April 2004 - Fractint - mailman.xmission.com

FOTD 22-04-04 (Rabbit Ears [6])
by Jim Muth 22 Apr '04

22 Apr '04

FOTD -- April 22, 2004 (Rating 6) Fractal visionaries and enthusiasts: To create the parent fractal of today's image, I took Z^(-1.6) and added 0.26 part of Z^(-6.1) to it before adding (1/C). The MandelbrotMix4 formula mixed these ingredients thoroughly. The 1200 iterations produced a fractal that retains many of the characteristics of the Z^(-1.6) and Z^(-6.1) Mandeloids, yet at the same time is something entirely new, with many features of the Z^2+C Mandelbrot set, such as bays, buds, valleys and midgets. Today's scene lies in one of the many valleys of this parent. The escape radius of the classic Z^2+C Mandelbrot set may be increased to as large a number as can be entered as a parameter, and the result will be nothing more than an outward shifting of the iteration bands. But when the escape radius of a fractal such as today's parent is increased, the image quickly falls apart. By the time the escape radius reaches one-googol, nothing is left but empty space. All the points have become trapped. I call this process 'evaporation'. Things are not lost however. All the points might be trapped, but they are still active, and the results of this activity can be made visible by rendering the image with the inside option set to something like 'bof61', which I believe colors the points according to which iteration takes them closest to the origin. All this stuff is relevant because the escape radius of today's image is indeed one-googol, and all the points have therefore been trapped. The original scene has evaporated. What we see on the screen are the things that the trapped points are doing in their confinement, made visible by the dynamic 'bof61' inside fill. What I see while staring at the image is a forest of rabbit ears. Maybe this means the residents of Fractal Land have over-the-air TV, but more likely it's just a coincidence. Whatever the reason, I named the image "Rabbit Ears", then rated it at a 6, which gives an overall value of a 66. Don't waste time investigating the detail inside the rabbit ears. This detail consists of moire patterns -- artificial patterns caused by limited screen resolution, which vanish faster than one can go after them. The only thing faster than a vanishing moire pattern is the download of today's pre-rendered GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> On Wednesday the temperature reached 73F 23C here at Fractal Central, while the sun shone frequently and the wind blew gently from the east. The cats enjoy such conditions, and made no exceptions on Wednesday, when they spent half of the morning and the entire afternoon lounging in the yard. Today is similar. The cats are already on their window shelves, gazing at the sun and planning a lazy afternoon. For me, it will be another in a seemingly endless string of days with work before play. The next fractal will hatch when the work is finished. Until next time, take care, and be back in 24 hours for the next fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Rabbit_Ears { ; time=0:09:08.16--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+3.20067893060894/+0.02108591826425907/\ 685450.6/1/-20/-1.18714037711242781e-007 params=1/-1.6/0.26/-6.1/0/1e+100 float=y maxiter=1200 inside=bof61 periodicity=10 colors=000ISTRYfXcrg_fpXUzTHzR2xXBnaKcgSTlZHpfIfnI\ XuINzIBz4zK8zXBrhEltHfzKevNenOefRcYTcPUcGWZOXWWYSa\ YOhZIo_EuaAza5zbDvcKkePZfWNf_8G8TOAUWBUaBWhDWnDWiI\ ZfObbTfYYiUbmRgockqpnrzqt0404PHBgZHxnTtlcpkmlhwhgz\ efxbep_chZb_XaSW_HGS70Ibz0hzBmzRhmYeZeaIlY0qXSgXnX\ z8zHiBSXW_IlhDmo8nv4oz0pz0pz0qz0rz0tx0tu0ur0vo2wm2\ wkEnhPegZXifSllNmqHoxBqz5rz0zzzzxwzpvzhuzZtzRrzHqz\ 7pz4mr2ii0f_0bX0aT0aP0_N0_I0ZE0ZL0OM0N52T58P5GL5LG\ 5SB5X7DZAKaBRcDWfGahHgkIigKo_frOzbRpNShYIahAUr0Ov7\ LzDIzIGzODzTAzPGzLLzHPzDUz8Zz4bz0gx0kkGlYXmKlnIhkI\ egHaeHYaGUZGRWGNTT_bcmlispmvrqwttxvzzzzzzzzzzzwzzu\ wzqvxotvlrtiqrgrveuxbvz_wzYxzUxxSxvOxtLxqIzoEzmBzk\ 8zh4zf0ze0wb0va0u_0rZ0qY0pX0nW0mU0lT0iS0hR0gP0fO0e\ N2eN8cLDcLIcKObKSbIXbI_aHeaHi_Gm_Gq_EvZEzZDzZDzHAx\ 08o4EmAKlGPkLUiSZgXcfahefmckpbokXteSxZNzTHzNBuULk_\ U_fbOmkBrr0xzzg7ze52E0BLE } 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==================================

1 0

Reading Digests
by Vortex Swirling 22 Apr '04

22 Apr '04

This is only a bit off topic since I receive the fractint list as a digest. Is there any sort of application that makes it easier to navigate the digest? --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.659 / Virus Database: 423 - Release Date: 4/15/2004

2 1

FOTD 20-04-04 (Gruesome-brot [3])
by Jim Muth 22 Apr '04

22 Apr '04

FOTD -- April 20, 2004 (Rating 3) Fractal visionaries and enthusiasts: Today's image takes us to the northeast shoreline of the main bay of the Mandelbrot set, where we examine the valley leading to the large period-4 bud there. This valley is centered at 0.25+0.5i, and the slope of the main bay at this point is 45 degrees, which makes it quite simple to examine the area from all kinds of strange four-dimensional directions. Today's view is halfway between the Parabolic and the Oblate directions. The tiny buds that line the edges of the valley do appear in the image, but they no longer appear as tiny empty circles. The circles have been stretched in one of their dimensions to infinity, and appear as parallel slits partially obscured by fractal debris. By changing the imag(p1) parameter, we can see many different views of the scene, all of which show the buds as slits. If imag(p1) is set at 180, the image is the same, but we are looking at it from the opposite direction. Some of these other views are quite interesting, though I had little time to investigate them. I might do so sometime in the future, but with today's image rating only a measly 3, I will be in no great rush. With a render time of almost 8 minutes, the image has an overall value of 39. I named the image "Gruesome-brot", not because it is horrifying to look at, but because it's not a very good example of fractal art. The completed GIF image is available on the FOTD web site at:. <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> It reached 91F 33C here at Fractal Central on Monday, a temperature that left the fractal cats with nothing to do but sleep. They passed the afternoon sleeping in the yard, dreaming whatever it is that cats dream. Their moods were good when the time came to come indoors, so I guess their day was satisfac- tory. Today is starting cooler, but still mild. We'll see how the duo takes things. I managed to trim half the grass yesterday. The second half will be finished sometime this afternoon. Until next FOTD, take care, and look for the best. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Gruesome-brot { ; time=0:07:45.55--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=1 float=y center-mag=-2.2204e-016/-0.00217442/11.20316/0.2086 params=-45/0/2/0/0/0/0.25/0.5 maxiter=32000 inside=0 logmap=6 symmetry=yaxis periodicity=10 colors=000ZZh__i``jaakablbcmcdndeoefpfgqehqegpdfod\ encdlbckbbjaaha`g`_f_Zd_YcZXbZWaYV_XUZXTYWSWVRVVQU\ UPSUORTNQSMOSLNRKMRKLSLMTMMUNNUONVPOWQOXROXRPYSPZT\ Q_UQ_VR`WRaXRbYSbYScZTd_Te`TeaUfbUgcVhdVhdWieWjfWk\ gXkhXliYmjYlkamjYmfVmcSm_PmXMmQVmJbmCjc6rU7qK8pD9p\ DAoDBnDCnDDmDElDFlDGkDHkDIjDJiDKiDLhDMgDNgDOfDPeDQ\ eDRdDSdDTcDUbDVbDWaDX`DY`DZ_D_ZD`ZDaYDbYDcXDdWDeWD\ fVDgUDhUDiTBkUDjTFjTGjTIjTJjTLjTMiTOiTPiSRiSSiSUiS\ ViSXhSYhS_hS`hSbhRdhRehRggRhgRjgRkgRmgRngQpgQqfQsf\ QtfQvfQwfQyfQyhHzjQzlYznexmfvmfulgslgrkhpkhojimjil\ ijjijiijghkfhkdglcglafm`fmZenYenWdoVdoTdoScpQcpPbq\ NbqMarKarJ`sH`sF`wG`sH`pI`mJ`jK`gL`cMZ`NXYOVVOTUOR\ S4PB6NC7LD9JEAJFCKGDKGELHGLIHMJJMKKMLLNLNNMOONQOOR\ PPTPQUQQVQRXQSYRT_RU`SVaSVcTWdTXfU_hWbjYel_hnakpcn\ reotfoveowenxdnycozcqzbszbuzawz`yz`zz_zzZzzZzzYzzY\ zzXzzWzzWzzVzzUzzUzzTkzSz } frm:multirot-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================

6 7

FOTD 18-04-04 (Fractal Splendor [7])
by Jim Muth 22 Apr '04

22 Apr '04

FOTD -- April 18, 2004 (Rating 7) Fractal visionaries and enthusiasts: Take (1/Z), mix it with 1/2 as much Z^(-2), and add (1/C). What do you get? Why, a fractal of course -- an oversized fractal that is too large to fit on the default screen and needs to be shrunk by an outzoom before it becomes completely visible. This fractal has X-axis symmetry, but only because the exponents of Z are whole numbers. Changing (1/Z) to Z^(-1.1) or Z^(-2) to Z^(-2.1) gives a pair of entirely new fractals with no symmetry. This parent fractal is far richer in detail that the classic Mandelbrot set. The detail might not be any more varied, but it covers a far larger area. The fractal has an interesting area around +7 on the real axis, where two graceful arcs of delicate filaments come together. Today's scene is located in one of these arcs, very near the point where it touches the X-axis. I have colored the image to resemble something like a brilliant star blazing away in empty space, and named it "Fractal Splendor". I seem to remember a somewhat similar FOTD image from several years past, but if today's image is a near-repeat, I will consider it simply a variation on a splendid theme. I rated today's image at a 7, mostly because of the extra effort I put into the coloring. The render time of 11 minutes gives the image an overall value of 59. As always, the image may be seen most conveniently by downloading it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Saturday was as close to being a perfect day as we have come in quite a few months here at Fractal Central. Warm sun, light winds and a temperature of 84F 29C gave the fractal cats all they could ask for. If they had been 10 years younger, they would have romped all afternoon. But being 14-year-old cats, they slept in the shade of the holly trees most all afternoon, and romped, (if what they did can be called romping), only a few minutes. Today is starting just like yesterday. I assume the cats will have an equal day. As for me, I'll put off the grass trimming one more day, and take it easy. The work is light and I should have lots of time to get it done on Monday. The next FOTD will appear in 24 hours. Until then, take care, and try to prove that fractals are not real without defining reality. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Splendor { ; time=0:11:55.35--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+7.02311504952539200/+0.000296216423795\ 89/7.833267e+008/1/-142.5/0.00233171123971526173 params=1/-1/0.5/-2/0/0 float=y maxiter=2000 inside=0 logmap=248 periodicity=10 colors=0007LK7LK7LK7LK7LL7LL6LL6KM6KM6KM6KN6KN6KN6\ KN6JO6JO6JO6JP5JP5JP5JP5IQ5IQ5IQ5IR5IR5IR5HS5HS5HS\ 4HS4HT4HT4HT4GU4GU4GU4GU4GV4GV4GV4FW3FW3FW3FX3FX3F\ X3FX3EY3EY3EY3EZ3EZ3EZ3EZ4F_4G_5H`5I`6Ia6Ja7Kb7Lb8\ Lc8Mc9Nd9OdAOeAPeBQeBRfCSfCSgDTgDUhEVhEViFWiFXjGYj\ GYkHZkH_lI`lI`lIamJbmJcnKdnLeoMfoNgpOhpPiqQjqRkrSl\ rTmsUnsVosWptXqtYruZsu_tv`uvauwbvwcvxdwxewyfxygxzh\ yziyzjzzkzzlzzmzznzzmzzlzzkzzjzzizzhzzgyzfxzewzdvz\ cuzbuzatz`tz_szZszYrzXrzWqzVqzUpzTpzSpzRozQozPozOn\ zNnzMnzLmzKmzJmzIlzHlzGlzGkzGkzFjzFjzEjzEizEizDizD\ izChzChzChzBgzBgzBgzAgzAfz9fz9fz9ez8ez8ez7fz8ez8ez\ 8dz9dz9cz9cz9bzAbzAazAazB`zB`zB_zBZzCZzDZzEZzFZzG_\ zH`zIazJbzKczLczMdzNdzOdzPezQezRezSfzTfzUgzVgzWgzX\ hzYhzZhz_iz_iz_izZjzZjzZkzYkzYkzXlzXlzXlzWmzWmzVnz\ VnzVnzUozUozTozTpzTpzSpzSqzRqzRrzRrzQrzQszPszPszPt\ zOtzOuzNuzNuzNvzMvzMvzLwz } 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==================================

2 1

(marks.par) Mark'sMandel by the documentation.
by SherLok Merfy 22 Apr '04

22 Apr '04

MarksBug { ; Attempt at speeding up Mark's Mandel with flexibility. ; Methinks that the similarity between manzpower and ; Mark's Mandel is the error, but the hard-coded formula ; does seem to allow for larger exponents before it ; decays. Maybe it's z(n+1)=c^(ex-1)*z(n) +c z=fn1(pixel), c=fn2(pixel), a=c^real(P1)-1: z=a*sqr(z) +c, LastSqr<= imag(P1) } default { ; Not even close, but I'm pretty sure that ; is what the documentation says (without functions ; or the realization that part of the documentation's ; results are constant per iteration). reset=2003 type=formula formulafile=marks.par formulaname=MarksMandel function=ident/ident params=7/4 maxiter=255 inside=0 } MarksHand { ; This might be kinda nifty. reset=2003 type=formula formulafile=marks.par formulaname=marksmandel function=ident/ident center-mag=-3.486/3.66155/0.1051468/1.1186 params=7/4 float=y maxiter=255 inside=0 outside=atan invert=1.13584734211722/0.5/0.7 periodicity=0 colors=(a)altern.map } Heart { ; Some habits are hard to break. ; I would finish the set, but I've worked ; hard to establish this account, and something's ; very wrong with my ISP's response time. reset=2003 type=formula formulafile=marks.par formulaname=marksmandel function=conj/ident center-mag=0.22319/0/1.01533/1.1992/90/0 params=7/4 float=y maxiter=255 inside=0 outside=atan invert=0.5/0.25/0 colors=(a)altern.map }

1 0

FOTD 21-04-04 (Invasion of the Pods [4])
by Jim Muth 21 Apr '04

21 Apr '04

FOTD -- April 21, 2004 (Rating 4) Fractal visionaries and enthusiasts: I still have a fondness for those junky old sci-fi and monster movies that were made in the 1950's. Those movies were populated by an incredible variety of giant spiders, crabs, ants, mantises, living plants, and blobs of all consistency, not to mention the invading aliens from outer space. Except for the specialty networks, those movies are gone from TV now -- they have been replaced by computer effects, car chases and explosions -- but I still have hundreds of the junkers safely stored away in my vast collection of junky old movies. Whenever I find myself in the mood for some TV junk, I pop in a tape and sit down to see how long I can watch before falling asleep. I mention junky movies because today's image reminds me of one of my favorites -- "Invasion of the Body Snatchers" -- in which alien pods drop from space, hatch into duplicates, and take over our minds. I have named the image "Invasion of the Pods". When I studied the image, I found myself looking up into a clear blue sky at a shower of pods raining down to earth. I guess we will never know whether the invasion is successful, but with a rating of a mere 4, the image is only marginally successful. The parent fractal is basically a shapeless hole, created by combining portions of Z^(-1.2) and Z^(-2.1), which lies in a sea of sand, with a vast expanse of fat twisting filaments extending far to the south. I have found no signs of midgets in this parent fractal, but the sea of sand proved interesting enough to produce today's image. The invading pods may be seen by running the parameter file or by downloading the complete GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With lots of sun and a temperature of 77F 25C, Tuesday was another fine day here at Fractal Central. The cats must have thought so also, since they spent almost six hours in the yard, mostly sleeping. Today however is starting cloudy with showers in the area. It remains to be seen how the dynamic duo will make out. For me it's work, then play. Until next time, take care, and see you in 24 hours, when the next FOTD appears. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ InvasionOf_ThePods { ; time=0:03:11.53--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-7.81089/3.08437/31.9843 params=1/-1.2/\ 0.57/-2.1/0/0 float=y maxiter=1200 inside=0 logmap=yes periodicity=10 colors=000M`uKZuHXuFVuCTuARuCTpEUlGVhHWcJX_LYWM_RO\ `NQaJRbETcAVd6We2Zb3``3bZ3dX3fV3hS3jQ3lO4wn8xn8yn7\ zn7r`8vn8n_8rn8oZ8vm8l`8rg8hc8kf8ea8fb8aa8d_8YY8`W\ 8UUcSScQRcOPcNNcLLUJJUHHUUczUczUczUczUczUczUczUczU\ czUczUczUczUczUczUczUczUczUczUczUczUczUczUczUczUcz\ UczUczUczUczVczWczXczYczZcz_cz`czaczbczcczcczcczcc\ zcczcczcczcczcczcczcczcczcczcczcczbczacz`czZczYczX\ czWczVczTczSczRczQczPczNczMczLczKczJczHczGczFczEcz\ DczBczAcz9cz8cz7cz8cz9czAczAczBczCczDczDczEczFczGc\ zGczHczIczJczJczKczLczMczMczNczOczPczPczQczRczSczS\ czTczUczVczWczVczVczVczVczVczVczVczVczVczVczVczVcz\ VczUczUczUczUczUczUczUczUczUczUczUczUczUczTczTczTc\ zTczTczTczTczTczTczTczTczTczRczTczVczXczYcz_czaczc\ czdczfczhczgczhcziczjczkczlczmcznczoczpczqczrczscz\ tczuczvczvczucztcztczsczrczqczqczpczoczncznczkczhc\ zfczcczcczcczcczcczcczccz } 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==================================

1 0

sorry about the fat.
by David Lowenstein 21 Apr '04

21 Apr '04

I will trim my further messages. -david

1 0

FOTD 19-04-04 (The Wine-Dark Sea [5])
by Jim Muth 19 Apr '04

19 Apr '04

FOTD -- April 19, 2004 (Rating 5) Fractal visionaries and enthusiasts: Today's discussion will be very short -- reason: I can no longer put off the trimming of the fractal grass, and there is significant other work to be done as well. This means that the image will have to speak for itself. But careful listening will be needed to hear the words. Like most of the FOTD images, today's image has a midget at its center. The scene is located in an 'East Valley' type valley in the fractal that results when some Z^(-5.1) is subtracted from Z^(-1.5) and (1/C) is added. I named the image "The Wine-Dark Sea". The phrase is not original, but I forget in which piece of literature it appears. The rating of a 5 seems appropriate for an image that I needed to hurry along. When the 7-minute render time is taken into consideration, the overall value rates a 70. The finished image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The temperature reached 87F 30.5C here at Fractal Central on Sunday, which was actually a bit too warm for the fractal cats, who did little more than lie motionlessly in the shade of the holly trees all afternoon. When evening arrived, they came indoors without hesitation to enjoy their meal. Today is starting even warmer. I expect a similar day. For me, the work is moderate, and the trimming of that grass is imminent. Until next FOTD, take care, and be lucky. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Wine-Dark_Sea { ; time=0:07:06.06--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+4.37697768075993700/-0.007125508732302\ 11/3.264379e+008/1/145/-0.000315981629220238314 params=1/-1.5/-0.294/-5.1/0/0 float=y maxiter=1200 inside=0 logmap=132 periodicity=10 colors=000RDIRFJTHLVJNXLPZNQ`PSbRUdTVfVXhaZje_lian\ mcppdqnfqkgqghrdir`jrYksUlsRmsNnsKooIikGcgEZcCT`AO\ X8IT6DP47M32Q83UD4YH5`M6dQ7hV8lZ9ocAsgBwlCzpCqiIhb\ N_WTRPYIIcABhDIbGPYJVTHYQF_ODaLBdJ9fG7hE5jCFiBOiBX\ hBehAngAwgAoa8hW6aQ4VL2YO3`Q3bT3eV3hX3j_4ma4pc4rf4\ uh4wj4vi8uhCtgGsfKreOqeRmbSj`TgZUdWV`UWYSXVQYSNZPL\ _LJ`IGaFEbCCc9Ad7QZ5dT3sN9tSEtWJt`OtdTuiYumburguvl\ uzivxgvvdvtbvr`wpYwnWwlTwjRxhPxfMxdKxbIx`KwaMwaNva\ PvaRvaSuaUuaVtaXtaZta_saasabsaamd`gf_biZXkYRmXMpWG\ rVBtYEq`GnbIkeLhgNfjPclS`oUYqWWmZViaUfdTbgT_jSWmRT\ oRSlQSiPSgPSdOSaNS_NSXMSULSSLSPKSNKURJVUIXYHY`G_dF\ `gEbkDcnCdqBbmE`iGZfJXbLVcOTdQReTPfVNgYLh_JibHjdFk\ fHldJmcLmbNmaPm_RmZTmYVmXXrWYlUZmT_mS`mQamPbmOYmx_\ msamncmiemdgo_iqVksQmuLowGnyLnzQnzVnzZnzcmzhmzlmzq\ mzvmzzoznqzcszTlzPfzM`zIUzFOzBIz8Cz5DzBDzGDzLDzQDz\ VDz_Gz`IzaKzaNzbQzFQzGRzH } 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==================================

1 0

FOTD 15-04-04 (Land of Fractals [5])
by Jim Muth 18 Apr '04

18 Apr '04

FOTD -- April 15, 2004 (Rating 5) Fractal visionaries and enthusiasts: Today's image takes us into the fourth dimension. I have always been fascinated by the fourth dimension. I was not yet a teen-ager when, having just finished a book, (I think its name was "One, Two, Three, Infinity..."), I asked my father where the fourth dimension is, and, thinking of relativity, he told me that it is in the past and the future. This was not a very satisfactory answer. The past and future are time, not space. I wanted to know where the fourth dimension of space is. He then explained to me that as far as we know, there is no fourth spatial dimension, and even if there were, we would perceive it in three-dimensional terms. This is the problem. We are brain-washed to perceive our surroundings as a three-dimensional world. We have not been wired to perceive a four-dimensional space, and it is too late to change that. If we were suddenly dropped into a four- dimensional world, we would not see the fourth dimension. We would see a three-dimensional world that obeyed different rules. Solid objects would change shape as we watched; objects would appear and vanish. We would think the world had gone crazy. We would probably go crazy ourselves, (as some say I already have), but we would be no closer to visualizing the fourth dimension. Even now, we are able to fully visualize and understand the shadows that would be cast by four-dimensional objects onto the three-dimensional surface of our space. A 4-D hypersphere would cast a spherical shadow if the ray of light fell perpendicularly onto our space. If the light struck our space at an angle, we would see an oblate spheroid, the eccentricity of which would vary with the angle of the ray of light. But even though we understand all of this, we are still totally unable to visualize the hypersphere that would be casting the shadow. We can also know and fully visualize the three-dimensional slices of four-dimensional objects. The 4-D hypercube may be sliced to give many curious prisms, as well as a tetrahedron and an octahedron, and of course the expected cube. But even this is of no help in our quest to realize the fourth dimension. Our lack of visualizing ability is curious. We can program our computers to 'think' in four dimensions almost as easily as in three. We could even give them three-dimensional screens on which to better display the 4-D worlds they would have no trouble in manipulating. Of course, we would then be unable to view the 3-D screens in the proper manner, from outside our space. We would of necessity need to view the screens 'edge-on'. We appear to be forever doomed, trapped in a world of three dimensions, while able to know of the far greater vistas that would lie before us if only we could rewire our minds. Since our minds are not about to be rewired, it's best we turn to today's image. Today's image is a two-dimensional slice of a four-dimensional object. In this case, the object is the 4-D Julibrot created by iterating the formula (1/Z)-Z+C. I have sliced the Julibrot in what I call the Oblate direction, which is determined by the imaginary C and real Z axes. The picture has a certain surreal quality about it, which inspired the above outburst about higher dimensions. It could almost be something we might see if we were suddenly dropped into a four-dimensional space. This is why I named the picture "Land of Fractals". Since the image is such a departure from my usual fractal fare, I was not sure how to rate it. I finally decided on a rating of an average 5. The short render time of 2-1/2 minutes raises the overall value to a mighty 202. An alternate way of seeing the other-worldly scene is to download it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Light rain fell steadily all day Wednesday here at Fractal Central, keeping the fractal duo confined to the indoors. Even if it had not been raining, the temperature of 50F 10C would have been a bit chilly for their sensitive ears. Today is starting windy and chilly, but sunny. We'll see how the dynamic fractal cats take these conditions. For me it's work before play. The problem comes in separating the two. Until tomorrow's FOTD, take care, and most likely it's fractals all the way down. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Land_of_Fractals { ; time=0:02:28.69--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=OblateMix2 function=ident passes=1 center-mag=-4.55271/3.10114/0.6584367/8.9718/-11.2\ 262659607652502/29.222244310548934 params=1/-1/-1/1/1/-0.2 float=y maxiter=1200 inside=255 logmap=yes periodicity=10 colors=000Di`Ei_FiZFhZGhYGhXHhWHhWHhWU_`fRfuHlsIkr\ JjpKjmLiUdkUckUbjUaiU`hU_gUZfUYeUXdUWcUWcUVbUVbUUa\ TUaST`QT`RS_PS_NRZMRZKQYJQYHPXGPXENWDLWBIVAGV8EU7C\ U8ET9MTANSBOSBPRCQRDRQETQFUPFWPGYOH_NIaMIcLJeKKgJL\ iIMkIMmINoIOqIPsINsHPtIQtIStITuJVuJWuJYvKZvK`vKawL\ cwLdwLfwLgxMixMjxMlyNmyNoyNpzOrzOszOtzOuvPusPupPum\ PvjPvgPvdPvaPubRtcTscVrdXqdZpe_oeanfcnfemgglgikhjj\ hliinhipgjrfhygjshlninhjpckrZltTmvOnxJozDpz8pz3lxE\ hrPdm_`gjYcvXbtXbsXbrXbqWbpWboWbnWbmVbkVbjVbiVbhUb\ gUbfUbeUbdUbcW`bY_bZZb`YbaWbcVbeUbfTbhRbiQbkPblObj\ NahNafM`dM`bL_`L_ZKZXKZVJYTJYRIXPIXNHWLHWJGVHGVFFU\ DFUBET9ET7DS5DS8GTBITELTGNTJQTMSTOVURXUU_UWaUZdUaf\ UgkVchU_fUXdTTbTQ`SMYSIWRFURBSQ2UJ8QQEMWKIbQEjPFhP\ GgPHfPIeOJdOKbOLaOL`NM_NNZNOYNPWNQVMRUMRTMSSMTQLUP\ LVOLWNLXMHUMLXLP_KTbJXeJ_gIcjHgmHkpGosFstCruFrvIrw\ LqxNqyQqzTqzWpzYpz`pzccwz } frm:OblateMix2 {; Jim Muth z=real(pixel)+flip(real(p3)), c=fn1(flip(imag(pixel)))+imag(p3), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2): z=(a*(z^b))+(d*(z^f))+c, |z| <= 100 } END 20.0 PAR-FORMULA FILE==================================

5 5

FOTD 17-04-04 (Polyester Minibrot [7])
by Jim Muth 17 Apr '04

17 Apr '04

FOTD -- April 17, 2004 (Rating 7) Fractal visionaries and enthusiasts: Once again the time has come to enter Fractal Land, that strange land that exists somewhere between the real world around us, which might not be totally real, and the imaginary worlds within us, which might not be totally unreal. The irregular real(p3) parameter of today's image shows that its parent fractal was found by the Fractint 'evolver' feature. Normally, I round off the odd numbers this feature produces, but for some reason I skipped the rounding process when I started working with today's parent. The parent fractal is a hugely bloated area of mostly disconnec- ted rings. Today's scene is located near a larger midget that lies in the interior of a ring in the distant north-northeast suburbs of the parent. The unusual detail inside the midget itself is a sign that the scene has been evaporated, and the ghost brought to life by the bof61 inside fill. Fractals in which all the exponents of Z are negative can be evaporated by raising the escape radius to a full googol, which is the amount entered as the imag(p3) para- meter of today's image. This trick usually traps every point. For reasons known only to myself and the 'intelligent designer', (whatever you consider this to be), I named the image "Polyester Minibrot". I might have done myself a favor when I rated it at a 7, but the image is really rather pleasant to look at, and I feel it earns its rating. The reasonably fast render time of under 4 minutes gives an overall value of 184. The render time is fast, but the fastest way of all to enjoy the image is to download it in finished form from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With a temperature of 67F 19C, gentle breezes, and warm sunshine to keep them happy, the fractal cats put on their best moods Friday. When the day was finished, they were so exhausted that they forgot their customary evening treats, and went right to sleep. Today is starting mostly sunny and warmer. I expect a similar day. For me, most of the graphics work is caught up. If I can muster the energy this afternoon, I'll give the grass the first trimming of the season. If not, I'll do it tomorrow or Monday. Until next time, take care, and don't get hot under the collar when a cool fractal appears. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Polyester_Minibrot { ; time=0:03:48.11--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+25.24771384422294000/+103.017140882474\ 40000/4599911/1/-22.5/6.18164318095387744e-005 params=2/-1.4/0.2/-8.6/-2.597094637897885/1e+100 float=y maxiter=1200 inside=bof61 periodicity=10 colors=00000U00o00u00x80zOAzdOzuazzozzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzdz0Iz00u50UX02x00zo0Dz00zG0zg0\ U0za0zg0zl0zu0rz0dz0Qz2Gz52zA0zD0zA0z80u50i20_05O0\ AA0G00L00Q00X00a00g00l00g00a00X02U08O0AI0GD0LA0Q50\ X00_00UD0NQ0LgGIoXDzhAsz5zz2zzzzxozodugQo_GiQ2KK00\ Q0ou8_f0zD0zD2zDDzDLgDXODm520a00z00z20z80uD0rI0lL0\ iQ0gX0aa0_g0Ul0Qo0Ou0Ux0_z0az0gz0iz0oz0rz0xz0zz0zz\ 0zz0zz0zz0zz0zz0zz2zzAzzIzuQzi_z_gzOozDxz2zz0zx0zu\ 0zr0zo0zl0zlIzlazluolzglzXlzOlzQozQozUozUozXrzXrz_\ rz_rz_rzdxzizzlzzrzzuzzzzzzzzuzzlzzgzz_zzUzzGzz5zz\ 0lz0Xa_dAzi5zl0zl0zo0zo0zr0zr0xu0uu0ox0lx0iz0gz0dz\ 0iz0oz0rz0xz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0z\ z0zz0zz0ro0da0UL2G822050080080000000000000A00O02a0\ 8r0Dz0Iz0Oz0UiG_QadAxi0zo0zu0za0zI5x2Qi0lX0zI0z800\ 00I0Gz0Gz0Gz0Gz0Gz0Gz0Gz0Gz0Gz0Lu0Oo0Ql0Ug0Xa0__0a\ U0dQ0gL0iG0lD0o80O0080008 } 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==================================

1 0