGKjEKi\ DKeDKdBKcAI`AIZ8IW7IV7IT5IQ4IO4IN4KN4LN4NN4ON2QN2R\ N2TN2VN2WN2WN05V05V0Ha0Tg }
frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l }
END PARAMETER FILE=========================================
------------------------------
Message: 2 Date: Mon, 20 Dec 2004 09:06:15 -0500 From: Jim Muth <jamth@mindspring.com> Subject: [Fractint] FOTD 20-12-04 (Fractal Flight [5]) To: fractint@mailman.xmission.com Cc: philofractal@lists.fractalus.com Message-ID: <1.5.4.16.20041220090808.29d757b6@pop.mindspring.com> Content-Type: text/plain; charset="us-ascii"
FOTD -- December 20, 2004 (Rating 5)
Fractal visionaries and enthusiasts:
For today's fractal we break out the MandelbrotBC2 formula, which takes advantage of the multi-valued nature of the complex 'log' function, and gets an infinity of fractals from formulas that would seem limited to only one.
The additional fractals are especially interesting when the exponent of Z is set to a value between 1 and 2. Today's image uses a value of 1.1 -- a value in the lower part of that range, where the images explode in size as we travel up the logarithmic spiral and the changes are the greatest.
The parent fractal is an oversized thing resembling a dead bird lying on its back, with its pointed bill facing upward. Today's scene is located in the valley that forms the lower edge of the bird's bill. Not wanting to make allusions to a dead bird in the name of the image, I decided to name it "Fractal Flight".
The question of whether fractals can fly is moot. Fractals are abstractions, and abstractions can do anything we wish them to, though usually they do nothing.
In today's image I saw a flight of fractal somethings taking off into a blue sky and vanishing beyond the upper left corner of the frame. Perhaps they have been frightened by approaching danger. (It is hard to imagine how a fractal could come to harm however.)
The 'objects' (if that's what they are) share a curious similar- ity. In some ways they are alike; in other ways, each has a character of its own. Even the larger groups of objects share this partial similarity. The image is a true fractal. In it, the same pattern is repeated again and again at the deeper levels. Of course, the deeper we explore, the slower the calcu- lation becomes.
With nothing really exceptional to raise its rating, the scene could be rated no higher than an average 5. Its render time of almost 23 minutes gives it an overall worth of only 22. It is still an interesting image to see however, and well worth the small effort of downloading it from the FOTD web site at:
<http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
Heavy clouds, a chilly temperature of 36F 2C, and a cold rain kept the duo indoors for the entire day on Sunday. Their moods were surprisingly good considering their confinement. As night fell, the rain changed to snow, which soon froze solid, making for tricky walking and worse driving. When the duo saw the bad conditions, they actually seemed glad to be indoors, where a generous serving of tuna was available to assure their content- ment. This morning is starting sunny, but with a temperature of only +7F -14C and a wind of 20mph 30kph, I doubt that the duo will want to go outside.
The work is still heavy in my department, but I hope to squeeze in a fractal or two before the day ends. The best of what I find will appear as tomorrow's FOTD. Until then, take care, and keep your cool when the snow falls.
Jim Muth jamth@mindspring.com jimmuth@aol.com
START PARAMETER FILE=======================================
Fractal_Flight { ; time=0:22:55.83--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=+0.77134655541610010/+0.189518755374709\ 60/3732.587/1/-12.5/-1.07880579469643578e-011 params=1.1/0/23.8/0 float=y maxiter=3000 inside=255 logmap=304 periodicity=10 colors=000HHUJIULJTNKSPLRSMRVOQXPPZQO`RNbSNdTMfULh\ VKjWKlXJoYIrZHs_Fr_Hp_Jn_Kl_Mi_Og_Pd_Rb_SZ_UX_WV_X\ T_ZQ_`O_aM_cK_dL`eL`eM`eM`fN`fN`fN`gOagOagPahPahPa\ hQahQaiRaiRbiRbjSbjSbjTbkTbkUbkUblUclVclVclWcmWcmW\ cmXcnXcnYdnYdoYdoZdoZdp_dp_dp_dp_dp`ep`fp`gq`gqahq\ aiqajrajrakrblrbmsbmsbnsboscpscptcqtcrtdstdsudtudu\ udvuevvewvexveyveyvfurfqofmmfmmgmmgmmgmmgmmhmmhmmh\ mmhmmhmmgmmfmmfmmemmemmdmmdmmcmmbmmbmmammamm`mm`mm\ _mmZmmZmmYmmYmmXmmXomWqmWrmXqmYqmZqmZqm_qm`pm`pmap\ mbpmbpmcomdomeomeomfomgnmgnmhnminminmjmmkmmlmmlmmm\ mmnlmnlmolmplmplmokmnkmnkmmkmmkmlkmlkmkkmkkojkpikq\ ikrhkshktgjugjvfjzfjxejydjzdjzcjzckzblzbmzanzaoz`p\ z`qz_rzZszZtzNuzNuzNuzOuzOuzOuzOuzPuzPuzPuzQuzQuzQ\ uzRuzRuzRuzSwzRvzRuzRtzRszRszQrzQqzQpzQpzQozPnzPmz\ PmzPmzPmzOmzOmzQmzOmzLmzJmzHmzFmzDmzAmz8mz6mz4mz2m\ z0mz3mz5mz7mz9mzBmzDmzFmz }
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=========================================
------------------------------
Message: 3 Date: Tue, 21 Dec 2004 12:34:25 -0500 From: Jim Muth <jamth@mindspring.com> Subject: [Fractint] FOTD 21-12-04 (Otherworld Fractal [6]) To: fractint@mailman.xmission.com Cc: philofractal@lists.fractalus.com Message-ID: <1.5.4.16.20041221123618.29bff2e6@pop.mindspring.com> Content-Type: text/plain; charset="us-ascii"
FOTD -- December 21, 2004 (Rating 6)
Fractal visionaries and enthusiasts:
WARNING -- I went beyond the topic in today's discussion, as I occasionally do. The discussion is rambling and rather philo- sophical. Those who have a 'knee-jerk' reaction to philosophy or mysticism should move on directly to the image and spare their knees.
Depending on where the observer is located, today is either the shortest or longest day of the year. For those living on the equator however, where all days are 12 hours long, it is just another 12-hour day, though it is still one of the two days of the year with the lowest maximum sun angle.
On a special astronomical day such as today, fractals are just as real or unreal as on any other day. The position of the sun has no connection to the world of fractals. This much everyone can agree on. But do other universes exist where such a connection might be possible? After all, the name of today's image is "Otherworld Fractal", and I gave it this name because it is unlike anything that might be seen in our familiar version of the 'real' world.
In the naive days of my youth, I was certain that there is only one real world and that world was the one I had learned to con- struct from the images I observed through my senses. Those who thought otherwise were confused and superstitious. True, I realized that my senses could detect only a tiny part of that real world, but there was still only one real outer world, and that world was the ultimate reality, which was out there whether anyone was around to observe it or not.
That was when I was young and naive.
I am no longer young, though I am still rather naive, (aren't we all), but I am not so naive as to believe that anything such as an ultimate reality can exist unless one is referring to the idea known as God. When one truly knows God, all questions about creation and existence become non-questions. When one asks why God created the universe, or where God came from, or even what happens to people after they die, then that person does not truly know the nature of reality.
When one asks, or even wonders about such things, that person is displaying his ignorance about both himself and the world he assumes he exists in. When one flees from such questions into the comfortable and easy-to-comprehend world of Atheism, that person is merely showing the arrogance that conceals his fear of the unknown. I know this because I was once there. When one realizes that God is an idea, yet uses this fact as evidence that there is no God, that person is closer to the truth. When one realizes that the physical universe is also an idea, that person is closer still. . . .
. . . to be continued . . . perhaps . . .
Just imagine it -- all this off-topic stuff came about because I had the thought that today's image is a scene that could never be observed anywhere in the universe as we know it. But it very easily could exist in the world of fractals, especially the world created by the formula Z^(1.1)+C.
The rating of a 6 is about what the image is worth. Its overall value could be anything, but calculates at a 90. The most convenient way to see the otherworldly image is to download it from the FOTD web site at:
<http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
With a temperature of only 19F -7C, Monday was far too cold here at Fractal Central for the dynamic duo to go outside. But they spent several hours on their shelf by the window, watching the chilled starlings huddle around openings of the neighborhood chimneys to keep warm. A surprisingly small serving of tuna was needed in the evening to make the duo happy. This morning is starting less cold, but still far from warm. We'll see how the duo adjusts.
For me it looks like another in the nearly endless string of similar days of work before fractals. The next FOTD will appear right here in 24 hours. Until then, take care, and be of good cheer at this time of year. Save the mysteries for next year.
Jim Muth jamth@mindspring.com jimmuth@aol.com
START PARAMETER FILE=======================================
Otherworld_Fractal { ; time=0:06:40.57--SF6 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=-2.14292936172586400/+0.027868278465541\ 99/374.3557/1/7.5/5.92893789619353129e-012 params=1.1/0/-28.3/0 float=y maxiter=500 inside=255 logmap=77 periodicity=10 colors=000K3HL4IM4JN5KO5LP6MQ6NR7OS4PT7QU9RVCSWETX\ GUYJVZLW_OU`QTaSTbVTcXSd_SeaSfcRgfPhhOikNjmMkoKnrJ\ qtIvyIswHqvHntGlsGirFgpFfoEdnEclDakD`jCZhCYgAXfFVd\ KUcPSbURaZP`cO_cNZcLZcKZcIZcHZcFZcEZcBZcCZcDZcEZcF\ ZcFZcGZcHZcIZdIZeJZfKZgLZhLZiMZjNZkOZlPZmPZnQZoRZp\ SZqSZrTZsUZtVZuVZvWZzXZxYZyZZzZZz_Zz`ZzaZzaZzbZzcZ\ zd_zd_ze_zf_zg_zh_zi_zh_zg_zg_zf_ze_zd_zd_zc_zb_za\ _za_z`_z__zZ_zZ_zY_zX_zX_zW_zV_zU_zU_zT_zS_zR_zR`z\ Q_zP`zO`zO`zN`zM`zL`zL`zK`zJ`zJ_zI_zH_zG_zG_zF_zE_\ zD_zD_zC_zB_zA_zA_z9_z8_z7_z7_z6_z5_z3Zz4_z5_z5_z6\ _z7`z7`z8`z8`z9azAazAazBazBbzCbzDbzDbzEczEczFczGcz\ GdzHdzIdzIdzJezJezKezLezLfzMfzMfzNfzOgzOgzPgzPgzQh\ zRhzRhzShzShzShzShzShzShzShzShzShzShzShzShzShzShzS\ hzShzShzShzShzShzShzShzShzShzShzShzShzThzShzShzShz\ ShzShzRhzRhzRhzRhzRhzQhzQhzQhzQhzQhzPhzPhzPhzPhzPh\ zOhzOhzOhzOhzOhzPhzPhzPhz }
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=========================================
------------------------------
Message: 4 Date: Wed, 22 Dec 2004 11:59:23 -0500 From: Jim Muth <jamth@mindspring.com> Subject: [Fractint] FOTD 22-12-04 (Super Something [7]) To: fractint@mailman.xmission.com Cc: philofractal@lists.fractalus.com Message-ID: <1.5.4.16.20041222120118.0d57799c@pop.mindspring.com> Content-Type: text/plain; charset="us-ascii"
FOTD -- December 22, 2004 (Rating 7)
Fractal visionaries and enthusiasts:
In today's fractal we take a trip to the Z^(2.02)+C fractal. We check it 20 levels up the logarithmic hyper-spiral. (Actually the scene lies 16.858... levels up the spiral. The level 3.14159... or 'pi' is better considered ground level.) The formula is very close to that of the Mandelbrot set, and the fractal it produces is very similar. But there are significant differences. To start, the entire set appears rotated 30 degrees. The greatest change however has taken place at the north branch of Seahorse Valley, which has broadened into a plateau with a spire at its inner edge. Today's scene lies on the main-bay side of this spire.
The midget I found there rates a lofty 7. I have never before seen a midget with such intricate decoration surrounding it unless it was produced by one of the fancy features of the program, which I feel are somewhat artificial. By contrast, today's scene, which was rendered with the outside set to the standard 'iter', shows what is 'actually there'. I named the image "Super Something", leaving it to the viewer to decide what that 'something' is.
Since the exponent of Z is fractional, discontinuities must exist in the image, and indeed they are there. But with an exponent so close to integer value, the breaks are minor, and at first glance may go un-noticed.
The rating of a 7 leaps to an overall worth of a rather disappointing 47 when the render time of almost 15 minutes is figured in. But the rendering may be eliminated entirely by downloading the finished image from:
<http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
With a peak temperature of 39F 3C, Tuesday was hardly balmy here at Fractal Central. But the dynamic cats, who had been confined indoors for almost two days, were willing to ignore the minor chill to enjoy an outing in the great outdoors of the holly thicket, where they passed the afternoon pretending they were stalking birds. Only a minor treat of tuna was needed to end their day on an up note. This morning is starting sunny and warmer, but rain is scheduled to move in before nightfall. I see a hint of trouble for the fractal duo.
For me, the pile of real work waiting to be done is minor. This should assure another fine fractal in 24 hours, and maybe another outburst of philosophy. Until then, take care, and remember that, regardless of how much we learn, we will never know more than an infinitesimal part of all there is to know.
Jim Muth jamth@mindspring.com jimmuth@aol.com
START PARAMETER FILE=======================================
Super_Something { ; time=0:14:48.75--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 periodicity=10 center-mag=-0.61120335469249380/+0.436965672671546\ 70/6345769/1/-92.5/1.01919733624944e-008 logmap=215 params=2.02/0/20/0 float=y maxiter=4200 inside=0 colors=000W2RUE_SQhQaqPiyOhwNguMfsLeqKdoJcmIbkHaiG\ `gF_eEZcDYaCX_BWYAVW9UU8TS7SQ6RO5QM4PK3OI2NG1ME0LC\ 0KA0J80I60H40G25F0AE5EDAFCFGBKHAPI9UJ8WK7XgV9eUBcU\ CaUE`UFZUGXUIWUJUUKSUMRUNPUPNUQMURKUTIUUHUVHQRIMNI\ JKIFGIBCI78I45L58N6AP6DR7FT8HV8KX9MZAP`ARbBTdCWfCY\ hD`jEblEdnFgpGirGksLgsQcsV_s_WsdStiOtnKtsGtxCtz9sz\ 8sy8sw8su8ss8sr8sp8sm8sk8si8sg8se8sc8sa8sZ8sX8sV8s\ U8tQDtNHtKLuHQuEUuBYLoUNmVPkWRiXSgXUeYWcZXaZZ__`Y`\ aW`cUaeSbfRb_XdTaeMffFkg8ph2ui8vgEveKwdQwbWx`ax_gy\ YmyWryVsvTstStqQtoPumOujMvhLveJwcIwaHsUJpMKmELj7Mf\ 6Oc6P`6RY6SV5US5VP5XM5YJ5_G4`D4bA4c74e44f88eBBdEEc\ IHbLKbONaSQ`VU_YXZa_ZdbYgeXkhWnkVqcVic_bccWchPclIc\ qBcuCctDctEctFctGctHctIctIctJctKctLctMctNctOctOctP\ ctQctRctSctTctUctUctZcnbcifcckcZocTscOccYbcWbcVacU\ acT`cS`cR`cQjcDlcGmcIncLocNpcQqcSrcQrcOrcNrcLrcJgc\ CfcEdcGccHbcJ`cL_cMYcOXcQ }
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=========================================
------------------------------
Message: 5 Date: Thu, 23 Dec 2004 11:52:10 -0500 From: Jim Muth <jamth@mindspring.com> Subject: [Fractint] FOTD 23-12-04 (Comb Filter [7]) To: fractint@mailman.xmission.com Cc: philofractal@lists.fractalus.com Message-ID: <1.5.4.16.20041223115405.29d75974@pop.mindspring.com> Content-Type: text/plain; charset="us-ascii"
FOTD -- December 23, 2004 (Rating 7)
Fractal visionaries and enthusiasts:
It's that time of year again, and I find myself with so much work and so many things to do that I will have no spare time for the FOTD for the next 3 or 4 days. The bad news is that there will be no FOTD until December 27th or 28th. The good news is that the FOTD will return at that time in its full glory, for another year, or twenty-five years, of stunning fractal images from nowhere.
With today's image, I stayed with the Z^(2.02)+C fractal, but examined it 154 turns up the hyper-spiral, where the figure is rotated 180 degrees, so that East Valley now lies on the nega- tive X-axis, where the most interesting discontinuities are located.
The inner details of this area are like nothing in the classic M-set. They vaguely resemble the elephant-like shapes that might be expected there, but are far more broken and chaotic. The midget in today's image is a typical example of the dis- order that exists in this part of the infinite-dimensional land of fractals.
I have named the image "Comb Filter" because some of the ele- ments resemble coarse-toothed combs. (I am in no way an elec- tronics technician.) The rating of a 7 seems fair, considering the unusual nature of the image, which needed no program trick- ery. The render time of just under 5 minutes raises the overall worth to a rather impressive 143.
The most convenient way to see the image is to download it from the FOTD web site at:
<http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
An absolutely gorgeous day on Wednesday here at Fractal Central resulted in angelic cats. The warm sun, light breezes, and temperature of 61F 16F were just what the duo needed to ease their disappointment over the recent cold spell. No tuna was necessary to make them happy in the evening. Today is starting mild but rainy. I hope the duo doesn't have too big a let-down.
For me, it's finish the work then get ready for the holiday craziness. As I said earlier, the next FOTD will appear in 5 days on December 28, (maybe the 27th if things go well). Until then, take care, and may Santa leave a real fractal, not just a picture of one, in your stocking.
Jim Muth jamth@mindspring.com jimmuth@aol.com
START PARAMETER FILE=======================================
Comb_Filter { ; time=0:04:53.58--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 periodicity=10 center-mag=-0.26350487612601/+0.02105654396608012/\ 1347270/1/-57.5/-2.69338237129934654e-009 logmap=79 params=2.02/0/154/0 float=y maxiter=1200 inside=0 colors=000H0RI0SI0UI0VK0WK0YL0_L0`M0cM0dM0eP0hP0jS\ 0kS0nW0oU0qS0rR0sP0uO0rM0oK0nI0kH0hF0gE0dC0a90L70K\ 60L40K21L11L01M04P06S07V0AY0C_0Ea0Fd0Ig0Kj0Lk0On0P\ q0Rs0Su0Vs4Wr9YqF_oKanOclSdkYejagjejhkkgokeskdxlcz\ nazn`zh_ze_zcYz_YyWYy_WxWWxUWwRWwMVuIVsEVn9Um4Ui0U\ n0Un0Wo0Yt0`w1ax1dw2ev4gt6js7kq7no9onAqkCsjEuhExeF\ ydHzcIz`Kz_KzYLzVMzUOzSOzUPzVRzVRzWSzWSzYUzYUz_Vz_\ Vz`Wz`WzaYzc_zc_zd`zd`zeazeazgczgczhdzhdzjezjezedz\ cdz_dsWdlUdePc`McUKcMFcFCc76`09c1Cd2Fe2Ig4Kj6Mk6Pl\ 7Sn9Uq9WrA_sAauCdwEeyEhzFkzHnzHozIrzKuzKxzLzzHyzLs\ zOnzShzVcz_YzaSzeMzhHzlAzo4zs0zz0zw0zr0wn0rj0ne0ja\ 1eY1aU1YP2UL2PH2LE7OFCSIHVKLYMPaOUdPYgSakUenWjqYnu\ `rxauzcqy`nxYjwVguUcsR`rOWqMUqKPrHMuFIxCFz9Az77z42\ z10z04z27z6Az9EzCHzFKzHMzKPzMUzPWzS_zUazWdz_gzajzd\ lzeSz0Uz0Uz0hz4hzzgzzezzezzUzzIzz6zy0zw`zazzIzzgIz\ IEzFAzC7z94z61z20z00z00z0 }
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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End of Fractint Digest, Vol 22, Issue 10 ****************************************