May 2004 - Fractint - mailman.xmission.com

FOTD 26-05-04 (Little Joe [6])
by Jim Muth 26 May '04

26 May '04

FOTD -- May 26, 2004 (Rating 6) Fractal visionaries and enthusiasts: Another busy day means another brief discussion. There is not much to be said about today's image, which was found in the same way as yesterday's. To add a bit of interest, I rendered the scene with the outside set to 'fmod' and the proximity set to the default 0.01. The midget at the center is another shapeless thing, though not quite as shapeless as the midget in yesterday's image. For some reason now forgotten, I named the image "Little Joe". I rated it at a 6 because blue is one of my favorite colors. The render time of 13 minutes results in an overall value of 45. The image is available, already rendered, on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunny very warm weather here at Fractal Central on Tuesday gave the cats a pleasant afternoon in the yard. The temperature reached 88F 31C, then at 7pm, a whopper of a thunder-storm moved in, but by that time the cats were inside for the evening. They took shelter in the closet until the noise passed, then came out for their evening treats. Today is starting cloudy and very humid, with more storms due. The cats are already checking the outdoor conditions. I have quite a bit of work to finish before I turn to fractals, so I had best start working. Until next FOTD, take care, and be decisive. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Little_Joe { ; time=0:13:17.96--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=+0.1814731907900935/-0.0169584462205538\ 5/8693.298 params=1.5/0/2.5/0 float=y maxiter=16000 inside=0 outside=fmod logmap=60 periodicity=10 colors=0006vy7ux7tw8sv8ru9rt9qsAprBoqBnpCmoCmnDlmD\ klEjkEijFhiGhhGggHffHeeIddIccJccKbbKaaL``L__MZZMZY\ NYXNXWOWVPVUPUTQUSQTRRSQRRPSQOTPNTPMUOLUNKVMJVLIWK\ HXLFWKHWKIVKJVKKUKLUKMUJOTJPTJQSJRSJSSJTRIVRIWQIXQ\ IYQIZPI_PHaOHbOHcOHdNHeNHfMGhMGiMGjLGkLGlKGmKFoKFp\ JFqJFrIFsIFtIFuIHtIIsIJsIKrILqIMqINpIOpIPoIRnISnIT\ mIUlIVlIWkIXkIYjIZiI_iIahIbgIcgIdfIefIfeIgdIhdIicJ\ ldIjcIhbIfaHd`Hb_H`ZGZYGXXGVWFTVFRUFQTFOSEMREKQEIP\ DGODENDCMCALC8KC6JD3IC4JC5JC6JC7JC7JB8JB9JBAJBBJBB\ JACJADJAEJAFJAFJ9GJ9HJ9IJ9JJ9JJ8KJ8LJ8MJ8NJ8NJ7OJ7\ PJ7QJ7RJ7RJ6SJ6TJ6UJ6VJ6VJ9SKBQLDOLFMMHJNJHNLFONDP\ PAPR8QT6RV4RW5SX5SX5TY5TY5TZ5UZ5U_5U_5V`5Va5Va5Wb5\ Wb5Wc5Xc5Xd5Xd5Ye5Yf5Yf5Zg5Zg5Zh6_h6_i6_i6`j6`k6`k\ 6al6al6am6bm6bn6bn6co6cp6cp6dq6dq6dr6er6es6es6ft6f\ u5ht6fs7er7dr8cq8bp9ap9`oAZnBYKlNJmQInTHnVGoYFp`Eq\ cDqfCriBskAtn9tq8ut7vw5wz } 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 20.0 PAR-FORMULA FILE==================================

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FOTD 25-05-04 (A Hot Midget [5])
by Jim Muth 25 May '04

25 May '04

FOTD -- May 25, 2004 (Rating 5) Fractal visionaries and enthusiasts: I have been doing some pondering since the last FOTD. Yesterday I received in the mail a special report from 'Scientific American' magazine with the title "Are You a Hologram?" At one place the article states that the three-dimensional world we see around us might be an illusion that we are creating, that in reality we are two-dimensional somethings. There is an illustration showing a two-dimensional woman imagining that she is three-dimensional. This revelation nearly knocked me flat! I thought that the assumed number of dimensions in our universe was increasing, not decreasing. And if we really are two-dimensional, then it must be possible to imagine more dimensions. So what is keeping us as 2-D beings from imagining four dimensions. Finally, I wonder about the nature of the 2-D things that are having the illusion of three-dimensional space. It is all so complex. I like things simple. Complexity brings confusion; simplicity brings ease of understanding. At least that's the way it's supposed to work. Of course, it often happens that things which at first appear quite simple turn out to be surprisingly complex. And nowhere is this unexpected complexity more evident than in the world of fractals. The iterated expression behind today's image is Z^1.5+C, as simple an expression as one could hope to run into in the arcane field of mathematics. Yet it has an infinity of infinite worlds hidden within it. Today's parent fractal is but one of these infinity of worlds. It is a shapeless thing with bits and pieces of itself lying scattered to the west of the main bay. This bay has a rudimentary East Valley, and today's scene is located in the chaos along the southern shoreline of this valley. (In this case, the northern shoreline is entirely different.) I named the image "A Hot Midget" because to me at least, the midget at the center looks overheated. It is a curious midget, almost giving the impression that it cannot decide what shape to take, and has decided to try to take all shapes. There is an obvious smaller midget lying on the midget's main filament. I have already checked this smaller midget and found it to be both less interesting and far slower to render. After carefully considering the situation, I rated the image at a 5, which is not good and not bad. After all, this is the kind of stuff I was doing 12 years ago. Back then it would have rated a 7 or 8. Nowadays, the 5 is all I could give it. When the render time of 22 minutes is considered, the overall value rates a 22 also. With images of such mediocre worth, perhaps the wisest way to view them is to download them from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Another very warm and sunny day here at Fractal Central, with a temperature of 90F 32C, was acceptable for the dynamic duo, who spent an hour in the yard, fighting off the cicadas that were threatening to overwhelm them. Actually, I think the ear-split- ting singing of the bugs disturbs the duo more than the bugs themselves. The singing masks the warning sounds of approaching threats. Today is starting sunny but less warm. The singing is very loud however, and it remains to be seen how the duo will react. As usual, my day will be much improved when the work is finished. Until next FOTD, take care, and see you in the fractal vicinity. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Hot_Midget { ; time=0:22:32.59--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=+0.16011719832039840/-0.003322865380414\ 47/305474.1 params=1.5/0/2/0 float=y maxiter=18000 inside=0 logmap=290 periodicity=10 colors=000XNQYORZOS_PT`PUaQVbQWcRXdRYeSZfS_gT`hTai\ UbjUckUelUfmUhnUigUjaUjVVjPTmIQoCNm5Dl6Ej6Ei7Eh7Eg\ 8Ef8Ee9Ec9EbAEaAE`BE_BEZBFYAHWAKUALT9OR9QQ9RO8SN8T\ L8UK7VI7WH7XF6YE6ZC6_B5`95a85b63c25d56e87eB8dE9cGA\ bJB`MC_PDZSFYUGXXHW_IUbJTeKSgLRjMQmNPpOOrPNsPMsPMs\ PLsQLsQKsQJsQJsRIsRIsRHsRGtRGtSFtSFtSEtSDtTDtTCtTC\ tTBtTBtRDpPEmNFjLGgJHdHIaFJZDKWBLT9MQ7NN5OK3PH1QE5\ RH9RKDRNGSQKSTOSWSSXRRYRRWRQURPSRORRNPRMNQLLQKJQJI\ QIGQHEQGCQFAQE9RDASDATCAUCAVCAWBAXBAYBAZAA_AA`9Aa9\ Ab9Ac8Ad8Ae8Af7Ag7Af5Bg7Ah9AiAAjC9kD9lF9mG8mI8nJ8o\ L7pM7qO7rP7sR6tS6tU6uV5vX5wY5xZ4yZ4z_4z_4wa8tbBqcF\ neIlfKkgLkhLkiLjjMjkMjlMjmNioNipNiqOjrOktOluPmvQov\ UqwYrwasxetxiuymvymwzmxzmyzmzzmzzmzzmzczz`zz_zzZzz\ ZzzYzzYzzXzzWzzWzzVzzVzzUzzUzzWzzYzz_zz`zzbzzdzzez\ zgzzizzjzzlzznzzozzqzzszztzzpzzlzzhzzdzz`zzXzzVzzU\ zzTzzRzzQzzOzzNzzLzzMzzGz } 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 20.0 PAR-FORMULA FILE==================================

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Franktal Gallery update
by Franktal Gallery 24 May '04

24 May '04

Franktal Gallery update (two updates in a month.... unbelievable !) - Couple of new Nature Fractals - A new IFS gallery Set your course to http://www.geocities.com/franktal2002 And don't be scared by those Geo@%#cities "bandwidth exceeded" messages, just try again later. Thanks for visiting ! Best regards, Miguel _________________________________________________________________ The new MSN 8: advanced junk mail protection and 2 months FREE* http://join.msn.com/?page=features/junkmail

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FOTD 24-05-04 (Fun in the Sun [5])
by Jim Muth 24 May '04

24 May '04

FOTD -- May 24, 2004 (Rating 5) Fractal visionaries and enthusiasts: Today's image is something different. It has no midget at the center, and it has been created by one of the built-in formulas -- the manzpower. To find the image, I drew the Z^(998.1)+C Mandeloid and examined it in the area of the negative real axis. Fractals of such a high order are normally very dull objects, appearing as circles with a multitude of identical tiny bays lying along the perimeter. The inner detail of these bays has a similarity that makes exploration boring. But today's image was drawn with a fractional power of Z, and that fractional part makes the difference. Most of the parent fractal consists of the expected identical bays. The difference lies along the negative real axis, where the fractal is splitting apart and new scenes are springing into existence. It is in this area that today's image lies. In today's image the view window has been rotated 90 degrees. East is up and north is left. The X-axis runs up and down the center of the screen. The magnitude of the scene is a nominal 2x(10^8), the maxiter an unimpressive 1500. The resulting image reminds me of a fantastic tree set against an alien sky, with smoky globules of light scattered among the branches. For reasons not recalled, I named it "Fun in the Sun". The tree itself is unlike anything that could be found on earth, but if one of the leading quantum theories is correct, and an infinity of alternate universes does exist, then this exact scene not only exists, but exists an infinity of times. The rating of a 5 is a fair representation of the image's worth. I found it almost automatically and spent very little time in rendering or coloring it. When the render time of 2 minutes is considered, the overall value is an exciting 226. For fractal convenience, the parameter file of the image has been rendered and the finished image posted to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunday was a repeat of Saturday here at Fractal Central. The temperature reached 91F 33C under lots of sun, and the cats spent several hours in the yard, watching cicadas and occasion- ally eating one that fluttered too near. In the evening they came inside and settled down without complaint. Today looks as though it will be another repeat. In my corner of F.C. the work is piling up, so I had best get started. Until next FOTD, which will most likely, but not certainly, appear in 24 hours, take care, and be kind to all types of fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fun_in_the_Sun { ; time=0:02:12.70--SF5 on a P200 reset=2003 type=manzpower passes=1 bailout=10 center-mag=-1.00064242478037900/0/2.137563e+008/1/\ 90/3.88578058618804789e-016 params=0/0/998.1/0 float=y maxiter=1500 inside=bof60 outside=real periodicity=10 colors=000F2LD3JC4IB5G96F87D78B59A4\ A82B63C73D73E73F73G74H74I74J84K84L85M85N85O85P81Q7\ 3R85S87T98U9AVACWAEXAFYBHZBJ_CL`CMaDObDQcDSdETeEVf\ FXgGZhH_iIajJckKdlMemOgnQioSkpUkqWmrYos_osapscprep\ qgppippkpompnopmqplrplsoktojunivnhwngxnfyoezodzocz\ ocztbStaTt`Tt_TuZUuYUuXVuWVuWWuVWuUWuTXvSXvRYvQYvP\ YvOZvNZvN_vM_wL`wK`wJ`wIawHawGbwFbxFawFbwFbvFbvFbu\ FbuFbuFctFctFcsFcsFcsFcrFdrFdqFdqFdqFdpFdpFeoFeoFe\ oFenFenFemFemFflFflFflFfkFfkFfjFgjFgjFgiFgiFghFghF\ hhFhgFhgFhfFhfFhhBmgDjfFhfHfeJdeLbdM`cOYcQWbSUbUSa\ WQcYRbXPaXO`XN_XMZXLYXKXXJWXIWWGVWFUWETWDSWCRWBQWA\ PW9PW8RVBSVDUUFVUHWTJYTLZSN_SPaRRbRTdQVeQXfPZhP`iO\ bjOdlNfmNhnNjnMkoMkoLlpLmqKmqKnrJnrIosIosHptHpuGqu\ GqvFrvFrwEswEsvFrqNquGruHrtIrtJrsJqsKqrLqrMqqNqYiO\ ZhPZhPZhQ_gQ_gR_gR_fR`fS`fS`eTaeTaeUadUadUbdVbcVbc\ WXSeVRcUQbSQ`RPZQOYONWNMVMLTKLRJKQIJOGIN } END PARAMETER FILE=========================================

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FOTD 23-05-04 (Z-Eexponent-Pi [3])
by Jim Muth 23 May '04

23 May '04

FOTD -- May 23, 2004 (Rating 3) Fractal visionaries and enthusiasts: Unless I am mistaken, today's image is the third consecutive one with a rating of a lowly 3. FOTD quality seems to be slipping. The work rush here at F.C. is taking its toll. There is an infinite family of 'zexpe' fractals with an exponent of epsilon, so why not a family of 'zexpi' fractals with an exponent of pi? In fact, there is a family of 'zexpi' fractals, (I just decided there is), and one of its infinite number serves as the source of today's image, which I have named Z-Exponent-Pi. The scene of the image is very near the negative real axis of its parent, in an area filled with discontinuities. The render time of 4-1/2 minutes gives an overall value of 65, which, depending on the individual fractalist, may or may not be worth the effort. The simplest and quickest way to see the image is to view it on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Saturday was quite warm and sunny here at Fractal Central. The high temperature of 90F 32C was near perfect for both fractal cats and cicadas. The cats watched from the yard while the cicadas sang in the trees, and as far as I could tell, everyone was happy. When evening arrived, the cicadas stopped singing and the dynamic duo came indoors for their treat. Today is starting the same. I'm going to take it as easy as possible today. It looks like a very busy week coming up. Until next FOTD, which I still hope to have ready in 24 hours, take care, and see you then. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Z-Exponent-Pi { ; time=0:04:34.96--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=-0.44889489820032070/-0.008655752583507\ 26/1687871/1/-80/1.02041138039243862e-009 params=3.14159265358979/0/0/0 float=y maxiter=1400 inside=0 logmap=114 periodicity=10 colors=000VMGIIDFF9BB8S84O400002604D06F29G4BG6DI8F\ I9P`O`qaeyghzlauhVhcPZZIMTG6GDBO9GT6MZ4Pc0Vh0`n0es\ 0Mw0hy0sz0zz0jw0Rs08p00n0DZ0aK0gR0jX2nc8shBwpFzuIq\ sMjsPcqRXqVPqZGp`9pc2ng0nh0n6az2`z0Zz0Xz0Vz0Tz0Rz0\ Pz0Zz0Oz0KzBFzMBzZ6zh2zs0zz0zz0yz0wz2uz8szFqzKpzPn\ zXlzalzgjznhzsgzyezzczzazz`zz`zzZzzXzzVzzVzzTzwRzs\ RzpPzlOzgMzcMz`KzXIzTIzPMzMPzKTwGXuF`qBcp9gl6hh2lg\ 0pc0sa0wZ0zX0zT0zR0zT0zV0zX0zZ0z`2z`4zyVzzuzzzgjzK\ Xz0Tz0Pz0Oz0Kz0Gz2Fz4Bz69z66z82z90zB0zB0zD0zF0zG0z\ F0zG0zG0zG4zIBzIGzIOzKTzKZzKezMjzMqzMwzOzzOzzOzzIz\ zOzzTzzZzzczzhwzlsyqpwwlszhpzelzlczajzTqzKyzBzu2zn\ 0zg0z`0zZ8yZKlXV`XgMXq9Vz0Vz0Vz0cz0jz6qzDyzKzzRzzV\ zzXzzZzzZzzZzz`zz`zz`zzazzazzazzczzczzczzezzczzazz\ `zzZzzZzzXzzVzzTzzRzzRzzPzzOzzMzzMzzIzzGzzFzzDzzDz\ zBzz9zz8zz8zz6zz4zz4zz6zz8zz9zzBzzDzzFzzGzzGzzIzzK\ zzMzzOzzPzzRzzTzzTzzPzz0z } 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 20.0 PAR-FORMULA FILE==================================

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FOTD 22-05-04 (Hexafault [3])
by Jim Muth 22 May '04

22 May '04

FOTD -- May 22, 2004 (Rating 3) Fractal visionaries and enthusiasts: I'm still far behind in the work, so the discussion will once again have to be brief. I think it was Lee Skinner who named the Z^(2.1828...) fractal the 'Zexpe' fractal. To create today's image, I have taken the 'Zexpe' fractal, and with the MandelbrotBC2 formula, calculated it at a different level to produce a different yet similar fractal. This fractal is indescribable, basically a Mandeloid standing on its nose, with branch cuts and irregularities everywhere. Several jagged spirals lie on the northwest part of this fractal; today's scene is rather deep in one of these spirals. I named the image "Hexafault", because the midget at the center is sliced almost perfectly symmetrically by six major branch cuts, or fault lines. It is rare to see such fault-line symmetry in a fractional-power fractal. Unfortunately, I gave almost no effort to the coloring, not that it would have made much of an improvement if I had. As a result, the rating is another lowly 3. But the very fast render time of 33 seconds raises the overall value to a very respect- able 534. Those who prefer to avoid rendering may download the completed image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather was pleasant enough here at Fractal Central on Friday, with some sun and a temperature of 81F 27C, but the cats had to be escorted as they took their daily walks in the yard, to keep them from overstuffing themselves with those easy-to- catch cicadas that are flying around by the millions. Today is starting sunny and quite warm, and the cicadas are quite active. It looks like another chaperoned day for the duo. For me, it looks like I'm going to try to get caught up. If I make reasonable progress in the work, the next FOTD will appear in 24 hours. If not, it might be 48 or 72 hours. Until next FOTD, take care, and who will be first to realize that the universe is a great fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Hexafault { ; time=0:00:33.67--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 center-mag=-1.3193191562\ 43292/+0.2253921211100132/1952924/1/-165/-5.999734\ 35516655e-009 params=2.71828182845905/0/0/0 float=y maxiter=1000 inside=0 logmap=23 periodicity=10 colors=000AMQ8OH6Q9DUAKXBR_CYbDdeEkhFrkGphIofKncLm\ aNkZPjXQiVShSUgQVeNXdLZcI_bGaaEbbHdcKfdNheQjfTlgWn\ hZpiarjdtkgvliwkkvjlujnuiotiqthrsgtrgurfwqfxqbsp_o\ pXkpTfpQbpNZpM`oLbnLcmKelJgkJhkNdgQ`cTY`WUX_RTbNQe\ KMhGIkDFlCIlBLlBOlARlAUl9Wm8Zm8am7dm7gm6jm6lk7EjCH\ iHKhMNgRPfWSe`VdeYcj_`hXYgUVeRTdPQcMNaJK`GI_EGaDEd\ CCfAAh98k86m74o68m7Bk8Fi9IgALeBPcCSaDV_EZYFaWGeUHh\ SIkQJoOKrMLuKMnPOgTP`XRU`SNeTGiV9mW3qX4rZ5r`6sa7sc\ 8se8tf9thAtiBukCumCvnDvpEvrFwsGwuGwvEtsDqqCqnArl9s\ i8tg6ud5vb4w_3xY2y_2za2zc1ze1zg1zi0zk0zm0zo0zp4zl7\ ziBzfEzcIz`LzYOzVQzTTzQVzOYzL_zJbzHdzEgzCiz9lz7nz5\ pz7rz9tzBvzDwzEdzaMzxMzwMzwMzwMzwMzwMzwMzwMzwMzwMz\ wMzwMzwMzwMzwQztTzqWznZzlazidzfgzdezcczbazb_zaZzaX\ z`Wz_UzZTzZRzYQzXOzWNzWCzN2zF8zKEzOKzSQzWVz_`zdfzh\ lzlrzpwztqzokzjfze`z`VzXQzSKzNEzI9zECzKFzQIzWLzaOz\ fEz3Iz5Lz7JzjIzmIzoFzfDzY } 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 20.0 PAR-FORMULA FILE==================================

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A fractal showing the fractional power Mandeloid "fault line" phenomenon (fractal "SierpinskiUnwoven")
by Hiram Berry 21 May '04

21 May '04

A few days ago I asked if anyone on this forum was familiar with the phenomenon whereby a Mandeloid, even when done as a union of the sets produced from all its critical points, ends up showing straight or smoothly curved lines on the boundary between inside and outside points, or else in the outside iteration zones in a discontinuous way (eg. smoothly sided polygons of iter=7 bordering a region with iter=15). I didn't get any answers on this, as to whether this is a genuine effect or not-- one doesn't see this in the classic M-set, nor as far as I have been able to tell in Mandeloids of integer power, but on encountering it once more and unintentionally, I am more confident that it is a genuine effect. Today though I came across an example of this phenomenon (accidentally) that was so thorough that the smooth lines actually extend on down fractally-- infinitely more such regions as the scale gets smaller. A couple of days ago Jim M. mentioned a Mandeloid using exponents 0.15 and -0.15, commenting that all the points were inside points (ie. there was no attraction to infinity to generate an outside). It got me thinking about the possibility of having the attractor for outside points being something other than infinity for fractals like this where the generator itself can't possibly go to infinity. So, on the way to writing a .frm that could display many orbits of outside points, I needed a sentry value to put in one of the parameters to indicate it was an orbit fractal and not the usual bailout kind; the number e came to mind since it would not likely be hit accidentally during the nonorbit iteration. I accidentally put this in the place for the exponent of the Mandeloid instead-- being a good approximation for an irrational number, an interesting thing happened on the _non_ orbit screen: the fractal generated had the "fault lines" all over one side of the fractal. Zooming in, they become so numerous in some areas that they become the dominant visual theme. One particular area is very reminiscent of the Sierpinski triangle-- with the triangles slightly rearranged and etched away, but trailing down into the infinitesimal (while blue-shifting as they get smaller). It can be generated by this .frm-.par pair: Sincerely, Hiram =================PAR BEGIN===================== SierpinskiUnwoven { ; The fault lines from fractional order Mandeloid powers ; proliferate @ exp=e. The torn triangles in fractal dimen ; sion remind me of the Sierpinski triangle with its parts ; distorted rearranged and partially covered. ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=exprmntl.frm formulaname=orbit_mandeloid passes=1 center-mag=-0.65861073150000000/+0.17502501600000000/86.33309/1/-47.5590\ 028298907441/0.159744895096057493 params=2.71828182845905/0/2.71828182845905/0/4/0 float=y maxiter=10000 inside=0; colors=(a)spectrm3.map colors=000oC8<7>uM4vO3vP3<2>yT1zV0zY0<3>xj0xm0wp0ws0vw1<3>hxHdxL`xPXyU<1\ 6>WyoWypWyq<2>WyuVzwWww<3>cgwdcwf_whWwjSw<4>e8wd4wc0w<9>Y0kY0jX0h<2>V0eU\ 0cU0c<118>TQTTQTTRT<3>SSS000000zzzc00<6>n00o00p00<3>w00<7>nE9mGAlIB<3>fP\ GeRHdTI<9>xU2 } ==================END PAR======================= ==================BEGIN FRM===================== Orbit_Mandeloid{ ; p1=A in z->z^A+C,p2=(sentry to do orbit,radius), ; p3=(bailout for nonorbit,angle subdivisions for orbit) IF(isinit==0) isinit = 1 A = p1 lim = real(p3), anglediv = trunc(imag(p3)), angle = 2*pi / anglediv sentry = real(p2), radius = imag(p2) rotfactor = cos(angle) + flip(sin(angle)) orbititer = trunc( (maxit - 1) / anglediv ) ENDIF isorbit = ( real(pixel) == sentry ) IF(isorbit) C_ct = 0 ; count C values on the radius i_ct = 0 ; count iterations per C value C = radius ; set initial C position to radius along +real axis continue = 1 ; the "do not bail out" flag ELSE C = pixel ENDIF z = 0 ; in either case z starts at 0 : IF(isorbit) IF(C_ct >= anglediv) ; should terminate continue = 0 ELSE ; normal iteration for orbit screen z = z^A + C i_ct = i_ct + 1 IF(i_ct >= orbititer) ; go to the next C value C_ct = C_ct + 1, i_ct = 0 z = 0 C = C * rotfactor ; rotate C-value around the circle ENDIF ENDIF ELSE z = z^A + C continue = ( |z| <= lim ) ENDIF continue } =================END FRM=========================

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FOTD 20-05-04 (A Tangle of Points [3])
by Jim Muth 20 May '04

20 May '04

FOTD -- May 20, 2004 (Rating 3) Fractal visionaries and enthusiasts: I have another very busy day ahead of me, so I must again be brief. Today brings another 'nothing' fractal, worth only a lowly 3. The low rating reflects the disappointment I feel with it. I have named the image "A Tangle of Points" because it reminds me of a tangle of vines. It is part of the larger fractal that is created when portions of Z^(-0.8) and Z^(-7.5) are combined and (1/C) is added. The image has been 'evaporated', and therefore consists totally of 'inside' points made visible by the 'bof61' inside fill. Other fills might have done better, but I had no chance to try them. The rating of 3 and render time of 7 minutes combine into an overall value of 41. All this becomes meaningless when the completed image is downloaded from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Clouds hung tough all day Wednesday here at Fractal Central. Combined with occasional light rain and a temperature of 82F 28C, the lack of sun kept the fractal cats safely ensconced indoors. They were only mildly annoyed however, and spent the afternoon sleeping by the window. Today is again starting cloudy, but at least it is dry. The cats are still sleeping. It is too early to predict what kind of day they will have. As usual, I have a lot of work to do. Unless the unexpected happens, the next FOTD will appear here in 24 hours. Until then, take care, and where is the world going, other than around the sun? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Tangle_of_Points { ; time=0:07:17.42--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+15.30615106164459000/+1.23468727139517\ 000/5.37212e+009/1/157.5/-0.00641920475950448488 params=1/-0.8/0.2/-7.5/0/1e+100 float=y maxiter=750 inside=bof61 periodicity=10 colors=000r_IvbYydmwcjvbgtbesabq``p`Yn_Wm_TlZQjYOi\ YLgXJfWGdWEcVBbV9_REXOIULMRIQOEULBYI8aF5eEAbEF`EJZ\ EOXETVEXTEaREfPEjNEoLEtJExH7vZ0tp4sf8rYCqPGqGQ0YT0\ ZV0_Y0``0ab0be0cg0dj0el0fo0gq0go3cm5`k7Yi9VgBSeDPc\ FMgBTj7_n3fq0mm6kjBjfHhcMg`SeXXdUbbRgaNm_KrZHwY9va\ 2vd6rd9ndCjdFfdJbdMZdPWdSSdVOdZKdaGddCdg8dj5dh9cgD\ cfHceLcdPccTbbXba_b`cb_gbZkaYoaXsaWwaVzahzLuz4sx6r\ w7qu8ot9nrAmqBgjJbcRYYZSRfNKnIEuPNlVVdUU`TTXSSUSRQ\ RQNQPJPOGPNCOM9NL5NL2SSDWZN_eXY`TWWQURNSMKQHHOCEM8\ BKGEIOGGWIEcKCkMAsO8zQDvPIrONnNSkMXgLacKf_JjXJX_UJ\ bd5do6ap6_q6Yr7Wr7Us7St8Qt8Ou8Lv9Jv9Hw9FxADxAByA9z\ A7z9Hl8RZ7`L6j78g6Ae5Bb5D`4EY4GW3HT3JR2KO2MM1NK1PJ\ 5QJ8RJBSJFUIIVILWIPXISZHV_HZ`HaaHd_GfZFgYFhWEiVEjU\ DlTDmRCnQCoPBpOBrMAsLAtK9uJ9v_LAZG8ZB6_E5_G5_J4`L4\ `N4`Q3aS3aV2aX2bZ2ba1bc1cf0ch0cj0ek1gk1ik2jk2lk2nk\ 3ok3qk4sk4tk4rg3qc3o_2nX2 } 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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FOTD 19-05-04 (Decorated Minibrot [4])
by Jim Muth 19 May '04

19 May '04

FOTD -- May 19, 2004 (Rating 4) Fractal visionaries and enthusiasts: I am still lagging behind in my regular work, so I must be brief. Z^(0.15) does not make a fractal; nor does Z^(-0.15). And combined they do not make a fractal. They make a blank screen consisting of trapped 'inside' points, but just as with the 'evaporated' images, these points can be brought to life by rendering them with an active inside fill. In today's case, the bof61 fill works best, though the main action lies just beyond the left border of the default screen. Hiding almost invisibly there lies the scene of today's image, which pictures a strange Mandeloid with unusual decorations. I named the image "Decorated Mandeloid". The rating of 4 combines with the render time of just under 2 minutes to give an overall value of 205. That value might be raised by downloading the completed GIF image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather here at Fractal Central on Tuesday was fair enough, with a temperature of 82F 28C. It was fair enough that is until it started thundering around 6pm. But by that time the fractal cats had long since come inside. The dynamic duo has taken a liking to the cicadas, which are in unlimited supply in the area. The bugs are good to eat and easy to catch, but the duo doesn't know when to stop catching and eating them. I guess the aging cats feel good about once again being able to catch prey at will, but I will likely have to limit their outdoor time until the cicadas are gone, which will be in about a month. I do not want the duo overstuffing themselves with wings. When the cicadas started singing, I thought there was a faucet running somewhere in the house, but now that I know what it is, I find the song rather enjoyable. It has a diffuse, direction- less, far-away quality about it that always raises feelings of nostalgia. The last time I heard it I had just discovered fractals, and had not even dreamed of leaving my designer position at the print shop to see what I could do on my own. A lot can happen in 17 years. If I don't fall too far behind in the work, the next FOTD will appear in 24 hours. Until then, take care, and search for the source of dark energy. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ DecoratedMandeloid { ; time= 0:01:57.10--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=t center-mag=-1.998748343088183/0/1139.953/1.1658 params=1/0.15/1/-0.15/0/0 float=y maxiter=256 inside=bof61 symmetry=xaxis periodicity=10 colors=000L2OD0ND1OB6T9BX8Ga6Ld4Qi1Tl0Yq0bt0gz0lz0\ qz0tz0uz2qz8qzEpzJpzOnzTlz_lzdkzikzniztgzzgzzfzzfz\ zgzzizwizskzpksklkgladnT_nJXpBTp2Rn6Qn8Qn9OlBNlDNl\ ELlGJkIJkJIkLIkNLVQQRaTQkYOwaNznTzzYzzbwzfzpizdlzT\ pzJszBzz2zz0zxtzzzfzzdzqbzgbz_awRanJdzDfz4iz0kz9gz\ LdzXazgYzsVqzTkdkgEzf0zd0za4z_DtYJkXRbVYVTdbqiiznp\ zQObz0zz0zz0zzDzzQztbznnzszzwzzzzzzzzxzzszwnzqizld\ zg_wbVpYRkT_p_ftfnzktzqzzxzzzzzzqzwgst_kqQdpIYl9Rk\ 8Tl6Vl6Xl4Yl2_l2al1bl1bl8kqEqtJzxQzzVzzzEfkEbXE_IE\ X2ET4zg6sl8lq8fw9_zBTzBNzDGzD9zLDzRGz_JzfNzwbxzssz\ znzzqzztqzxfzzTwzItzIwzIwzIxzIxzLzzOzzRzzVzzXzz_zx\ bzxfzwiztkztnzsqzqtzqzzkxzpzznzznzzlzzk19T8EVDJXIN\ YNR_RX_X_aadbgidllfqqfwwgzzizzkqxzszzszzszztzztzzt\ zzwzzwzzwzzxzzxzzxzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzxzzwzzwzztzzszzqzzqzzpzznzznzzlzzkzzRzz\ VzzXzzYqgxkaqfVkaNfVG_Q9V } 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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how do I generate a file par
by Alessandro Flamini 19 May '04

19 May '04

Hi, I've just started to use Fractint and I don't know how to create a new fractal starting from scratch. My understanding is that I should create a file.par and a file.frm (the second with wordperfect) which contain the code, am I right? Furthermore, how do I generate a par file? Thanks in advance. Alex

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