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FOTD 21-11-03 (Mandelbrot-09 [8])
by Jim Muth 21 Nov '03

21 Nov '03

FOTD -- November 21, 2003 (Rating 8) Fractal visionaries and enthusiasts: Today's image takes us to the region of the Mandelbrot set that produces Siegel disks when sliced in the Julia direction. It is not exactly Siegel disk territory however. True Siegel disks are found in the Julia sets of the total chaos on the exact edge of the main bay, and are of infinite iterations, which makes them impossible to calculate even though they do exist. Today's image contains things that are almost Siegel disks however. The things that resemble stuffed olives are about as close as one can come to Siegel disks in the M-set. By striking the space bar twice with today's image on the screen, one may draw a Julia fractal that is virtually a 'Siegel disk' fractal, but that's another story. (Still another story is the appear- ance of this part of the Julibrot when sliced in the odd direc- tions.) Yet another story is the things known as 'Herman's rings', which I remember being discussed on one of the fractal lists a number of years ago. Unfortunately, I have no idea what 'Herman's rings' are. Today's image is actually a rather new appearing fractal in the M-set, and deserves its rating of an 8, especially since the parameter file renders in a speedy 3 minutes plus 1/100 of one second, at least on my tired old machine with the exhaust fan that must be started by hand. The location of today's image is in the tip of a curving area of chaos in a valley of a tiny bud on the northwest shoreline of the main bay. Much of its impact is due to the coloring, on which I spent some extra time. This would appear to make it somewhat a work of art, though I claim no credit for the things actually done by the numbers. The three-minute render time may be escaped by downloading the image from Paul's web site, which hopefully is up and running at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Thursday here at Fractal Central dawned brilliant and stayed brilliant all day. The afternoon temperature of 59F 15C was perfect for cats and man alike, with a wind that stayed within reason. While the cats enjoyed these great conditions in the yard, the man finished the nominal amount of work that had accumulated since the preceding day ended. The day came to a close with everyone happy, which is quite an unusual event. Today and tomorrow promise to be repeats, so it looks like happi- ness will be the rule. Until next FOTD, take care, and the old M-set is not exhausted yet. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandelbrot-09 { ; time=0:03:00.01--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=-0.4166\ 3907681894050/+0.57331389272568470/2.33453e+007/1/\ -102.5/9.46314000424552937e-008 params=0/0 float=y maxiter=30000 inside= logmap=-712 periodicity=10 colors=000nRznUznVznYzn_znazncznezngzniznkznnznosn\ rmnsfnvenwekucjubisbfsafrafr_foUfoNfoUfoYfoXfq__rf\ UrmSssRszQszOszNssMsmKrfJr_IrUHrNFmMEfKD_KEUMENN0K\ 30J30J20I20I20E00F20H20I20J20K20M22N23N33O34Q36R37\ S37U38V3AV4BX4BY4DZ4E_4Fa4Fb4Hb6Ic6Je6Jf6Kg6Mi6Nj6\ Ok6Om6Nj6Mi6Mg6Mg6Mf6Mf6Ke6Ke6Kc6Kb6Kb6Ja6Ja6J_6J_\ 6JZ6JY6IY6IX6IX6IV6IV6HU6HS6HS6HR6HR6HQ6FQ6FO6HO6I\ N6JM6KM6MK6NK6OJ6RJ6UI6UH6UH6XF6ZF6aE6cE6fD6fB6fB6\ fA6fA6f86f86f76f76f66f46f46f36f36f26f26f06f06f06f0\ 6f0Af0Hf0Nf0Of2Qf3Rf4Sc6Ua7VZ8XXAYUBZOD_JEaEFb8Hc8\ Ie8JfAKgAMiANjBOkBQmDRnDSoEUqEXrEYsFZvF_wHayHbzIcz\ IezIfzJgzJizKjzKkzMmzMnzMozNqzNrzOszOszQszQszRszRs\ zRszSszSszUszUszVszVszVszXszXszYszYszZszZszZsz_sz_\ szaszaszbszbszbszaszasz_sz_sz_szZszZszZszYszYszZsz\ YszYszXszXszVszVszUszUszUszSszSszRszRszQszQszOszOs\ zOszNszOszQszRszSszUszVsz } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD 20-11-03 (Mandelbrot-08 [6])
by gnome＠hawaii.rr.com 21 Nov '03

21 Nov '03

Strange, went to Paul's site, I get the main FOTD page, but the links to the individual FOTD pages keep giving me the ATT message page not found message. David gnome(a)hawaii.rr.com >FOTD -- November 20, 2003 (Rating 7) > >Fractal visionaries and enthusiasts: > >With today's scene, we again take a trip into the depths of the >Mandelbrot set. We choose the basin of the midget at -1.47 on >the X-axis to be the scene of our trip. This midget is >surrounded by radiating filaments, with the location of today's >scene found on a small filament on the northeast shore.

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FOTD 20-11-03 (Mandelbrot-08 [6])
by Jim Muth 20 Nov '03

20 Nov '03

FOTD -- November 20, 2003 (Rating 7) Fractal visionaries and enthusiasts: With today's scene, we again take a trip into the depths of the Mandelbrot set. We choose the basin of the midget at -1.47 on the X-axis to be the scene of our trip. This midget is surrounded by radiating filaments, with the location of today's scene found on a small filament on the northeast shore. The midget in the image is of the fourth order, meaning it is located near a midget, near a midget, near a midget, near the midget at -1.47. For some reason known only to the mathematical illuminati, when a midget is located in one or more basins of attraction of larger midgets, the number of elements surrounding the midget resets itself several times as the midget is neared. Thus, instead of having the series 4,8,16,32...infinity, we have 4,8,16,32,...infinity, 8,16,32,64...infinity, 16,32,64,128... infinity, and so on. Today's midget shows this quirk quite clearly. And other than having this curiosity, it is a fairly lively scene, maybe not quite worth the half-hour required to render it from the para- meter file, but certainly worth the effort to go online and download the completed GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Rating the image was no problem. Considering the image itself and the time required to render it, I could rate it no higher than a 6. Pictures of scenes such as this are fairly common. (Had I found today's image 10 years ago, it might have rated an 8.) The weather in the Fractal Central area on Wednesday was violent to say the least. Torrential rain in the afternoon caused the local streams to flood, resulting in three deaths and several rescues. The temperature reached 68F 20C, but with flash flood conditions prevailing, the fractal duo wisely chose to remain indoors, asking for tuna. Today is starting sunny, but the wind is blowing, and the duo does not like wind, which hides the subtle sounds of approaching danger. They may be reluctant to venture out of doors. The fractal basement escaped with only a small puddle in the corner. My graphic work is reasonably under control. Another Mandelbrot fractal in 24 hours is a virtual certainty. Until then, take care, and keep your fractals dry. (Come to think of it, I have never seen a wet fractal.) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandelbrot-08 { ; time=0:31:08.32--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=-1.47539451765734098536/0.0079188952178\ 53054469/2.528066e+016/1/27.5/3.88578058618805e-016 params=0/0 float=y maxiter=7200 bailout=9 inside=0 periodicity=10 colors=000NUWTUVYVUcVTiWSnWRjOWfH`b\ 9eZ2ia3kd4lg4mj5nm6op6pjCodInZOmTUlN_kHejBki5qh7pf\ 9odBncDmaFl_HkZJjXLjWbkKtl9pnNmp_jrlVupZrqaordlsgi\ tjfumduhgncjgZm`UpUQrNRkORdPRYQSRRSKSSDTTNRUWPVeNW\ nLWwKVwKVwKUwKUwKUwKmX9k`BjcDhgFgjGemIdqKbtMawNfrQ\ knSoiVteXxaZo`ag`d__gS_jK_mRVjXRgSJmOCsQDpSEnUFlkz\ glmcla`mPXmDUiLQeSMaZIYfEUmAQt6PoEOjLNeSM`_LWfKRmJ\ NtYdbWfZVgVUhRTiNSjJRkFQlBPm7RfDT_JUUPWNVXH`ZAf_4l\ VFgQPcL__GiWCsSGnPKiNNdLR`JVWGYREaMCdIAbNBaSC`WDZ`\ EYeFXiFiVBuG7mLBePFYUJQYNJaQHZWGW`FTesVKpYLm`OjcRg\ fVeiZbma`peZqhUobPlYKiSGeNBbH6_CKXKPXUUWcZWicVnhVs\ kVviWtgXpeYkcZga_b_`ZYaUWbQ`ZMdVJhUGmcCqq9zz6qmAmc\ EjUIfKMbTQ_VUWYYT_`S`XSaTVeUXiU_mUaqUZjTWcSTXRQQQN\ JPTLPYMPbNPgOPjJUmEZoAbr5gt1kk6YcALWE8QJKKNWPMYTL_\ YKaaJbfIdjHfoGhsGijKfaNcUQ`LTYCWV4ZSCSNKLJREFVKKZP\ PbUUgZYldbqjgvplzvpsrkmnggkbagZVdUQbQHTY } END PARAMETER FILE=========================================

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FOTD 19-11-03 (Mandelbrot-07 [6])
by Jim Muth 19 Nov '03

19 Nov '03

FOTD -- November 19, 2003 (Rating 6) Fractal visionaries and enthusiasts: (Please direct any non-fractal comments to the philofractal list.) Too many years ago, when I was a curious young boy, (age 13 or so), I found my share of unbelievable claims in columns and books such as Ripley's 'Believe it or Not'. I remember one claim in particular -- that the botfly can fly 808 miles per hour, which is faster than sound. I wondered where the tiny fly found the energy. As it turned out, that particular claim was false, but many of the things that appeared in the column, such as the 'Pyramid of Hanoi', are true. At that time, as today, the newsstand shelves were filled with publications dealing with things such as lucky charms and Astrology. Being a reasonably intelligent young fellow, I felt proud that I was too smart to believe in such nonsense. Of course, when I grew older I found that things such as lucky charms and Astrology are only a mild form of nonsense compared to the super-nonsense (we call it non-intuitive stuff) seriously considered nowadays by physicists and to a lesser degree by cognitive scientists. The acceptance of the nonsensical is where science is inexorably leading us. If it is seen as superstitious to believe in the real but invisible worlds and the invisible spirit beings of occultism, why should it not be seen as even more superstitious to believe in the infinity of real but invisible parallel universes and the infinity of alternate versions of ourselves which are being seriously considered by physicists? And, is it truly so absurd to wonder if the scientific and occult views of other worlds are merely two different aspects of the same thing? The modern-day realization that the world is non-sensical is amazing, but the most amazing thing that has come about in the past quarter century is IMO the development of computers and the means to rapidly calculate fractals, which led to the discovery of their infinite richness. This is something which neither occultist nor scientist could have imagined back at the time I was reading 'Believe it or Not'. The best known and most basic of all fractals is the Mandelbrot set. And the best known area of the Mandelbrot set is perhaps Seahorse Valley. Today's FOTD takes us to the bud side of the north branch of the valley to view a midget that lies there. With its many seahorse-like twists and whorls, the image fairly reeks of 'Seahorse Valley', though it is still a rather pleasant scene to see. Because the area has been explored to the point where it is becoming boring, I could rate the image no higher than a 6, but what could one expect from an image that renders in 35 seconds? The alternate way of seeing the image is to download it from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> A raw, cloudy, damp, chilly day here at Fractal Central on Thursday kept the cats confined to the porch. The temperature of 50F 10C and occasional drizzle made their confinement a short one. After 20 minutes they were back indoors, asking for tuna. Today is starting milder but still cloudy. And rain is due. I expect sulky cats before the day ends. But before the sulking begins, I must finish the work. Until next time, take care, and watch out for that invisible dark matter and energy. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandelbrot-07 { ; time=0:00:35.37--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=-0.7659\ 7715297031940/+0.09328995436879066/2.980249e+011/1\ /-177.5/-0.0303889026000893486 params=0/0 float=y maxiter=6000 inside=0 logmap=808 periodicity=10 colors=0500IAf6_r6Xv6VyE_sKajQddViYalSfoMnsFtv9zy1\ zz0zz0zz0zz0zz0zz0zz1zz4wz6tz9ozAlzDiyFfyShzcizpkz\ zkzvnzrozlrzgtzawzYxzSzzOzzIzzDzz7zz3zz0zz0zz3zzCz\ zLxvTtrcnlligudcz__zVVzXSzXQvXPrXOmXLgXJcXI_XGTYDP\ YCJYAFY9Al64f40e30b14aJDX`MFpOIoPKmQLlQOjSQiTRgTUf\ VVdXXcX_aYa`_b__d_aicdnggrliwplzuozypzzrzxrrssiosa\ juTfuKavBYv5Tv5Ps5Tp6YmCalIfiOjfUoc_saev`Xx_QyYIzX\ BzV5zT5zX5xY8r_El`KfaO`dUVf_PgeJikDjo7olGriOufVseS\ sdQrbPrbMpaLp_Jp_ImUQjQ_gKfdFoa9x`5zc5vd5of5gi5_j5\ Sl5Lo5Cp54r50v5Ay5Oz5`z5mz5zz5zzBJzCMzEOzFPzFQzHSz\ ITzIVzKXzL_zL`zNazOczOdzQfzRgzRiuX`oaSgfLakCXo4Yr3\ Yt3Yu3Yw3_z3_z3_z3_z3`z3`z3`z3`z3az6cz7dz9fzCgzDiz\ FjzGlzJmzLozMpzOmzLjzJgzGfzFizDlzCmzApz9sz7uz6xz4y\ z3zz1zz0zz0zz0zz0zz4zzCzzIzzPzzVzzazzizzozzvzzzizs\ Qzj6za0zT0za0zi0zp1zy6zz9zzDzzGzpLzdOzTMzQLzPLzMJz\ LJzIIzGczmfzjjzimzfrzcuza } END PARAMETER FILE=========================================

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FOTD 18-11-03 (Mandelbrot-06 [6])
by Jim Muth 18 Nov '03

18 Nov '03

FOTD -- November 18, 2003 (Rating 6) Fractal visionaries and enthusiasts: I just heard an item on the radio, which for some reason strikes me as unbearably funny. The enlightened city council of our fair city, which recently ordered the police commissioner to crack down on crime but stop harassing the criminals, has just suggested an ordinance making it illegal for homeless people (in non-PC language, bums) to ask for a handout unless they sing or dance, or perform some other form of entertainment. The penalty would be a 50-dollar fine or a month in jail. To help the homeless in their plight, I suggest we give every homeless person a lap-top computer and a copy of Fractint, so they can entertain the gathered crowd with fractals. Nothing could be more entertaining. Besides, homeless people do not have 50 dollars to pay the fine, and, with winter coming, might actually appreciate a month in a warm jail. (This situation is not politics; it is comedy!) While I'm trying to figure that one out, we have another fractal to discuss. Today's scene is located on a filament extending out from the large midget at -1.75. It is located just beyond the point where the filament changes from a jagged, totally chaotic line to a rather straight line with occasional zigzags. At this point on the filament, there are still occasional areas of chaos, but they are disconnected. This characteristic is reflected quite well in today's image, and is made even more clear by half an outzoom. Once again, I can find nothing in the image to earn it a rating over a 6, which equals just a little above average. And there is no mistake in the render time -- the image actually renders in 6 seconds. But there are those who prefer their fractals pre-rendered. These fractalists can find the completed GIF image ready for download on the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Monday started foggy here at Fractal Central. The fractal cats watched the outside conditions carefully, but did not ask to go out until the fog burned off shortly before noon. When they did go out, the sun and temperature of 61F 16C made their afternoon enjoyable. Today is starting cloudy, with rain threatening by the afternoon. The cats might not like this. I have a bit of work to do before I can dive into the Mandelbrot set in search of tomorrow's FOTD, and have a clear conscience. Until that cosmic moment arrives, take care, and gosh, how the old CD that came with the second edition of "Fractal Creations" brings back memories! Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandelbrot-06 { ; time=0:00:06.26--SF5 on a P200 reset=2002 type=mandel center-mag=-1.7778134544542\ 82/+0.0075774298300826/1.079544e+012/1/-121.11035/\ 0 params=0/0 float=y maxiter=600 passes=1 bailout=9 inside=0 logmap=122 periodicity=10 mathtolerance=/1 colors=0002N`3QY4SV5US6WP7ZM8aJ9fHJkJTnLgpMssOzzPz\ nWmYb`OiMFoOFgPF_RFTSFLUFDVF6SD5PB5N94K74I53F33D13\ BAAAJH9SN8`c7nm3Vg0Go8LlGPjOThWXfb`daYb`V`_TZZQXYN\ VXLTWIRVGPXFTYFWZFZ_Fa`FeaFhbFkcFnXeAZ_Q`UdYXeWZfU\ agSchPeiNhjLjkJlkIklHkmHknGkoFjpFjqEjrEjsDltDnuCou\ CqvCrvPlx`fyl`zgbqcch_e_WfSShJOiAKj2Pd8U_DZVIcQNhL\ SmGX`L5_NH_OSZPbZQmZRxYStYTpXUlXUhXVdWW`WXXWXUPePI\ mKCuGVvMHl2Nf6S`AXWEaQIgKMlFQq9Uv4Yj7UZAQNDMBFJLHG\ UIEbJBkK9WEPG8d12shJl_OfSTaJYWBbRCXQCSPDMODHOHLLKO\ INRGQVDTYBW`8Zc6abCcaHf`Nh_SkZYmYboYgjzhfziazjYzkU\ zlPzmLznHzoJzkKzgMzdNz`OzXQzURzQSzNPzLNzJKzHIzFFzD\ DzCzzcHz8TzCSzdAzN8zH5zB3z55zC7zJ_zBlzQxzcnzLdz2gz\ fez`dzVbzPazJLz4Pz6Sz8VzAYzC`zEyzpvzkszfpzbnzYkzTh\ zPezK_zw`zoazhazabzUczNZzv5znEzeNzXWzOqzalzUgzNwzu\ szlozdkzWgzOPzRXzLez4dz7dzAczDizWgzQezL3zcGzWSzO2z\ tFzfSzTXz5Yz7lz7`zFPzMDzU } END PARAMETER FILE=========================================

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FOTD 17-11-03 (Mandelbrot-05 [6])
by Jim Muth 17 Nov '03

17 Nov '03

FOTD -- November 17, 2003 (Rating 6) Fractal visionaries and enthusiasts: When I began my series of Mandelbrot images 6 days ago, I said that I would use arbitrary precision math as little as possible. I did not say that I would not use it at all. Today, I inten- tionally enter the range of arbitrary math to demonstrate a point. With today's image we are in the dark and mysterious world of the depths of the Mandelbrot set, a world where tiny things are exaggerated. In these remote depths, one of the things that becomes exaggerated is the size of the basin of attraction surrounding the midgets. With a magnitude of 7x10^23, today's scene lies in the shallowest range of arbitrary precision math, but even at this mildly-extreme depth, the basin of attraction around the midget in the image would be about 100 meters across if displayed at the same scale as the image on the screen. The scene lies in the basin of attraction of a larger midget, which lies in the basin of a still larger midget, etc. I have forgotten the exact count of midgets, but repeated outzooms will end up in a filament extending from a midget on the main stem of the M-set, a little to the east of the large midget at -1.75. A quick glance at today's scene will reveal that the number of elements surrounding the midget resets itself several times as the midget is neared. This resetting is typical of midgets that are part of the field of attraction of larger midgets. It will also become apparent that the elements around the midget are arranged in the form of circles. This is also typical of deep midgets. The rating of a 6 appears justified. The render time of 1-1/4 hours is harder to justify, but justice may be found by download- ing the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather was totally bland here at Fractal Central on Sunday, with a partly cloudy sky and a temperature of an average 55F 13C. To make things even more average, in the evening, a few drops of rain fell. The cats had an average day, doing average things. Today is turning milder; the work is under control; all is well. The next wonderful fractal will appear in 24 hours. Until next time, take care, and it will all work out in the end. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandelbrot-05 { ; time=1:17:31.32--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=-1.6341597430013676141250535918/0.00612\ 498599892884329038326681/7.325171e+023/1/132.5/3.8\ 8578058618804789e-016 params=0/0 float=y maxiter=3600 bailout=16 inside=0 logmap=770 symmetry=none periodicity=10 sound=off colors=000FETAGTAHSAGSAFRAFRAEQADPADOACNACMBBLCAJD\ AHE9FEP0IU0LZUPcQShMVmJZhLadMdbOgaPj_RmZSpXUsWVnV`\ iUeeTj`SpWRuSQzRStRTnRUhRVbQXYQYSQZMQ_GQ`BLZAGXABV\ 96T91S94RB7QDAPFCPHFOJINLLNNNMPQLRTLTWKVYJX`JZcI`f\ HbhHdfEWdBOc9Gf6Ti3el1rfAfaJWXSLS`AXbC`cEadGbdIbeK\ ceLceNdfPdfQefSfgUfgVghXghZhh_hialicoidqjarjZwkWxk\ TzkQphPmfOjdNhaMe_LbYK_VJYTJVRISOHPMGNKFKHEHFDFDDC\ SAAe78s4Bq8EpCGnGJmJLkNOjRRhVTgYWeaYde`bibalbam_Zk\ XWiUThSQfPNeMLcJIaHF`ECZB9Y86W64VG4PP4JV3G`2Ef2Cl1\ Aq18tV9wwAuvJsuRqtZosgmrokcwB2DNFBYS9hc7j_HkWRlT_f\ MYaFWcFZmFawFdzFgwFjmJccMYaPR_SLZVEXYzW`zRVzNPBJJF\ FDJB7N72RIJ`T_jbrtR00VC3ZO6b_9fkCiwEctJYrNToSNmWIk\ _T3XXBY`IZdP_hW`aTaWRaPPbJNbCLc6Lc0Oc7R_DUWKXSQ_PX\ bLbeHhhEekGcnH`qIZtKWwLUzMOzKIzRCzX6zb1zh8zjFzkMzl\ SzmZznezolzprzqdzoRzmWzd`zWezNizEfzFdzGazG_zHXzIVz\ ISzJQzzNzzLzzIzzGzzEzzBzz } END PARAMETER FILE=========================================

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FOTD 16-11-03 (Mandelbrot-04 [5])
by Jim Muth 16 Nov '03

16 Nov '03

FOTD -- November 16, 2003 (Rating 5) Fractal visionaries and enthusiasts: There was no FOTD on Saturday, the 15th of November. This was because I found a small pile of unfinished graphic work, and wanted to get it out of the way before the week ended. As I learned recently when I fell a week behind in the work, small tasks left unfinished soon pile up, and merge into a large task that takes several weeks to clear away. Rather than start falling behind again, I decided to forego the daily FOTD and clear away the work. Now I can search for fractals without the feeling of guilt. I may occasionally miss other FOTD's in the future. If so, do not feel concern. I am not growing tired of doing the FOTD; I am merely tending to first things first. With today's fractal comes good news and bad news. The good news is that the image takes only 15 seconds to render. The bad news is that the image rates only an average 5. In search of the image, I went to a midget on a filament extending from a sub-bud on the northwest shore of the large period-3 north bud of the Mandelbrot set. I zoomed in on a point of the filament just beyond the end of the main stem of the midget. To no one's surprise, I found a midget there. Since the location of the second midget is just beyond the tip of the stem of a larger midget, the second midget, which appears in today's image, is surrounded by not-quite-connected sword- like elements quite accurately mirroring the overall location of the scene. (Four much larger 'swords' appear out beyond the borders of the screen, and can be seen by outzooming and turning off the logmap.) If I were giving the image a proper title rather than a catalog number, the name would be something such as "Sword Play". The pre-rendered GIF image is available on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and on Scott's site at: But even a high-speed download cannot be faster than rendering today's image from the parameter file. <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The winds remained brisk Friday here at Fractal Central, but slacked enough in the afternoon for the fractal cats to venture into the yard. Tippy even managed to climb a few feet into a tree and sit there on the lowest branch, enjoying the sun and temperature of 46F 8C, and remembering the days when he could dash 20 feet up the trunk in a single bound. Thomas watched the action with disinterest. Saturday was sunny and warmer, with almost no wind, and a temper- ature of 55F 13C that made outdoor conditions quite pleasant for the duo. They spent several hours in the holly thicket, and needed to be coaxed indoors when the day ended. Today looks to be a not-so-sunny repeat. I'll try to take it reasonably easy today. If I try hard enough, I might even succeed. Until next FOTD and next trip into the infinite depths of the Mandelbrot set, take care, and where oh where did it all come from? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandelbrot-04 { ; time=0:00:15.60--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=-0.18985803257882940/+0.852822417465450\ 00/2.285195e+012/1/-102.5/0.00326419793650863793 params=0/0 float=y maxiter=1600 bailout=16 inside=0 logmap=332 periodicity=10 colors=000YuZYuaXueXuhWulWuoXtnXsnYrmYrmZqlZpl_ok_\ ok`nj`mj`mialiakhbjhbjgcigchfdgfdgeefeeedeedfdcfcc\ gbbgbbhaah`ai_`i_`jZ_jY_jYZkXZkWYlVYlVXlUXkTWkSWjS\ VjRViQUhQUgQUfRTeSTeTTeUSeVSeWSeXReYReZReZRe_Qf`Qg\ aQhbPicPjdPjeOkfOkfOlgOlhNmiNmjNnkMnlMomMonLonLooL\ opLoqKorKosKotJouJovJrwLpxKoxJmzJlzIkzHiyHhxGgwFeu\ FdsEcqDaoD`mC_kBYiBXgAWe9Uc9Ta8S_7QY7PX6OV5MU5LT4K\ R3IQ3HP2GO2EP5DP7CP9BPCAPE8QG7QJ6QL5QN2OJ3PM4QP5RS\ 6RV7SY8T`8Tc9UfAViBVlCWoDXrEZuDXuCWuCVuBUuBSuARu9U\ u9Zu8cu8hu7mz6mz6mz5mz5mz4mz3mz3mz2mz2mz1rz1wz2zz2\ zz2zz2zz2zz2zz3zz3zz3zz3zz3Gj3Hi3Hh4Ih4Jg4Jf4Ke4Ld\ 4Lc4Mb5Na5O`5O_5PZ5QY5QX5RW6SW6SV6oU6qT6rS6sR6sQ7s\ P7sO7rN7pM7nL7lK8iJ7fK7eK7dL7cL6bM6bM6cN6dN5fO5gO5\ hP5jP4kQ4kQ4kQ4lR3mRAnSFoSKrTPuTUwUZyUczVhzVmzWrzW\ wzWzzVzzVzzVzzUzzUzzUzzTzzTzzTzzSzzSzzSzzSzzRzzRzz\ RzzQzzQzzQzzPzzKzzOzzRzzV } END PARAMETER FILE=========================================

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No FOTD for 15-11-03
by Jim Muth 15 Nov '03

15 Nov '03

Fractal fans: Due to unexpected work, there will be no FOTD for November 15. The FOTD for Nov. 16 will appear on schedule. There is no problem. I merely want to avoid another work backlog. Jim M.

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FOTD 14-11-03 (Mandelbrot-03 [6])
by Jim Muth 14 Nov '03

14 Nov '03

FOTD -- November 14, 2003 (Rating 6) Fractal visionaries and enthusiasts: I realize that today's FOTD is late. During the wind-storm on Thursday we had another of our traditional power failures, which, though brief, was just long enough to put me behind in the graphics work. Wanting to avoid another work back-up situation, I spent the first part of today catching up on the work that should have been finished yesterday. Fortunately, when the work was caught up, I had good luck in my fractal quest. That quest took me out the negative stem of the Mandelbrot set to the East Valley of the large midget at -1.75, where I found a world quite similar to the East Valley area of the M-set itself, yet strangely different. The scene I found there reminds me of a display of caladium leaves, and I could easily have named it "Caladium", but I decided to stick with the bland but orderly consecutive 'Mbrot**' numbering system. The rating of 6 might be a bit conservative, but it's hard to give a fractal that has been found almost automatically a rating higher than 'a little above average'. The render time of 4-1/2 minutes is fast enough to make running the parameter file practical, and slow enough to make downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> more convenient. Tuesday was partly cloudy with a temperature of 46F 8C, but the wind gusted over 60mph (near 100kph) during most of the after- noon. The constant roar kept the intrepid duo very skittish, removing all thoughts of going outside from their heads. They passed the day on their shelves by the windows, watching the packs of empty trash cans clattering down the street. Today has been a bit on the busy side, but it is nothing that I cannot finish by later this evening. And then it's back to the Mandelbrot set to find tomorrow's FOTD. Until tomorrow, take care, and there will always be fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandelbrot-03 { ; time=0:04:39.13--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=-1.74999488467703500/-0.000000136207487\ 40/1.425142e+011/1/-100/-0.00196521785314480307 params=0/0 float=y maxiter=100000 bailout=16 inside=0 periodicity=10 colors=000ksalsdpsiqtlstpwtsxwwzwzzwzzxzzxzzxzzszz\ nzzizzdzx_zwVzsQxqLtpGslBqk6ni1lf0id0gd0gb0fb0fa0f\ a0d_0d_0d_0bY0bY0bX0bX0aX0aV0aV0_T0_T0_T0YR0YR0YQ0\ YQ0XQ0XO0XO0VN0VN0VL0VL0TL0TJ0TJ0RI0RI0RI0QG0QG0QE\ 0QE0OE0OD0OD0NB0NB0N90OB0NB0NB0NB0ND0ND0LD0LD0LE0L\ E0LE0LE0JG0JG0JG0JG0JI0JI0II0II0IJ0IJ0IJ0IJ0GL0GL0\ GL1GL1GL1GN2IN4JN6JN8LN9LNBNNDNNEOOGOOIQOJQOLRONRO\ OTOQVORVOTXQVXQXYQYYQ__Q__QaaQbaQdbRfbRgdRidRkfRlg\ RngRpiRqiRskTtkTwlTxlTznTznTzpTzpTzqQzsTzqVzqXzqYw\ q_sqapqblqdiqffqgdqiapkYplVpnRppOpqLpsIptEpwBpw8nx\ 9pxBpxBpxDqxEqxEqxGszIszIszJtzJtzLtzNwzNwzOwzQxzQx\ zRxzRxzTzzVzzVzzXzzYzzZzz`zzbzzbzzczzdzzezzfzzgzzh\ zzizzizzjzzjzykxxjztktpkqilkdkf_j_ViVOhOJgJEfD9e82\ d10d00d00d00d00d00d00d00d00d01d02d06d08d09c0Dc0Ec0\ Gb0Jb0Lb0Nb0Qb0Rb0Tb0Xb0Ya0aa0ba0da0ga0ia0ka0na0bi\ ObkQblQblQbnQbpQbpQfqVgqY } END PARAMETER FILE=========================================

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FOTD 13-11-03 (Mandelbrot-02 [6])
by Jim Muth 13 Nov '03

13 Nov '03

FOTD -- November 13, 2003 (Rating 6) Fractal visionaries and enthusiasts: Today's trip into the Mandelbrot set takes us to East Valley, which is sometimes known as Elephant Valley. The elephants do not appear in today's image however. Instead, the place we visit is the north shore of the valley and the 'star' at the tip of a filament extending from a bud with a periodicity of 24. The scene of today's image lies on a filament of the 'star'. The midget at the center of the image is surrounded by 8 groups of 24 radiating filaments, making 192 filaments in all that lead beyond the frame. This multitude of filaments blends the otherwise jagged iteration bands into a smooth color gradient that is not at all justified by the palette color itself. Naming the image was no problem. Since it is the second in the series of scenes in the Mandelbrot set, I named it "Mandelbrot- 02". Rating it was an equally simple task. The picture is just a little above average -- a perfect candidate for a rating of 6. I avoided the use of arbitrary precision math, thereby enabling the image to render in 3 minutes, at least on my antiquated 200mhz 80586 (P-200) unit. Since the magnitude of the image is close to the range where arbitrary precision math kicks in, I included the mathtolerance=/1 command in the parameter file. This prevents the program from shifting to arbitrary precision math and avoids unpleasant surprises, such as two-hour render times, when the image is calculated at resolutions higher than 640x480. All rendering problems may be avoided however by downloading the finished GIF image from either Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Heavy clouds and rain kept the fractal cats indoors all day Wednesday. The temperature reached 55F 13C, but the duo had no chance to test it. This morning is starting with lots of clouds but some sun. The winds are high however, and this will again put a damper on the cats' outdoor activity. Fractal cats dislike strong winds. I have about 4 hours work to finish before I will have a chance to look into the M-set. What I find there will be tomorrow's FOTD. Until then, take care, and be happy in your fun. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandelbrot-02 { ; time=0:03:01.58--SF5 on a P200 reset=2002 type=mandel passes=1 mathtolerance=/1 center-mag=+0.26649584743215790/-0.003450374208644\ 80/6.476097e+012/1/-69.0025124098784488/-0.0022269\ 2079104778312 params=0/0 float=y maxiter=18000 inside=0 logmap=-3400 periodicity=10 colors=000qcUmcUmcUmcUmcUucUmcUmcUmcUucUocUpcUqdTr\ aSseQrcPpaNn`MmZLkXJiWIgUGeSFdREbPC`NBZL9XK8WI7UG5\ SF4QD2OB1NA0P93R86S89U7CV6EX6HY5K_5N`4Pb3Sc3Ve2Yf2\ _g6`hAaiEajIbkLblPcmTcnXdo`dpceqgerkfsoftsguvgspaq\ gXoURmKMk0Gi0BkKDlPEmUFoZGpcHqhJsmKtrLuwMzzNzzOzzO\ wxOuvPstPrsPqrQqqQppQpoRonRpmRqkSrjSsiStgTweTzbTz_\ U`XU_UUPMVZUVZVVXZXXaYXdZXe_Xf`XhbVicTjdRkePlfQkdR\ kcRkbSk`Sk_TkZTkXUkWUkVVlTVlSWlRWmSXmTXmUYmWYmXZmY\ ZmZ_m__m`YmaXmbWmcUmdUmeVmfWmgXmhYmiZmj_mk`mlammbm\ ncmodmpemqfmrgmshmtimujmvkmwlmxmmymmzmmzmmzmmzmmzm\ mzmmzmmzmmzmnzmnzmnzmnzmozmozmozmozmpzmpzmpzmpzmqz\ mqzmqzmqzmrzmrzmrzmrzmszmszmszmszmtzmtzmuzmuzmuzmv\ zmvzlvzgvzbwyYwxTwwOwvJwuEwt9wsBznDzjFzfHzbJzZKzXL\ zVMzTMzRNzQOzOOzMPzKQzIRzHRzFSzDTzBTzAczBbzDazF`zG\ _zI_zJZzLYzMXzOWzQWzRVzTUzUTzWTzXUzVUzUUzTUzSUzRUz\ QUzPUzOUzNUzMUzLNz_mzUmzU } END PARAMETER FILE=========================================

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FOTD 12-11-03 (Mandelbrot-01 [7])
by Jim Muth 12 Nov '03

12 Nov '03

FOTD -- November 12, 2003 (Rating 7) Fractal visionaries and enthusiasts: The Mandelbrot set was the first fractal I explored those many years ago when I found my first fractal program. (A blow-up of the large midget on the negative stem was the first zoom I ever made.) In all the years that have passed since that day, I have yet to find a fractal with more richness and variety of detail. In a way, the Mandelbrot set is the ultimate fractal, the fractal to which all others must be compared. In order to do justice to this king of all fractals, I have decided to devote the second half of November to the Mandelbrot set. To make things more interesting, more convenient, and more challenging, I will limit the magnitude of the images to the range of conventional math. This will avoid the render time of hours that often results when arbitrary precision math is used. And I will try to limit myself to the equal-iteration-bands method of coloring. I will however explore the high-iteration areas that were beyond the reach of the 8mhz machine I was using when I first ventured into the M-set. Today's image, the first of the Mandelbrot series, is named "Mandelbrot-01". This is more of a catalog number than a name. The succeeding images will be named -02, -03 and so on. I have rated the image at a 7. Despite being a scene in such a well- known fractal, it equals many of my more exotic MandelbrotMix4 images, and easily earns its rating. The midget in the image lies rather deep in a spiral in the bud side of the east branch of North Valley of the M-set. This valley has a more descriptive name, which I cannot remember at the moment. There is not much to be said about today's FOTD. The image speaks for itself. (Though not in words!) Despite the high iteration count of the image elements -- the logmap is 7740 and the maxiter is 45,000 -- the parameter file renders in a zippy 6-1/2 minutes on my tired old machine with the balky fan. The fastest machines will render it in only a minute or two. The rendering can be bypassed completely by letting Paul and Scott do the rendering and picking up the completed image from one of the following web sites: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Tuesday brought cloudy skies and showers to Fractal Central, and disappointment to the dynamic duo. The temperature of 57F 14C was mild enough, but the wet grass dampened the paws of the cats and their spirits as well. It took a feather on a string to get them out of their lethargy. Unfortunately, today promises to be even wetter. I hope the cats' spirits hold out. I have a bit of work to accomplish before returning to the Mandelbrot set. And the sooner I get started, the sooner I'll finish. Until 24 hours have passed, take care, and become one with the Mandy. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandelbrot-01 { ; time=0:06:21.73--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=-0.1125\ 432147408424/+0.6501357215415452/1.112385e+010/1/\ -45/-4.45623187553881306e-005 params=0/0 float=y maxiter=45000 inside=0 logmap=7740 periodicity=10 colors=000m_npXqtUtwSwuRtsQqrPnpOloOimNfkMdjLahKZg\ KXhMWiOWjQWkRWlTWmVWnXWoYVp_VqaVrcVsdVtfVuhVviVVki\ 3lw5ku6ks8kq9koBkmCkkEkiFkgHjeIjcKjaLj_NjYOjWQjURj\ TWnW_rZdrahqdcnVZjLSfOMhRFjU9lWChYFe_HbaK_cMXePUgR\ RiUOkWLmZIo`FqcCse9uh6wj3xg5ue6sc7qa8oZAmXBkVCiTDf\ REdOGbMH`KIZIJXGKVJQ_LVdN_hLZfKZdIYbHYaFX_EXYDXXKU\ UKUUKUUKUUKUUKUUMUUGUUBUU5UU0VUcTmaPm`Lm_HmZDmXBgV\ AbU9YS8TQ6OP5JN4EM39N58N67N77O86O96OA5PB4PC4PD3QE3\ QF2QG1RH1RI0RJ0PM1NO1MQ1KS1JU2HW2GZ2E`2Db3Bd3Af38h\ 37j39l6An9KpCUsFcuImxLrzNmuRhpVcnPUlJRiEXh8bh3di4e\ i4fj5hj5ik6jk6ll7ml7nm8pm8qn9rn9toAuoAvoAugDt`GtUI\ sMLsFNp8Qn1Sj3Vf4Xb5Z`6UXAKZFK`KUbPc`UmZZwXczVhzTm\ zRrzNrzJrzFrzBwzDrzEmzFhzGczIG0JSXKT`LUcNVfOWiPXlQ\ YoSZiT_cU`ZVaTWbNXcIZdO`eUbf_djefkj6l8BmBGnEKoHPpK\ UqNYrPbsSgtVkuYpv`uwcyxezybzz_zzXzzVzzSzzPzzSzzSzz\ SzzSzzSzzWzzZzzazzdzzgzzk } END PARAMETER FILE=========================================

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[Fractint] Zoom into Lee Skinner's Dumbell.gif from the Fractal Creations 2nd Ed CD
by Hal Lane 11 Nov '03

11 Nov '03

######################################################################## This is a zoom into Lee Skinner's Dumbell.gif from the Fractal Creations 2nd Ed CD. Thanks again for the copy of the CD, Tim! The color map is from the image "Leather Gem" by Damascena Korwen, an entry in the Fractal-Art 1998 Contest: http://www.fractalus.com/contest98/entries/09-013.htm When I rotated the color map approximately 96 steps at a time I could watch the 'medallions' ('eyes' with spirals in them) be highlighted in the ring of 16 'eyes', then 32, 64, 128, 256, 512, and then 1024 'eyes' in a 1024 x 768 version of the image. I like to trace this 'period doubling' of features as they approach the Mandelbrot set. Btw, does anyone know if it has been determined if these miniature Mandelbrot Sets are exact copies of the full size Mandelbrot Set? - Hal Lane ######################### # hallane(a)earthlink.net # ######################### =================== FRACTINT PAR ===================== Medallion_Weave { ; Zoom by Hal Lane into Lee Skinner's Dumbell.gif - ; from the Fractal Creations 2nd Ed CD. ; Color map from "Leather Gem" by Damascena Korwin - ; an entry in the Fractal Art 98 contest. ; Version 2002 Patchlevel 5 reset=1720 type=mandel passes=1 center-mag=+0.25372693451716730/+0.00036640736338332/4.538746e+011/1/-37\ .5009262932441132/0.000734303369271584183 params=0/0 float=y maxiter=100000 inside=0 sound=off colors=000IbLJdMKfNLhM<5>bmDenBhoA<3>ts3wt1sr2<5>Zf8Vd9SbA<3>DVF<4>CPCCN\ BCMA<2>BI9BH8BH8<3>AE79D6DE6<3>UI9YJAaLBeMCgODjQF<9>tgGuiGvjG<2>ypGzrFzr\ K<3>yufxukxvqwww<3>rhh`F0`F0<5>UA0T90S80R80Q70P60<3>L30K30J20I10I10<16>U\ B2UB2VC2<3>YE3<3>Q82O61M41<3>Q71R81S91fM5<3>iO5jP5kQ6<9>UB3S92Q82<3>I109\ 31A00<3>VK0_P0dU0<3>zm0<3>zb0z_0zX0zU0<3>`F0UC0O80H40<2>A4773A73C<3>56K4\ 7M48O39Q2AS<8>9QaASbATc<3>E`hFbiGdi<3>JklKmmJkj<7>CURBSOAQM<3>6GB5E86G9<\ 12>H`K } =================== FRACTINT PAR ===================== ######################################################################## --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.537 / Virus Database: 332 - Release Date: 11/6/03

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FOTD 11-11-03 (Triangles of Doom [7])
by Jim Muth 11 Nov '03

11 Nov '03

FOTD -- November 11, 2003 (Rating 7) Fractal visionaries and enthusiasts: I have named today's image "Triangles of Doom". I can give no logical reason for choosing such a name -- the triangular holes in the image certainly appear harmless enough -- I simply felt like naming the image that way. And there certainly are enough junky old sci-fi horror movies with similar names. The most likely reason for the name could be the doom the triangles would bring if the fractalist who found them were to become obsessed with them, and stare at them until he starved. The rating of an above-average 7 was earned by the coloring, most notably the effect of the translucent foreground features being illuminated from behind. This effect is achieved by filling the holes with the maximum value of blue, and varying the red and green only slightly from the maximum. This tricks the mind into thinking that it is actually viewing the sky through holes in trees. The parent fractal of today's image appears as a scattering of small Mandeloids and an assortment of other, more oddly shaped holes. The most prominent Mandeloid has both a negative stem that points northwest and a positive stem that points southeast. The positive stem springs from East Valley and terminates in an irregularly shaped hole that passes through the neck of many smaller hourglass-shaped holes on the way. Today's scene is found close to the point where this spurious stem terminates. When colored in my usual inside=0 outside=iter manner, today's scene is dull and flat. But rendering the image with the inside=bof61 and the outside=tdis, results in the interesting terraced effect seen in today's image. I am not an absolute purist when it comes to fractals, but when I work with them, I try to keep the simplicity that existed when I first discovered them some 16 odd years ago, and had only the Mandelbrot set to explore. Maybe one of these months I'll devote a month to scenes in the M-set, just to show that it is nowhere near being exhausted. The render time of 2-1/2 minutes is reasonably short. And this time can even be cut a bit more by downloading the completed GIF image from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Monday featured nothing but blue skies and sun here at Fractal Central. The temperature of 50F 10C was a bit on the chilly side, but the fractal cats ignored the chill as they explored the holly thicket at the bottom of the yard. The day ended with happy cats sleeping soundly (Thomas snores). Today is starting sunny and promising to be warmer. The warmth is due to be temp- ered this afternoon however by clouds and perhaps a few showers. We'll just have to wait and see how it goes with the dynamic fractal feline duo. As for me, I have a bit of work to accomplish before the fractals can be found. Until next FOTD, take care, and don't take life too seriously. It won't last forever. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Triangles_of_Doom { ; time=0:02:23.90--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.72147391460799470/+2.077828375552933\ 00/16687.84/1/25/6.03698577933409197e-009 params=-1.5/-1/0.15/5/0/0 float=y maxiter=1250 inside=bof61 outside=tdis periodicity=10 colors=000Kt_MubOudQufSvhUvjWvuYwn_wpawrcwtcvrcuqc\ upctocsncsubnlajzafj`bi_Zh_Vgb_hedhhihknvrsznrzjre\ frcbq`ZqYVqWRpTNpQJpOFoLBoI4qDAtGAmJDiMGePIaRK`QL`\ PM`ON`NPXMQTLRSKSMJULIVKHWJGXIFZHE_FD`ECaDBcCAdB9e\ A8f97gC6gF6hH6hK6iM5iP5jR5lU5mX5oZ4pa4rc4rf4rh4ni6\ li8iiAgiCdiEbjG_jIYjKVjMTjOQjQOkSMkUKkWIkYGk_ElaCl\ cAle8lg6li4ljHkoUksTgrTdrS`rSYqRUqRRqRNpQKpQGpPDoP\ 9oP6oQ8nR9mSAmTBlTDkUEkVFjWGiXIiXJhYKgZLg_Nf`Oe`Pe\ aQdbSccTcdUbdVaeXafY`gZ_g__fRSeILd9Ed17f79gCAhHBiN\ CjSEkXFlbGmhHnmHnlIljJjhKhfKfdLcaMa_M_YNYWOWUOTRPR\ PQPNQNLRLJSHERJHSLJSNLTPOTRQUTSUVUVXXVZZW``WbbWcaX\ c`Xd_XdZXeYXeYXfXXfWYgVYgUYhUYhTYiSYiRYjQZjPZkPZkO\ ZlNZlMZmLZmLZeQVZVRR_NKdJCiF5mB6nF7nJ8nN9nRAnVAnYB\ naCneDniEnmEnnEnoGlnIkmJjkLijMghOfgPeeRddSbbUaaV`_\ X_ZYYX_XW`WUbVTcTReSQfROhQNmPGiPMePRbPWZP`VPeSPjOP\ oKPtHPyJRuKSqLTmMViVjUPoX } 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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SPAM
by cjsonnack＠mmm.com 10 Nov '03

10 Nov '03

wrote: >> Jim. I, for one, could do without hearing about your spam. >> We all get it (in both sense of the phrase). > > The solution to your (or is it my) problem is simple -- > don't read the paragraph(s) that mention spam. ROFL! "Don't Read This Sign" Yeah, that'll work... -- |_ CJSonnack <Chris(a)Sonnack.com> _____________| How's my programming? | |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL | |_____________________________________________|_______________________|

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SPAM
by cjsonnack＠mmm.com 10 Nov '03

10 Nov '03

Jim Muth wrote: > In addition to the obvious junk, my e-mailbox held a... Jim. I, for one, could do without hearing about your spam. We all get it (in both sense of the phrase). -- |_ CJSonnack <Chris(a)Sonnack.com> _____________| How's my programming? | |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL | |_____________________________________________|_______________________|

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Sorcery
by cjsonnack＠mmm.com 10 Nov '03

10 Nov '03

Jim Muth wrote: > Real sorcery, like real magic, is all in the mind, a fact that > all true sorcerers admit. But that doesn't make it any less > real. Er,... Wouldn't that be the Very Last Thing a "real" sorcerer would admit? Also, once again, ... define "real". > Sorcery, which need not be used only for evil purposes,... Actually, at least one dictionary has the primary definition: 1 : the use of power gained from the assistance or control of evil spirits especially for divining . Compare this to "Wizard" (which lacks the "use of evil" connotation). > ...involves a different kind of reality, and it is up to its > practitioners to shift their awareness to the reality where > sorcery is a true fact of nature. But if it's, as you say, all in their minds, what's the point? What makes it any different from any other aspect of the imagination? And if we agree the mind IS a part of nature, then what makes it a different reality? > Fractals are also a true fact of nature, and like sorcery, they > exist in a different kind of reality -- the reality of the world > of numbers. Is that a "different" reality or just an aspect of the plain ol' one we enjoy every day? -- |_ CJSonnack <Chris(a)Sonnack.com> _____________| How's my programming? | |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL | |_____________________________________________|_______________________|

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FOTD 10-11-03 (Basic Mandelbrot [4])
by Jim Muth 10 Nov '03

10 Nov '03

FOTD -- November 10, 2003 (Rating 4) Fractal visionaries and enthusiasts: In addition to the obvious junk, my e-mailbox held a letter from Citibank when I checked it at 7:30 this morning. The letter told me that they were having confusion with some of their customers' e-mail addresses, and needed to verify the addresses. The letter had been posted at 5:59am -- a strange hour for a bank to be doing business. The instructions in the letter were to click on the included web link and enter my ATM card number and PIN number in the proper spaces. Now the mystery deepens. To start, I do not have a Citibank ATM card, but more important, why would they need both card number and PIN number to verify an e-mail address? The letter was hastily written, and in broken english. It looked most unprofes- sional, almost childish. And finally, why did it include a string of the gibberish that clutters almost all spam e-mail? It was another scam. After a short laugh, I deleted it. ;-) Now on to the day's fractal. Perhaps I should have deleted it also. It's nothing more than a basic image of a double seahorse tail in a valley of the M-set. The scene is not located in Seahorse Valley however. It is in a remote 5th-order valley on the northwest shoreline of the large north bud of the M-set, in a rather chaotic area of very high iteration. The chaos fills the image with distracting, apparently disconnec- ted bits and pieces. These dots are actually unresolved frag- ments of features connected to the main body of the M-set. The coming together of two similar elements, such as we see in today's image, is almost always a give-away that a midget lies hidden in the center of symmetry. This is the case in today's image. If the area is not quite critical, something I call a 'dry lake' may appear, but usually a midget is found. I have given today's image a color palette that emphasizes the symmetrical features. The logmap has been set artificially high, so that the features, as well as the unresolved bits and pieces, will stand out against an otherwise flat background. Even with all the work I put into the image, I can still rate it no higher than a 4, which is somewhat below average. It's kind of hard to give a high rating to the type of image a neophyte fractalist would find on his first trip into the Mandelbrot set. Recognizing its worn-out-warhorse appearance, I have named the image "Basic Mandelbrot" The parameter file's excessive render time of 39 minutes is caused by the very high iteration count of most of the features in the image. But the wait may be bypassed by letting Paul and Scott render the image, and then picking it up from one of their web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Since the fractalist and fractal lady were away all afternoon Sunday, the fractal cats had no time in the yard. Most likely, due to the cold, they would not have stayed outside longer than a few minutes anyway, but the fact that I was away all afternoon gave them reason to blame their confinement on me. An extra large dose of tuna was needed to restore their good spirits. Today is starting sunny with a temperature of only 25F -4C, but there is no wind and a rapid warm-up is due. The duo will likely have a far better day. My day will turn good when I find a fractal really worthy of being a FOTD. And that will have to wait until the other work is finished. So until the next time, take care, and do people actually fall for those obvious internet scams?. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Basic_Mandelbrot { ; time=0:39:40.38--SF5 on a p200 reset=2002 type=mandel passes=1 center-mag=-0.22124326809773450/+0.800438909970306\ 90/1.057015e+009/1/150/8.90265827794833875e-005 params=0/0 float=y maxiter=500000 inside=0 logmap=24097 symmetry=none periodicity=10 colors=000ApzUmAUlAVl9Vl9Vl9Wk8Wk8Xk7Xj7Yj7Yj6Yi6Z\ i6Zi5_h5_h4`h4`g4`g3ag3af3bf2bf2bf2ae4ae5`e6`d7`d8\ _dA_cB_cCZcDZbEZbFYbHYbIYaJXaKXaLX`MW`OW`PW_QV_RV_\ SU`SV_TWZTXYTYXTZXT_WT`VTaUTbTUcTUdSUeRUfQUgQUhPUh\ OUiNVjMVkMVlLVmKVnJVoJVpIVqHWrGWsFWtFWuEWvDWwCWy7V\ xAWwCWvEWvHXuJXtLXtOYsQYrSYqUYqXZpZZo`Zoc_ne_mg_mi\ _jh`hhaegbcgc`gdZfdXfeUffSegPehNeiLdiIdjGdkDclBcmA\ ej9cm8bo7aq7_s6Zu5Yw5Xy7Wv9VsBVpCUmETjGTgHSeJSbLR_\ MQXOQUQPRQQQRPPRPPRPPRPPRPPRPOSPOSPOSPOSPOSPNSONSO\ NTONTONTOMTOMTOMTOMUOMUOLUOLUOLUNLUNLUNKVNKVNKVNKV\ NKVNJVNJWNJWNJWMJWMIWMIWMIWMIXMIXMHXMHXMHXMHXMHWLI\ XMHXMHYMHYNHZNHZNH_OH_OG`OG`PGaPGbPGcQGdQGdQFeQFfR\ FgRFhRFjSFkSFlSEnTEoTEpTEqUEsUEtUEtVKtWPuUEtT2uS3u\ S4vS5vR6vR7vR7vR8vQ9vQAvQBvQCvccvccvccvccvccvccvcc\ vccvccwccwccwccwccxccxccxccyccyccycczcczcczcczcczc\ czcczcczcczcczcczcczcczcc } END PARAMETER FILE=========================================

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FOTD 09-11-03 (Construction Job [6])
by Jim Muth 09 Nov '03

09 Nov '03

FOTD -- November 09, 2003 (Rating 6) Fractal visionaries and enthusiasts: I have won no further lotteries since yesterday. I'm not sure whether this is bad news or good news, but it is most curious that, despite having won close to a dozen lotteries over the past month, I am no wealthier now that I was before my good luck arrived. ;-) The parent fractal of today's image can be best described as 'mostly blobs with scattered Mandeloids'. And amid the Mandel- oids lurk some holes that are decidedly not Mandeloid-shaped, yet have buds along their borders that indicate the presence of a critical area. Today's scene is located on a filament exten- ding from one of these buds, near the point where the filament passes a hole shaped like a figure eight. I named the image "Construction Job" in honor, or dis-honor, of the construction that is taking place two blocks from Fractal Central, down at the bottom of the hill, where a new storm drain is being installed, which hopefully will eliminate the flooding that seems to happen down there on a regular schedule. I also chose the name because, by the coloring, I rather constructed something from nothing. I guess this makes today's image another piece of fractal-art. After studying the image for a few minutes, I decided it is just a little above average, which equals a 6 on my arbitrary 0-to-10 scale of fractal worth. The image does have a kind of glowing effect to it, but the colors, especially around the perimeter, are not all that pleasant to look at. The 'passes=g' option is extremely efficient with today's image. The render time when passes=1 is 17 minutes; 'passes=g' does the job in only 7 minutes. Since the result in either case is exactly the same, I have removed the 'passes=1' entry from the parameter file and cut the render time by 60 percent. But if 7 minutes is still too slow to fit into a busy schedule, the completed GIF image may be downloaded from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Though it was chilly here at Fractal Central on Saturday, with a temperature of only 46F 8C, the sun was warm, and the cats enjoyed a couple hours in the yard. This was enough to prevent the sulking that happens when they get too little time outside. When evening came, the duo settled down quite peacefully, and passed the rest of the day as decorations. But this morning's temperature is only 26F -3C, cold enough to put a film of ice on the water dish on the porch. I wonder how the duo will take this sudden cold weather. I'll know the answer in a few hours. For the rest of the day, I'll be trying to take it easy, but the fractal lady has that 'lets go look at antiques' gleam in her eye. So we'll have to see how the day goes. Regardless, in 24 hours I'll return with another fractal. Until then, take care, and keep those spirits up. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Construction_Job { ; time=0:07:29.56--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip center-mag=+0.09925390891872346/+1.894791001828095\ /1.868638e+008/1/115/-9.1173630439880804e-005 params=-3.1/-1.3/1.3/-3.1/0/0 float=y maxiter=1500 inside=0 logmap=245 periodicity=10 colors=000SYASX9RV8RU7RT6SU8TU9UVAVVBWWCXWEYXFZXG_\ YH`YIaZJbZLc_Md_Ne`Of`PgaQhaSjbTkbUmcVncWrcXsaPxaL\ xcKxdMxgOxiQxkSxnUxpWxsYxu_xw`xubxscxrexpfxohxmixl\ kxjlxinxgoxfqxdrxcswZivU`uT_tS_sRZrQZqPYpOYoNYnMXm\ LXlKWkJWjIWiHVhGVgFUfEUeDTdCTcBTbASa9S`8R_7RZ7RYCV\ XGZWKaVOeUShTWlS_oRctRgxSgxSfySfzTezTeyTdxUdvUduUc\ tVctVbtVbtVbtXcpZcm_cmZcmUcmPcmKcmBcnCcmDcmDfmEclE\ `lFZlGWlGTkHRkHOkILkJJjJGjKDjKBjJDlIFmHHoGJpFLrENs\ DPuCRvBTxBUyDVwFVuHWsJWqKXpMXnOYlQYjRYiwWjtXiqXhoX\ glXfjYegYddYcbYb_YaYZ`VZ_TZZQZYNZXL_WI_VG_UD_TB_TF\ ZRIYQLXPOWNRVMUULXTJ_TIbSHeRFhQEkPDnOBqNAtM9wM8xLA\ xKBxKDxJExJGxIHyIKyHOyHSyGWyFYyFazEezEgzDizDkzCmzC\ oyBqyBsyBtyBuyBvyBwyBxyByyBzxBzxBzxBzxBzxBzxBzxBzy\ BzyBzyBzxBzxBzxBzwBzwBzwBzvBzzBzzBzzAzzAzz9zz9zz8z\ z8zz7zz7zz6zz6zz6zz5zz5zz4zz4zz3zz3zz2zz2zz1zz1zz1\ zz4zz7zzAzzDzzGzzJzzMzzOz } 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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Re: Hal Lane
by JackOTradez 08 Nov '03

08 Nov '03

BTW, My screne resolution is at 1280 x 960; it is also my development environment. My web site loox fine there - it didn't occur to me that others had lower resolution and it would look wierd. Oh Well ... I hope(d) my Fractint utilities would increase the usage and lifetime of Fractint ... Long live the Fractint cult! But beware - Manpwin is comin' atcha ... JoTz

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Re: Hal Lane - Thanx!
by JackOTradez 08 Nov '03

08 Nov '03

Hal - thanx 4 the info. I guess I gotta go back and re-render all my viddies now to correct this :( I thought I had stumbled upon something really cool - now it seems 2B just a program tweak! I hate it when that happens! Ahhh - HellWidIt! They look cool as they iz - I just leave 'em be. The Excellent program I use to convert the GIF images to AVI viddie is called VideoMach and you can get it here: http://www.gromada.com It is shareware, costs very little, but well worth it. It can handle all formats you need. The shareware version is fully functional. Check it out! To convert (compress) to WMV format (it is a MPEG-4 derivative) use the free MicroSoft Windows Media Encoder and you can fetch it here: http://www.microsoft.com/windows/windowsmedia/default.aspx Although I am using version 7 not 9. Stay Amazed! JoTz

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FOTD 07-11-03 (Midget Starburst [8])
by Jim Muth 08 Nov '03

08 Nov '03

FOTD -- November 07, 2003 (Rating 8) Fractal visionaries and enthusiasts: Today's image, which combines portions of Z^(-0.75) and Z^(-7), is an 'evaporated' one. The escape radius has been increased to such an extreme value (one-googol) that basically all the points have been trapped. The trapped points do interesting things in their trapped state however, and these things form the basis of today's image. The image consists entirely of 'bof61' inside fill, which colors the trapped points according to which iteration comes closest to the origin. In today's scene, this fill is by far the best of the inside fill options. It works so well, in fact, that I rated the resulting image at an 'exceptional' 8. In its unevaporated state, the parent fractal consists of an oversized Mandeloid with a twisting fractal trail extending far to the northeast. Today's scene is located just beyond a crossroads on a filament extending from a sub-bud of the main bud of the parent. After a bit of consideration, I decided to name the image "Midget Starburst" I see no real reason for the name other than the fact that it sounds good. The render time of 9 minutes on my old worn-out 80586 machine is within the realm of reason. But the minute or so required to download the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> is even more reasonable. Weather conditions have deteriorated greatly here at Fractal Central over the past two days. Steady rain all day Thursday kept the aging fractal cats confined to the indoors, where they passed the day on their window shelves, waiting futilely for the sun to appear. The temperature of 63F 17C was mild enough, but fractal cats do not like wet ears. Today is starting cloudy and a bit cooler. If it stays dry, the dynamic duo might get in some quality outdoor time. My day will be good enough, especially if the work is finished by early afternoon. But to finish, I must first start. Until next time, take care, and see you soon. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Midget_Starburst { ; time=0:09:22.92--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+4.4291003385551/-0.6013162185079/2.309\ 104e+009/1/-67.5/0 params=1.2/-0.75/1/-7/0/1e+100 float=y maxiter=1500 inside=bof61 periodicity=10 colors=000QdOOdNOfLOfJOgJOgIOiGOiEOkDOkBOl9Ol8Ol8Q\ n9QnBQnDQpDQpERpGRqGRqIRqJRqJTsLTsNTsOTtOTtQVtRVwR\ VwTVwVVwVTxVTxXTxYTxYRz_Rz_RzaRzaQTLO04N04N14N24N4\ 4N64N64N84N94NB4ND4ND4NE4NG4NI4NJ4NJ4NL4NN4NO4NQ4N\ Q4NR4NT4NV4NX4NX4NY4N_4Na4Nb4Nb4Nd4Nf4Ng4Ni4Ni4Nk4\ Nl4Nn4Np4Oq2Np4Np4Lp4Lp4Jp4Jp4Jp4Ip4Ip4Gp4Gn4En4En\ 4En4Dn6Dn6Bn6Bn6Bn69n69n68l68l66l66l66l64l64l62l82\ l82l81l81k80k80k80k80k80k80k80k80k80k80k80g60f60d6\ 1b62a64_64Y66X68V69T6BR6DQ6DO6EL4GJ4II4JG4LE4ND4NB\ 4O94Q84R64T44V24V14_8DhRLgJTrXapXgzfpxgxzwzzzzzwzz\ pzzlzzizzdzxazwYztVztRzsNxqJwpGtnDsl8qk4pi1ng0lk0n\ g0ld0ka2iY6gVBfREdOJbLNaIR_EVYB_X8bV4gT1kR0pQ0sO0x\ N4zLDzLLzNTzNazNizNqzNzzNzxNzxNzxOzwOzwOztOztOzsOz\ sOzqOzqOzqQzpQzpQznQqnQilQalQVkQYkR_kRaiRbiRdgRfgR\ gfRifRkfRlbVlaXlYYlX_lValRdlQflNglLilJknGnnEpnBqn9\ sn8tn4xQ_XQaVQaVQbTQbRQdQ } 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 08-11-03 (Cave of Dreams [7])
by Jim Muth 08 Nov '03

08 Nov '03

FOTD -- November 08, 2003 (Rating 7) Fractal visionaries and enthusiasts: Great news! When I checked my e-mailbox earlier this morning, I found not one but two letters informing me that I have just won twelve-million-dollars in a lottery. All I have to do is send my bank account number so that the lottery commission can deposit my winnings in my account. But I must keep my good luck a secret. If the I.R.S. hears of it, they will take over half for taxes. No problem! I am not stupid enough to let the I.R.S. know I am rich. Oh happy day! It's nothing but fractals for me from now on. ;-) Today's image reminds me of a light at the end of a tunnel. My first instinct was to name it "N.D.E.", but on second thought I named it "Cave of Dreams", which can be interpreted to mean any- thing one wishes. The rating of a 'very good' 7 may be a bit overblown, but the image is at least somewhat above the usual mass of FOTD images, so with not too much stretching, the rating is justified. The image was found in a parent fractal which combines Z^(5) with some negative Z^(-2) before adding (1/C). This parent can hardly be called a fractal. It is more like an oversized scat- tering of fractal debris -- the remnants of a fractal explosion. But it does hold one very obvious though undersized M-set. This small M-set is surrounded by smaller bits and pieces, and is rotated so that its negative stem trails off to the south- east. The stem is unusual in that it does not come to a defi- nite end, but slowly loses definition, trailing off into nothing- ness and breaking up into ever more fragmented clouds of fractal stuff. The scene of today's image is located in this cloud of dissipating stem-stuff. The image itself was created by rendering the scene with the outside option set to 'tdis', which colors the points according to how far they travel before passing beyond the escape radius. The effect of light reflecting off the damp walls of a cave was intentionally produced by manipulating the colors. Today's image therefore may be considered more a work of 'fractal-art' than my usual images. The short render time of only 2 minutes makes watching the cave interior emerge on the screen a pleasure. It is almost as much fun visiting one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> and downloading the completed GIF image from there. Friday was a very average day here at Fractal Central, with a temperature of 61F 16C and enough sun to keep the cats happy. Since the work went smoothly, the fractalist was happy also. Today is starting sunny but notably colder. It remains to be seen whether the cats will approve of midday temperatures in the 40's (on the Fahrenheit scale). Since the evening is due to be clear, I'll probably take an hour or so to watch a lunar eclipse that will start around 8pm this evening. And when the eclipse has ended, I will likely travel to Fractal Land. Until next time, take care, and where is Fractal Land located? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Cave_of_Dreams { ; time=0:02:08.85--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.84707662108601570/-0.077027415795625\ 03/4.34485e+011/1/5.4998732086033213/0.00317742443\ 842483624 params=1.25/5/-0.3/-2/0/0 float=y maxiter=600 inside=0 outside=tdis periodicity=10 colors=000Jq_InYHkWGhUFeSEbQD_OCXMAUK9RI8OG7LE6IC5\ FA4C8396264132aLxYJrVHmSFhPEcMCZJAUF8PC7K95F63A315\ 0G90E80D70C60A6095084063053042021210juvgqtajsYcqTX\ pPNoPKkQHhPFeQCaQ9ZQ7WUDVYJUaPTdVSh`RlfQolQofOoaMo\ WKoRIoMGoGEoBCo6BnTfmXfm_flbflefkifklfjofjrfiqahpX\ hpSgoNgoIfnDfn8RgyhjzzmzxknwjbviRuhGvfLvdPwcTwaXw_\ `xZdxYhxZlt_fq``maVjbQgcKcdE`e8Yf3QgIPhWUijZjxckrh\ lmmmhnncoohppmqqrrrwssjttYuu_vvbwwexxgyyjzzlzzozzq\ zztzzvzznzzfzzZzzXzzVzzTzzRzzPzzNzzLzzJzzHzzFzzDzz\ Bzz9zz7zz6zz6zz6zz5zz4zz5zz5zz4zz4zz4zz4zz3zz3zz3z\ z2zz2zz2zz2zz1zz1zz1zz0zz0zz0zzzzzjzzVzzFzzozzbzzQ\ zzDzzdzz`zzYzzVzzSzzPzzMzzIzzFzzCzz9zz6zz3zzxzztzz\ qzznzzkzzgzzdzzazzZzzWzzSzzPzzMzzJzzGzzCzz9zz6zz3z\ zLzzJzzIzzGzzFzzDzzCzzAzz9zz7zz6zz4zz3zz1zzTzzQzzO\ zzLzzJzzGzzEzzCzz9zz7zz4zz2zzTzzOzzJzzEzz9zz4zzozz\ gzz`zzTzzMzzEzz7zzfzzczza } 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 06-11-03 (Both Ways at Once [5])
by Jim Muth 08 Nov '03

08 Nov '03

FOTD -- November 06, 2003 (Rating 5) Fractal visionaries and enthusiasts: Today's fractal is a gift from Thomas, the yellow-orange fractal cat. It is a very high magnitude image of a midget lying in the eastern suburbs of a larger midget. The larger midget lies on the negative stem of the M-set, just beyond the stem of the large midget at -1.75. This curious location gives the midget in the image the characteristics of both the sword-like elements of the negative stem and the brain-like elements of East Valley. This combination of elements inspired the name "Both Ways at Once". The rating of 5 means 'average'. The original image had a color palette that earned it a 7, but before I saved the colors, I got up to check on a waiting job. While I was out of my chair, Thomas decided to jump up and walk on the keyboard. I don't know which keys he pressed, but when I returned, the colors that I had created had been totally lost. After giving Thomas a friendly scolding, I found another, unfortunately not as good, palette. So, thanks to Thomas, we have an image that rates only an average 5 instead of the original above-average 7. Lying at a rather extreme depth, the image requires arbitrary precision math, and therefore takes 47 minutes to render. The wait can be eliminated by downloading the completed image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather deteriorated rapidly during the day Wednesday here at Fractal Central, with the climax arriving at 4pm when a heavy thunder-storm passed over. There were reports of a possible tornado sighted around 25 miles to the southwest, but F.C. escaped untouched. The cats managed an hour or so in the yard before the rain arrived, when the temperature was 73F 23C. This appeared to satisfy their urge to be outside. The day passed uneventfully for me. (Which means the work went smoothly.) Hopefully, today, which is starting rainy, will pass equally uneventfully. Check back in 24 hours for another stunning (IMO) fractal. Until then, take care, and how many fractals would be needed to weigh a ton? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Both_Ways_at_Once { ; time=0:47:15.43--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=-1.7919\ 569696643180421863582/2.4197474875995613452e-6/2.7\ 25467e+021/1/-85/1.1094160312641321e-011 params=0/0 float=y maxiter=3200 inside=0 periodicity=10 colors=000fdteaud_ucXueXqhXljXgmXboXZrXUtXPwXKzYFw\ XIsWLpVOlURiTUeSXbQ_ZPbWOeSNhPMkLLnIKqEIuMLiVPYbTM\ kXAt6jr7jo9jlAjiCkfEkcFk`HlYIlVKlSMmPNmMPmJRnMQlPO\ iSMgVKdZJaaH_dFXgDVkCSnAPq8Nt6Kx4Hv6Hs9IpCImFJkHKh\ KKeNLbQL`SMYVNVYNS`OQbONePKhQHkQFmRCpR9sS6vTNbhcIx\ cJwdKveLtfMsfNqgOphQniRmjSljTjkUilVgmWfnYdndeolfpt\ gfseXqcNoaDm_2kX3eY4Z_6S`7Mb8FcA8eDFbHM_KTWO_TRfPV\ mMZuIcjJh_LnONsDPy1Rv4Ss8UpBWlFYiI_fMacQb_TdXXfU_h\ RcjNglOglPgmQgnRfnSfoUfpVfqWeqXerYesZds`dtadubdvcc\ vdcwecxgby_YoSTeJOWBJM2DB2FB2HB2JA2MAIOAKQ9MT9OV9Q\ X8S_8Ua8Wc7Ye7_h7aj6cl6eo6jq5ks5kv4mw7kxAiyDgzGczJ\ _zMWzPSzSOwVKtYGr`8pc9mf9ji9gl9doAasCZsEVrGSqIUqKU\ pMUoOUnQUnSUmUUlWUkYVk_WjaXicXieYhgYgiXfkWfmWeoWdr\ VcrWcrXbrYar_ar``ra_rbZqdZqeYqfXqgWqiWqjVqkUqlTpnT\ poSppRpqQpsQptPpuOowNhrMamLVgJObIHYHASFN7PN8QNASNB\ UNDWNEYNG_NHaNJcNKeNMgNNi } END PARAMETER FILE=========================================

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[Fractint] Horizontal line (and other) artifacts due to periodicity testing
by Hal Lane 07 Nov '03

07 Nov '03

################################################################# JoTz, What I understand of Periodicity Logic is that it is a speedup whose purpose is to decrease the calculation time of fractals by terminating a pixel's calculation early when Fractint detects that the values of the iterates have fallen into a repeating loop. This feature, which is on by default, operates on essentially all fractal calculations (probably not while calculating Iterated Function Systems) and can occasionally cause image artifacts most usually in the form of horizontal lines if the assumptions made for its correct operation are not met. Damien M. Jones notes that sometimes "'Holes' in an image while it is being drawn" can be an artifact caused by periodicity checking terminating an iteration too soon in certain circumstances. (See below.) Fortunately these problems seem not to happen too often -- since Mark Peterson's Periodicity Logic in Fractint has saved countless years while calculating fractals... :) >"...I think the effect looks rather cool..." The horizontal lines are really not supposed to be there. The lines are caused by the speedup algorithm going awry. However, one person's artifact can be another's nifty effect. I certainly have created some nice looking fractals with artifacts in them when writing my own code... If I am correct, you can only turn this off with the command line parameter PERIODICITY=no (described below). There is no parameter on the V, X, Y or Z pages to turn this off. [Aside: A quick way to add a command line parameter to a calculation is with Robin Bussell's tiny (15kB) Windows 'front end' to DOS Fractint, called Paste 'n' Go. http://web.ukonline.co.uk/robin.b2/pastengo.htm You can specify any command line parameter in his Setup page as a 'Custom parm'. And of course you can paste (or type in) Fractint parameters and formulas into the text windows. Clicking 'Launch' copies the parameters and formulas to files which it 'feeds' to Fractint in an appropriate way. I use this program (under Win98) often and really like it a lot. Further Aside: I keep viewwindows=4/0.75/yes/0/0 as one of my custom parameters and always have it enabled so any fractal I start calculating appears in a 1/4 screen size viewing window to let me quickly see if things are going well. Then a quick 'v', 'n', 'Enter' starts drawing the fractal at full screen size. I am able to type all three characters without waiting for the text mode View Window Options screen to appear. Thanks again for a great program, Robin!] Note that PERIODICITY=no and PERIODICITY=0 do not do the same thing. Also, note that Ken Shirriff's inside coloring option 'Periodicity' (on the 'X' page and as a command line parameter - see below) determines pixel coloring. This setting/parameter does NOT turn on or off periodicity checking during the calculation of the fractal: "Inside=period colors pixels according to the period of their eventual orbit..." Btw, JoTz, Lee's recommendation of turning periodicity checking off while calculating your 'zoom2' fractal removed the horizontal lines from the image. JoTz's web site is at: http://www.sonic.net/~jot/ Click "The UlÂimaÂe FracÂal Video ProjecÂ!" link at the bottom of the page to see the animations he mentions in the message I quote at the bottom of this email. I am able to see this artifact in both 'Eye Of Hell #2' (very clearly) and 'Triskaidekaphobia'. Although I have not used them, JoTz appears to have written some very nice utilities for use with Fractint. JoTz, If you recalculate an image from one of your zooms would you please let me know whether turning periodicity checking off removes the horizontal lines from the image? Thanks... <--<< Also, what software do you use to combine Fractint's .gifs into an .wmv or .avi animation? <--<< Btw, your http://www.sonic.net/~jot/ufvp.html page is wider than my IE 6.0 browser set to full screen in 1024 x 768 screen size using 'Medium' (default) size characters. It only appears to exceed the screen width where PenÂaGoÂh, KaLieÃesÃope and PyraMid appear side by side in a horizontal row not too far from the top of the page. Nice web site! Here is some info from the Fractint 20.0 docs about periodicity: - Hal Lane ######################### # hallane(a)earthlink.net # ######################### ====================== Fractint 20.0 Docs =========================== 8.2.1 Periodicity Logic The "Mandelbrot Lake" in the center of the M-set images is the traditional bane of plotting programs. It sucks up the most computer time because it always reaches the iteration limit -- and yet the most interesting areas are invariably right at the edge the lake. [Note: 'Lake' ares in other fractals have this same problem - Hal] (See The Mandelbrot Set (p. 35) for a description of the iteration process.) Thanks to Mark Peterson for pointing out (well, he more like beat us over the head until we paid attention) that the iteration values in the middle of Mandelbrot Lake tend to decay to periodic loops (i.e., Z(n+m) == Z(n), a fact that is pointed out on pages 58-61 of "The Beauty of Fractals"). An intelligent program (like the one he wrote) would check for this periodicity once in a while, recognize that iterations caught in a loop are going to max out, and bail out early. For speed purposes, the current version of the program turns this checking algorithm on only if the last pixel generated was in the lake. (The checking itself takes a small amount of time, and the pixels on the very edge of the lake tend to decay to periodic loops very slowly, so this compromise turned out to be the fastest generic answer). ... PERIODICITY=no|show|nnn Controls periodicity checking (see Periodicity Logic (p. 153)). "no" turns it off ... Type lambdafn function=exp needs periodicity turned off to be accurate -- there may be other cases. [And you seem to have found one in your 'zoom2' fractal and your Julia Set zooms -- Hal] ... Note that fractint normally uses periodicity checking to speed up bifurcation computation. However, in some cases a better quality image will be obtained if you turn off periodicity checking with "periodicity=no"; for instance, if you use a high number of iterations and a smooth colormap. ... "Holes" in an image while it is being drawn: Little squares colored in your "inside" color, in a pattern of every second square of that size, in solid guessing mode, both across and down (i.e., 1 out of 4), are a symptom of an image which should be calculated with more conservative periodicity checking than the default. See the Periodicity parameter under Image Calculation Parameters (p. 116). ... inside=atan colors by determining the angle in degrees the last iterated value has with respect to the real axis, and using the absolute value. This feature should be used with periodicity=0 ... Periodicity is a new inside coloring option. Thanks to Ken Shirriff. ... 5.9 Color Parameters INSIDE=nnn|bof60|bof61|zmag|attractor|epscross|startrail|period|fmod|atan Set the color of the interior ... Inside=period colors pixels according to the period of their eventual orbit. ... ====================== Fractint 20.0 Docs =========================== ################################################################# >Date: Sun, 2 Nov 2003 10:24:01 -0500 >From: "JackOTradez" <JackOTradez(a)email.msn.com> >Subject: [Fractint] Re: Hal Lane;"zoom2"" >To: <fractint(a)mailman.xmission.com> >Message-ID: <000a01c3a155$5929ce70$06ec8041@skynet> >Content-Type: text/plain; charset="iso-8859-1" >Hal, >I have seen this effect quite often over the past year; it is quite common >in some Julia Set zooms, when you zoom into the black lake multicolored >horizontal lines appear and finally the lake is filled with color. This can >be seen in some of my animations, such as Eye Of Hell #2 and >Triskaidekaphobia, and especially "Star Gate", which is no longer on my site >(I can put it back up if anyone wants to see it). I also noticed it with >some of the "multifractals" and other "unusual" fractals I have been playing >with. >Up till now I assumed it was a normal, if not understood, fractal >phenomenon, and I have been pulling my hair out trying to figure it out. In >animation sequences, it looks not unlike a "bifurcation" effect. Actually, I >think the effect looks rather cool, especially with zoom animations. >It never occured to me that it could be a "bug", or due to a fractint >version, or a parameter tweak, as Lee suggested. I still don't know that it >is. I will try Lee suggestions; I have not played much with periodicity >setting, so I can tell you nothing about that. However, lowering the >iteration count will often generate a fractal that looks completely >different. >BTW, I made an animation on a variation of the "Julia Rectangle" image, it >is called Bad Trip and it is now on my site. >Stay Amazed! >JoTz ################################################################# --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.534 / Virus Database: 329 - Release Date: 10/31/03

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FOTD 05-11-03 (Total Sorcery [6])
by Jim Muth 05 Nov '03

05 Nov '03

FOTD -- November 05, 2003 (Rating 6) Fractal visionaries and enthusiasts: The parent fractal of today's image is a whimsical thing created by adding a lot of just plain Z to a little bit of Z^11. The resulting fractal appears as a tiny Mandeloid surrounded by a galaxy of even tinier satellite Mandeloids. Today's midget is located in one of these satellites in the southeast suburbs of its parent. The midget is quite 'disconnected', or cut off from the main body of its parent, which makes the traditional 'equal-iteration- band' rendering rather dull, and at the same time makes the other 'outside' options worth a look. The 'outside' option that works the best with today's scene is the 'fmod', with the proxim- ity set to a rather high 1.9. This rendering creates a scene of terraces, which for some reason I have named "Total Sorcery". The rating of a 6 might be a bit liberal. Real sorcery, like real magic, is all in the mind, a fact that all true sorcerers admit. But that doesn't make it any less real. Sorcery, which need not be used only for evil purposes, involves a different kind of reality, and it is up to its practi- tioners to shift their awareness to the reality where sorcery is a true fact of nature. (Is not the mind a part of nature?) Fractals are also a true fact of nature, and like sorcery, they exist in a different kind of reality -- the reality of the world of numbers. Luckily, this world of numbers has been made visi- ble through the modern computer. One of these days, someone just might devise a way for computers to make visible the world in the mind where sorcery exists. And then . . . who knows . . . magic might become as real as fractals. It is almost magical that today's image renders in a mere 53 seconds. That is even faster than the time required to download the already-rendered image from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather was perfect all day Tuesday here at Fractal Central. The light winds, sunny skies, and high temperature of 80F 26.5C that prevailed are most unusual in early November. The fractal cats took full advantage of the perfection by romping in the yard and sleeping on the porch. Tippy even made a leap at a bird that landed on the railing, but the bird was far too quick, and Tippy went without his tidbit. A bit of tuna eased his disappointment. Today is starting much less perfect. The heavy clouds, fog, and drizzle that moved in overnight are firmly ensconced. The rain that is due later this afternoon will make things only worse. The cats will likely have a bad day. But, if the moderate amount of work now before me goes smoothly, I will finish by 2pm, and my day will be acceptable, especially if I have a good evening in Fractal Land. Check back tomorrow to see how things go. Until then, take care, and where is nowhere? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Total_Sorcery { ; time=0:00:53.66--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident center-mag=-1.008324354763536/-0.2658996081493412/\ 4.908143e+007/1/-97.5/2.4234396733824326e-007 params=1/11/11/1/-0.8/0 float=y maxiter=275 inside=0 proximity=1.9 outside=fmod periodicity=10 colors=000nWPmVQlURkTSjSTiRUhQVhPWhOXhMZhL_gK`gIbg\ HcgFegEfgDggBifAjf9kf7mf6nf5of3qf2re0tgAqiLmlVin_f\ mcbmcZmdekbciaag__eZYcXWbWV`UTZTRXRPVQNTOLSNKQLIOK\ GMIEKHCIFAGD8IGAIHAIIAHKAHLAHMAHNBGPBGQBGRBFTBFUBF\ VBFWCEYCEZCE_CE`CDbCDcDDdDCfDCgDChDCiDBkDBlEBmEBnE\ ApEAqEArE9tFAnFAjGAfHAbJAZKAVLBVNAVLBVKBVKCVJCVJDV\ IEVIEWHFWHFWGGWFHWFHWEIWEIXDJXDJXCKXCLXBLXAMXAMY9N\ Y9OY8OY8PY7PY7QY6RZ5PY7PY8PY8PY9PZAPZAPZBPZBP_CP_D\ P_DP_EP`EP`FP`GP`GPaHPaHPaIPaJQbJQbKQbLQbLQcMQcMQc\ NQcOQdOQdPQdPQdQQeRQeRQeSQeSQfTQfUQfUQfVRgWRf_TfeV\ fkXfqZewZevYduXctXcsWbrVaqV`pU`oT_nTZmSYlRYkRXiQWh\ PVgPVfOUeNTdNScMSbLRaLQ`KP_JPZJOYINWHMXHMUGLTFKSFJ\ REJQDIPDHOCGNBGMBFLAEK9DI9DH8CG7BF7AE6AD59C58B47A3\ 7936825714525726827928928A29B2AB2AC2AD2AD2AE2AF2AF\ 2AG2BH2CI2DI2EJ2FK2GK2HL2IM2JM2KN2LO2MO2NP2OQ2PR2Q\ R2RS2ST2TT2UU2VV2WV2XW2YX } 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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FC2E CD
by Tim Wegner 05 Nov '03

05 Nov '03

I have uploaded an ISO image of the companion CD to "Fractal Creations 2nd Edition" here: http://www.fractint.org/ftp/iso The CD is for personal use, the same as if you had gotten the CD with the book. The offer of sending a copy of the CD to anyone who sends me a self- addressed stamped mailer with a blank CD still holds. Several people have taken advantage of this. My address is in the fractint online help under "Contacting the Authors". To those who mirror www.fractint.org: the main html file has changed, and there's a new ISO directory. The mirror of fractint.org now takes up a lot more space. :-) I have yet to update my own mirror. Tim

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FOTD 04-11-03 (Fractal Arrowheads [7])
by Jim Muth 04 Nov '03

04 Nov '03

FOTD -- November 04, 2003 (Rating 7) Fractal visionaries and enthusiasts: Today's image reminds me of the indian (Native American in PC language) artifacts that are sometimes found in the Fractal Central area. Lots of these are still lying around the area, waiting to be discovered. But it is not a matter of going out and picking up a relic. The difficulty lies in distinguishing the artifacts from the natural stones. It takes an expert to pick out an old arrowhead among the pebbles littering a river bank. There is no such difficulty in today's image. The reddish- orange bits that fill the image and seem to be swirling around the small midget in the center could easily be old arrowheads that have been lying in the ground for hundreds if not thousands of years. They could be, but they are actually fractals. I named the image "Fractal Arrowheads accordingly. The formula Z=(-1*(Z^1.1))+(11*(Z^(-1.11)))+1/C was iterated to create the parent fractal, which consists of two Mandeloids -- a rather intact one on the left, and a rudimentary one on the left, which is partly cut off. Today's scene lies in what remains of the East Valley of the left Mandeloid. Today's scene is unusual in that almost all the outside options work well with it. I chose the 'summ' option because that one impressed me the most when I saw at thumbnail size how it worked. The rating of today's image lies somewhere between 7 and 8. Feeling conservative, I rated it at a 7, though an 8 would have been nearly as accurate. The render time of 11 minutes borders on the excessive. The better way to see the orange arrowheads in today's image is to download it from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Monday started perfect and stayed perfect all day here at Fractal Central. Cloudless skies, balmy south winds and a temperature of 81F 27C kept the dynamic fractal cats coming and going from 11am until sunset, which comes at 5pm in this part of the world at this time of year. It might be winter in Minnesota, but it's summer in Maryland. Today looks to be another perfect one. The cats are waiting with anxious anticipation. As for me, I've got a couple hours of work to wrap up before I return to Fractal Land. The next FOTD will appear in 24 hours. Until then, take care, and could a fractal ever be complex enough to be considered alive? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Arrowheads { ; time=0:11:75.43--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.07936380134388553/-0.063807105970711\ 40/2.109278e+009/1/175/-3.97646805857798658e-005 params=-1/1.1/11/-1.11/0/525 float=y maxiter=1800 inside=0 outside=summ logmap=250 periodicity=10 colors=000KDJNEKQFLTGMWHNZIOaJPdKQgLRjMTmNVpOXsP_u\ QbwReyShzUkzWnzYqz_tzawzcwzcwzcwzawzawz_wz_wzYtzYq\ zWnzWkzUgzUczSazSZzSVzVRzYPz`LzcGyaBw_9wY4wU0wR0uP\ 0nS0fS0_S0SS0JS0AU0AW0QZ0Ua0Yd0ag0ej0im0mn0il0ej0a\ i4Yf7UdBQcGMaLH_N0YR2YV4WZ7U`AScCQgEOkHLnJJqLHtLCo\ OHvOJwOLwOOwOSwOUwOWwJ_wOYwQYwSWwWWwYUw_UwcUwdSwfS\ wjQwlQwnQwrOwtOvuLtyLqzJnzJkzJgzHczHazEZzEVzCVzETz\ HRzJPzLNzOLyOIuQGtSEqUBlW9iY7dY4a_1Ya0Uc0Sd0Of0Jf0\ Ei0Aj04l00n00n0Hr0Wu0jy0wz0zy0zz0zz0wz1rz7lzBdzG_z\ LWzRUzPUzNUzLSzISzGSzESzBQz9Qz9Qz7Oz4Oz1Oz0Oz0Lz0L\ z0Lz0Sz0Lz0Ez0Az02z00z10z40z70zE0zL4zPCzVHyZOwcUti\ Yrncqrflvljwqiwnjwnlwnnwlqwlrwlrwltwjuwjwwjyvjyviz\ viztiztfzrfzrfzrfzqdzqdzodzodzoazk_zgYzfWzaUzZQzXO\ zTLzRJzNHzICzGAzB7z74z42z00z04z0Az1Ez4Jz7Oz9SzBWzE\ _zGczIfzLjzNnzPrzRuyTyyVzyXzyZzy`zwazwczwfzwgzzfzz\ gzzizz0zz0zz0zz0zz0zz0zz0 } 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 03-11-03 (Retweaked Midget [8])
by Jim Muth 03 Nov '03

03 Nov '03

FOTD -- November 03, 2003 (Rating 8) Fractal visionaries and enthusiasts: When I opened my e-mailbox this morning, the usual load of junk was there, which I immediately discarded. But I also found a letter from the Fractint list, in which Hal Lane shows a midget that he found near yesterday's FOTD. Though the scene resembles yesterday's, the midget is quite attractive, and worth being touched up a bit to become the FOTD for today. But before discussing the image, I would like to answer the questions asked in Hal's letter. First, I find my color maps by using the 'enter' and function keys generously. Then, when a potentially good color map appears, usually by accident, I fine- tune the registers by hand. This can easily be done with the 256 colors of the GIF format. It is a bit more difficult, at least for me, with the gradients that must be used with true- color formats. Second, Hal's spell-checker is mis-informed. ;-) My name is correctly spelled 'Muth'. It is a German name. In Germany, it is pronounced 'moot'. In english-speaking countries, it can be pronounced mooth, to rhyme with tooth. It is not pronounced 'mewth' as the fractal cats address me, nor is it pronounced 'muhth' as though the final 'st' of 'must' were changed to 'th'. These two mispronunciations tell me that the voice on the phone is most likely a telemarketer trying to sell me something. To get today's image, I took Hal's image, did a modest outzoom and rotated the midget to the 'normal' position, with the main stem facing west. Then I noticed that several spurious holes appeared in the image. This could be corrected by resetting the logmap to 1, but doing this changes the colors too much. I decided instead to raise the proximity value from 0.4 to 0.53, which just barely closes the holes. Then I noticed a few minor irregularities in the color map, which I adjusted to make the map a bit smoother. I did this by equalizing the increments between bands by hand. The effect is subtle and is most noticeable where the yellow blends into the red and green. To conclude my tweaking, I reduced the maxiter to 1000, which cut the render time notably without degrading the definition of the midget. Since the scene is basically a repeat of yester- day's, I gave it yesterday's rating of an 8. The image is basically a tweak of a tweak, so I named it "Retweaked Midget". The 1-1/2 minute render time of the parameter file is very fast. But the download from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> might be a bit faster. The weather was absolutely perfect here at Fractal Central on Sunday. The sun shone brilliantly, the temperature reached 79F 26C, and the wind was light. True, in the afternoon, I was abducted and taken to one of the local antique emporiums, where we browsed for a couple hours, but with such a beautiful day surrounding me, even that was almost fun. The duo of fractal cats had a full morning and a late afternoon in the yard, so there were no complaints from them. The day ended peacefully, with everyone watching for more abductions on the sci-fi channel. The day is starting near perfectly once again. I have high hopes of it remaining so until evening. The next in the endless series of FOTD images will arrive in 24 hours, so until then, take care, and one good tweak is worth another. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Retweaked_Midget { ; Time=0:01:39.46--SF5 on a P200 reset=2002 type=formula formulafile=allinone.par formulaname=mandelbrotmix4 function=ident passes=1 center-mag=-2.03524527280745500/-0.010778095131324\ 12/941.8878/1/130/6.8422719449665e-006 params=1/2.\ 03/-0.2/2.97/0/0 float=y maxiter=1000 inside=0 proximity=0.53 outside=fmod periodicity=10 colors=000EKaGM`IO_KQZMSYOUWQWUSYSU_QWaOYcM_eKagIc\ iGekEilAlm1mm4ll6kj8khAjfDjdFibHi`JhZMhXOgVQgTSfRV\ fPXeNZeL`dJbdHdcFgcDibBkc9lb7ma5la3k`3j_4i_4hZ5gY6\ fX6eX7dW8cV8bV9aU9`TA_TBZSBYRCXQDWQDVPEUOFTOFSNGRM\ GQLHPLIOKINKIMJJMJJLNJOQIRUITXHW`HZcH`gGcjGfnGiqFk\ tFnwFptGmrGjoGhmGejHchH`eHZcHWaHTZHRWIOUIMRIJPIHMI\ EKJBHJ8FJ6CJ3AJ19J29I38I37H46H56G55G65G6CHDJIKQJRX\ KY_NabKc_HdWEeCBf38g58e78d98bA7`C7_E7YG7XI7VK7TM7S\ N6QP6OR6NT6LV6JX6IZ6G`6Fb6Dd6Bg10f6AeBJcGTbLaaQjZP\ iXOhUNgSNfQMeNLeLKdJKcGJbEIaCH`AH_8GZ6GZ3FY1EX6K_B\ QcFVfK`iPflTkoRhkQegOcdM``LYXJVTHSPGQLENHDKDBH9AF6\ AHBAJGAKLAMQANVAP_ARdASiAUmAVrDTqHQoKOnNLlRJjUGiXE\ g_Cf`CdaCcbBacB_eBZfBXgAVhAUiASjAQkAPlANnAMo9Kp9I`\ VGbUFaUF`VG_VGZWHYWHXXIWXIVYJUYJTYJSZKRZKQ_LP_LO`M\ N`MMaNLaNKaOJaOIbPHbPGcQFcQGbKFcPFeVEg_EieDkj5mmDo\ oMqgLshKphKnhJlhJjhIhhHfi } 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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Another midget in the FOTD for 03-11-02 (Nov 2,'03)
by Hal Lane 03 Nov '03

03 Nov '03

For those who like their Mandelbrot midgets more clearly defined I found a larger one near Jim Muth's Fractal of the Day for Nov 2, '03, 'Rainbow Vision'... This fractal calculates relatively quickly. Jim, That's quite a cheery color map! How did you happen to come up with that one? <--<< BTW, my spell checker says that you've been spelling your last name wrong all this time -- its actually supposed to be: 'Moth'... ;-) - Hal Lane START 20.02 PAR-FORMULA FILE================================ A_Bigger_Midget{ ; Another midget in the Nov 2,'03 FOTD ; Version 2002 Patchlevel 4 ; Hal Lane reset=2002 type=formula formulafile=_pastarc.frm formulaname=mandelbrotmix4 function=ident passes=1 center-mag=-2.03526564794305300/-0.01076099836157466\ /1216.695/1/157.4999928593476/1.06854042177251252e-0\ 05 params=1/2.03/-0.2/2.97/0/0 float=y maxiter=5000 inside=0 proximity=0.4 outside=fmod periodicity=10 sound=off colors=000Kph<3>IhhHfiHdi<3>E_iEZjE_iI`gLaeGcYSdU<3>\ ekEilAlm1mm4ll6<12>eIZeF`dDb<2>c5ib3kc0lb1m<22>NGRMG\ QLHPLIOKIN<2>JJL<4>`HZcH`gGc<3>tFnwFptGm<6>cHWaHTZHR\ WIO<3>MIEKJBHJ8FJ6CJ3AJ1<3>7H46H56G55G65G6<3>XKY_Nab\ Kc_HdWEeCBf38g<13>T6LV6JX6I<3>d6Bg10<3>bLaaQjZPi<8>E\ IaCH`AH_<3>1EX<3>K`iPflTko<5>JVTHSPGQL<2>BH9AF6AHB<3\ >ANVAP_ARd<2>AVr<3>NLlRJjUGiXEg_Cf<8>iASjAQkAP<3>p9I\ `VGbUF<17>LaNKaOJaO<2>GcQFcQGbK<4>Dej5TwDeoMugLsh } 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 20.02 PAR-FORMULA FILE================================== ######################### # hallane(a)earthlink.net # ######################### --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.534 / Virus Database: 329 - Release Date: 10/31/03

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Re: Hal Lane;"zoom2""
by JackOTradez 02 Nov '03

02 Nov '03

Hal, I have seen this effect quite often over the past year; it is quite common in some Julia Set zooms, when you zoom into the black lake multicolored horizontal lines appear and finally the lake is filled with color. This can be seen in some of my animations, such as Eye Of Hell #2 and Triskaidekaphobia, and especially "Star Gate", which is no longer on my site (I can put it back up if anyone wants to see it). I also noticed it with some of the "multifractals" and other "unusual" fractals I have been playing with. Up till now I assumed it was a normal, if not understood, fractal phenomenon, and I have been pulling my hair out trying to figure it out. In animation sequences, it looks not unlike a "bifurcation" effect. Actually, I think the effect looks rather cool, especially with zoom animations. It never occured to me that it could be a "bug", or due to a fractint version, or a parameter tweak, as Lee suggested. I still don't know that it is. I will try Lee suggestions; I have not played much with periodicity setting, so I can tell you nothing about that. However, lowering the iteration count will often generate a fractal that looks completely different. BTW, I made an animation on a variation of the "Julia Rectangle" image, it is called Bad Trip and it is now on my site. Stay Amazed! JoTz

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FOTD 02-11-03 (Rainbow Vision [8])
by Jim Muth 02 Nov '03

02 Nov '03

FOTD -- November 02, 2003 (Rating 8) Fractal visionaries and enthusiasts: I got quite a shock this morning when I opened my e-mail box. Among the hundred or so letters destined for immediate deletion I found one with the subject 'jamth, I met your mom last night xvztgsh hltbrs'. I was both shocked and elated. My mother has been dead over 10 years, which meant that spirit communication with the dead through the internet must have at last been achieved. But my wonderment did not last long. When I opened the letter, off-line of course, my web browser came up, and a message appeared telling me that the server could not be found. My disappointment was beyond words. The whole letter was just a ruse to lure me to a web site where someone wanted to sell me something I neither needed nor wanted. I drowned my sorrow in a glass of orange juice. ;-) Today's image however is no disappointment. It is a scene in the fractal that results when 0.2 parts of Z^2.97 are subtracted from Z^2.03 before C is added. In this fractal, the infinite splitting that normally occurs on the negative stem of a fractal such as Z^2.01+C occurs on a spurious stem that has magically appeared in the 'East Valley' area. This area of today's parent fractal is interesting enough when rendered with the normal equal-iteration-band method, but it is really outstanding when rendered as it has been in today's image, with the 'fmod' outside option with the proximity value set to 0.4. I named the image "Rainbow Vision" because of its rainbow-like palette of colors. The rating of 8 is justified, as will become obvious 2-1/2 minutes after the parameter file is started. And one of those 2-1/2 minutes can be knocked off the waiting time by going directly to Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or to Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> and downloading the completed image from there. Near perfect weather on Saturday made for near ideal cats. The sunny skies and temperature of 81F 27C were perfect for cats and man alike. Both enjoyed an afternoon of doing little in the yard. When evening came, (and it comes early at this time of year), the duo were ready to eat, and the man was ready to venture into Fractal Land. The day ended peacefully with a junky old sci-fi 'creature' movie on the TV. Today is starting just as pleasantly. If all goes well, the day will be as pleasant as yesterday. If not -- well, that's a different story. But regardless, 24 hours from now, another fractal will appear from nowhere. Until the next apparition, take care, and be kind to your fractals, for you might come face to face with one in the next world. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Rainbow_Vision { ; time=0:02:28.96--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-2.035785276340843/-0.01093006104338/10\ 0742.8/1/-122.5/-1.11086558701734e-009 params=1/2.\ 03/-0.2/2.97/0/0 float=y maxiter=500 inside=0 proximity=0.4 outside=fmod periodicity=10 colors=000KphKnhJlhIjhIhhHfiHdiGbiFaiF`iE_iEZjE_iI\ `gLaeGcYSdUWeQZgMbiIekEilAlm1mm4ll6lj8khAkeDjcFj`H\ iZJiWMhUOhSQgPSfNUfKXeIZeF`dDbdAec8gc5ib3kc0lb1ma2\ l`2k`3j_4iZ4hZ5gY6fX6eX7dW7cV8bU9aU9`TA_SBZSBYRCXQ\ DWQDVPEUOETNFSNGRMGQLHPLIOKINJJMJJMJJLNIOQIRUITXHW\ `HZcH`gGcjGfnGhqFktFnwFptGmrGjpGhmGekGchH`fHYcHWaH\ TZHRWIOUILRIJPIGMIEKJBHJ8FJ6CJ3AJ19I28I38H37H46H56\ G55G65G6CHDJIKQJRXKY_NabKc_HdWEeCBf38g57e77c97bB7`\ D7ZF7YG7WI7VK7TM7RO6QQ6OS6MT6LV6JX6IZ6G`6Eb6Dd6Bg1\ 0e6AdBJcGTbLaaQjZPiXOhVNgSNfQMeOLdLKcJKcHJbEIaCH`A\ H_7GZ5FY3EX1EX6K`BQcFVfK`iPflTkoRhkPegObcM`_LYWJVT\ HSPGQLENHDKDBH9AF6AHBAJGAKLAMQANVAP_ARdASiAUnAVrES\ pHQoKNmNLlRJjUGiXEg_CfaBdbBbcBadB_eBYfBXgBVhATiASj\ AQkAPmANnALoAKp9I`VGbUFaVG`VG_WHZWHYWIXXIWXJVYJUYJ\ TYKSZKRZLQ_LP_MO_MN`NM`NLaNKaOJaOIbPHbPGcQFcQGbKFc\ QFcVEd_EdeDej5TwDeoMugLsh } 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 01-11-03 (Rebirth of the FOTD [7])
by Jim Muth 01 Nov '03

01 Nov '03

FOTD -- November 01. 2003 (Rating 7) Fractal visionaries and enthusiasts: I named today's image "Rebirth of the FOTD". Actually the name is kind of a misnomer, for the FOTD has never really died. It merely slowed down a bit while I was catching up on the work that had fallen behind during the previous month. But the work is now up-to-date, and the FOTD is back on track. Today's rather baroque-looking fractal is a not-bad resumption. It is an 'evaporated' scene in the fractal that results when 9 parts of Z^(-0.9) are combined with one part of Z^(-9) and (1/C) is added rather than plain C. The scene is then 'evaporated' by raising the escape radius to one-googol, resulting in a screen of nothing but 'trapped' 'inside' points. The blank screen is then re-rendered with one of the dynamic inside-fill options. In today's case the 'bof61' inside fill works best. Trying to decide on a rating for the image was no problem. IMO, it is clearly fancy enough and different enough to be considered above average, which requires a rating of a 7. With a few interruptions, the FOTD has been ongoing for 6-1/2 years, but in that time I have never posted a fractal honestly worthy of a 10. I have posted a few 9's, and I did once post an image of the Mandelbrot set, which I rather artificially rated at a 10. The rating was justified. After all, the M-set is rather the perfect fractal, to which all others must be compared. But I have never posted another image that rated a 10. Perhaps I never will post an image that rates a 10. To rate an honest 10, an image must honestly be 'the best of all time'. Since rating fractals is such a subjective thing, and I want to avoid the 'grade inflation' like that which is afflicting so many of our schools, an image would need to be truly supercalli- fragillisticexpialidocious to move me to give it a rating of 10. But the goal of a perfect 10 still remains. And who knows? One of these days or years, I might achieve it. Today's image may be viewed by saving this letter as a text parameter file and then running it in Fractint and waiting 6 minutes, or by downloading the completed image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Friday was a near ideal Autumn day here at Fractal Central, with the blue of the sky being marred by only a few unusually dense cirrus clouds. Accompanied by light winds and a temperature of 70F 22C, these conditions gave the cats a comfortable afternoon in the yard. At one point, a small flock of starlings settled in a nearby tree. When Thomas saw them, he chattered at them, but the birds flew away and the day ended peacefully. Today is again starting near perfectly, with only a few scraps of work lying around waiting to be done. I should have plenty time to find a fractal to knock your socks off. But if I do, I'll then need to find one to put the socks back on. And I am currently reading a newly released book titled "Consciousness -- a user's guide". It should supply action on the philofractal list in the not-too-distent future. But before then, I shall return in 24 hours with fractal action. Until tomorrow, take care, and where will it all end? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Rebirth_of_theFOTD { ; time=0:06:34.64--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+3.95208506849724700/+1.024358072558484\ 00/259242.9/1/20.0000000007082015/-1.4442258847169\ 3203e-009 params=1/-9/9/-0.9/-0.9/1e+100 float=y maxiter=750 inside=bof61 periodicity=10 colors=000FjfHlcJn`LoZQjbUefYaiaXmeTpiOtmKwjOphRie\ UbcXWa_Qb`Tb`Wb`Yba`bacbaebbhbbkbbmaci`df_ecZf`YgY\ XhVWiSVjPUkMTlJSmGRnDQoAPo7NmHMkRLi`KgjJftLdrMcpNa\ nO`mPZkQYiRXgSVfTUdUSbVR`WQ_XPZXOYYNXYMXZLWZKV_JU_\ IU_HT`GS`FRaERaDQbCPbBObAOdGReLTfQVhWYi`_jeaZUjNIs\ MIrMIrMIrLIrLIrLIrKIrKIrKIrOGa`Y_ieQqmHyu8vp7tl7qh\ 6od6oe7of8og8oh9oiAojAojBokColComDonEooEopFopFmiGk\ cGjXGhRHgKHeEHd8H09V5FPALKFRFJWAMYDPZGR_JUaMWbOZcR\ adUcfXfg_hhakidnkgpljsmmunoYgjAafB_gCYhDWiDUjETkFR\ lGPmGNmHLnIKoJIpJGqKErLCsLBsOErQHqSKqUNpWQoZTo`Wnb\ Ynd`mfcliflkikmljoojqristioujkujhujduk`ukYukUulRul\ NulJumGumCum9umBrmDpmEnmGlmHjmJhmLfmMdmObmP`mRZmTX\ mUVmWTmXRm_UjaWgcZde`bgc_ieXkhUmjSlgQkdPjaNj_MiXLh\ UJgRIgPHkOGnOGrNFuNFpOGkPHgQIbRJZSKUTLQTMNQELO7jNX\ dR_ZVaTZdObfIfiCjk6nn1qp4pq6pr8psAptCpuEpvGpwIpwGk\ iEgWCcJBaMA`P9_S9eoBglDii } 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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[Fractint] Apparently erroneous horizontal streaks in black 'lake' areas in "zoom2"
by Hal Lane 31 Oct '03

31 Oct '03

JackOTradez's "zoom2" (as well as most of his other zooms) has apparently erroneous horizontal streaks in its black 'lake' areas when I calculate it with Fractint 20.02.4 on my Win98 SE vanilla Gateway. I've not had this problem on other images. This happens at any size image / any viewport of the image. I once saw this a long time ago in another fractal on another machine but was unsuccessful in determining what was going on at that time. Since I had not seen this particular artifact in at least six or eight years I assumed that its mechanism had been uncovered and dealt with. I have been 'given' a 2nd chance to see and ask for assistance with this particular artifact and I don't want to drop the ball this time... Does anyone else see these horizontal streaks in the 'lakes' when they create this image? <--<< ================ original message =============== Date: Mon, 20 Oct 2003 23:33:51 -0400 From: "JackOTradez" <JackOTradez(a)email.msn.com> Subject: [Fractint] Re: The Julia Rectangle ! To: <fractint(a)mailman.xmission.com> Message-ID: <000601c39784$2677f9a0$06ec8041@skynet> Content-Type: text/plain; charset="iso-8859-1" Here it is: ;;;;;;;;;;;;;;;;;;;;;;;START PAR;;;;;;;;;;;;;;;;;;; zoom2{ reset=2002 type=formula formulafile=juliax.par formulaname=test passes=1 corners=-0.1779712/0.1779712/-0.1334784/0.1334784 params=-1.7435/0/0/0 float=y maxiter=2110000000 fillcolor=0 inside=0 logmap=7 colors=000000000c00zW0zz00k000zc0cc00nG0zW0zz00c000zc0cc00<3>p_0sh0wq0zz\ 0<2>0c0<2>00zK0oc0cc00<9>qb0sf0tj0<3>zz0<3>Cg00c00WC<3>00z<3>W0gc0cc00<2\ 5>vn0wp0wr0<3>zz0<3>aq0Wo0Pl0<3>0c0<3>0OP0KV0Ga<3>00z<3>E0rI0pL0n<3>_0ec\ 0cc00<57>xt0xu0yv0<3>zz0<13>Jj0Gi0Cg0<3>0c0<13>0Cg0Aj08n<2>02w00z10y<21>\ c0c } frm:test { ;Julia-X z = pixel: z = z ^ (2.003) + p1 |z| <= (4 + p2) } ;;;;;;;;;;;;;;;;;;;;;;;END PAR;;;;;;;;;;;;;;;;;;;;;; =============== end original message =============== - Hal Lane ######################### # hallane(a)earthlink.net # #########################

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Fractal from 27-11-87 (Earliest)
by Jim Muth 31 Oct '03

31 Oct '03

FOTD October 31, 2003 ================================================ Fractal from November 27, 1987 Today's FOTD is the last that will recycle old images. The ongoing series of new images will resume tomorrow. But before resuming the new images, I thought it appropriate to show my humble fractal beginnings. Today's image was saved on November 27, 1987. It is not the first fractal I ever found, that fractal has long been lost, but it is the earliest fractal that I could find in my fractal archives. The image is that of a simple Mandelbrot midget in 16 colors. I have no idea which of the primitive fractal programs created it. Like the other old images, it was saved without parameters, making a trip to one of the FOTD web sites necessary in order to see it. Those web sites are: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Hopefully, the images will be posted by the time you visit the site. I forgot to e-mail it ahead of time last evening, as I usually do. It's a beautiful Autumn day here at F.C. The cats are happy, and, with the backlog of work finally cleared away, I am happy also. The ongoing series of FOTD's will re-appear in 24 hours. Until that glorious moment arrives, take care, and don't get a little behind in your work. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com

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Fractal from 08-05-97 (Horseshoe)
by Jim Muth 30 Oct '03

30 Oct '03

FOTD October 30, 2003 Today's image and discussion originally appeared as the FOTD for May 08, 1997. Both are reproduced here as they originally appeared. ================================================== Fractal of the day, May 08, 1997 Fractal visionaries: Today's fractal again comes from my most prolific and unpredictable formula file -- mandnewt.frm. Sometimes these formulas produce blank screens, sometimes they produce blank screens when the inside fill is set to a single color, but rich fractal images when the inside is set to bof60 or bof61, sometimes they produce Newton's images, sometimes they produce mandeloid images, and sometimes they produce a combination of all of the above. Today's fractal falls into the all of the above category. To see how much of it is inside fill, redraw the image with the inside set to 0 and the passes set to t. With the detail removed it will take only a few minutes. To add my part to the survey, let me say that I use Fractint about 80 percent of the time, an old shareware program by Scott Jones called "Recursive Realm" about 15 percent of the time, and all the other fractal programs about 5 percent of the time. I haven't yet had time to check most of the other fractals posted here, but things are beginning to slow down now businesswise, so over this weekend I'll see how many of the other posted parameter files I can find time to draw. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START FORMULA FILE======================================== frm:MandNewt03 {; Jim Muth z=c=pixel: a=z^3+(c-1)*z-c b=p1*z^p2+c-1 z=z-p3*a/b .0001 <= |a| } horseshoe { ; time=0:03:17.35--SF5 on a P200 reset=1950 type=formula formulafile=mandnewt.frm formulaname=MandNewt03 passes=1 center-mag=-1.01\ 365/2.22045e-016/0.7408645/1/90 params=5/0/2/0/4/0 float=y maxiter=304 inside=bof61 logmap=yes periodicity=7 colors=000F5f<2>I1fI0fK4g<17>dyw<19>\ pOu<4>Gey<7>A1C<7>g24<15>2Np<12>qzn<24>EZD<20>PlnP\ loQkm<17>Q`G<10>yGs<17>ifN<3>5Qm<9>yfC<30>bgpbgqaf\ p<8>Zeo6Kg<8>E7f } END PARAMETER FILE========================================

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Fractal from 08-01-89 (Mandelbrot Landscape)
by Jim Muth 29 Oct '03

29 Oct '03

FOTD October 29, 2003 Fractal image from January 08, 1989 Today's image is another blast from the past. In fact, when the time scale of personal fractal programs is considered, it is from ancient times. I found and saved the original PCX format image (now GIF) in January of 1989, at a time when I was still fascinated with the ghost-like remnants of buds that exist in the high-iteration background of many perturbed Mandelbrot sets. The name of the original image file is 'mndlscap', which I assume stood for "Mandelbrot Landscape". If I were naming the image today, I might choose something more like "Celestial Skyscape", but we'll stick with the original name. As was the case with yesterday's ancient image, the parameters of today's image were not included in the old image file, and have long since been lost. This means that the only way to see the image is to visit one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> and download the scene from there. Like yesterday's image, today's exceeds the limitations of its meager 16 colors. When I started working with fractals, I had only 16 colors to work with. This might be why I am little disturbed by the 256-color limit of the present Fractint GIF format. If millions of colors were available however, I of course would use them. While admiring today's image from the past, I was struck by the fact that it is better than some of my present day images. If I had to rate it, I would rate it around a 7. As a final note, I wonder what would happen to images like today's if the program were told not to draw to the screen until a certain number of iterations had been reached. Additional blank 'inside' areas would certainly appear, but what would they be shaped like? Today here at Fractal Central is starting rainy, but despite the rain, things are going well. (Unfortunately, they are not going so well in dried-out southern California, but then California does not get hurricanes, violent thunder and lightning storms, or blizzards.) The work backlog is down to one job that arrived yesterday morning. If nothing large comes in today, I will be caught up by the time the late news comes on TV at 11 this eve- ning. Turning to my left, I see Thomas on his shelf, looking wistfully out the window. Tippy is sleeping peacefully on a blanket by the radiator. The rain is due to end by noon, so if the fractal cats do not mind getting their paws wet, they will have a half- pleasant afternoon in the yard. I'll be back in 24 hours with another fractal, quite possibly another one from long ago. And in 3 days, the present-day FOTD will resume its daily schedule. Until tomorrow, take care, and don't lose your cool. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com

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Fractal from 11-11-88 (Alpha-Beta)
by Jim Muth 28 Oct '03

28 Oct '03

FOTD October 28, 2003 Fractal image from November 11, 1988 Fractal visionaries and enthusiasts: With today's fractal we take a trip back quite a way into the past century, to the year 1988, to an image that was saved in 16-color PCX format, without parameters. Whatever program created it apparently had no ability to write parameter files. As a result, the only way to see the image is to download it from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> I converted the original PCX image to GIF format and sent it to Paul and Scott separately late last evening. Hopefully, it will have been posted by the time I post this discussion. I do not recall what program created the old image. I was using several primitive fractal generating programs at the time. The earliest version of Fractint I ever used is version 2.0, which was released around that time. I still have it stored on a disk somewhere, but I don't think that version 2.0, which had a very limited range of magnification, created the image. The image is apparently a scene in a perturbed Mandelbrot set. At the time, I was fascinated by the 'ghosts' of the original M-set that remained in the background of 'perturbed' sets. Today's image is a study of one of these 'ghost' buds, with two prominent spiral loops in the foreground, and many thread-like tentacles leading to a 'bulls-eye' at the head of the bud in the background. The two loops most likely inspired the original name "Alpha_Beta". The image stands out as the exception among the scores of humdrum images from the same period. If I knew the parameters, I would like to re-do it in the latest version of Fractint, but that is impossible. And if I don't cut this short, it will be impossible for me to catch up in the other work. So until my next appearance, take care, and it's only four days until the ongoing FOTD resumes. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com

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Fractal 18-12-91 (Ancient Mandeloid)
by Jim Muth 27 Oct '03

27 Oct '03

FOTD October 27, 2003 Fractal from December 18, 1991 Fractal visionaries and enthusiasts: Today, we have a truly ancient fractal -- one from long before the FOTD was even dreamed of. The date of the original image file is December 18, 1991. I have no idea what version of Fractint it was created with, though my guess is that it was created with version 15.13, which came with the first edition (1991) of 'Fractal Creations'. The second edition was not published until 1993. Regardless of its origin, the image represents the kind of fractal work I was doing 12 years ago, at a time when I was fascinated with high-order fractals. The high-order period was brief, as I soon discovered that the images all look pretty much the same. But a few high-order images, such as today's scene in the Z^10+C Mandeloid, still stand out. Since the image is so old, I have named it "Ancient Mandeloid". I gave it no rating, feeling that it would be meaningless to compare a 12-year-old image to those I am producing today. The parameter file, which was created by the current version of Fractint from data encoded in the original GIF image file, runs in a speedy 4+ minutes. And to save even more time, the completed image has been posted to: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and to: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> A partly sunny, 73F 23C day here at Fractal Central gave the dynamic but gradually-slowing-down cats a pleasant Sunday in the yard. As for myself, the work backup is down to around one day -- small enough to be eliminated with a few more extra-long workdays. It looks as though the ongoing FOTD is still on schedule for a resumption this coming Saturday. For tomorrow, the good news is that I'll post a image from the 1980's, when I was just discovering the world of fractals. The bad news is that it will have to be picked up from one of the FOTD web sites. The image was originally saved in .pcx format and the parameters have long since been lost. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Ancient_Mandeloid { ; time=0:04:15.56--SF5 on a p200 reset=2002 type=manzpower center-mag=-1.0735586619\ 6815300/0/8.899924e+011 params=0/0/10/0 float=y maxiter=2500 bailout=7 inside=0 logmap=365 colors=000YlbZm__nX`nUanQbnNcnKdnHenGfnFfoEgnGhnHi\ nIjnJknKknLlnMmnNnnOonPpnQpnRjhSdcT_YUUTVONWJIXDCY\ 77Z22_74UB6PG8JK9ELEFLIGLNGLRHMWIM_IMdJMhKNmKNqLNv\ MNzMLtOJnPHhQFbREYSCSUAMV8GW6AX55YQR_jkahlcgmdened\ ofbpgaqi_rjZrkYslWtmVuoTvpSwqQxrPysOytOvuOtuOruOpv\ OmvOkvOiwOgwOdwObxO`xOZxOXxPWvQVuRUsSUrTTpUSoVSnWR\ lXQkYPiZPh_Of`NeaNdZNeXNeVNeTNeRNePNeNNeLNeJNeHNeF\ NeDNeBNe9Ne7Ne6Pd6Qd6Rc5Sc5Ub5Vb5Wa4Xa4Y`4_`3`_3a_\ 3bZ3cZQ2yP6vPAsPEpPImPMjOQgOUdOYaOaZOeWNiTNmQNqNNu\ KNxHLwIJwJHwKFvLDvLBvM9uN7uO5uP4uP6rO7oN8mM9jLBgKC\ eJDbIE`HGYGHVFITEJQDLNCMLBNIAOGAPFCQEERDGRCISBKTBL\ UANU9PV8RW7TW7UZ9R`APbCNdDLfEJhGHjHElJCnKApL8rN6tO\ 4vP2uR3tS3sT3rU3qV4pW4pX4oY4nZ5m_5l`5ka5kb5l`7m_8n\ Z9oYApXBpVCqUDrTEsSFtRGtQHuSJuULuWMuYOv_QvaRvcTveU\ wgWwiYwkZwm`woaqqblsbgucbwcXzcSzdNzdIzdKzcLzbMzaNz\ `Oz_PzZRzYSzXTzWUzVVzUWzT } END PARAMETER FILE=========================================

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FOTD 26-10-03 (Snake Tree)
by Jim Muth 26 Oct '03

26 Oct '03

FOTD October 26, 2003 (Snake Tree) Here is an improved version of the first entry in my collection of FOTD's. It was originally posted to the Fractal-Art mailing list on April 11, 1997. It is not the first fractal I ever posted to the F.A. list. That honor belongs to some forgotten image that I did not save because I had not yet realized how important the FOTD would become. START ORIGINAL MESSAGE=================================== FOTD 11-04-97 Fractal fans: Here's the formula and par file for an eye-catching fractal. Notice the simplicity of the formula, and especially the ridiculously low power of Z. Take a few minutes to run the par file to see a sample of what can be done with well-chosen but unlikely parameters used in simple formulas. I'll try to post a different image every day, until I make my point that complicated formulas are not necessary for new and unusual fractals. My point is not so much that complex formulas are wrong, but rather that there is much to yet be found in simple formulas such as the one attached below. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PAR-FORMULA FILE====================== frm:SnakeTree {; Jim Muth z=pixel: z=(-z)^1.095+3.4 |z| <= 100 } snaketree { ; time=0:01:58.56 on a P200 reset=1950 type=formula formulafile=outdated.frm formulaname=SnakeTree center-mag=1.75692/2.77556e\ -015/2.76818/1/90/3.88578058618804789e-016 float=y maxiter=500 inside=0 logmap=yes periodicity=10 colors=000FNN<25>hpk<27>GHW<18>9dI9eIAfK<34>TjrTj\ sWhi<3>c`8<45>Jd1Jd1Kc3<27>WbvWbwYav<23>wZaxZaxZa\ <24>yOd5CE<7>ELM } END PAR FILE================================

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FOTD 25-10-03 (Inside-Out Midget [7])
by Jim Muth 25 Oct '03

25 Oct '03

FOTD October 25, 2003 I include the original discussion that went with today's fractal, but the image is almost totally new. The original image as it appeared on May 15, 2001 consisted of a Mandeloid- shaped object at the center of a largely empty frame. As it appears today, the Mandeloid has been turned upside down, and I have zoomed in much tighter. The color is also entirely new. All these changes make the image virtually a new one and have justified a name change from "All Pooped Out" to "Inside-Out Midget". The sizzling render time of one minute should make running the parameter file almost a joy. =========================================================== Classic FOTD -- May 15, 2001 (Rating 7) Fractal visionaries and enthusiasts: Where are all those extra FOTD's coming from? Every time I post through AOL, it seems to happen. Today's FOTD holds a surprise. During the first half of the render, it looks notably unimpressive, but the lower half features a most unusual Mandeloid. This is not a midget -- it is the whole fractal, which explains why the render goes so fast. The iterated formula is a simple one, subtracting a portion of Z^(-0.7) from Z^(0.7) then adding 1/C. The result is a picture of a totally pooped-out Mandeloid lying flat on its face. I had no choice but to name the image "All Pooped Out". I rated it a 7 because I think it's kind of cute, though I really don't care much for funny-face fractals. The render time of under 3 minutes is reasonable. If it is not reasonable enough, the GIF file of the image is available on the Web at Paul's site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather today was reasonably pleasant, though a dry squall spoiled the evening. The afternoon temperature of 73F (23C) kept the cats happy. I've got a busy day coming, so that's it for now. Until next FOTD, take care, and see you soon. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Inside-Out_Midget { ; time=0:01:17.94--SF5 on a P200 reset=2001 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip float=y center-mag=-0.0158567/-0.125422/53.23071/1/-32.5/\ -1.7772588956e-013 params=1/0.7/-1/-0.7/-4.5/5000 maxiter=440 inside=atan logmap=yes periodicity=10 colors=000ZWSZWS_VR`VQ`VQaVPbVPbVO7MM7MM7MM7ML6ML6\ Ma6M`6M_6MZ6MY6MW6MV5MU5LS5KR5JQ5IO5HN5GM4EJ5EK6EK\ 6DK7EK7EL8FM8FN9GP9HQAHRAISBITBJUCJVCKWDVYDVZEW_EW\ `FXaFXbGYcGYdHZfH_gI_hI`iJ`jJakKalKbmLcoLcpMdqMdrN\ esNetOfuOfvPeuQetQdsRdrRcqScqTbpTboUanUamV`lV`lW_k\ X_jXZiYZhYYhZYgZXf_Xe`Xd`WcaWcaVbbVabU`cU_dT_dTZeS\ YUFKUA0UFKUFKeQUePTePSeOPeOKeNFeNAeN5eM0fM0gL0hL0i\ K0jK0kJ0lJ0m00n10o20p30q40r50s60t70u80v90vK0v90u80\ t70s60r50q40p30o20n10m00l00k00j00i00h00g00f00eTOdU\ PcUQbVRaWR`XS_YTZZUXZVV_WU`XTaYSbYRcZQc_Pd`OeaNfbM\ gcLhcKidIieHjfGkgFlhEmiDniCnjBokApl9qm8rn7so6so7rn\ 7rn7qn7qn8qn8pm8pm8pm9om9om9nl9nlAnlAmlAmlAmlBlkBl\ kBkkBkkCkkCjjCjjCjjDijDijDijDhiDhiEgiEgiEgiEfhFfhF\ fhFehFehGdgGdgGdgGcgHcgHcgHbfHbfIafIafIafI`eJ`eJ`e\ J_eJ_eJ_eKZdLZcLZcMZbNZbNZaOY`PY`PY_QY_RYZRYZSXYTX\ XTXXUXWVXWVXVWWUXWUXWTYWT } 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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Classic FOTD 11-04-01 (Veiled Objects [7])
by Jim Muth 24 Oct '03

24 Oct '03

FOTD October 24, 2003 All is going well here at Fractal Central, both with the work and the cats. And I have some great news. No, I have not saved a bundle on my auto insurance, I have won one-million dollars in a lottery sponsored by Bill Gates. I received the e-mail notification about an hour ago. Some minor bad news is that I must have a touch of amnesia, since I do not recall entering such a lottery. All I must do now is send a check for 750 dollars to cover expenses, and I will receive my million. Now I will be able to forget the graphic-design hassle and devote full time to fractals. The weather today is sunny and chilly. The classic FOTD appears below. ===================================================== CLASSIC FOTD April 11, 2001 (Veiled Objects [7]) Fractal visionaries and enthusiasts: Today's FOTD is late again . . . no surprise in that. I'm still busy. But I have finally managed to find an image that rates above a 6. True, at a rating of 7, it's only a single step above 6, but it's a start. I named the image "Veiled Objects" when I noticed that the smaller features seem to be draped over the larger objects like a gossamer veil. To create the image I unpacked number 6 in my series of 12 MandNewt (Ikenaga) formulae. This formula is a random variation of the Ikenaga function, and the Ikenaga function is a minor mystery. The image takes 8-1/2 minutes to render at a low-resolution SF5, but the highest resolution available is needed to do it justice. The image may be seen by running the parameter file at the resolution of your choice, or by downloading the GIF file from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://home.swbell.net/sdboyd56/fotd/> once it has been posted. The fractal weather today was cloudy but dry, with a temperature of 68F (20C). The fractal cats approved of the conditions. That's it for today. I've got a busy day ahead of me, and it's time to get to work. Until next time, take care, and hug at least one fractal every day. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Veiled_Objects { ; time=0:08:38.44--SF5 on a P200 reset=2001 type=formula formulafile=mandnewt.frm formulaname=MandNewt06 passes=1 center-mag=0.277319/-1.04425/35.70909/1/82.499 params=-2.37/2.17/-1.56/-1.05/3.29/-3.17 float=y maxiter=254 inside=bof60 logmap=yes periodicity=0 colors=000jwpjwqjwqhuogsmfqlepjdniclgajf`id_gcZeaY\ c`XbZV`YUZWTXVSWTRUSQSQOQPNPNMNMLLKKJJJIHHGGGEEFCD\ EBBD9AC78945B67D78F8AH9BJACLBENCFODGQEISFJUGKWHMYI\ N_JO`KQbLRdMSfNUhOVjPWlQYmRZoS_qTasUbuVcwWexXfxYgr\ ZdkZadZ_XZXQZVJZSAYRCZQDaNFeKGhHIlEInBJoCKoCKoCLoC\ LoCMoCMoCNoCNoDOoDOoDPoDQoDQoDRoDRoDSoESoEToEToEUo\ EUoEVoEWoEWoFXoFXoFYoFYoFZoFZoF_oF_oF`mG`lH`kIajIa\ hJagKafLbeLbdMbbNbaOc`Oc_PcYQcXRdWRdVSdUTdSUeRUeQV\ ePWdMYeOWeQVeRTeTSeUQeWPeXOeZMe_LeaJebIedHeeFegEeh\ CejBekAdj9dj9cj9cj8cj8bj8bi8bi7ai7ai7ai7`i6`i6`h6_\ h6_h5_h5Zh5Zh4Yh4Yg4Yg4Xg3Xg3Xg3Wg3Wg2Wf2Vf2Vf2Vf1\ Uf1Uf1Uf1Te3Td4Td5Tc6Tc7Tb8Tb9TaBSaCS`DS`ES_FS_GSZ\ HSZJSYKSYLRXMRXNRWORWPRVQRUSRUTRTURTVQSWQSXQRYQR_Q\ Q`QQaQPbQPcQOdPOePNgPNhPMiPMjPLkPLlPKmPKnRMmTNmUOm\ WQmXRlZSl`UlaVlcWkdYkfZkh_kiajkbjlcjnejpfiqgisiitj\ ivkhxmhxnhxohkunkunkvojvp } frm:MandNewt06 {; Jim Muth z=c=(pixel*p1): a=z^3+(c-p2)*z-c b=p3*z^2+c-1 z=z-1*a/b 0.000000000000000000000000000001 <= |a| } END 20.0 PAR-FORMULA FILE==================================

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Classic FOTD 17-03-01 (Mandelbrot Glory [6])
by Jim Muth 23 Oct '03

23 Oct '03

FOTD 23-10-03 (Mandelbrot Glory [6]) Here's a golden not-so oldie from 2-1/2 years ago, around the time I was moving the F.C. workshop from its old to its present location. The move actually caused less of a backup than the one that developed over the past few months and was exacerbated by the 5-day power failure about a month ago. Luckily, the backlog is now down to just under 2 days, and if the present trend continues, will be eliminated by the end of the month. The odds still look good for the ongoing FOTD to resume on November 1st. ========================================================= FOTD 17-03-01 (Mandelbrot Glory [6]) Fractal visionaries and enthusiasts: It's Saint Patrick's day and all is in confusion. I'm at the stage where the new Fractal Central is operating, but I have no idea where anything is. Nevertheless, I found an average fractal, which appears almost by magic if the parameter file is run. I named the image "Mandelbrot Glory" and rated it a 6. Searching for things such as certain computer disks in dozens of packed cartons leaves little time for discussing fractals, so I'll end my short discussion here. The GIF image will be available at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://home.swbell.net/sdboyd56/fotd/> The fractal weather today was cloudy with rain in the afternoon and a temperature of 48F (9C). Having been marooned indoors for two consecutive days, the fractal cats were testy most of the day. I'll return on schedule in 24 hours with another FOTD. Until then, take care, and watch the time fly. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Mandelbrot_Glory { ; time=0:12:49.07 -- SF5 on p200 reset=2001 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+23.153685954444/-41.66830373638096/2.4\ 33538e+007/1/-174.999 params=1.1/-11/11/-1.1/0/300 float=y maxiter=1800 inside=0 logmap=275 periodicity=10 colors=00000F00F00I00L00O00Q00U00X00_00b00e00h00k0\ 0n00r00u00x00z00z00z00z00z00z01z28z5Fz8MxAUsC`pIbi\ MbeQd`WdXbeSgeOmeJrgFzgAzh6zh2zh0zeAzbOz``zedxhgzk\ izpkzrnzurzxszzpzznzzmzzkzzizzhzzgzzezzdzzbzz`zz_z\ z`zzbzvdzsexpgvmhuiishipeknbmm_nkXphUrgQseOudMukOz\ sOzzOzm9rb0bW3gPAiIImCPp6Yu0ex0mz0uz5GM9CQC9WG5_J2\ dO0gQ0kW0pY0u`0xb0zd0zd0ze0ze0zg0zg0zh0zi0zi0zk1zk\ 2zm3zm5zn6zn8zp6vr5sr3ns2ks1gu1du0_v0Xx0Ux0Pz0Mz0I\ z0Fz0Az08z05r08h0AY5CP9FGFI6JJ0PM0UOFMAdF0z90sG0iO\ 2_W8Q`FGhM8pS0x_0ze0zk0zr0zxF2z9Dz5Oz1Yz0hz0sz0zz0\ zi0zn0zr0zv0zzzA3kOGW`SFnd0zpzXvLszU0C6Yb0Qp0gu0xz\ OirPhvQgzSezSezDYi1SM6UQCUUGUXMU`QUdXWgbWkgWnmWrrW\ urYvr`vrdvrgvrixrmxrpxrrxruzrxzrzzrzzrzzrzzrzzrzzn\ zvmzsizphzmgzhdzebzb`z_YzXXzSWzPSzMQzJPzGXzMbzShzY\ nzduzizznzzhzzdzz_xzWxzQxzMvzIvzDvz9uz5uz1uz0sz0sz\ 0sz0nz0kz0gz0dz0_z0Xz0Sz0 } 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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Re: Classic FOTD 03-10-1997 (Cirrus)
by Jim Muth 22 Oct '03

22 Oct '03

At 10:13 AM 10/22/03 -0500, Paul Lee wrote: >... would it not be just as easy to make [the altered >old FOTD's] whole new postings?? Yes. maybe I'll do this. >... why not just as well add in Scott's web hosting URL?? I'll do this. >And all of this leads to another question. Will the >"FOTD CD" have both versions of these postings (the >original and the modified)?? This I must consider. My original intent was to simply repost the old FOTD's unchanged, but then I started noticing obvious improvements that could be made to the old images and discussions. I could easily include the classic FOTD's on the impending CD. Jim M.

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Re: The Julia Rectangle !
by Jim Muth 22 Oct '03

22 Oct '03

At 11:33 PM 10/20/03 -0400, JackOTradez wrote: >Stay Amazed! Far more than rectangles lie in the vicinity of the julia rectangle. The attached parameter file draws an octagon. To see triangles, hexagons, etc. vary the real and imag p1 parameters + - 0.0001, and toggle the functions between ident/flip and flip/ident. ======================================================= Julia_Octagon { ; time=0:70:48 at 200MHZ SF5 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip center-mag=0/0/2500 params=90/90/2.003/0/0/0/-1.74\ 35027247539/7.707258e-008 float=y maxiter=1200 inside=0 logmap=393 periodicity=10 colors=000cccTnaYkXbiTgfOldJpbFcXBSS8FN43I13QD3YP3\ e`9`ZFXYLTWQPVWKUaGSgCRl8QhAMeBJbCFZDCWE8TF5QG2SJ7\ TMBVPGWSKXVPZYT_`Yacabffchjegkfflhemidnjdolcpmbqoa\ rp`sq`tjiTdr1bs3at4`u6_v7Zw9YxAXyCWzDVzETqIRiMPaPN\ UTMMWPNVSNUVOTYOS`PRcPQfQPiQOlQNfRJaSGXTDSUANU7MX9\ M_BLbDLeFKgGKjIJmKJpMIsOIuPKrQLpRMnSNkTPiUQgVRdWSb\ XT`YR__QZaPYcOYeNXgMWiLVkKVmJUoITqHSsGStHXuIauJfvJ\ kvKpwLuwLzwNvrPrmRohTkcVgZWdVZeU`eTbeSeeRgfRifQlfP\ nfOpgOsgNugMwgLygLuhJqhImhHiiGeiFaiEZjCVjBRjANk9Jk\ 8Fk7Ck6GiAJgDMeGPdJTbMW`PZZSaYV_ZWY_WW`XVaXTbYRcYP\ dZOeZMfZKg_Ih_Hi`Fj`DkaBlaAlaQF_VJW_NScROhVKlZHk_I\ k`IkaIjbIjbIjcIidJieJieJhfJhgJhhJhhJfcOeZTcVYbQb`M\ g_HlZDqaGrdIrfLsiNslQtnStjTnfThbUb_UXWVRSVLOWFLWAP\ cESjIWqMZxP3XM5YP7YS9YUBYXDY_FYaHZdJZfLZiNZlPZnRZq\ SZsQWsOTsNQsLOsJLsIIsGFsFDsGHoGLkHOgHSdIW`IZXJbUJe\ QKiMKmJLpFLtBLw8IrFFmMDiT } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } =======================================================

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Classic FOTD 03-10-1997 (Cirrus)
by Jim Muth 22 Oct '03

22 Oct '03

NOTE: This image has been changed from the original version. ===================================================== CLASSIC F.O.T.D., October 03, 1997 (Cirrus) Fractal visionaries: Today's unusual fractal is a view of the sky -- nothing solid, just vapor and ice crystals. I was undecided whether to name it "Cirrus" or "Skyscape". I finally decided on "Cirrus", but I could just as easily have given it the other name. There may still be some who doubt that clouds are one of nature's fractals. If so, today's picture should end that doubt. It is a photograph taken from a window of F.C., showing a clear blue sky filled with cirrus streamers. Well, actually it's not a photograph at all, but rather a scene in the Z^2+C Julibrot, sliced in the oblate direction, in the area of the second valley beyond Seahorse valley, the one at -1.368 on the X-axis. One of my fractal projects is to collect fractal representations of all the cloud types. I have had several fine cumulonimbus cloud fractals for quite some time, but today's cirrus fractal is my best cirrus scene to date. That leaves nimbus and stratus fractals yet to be found. And of course I'll also want all the combination clouds, such as cirro-cumulus and alto-cumulus, etc. The formula draws the oblate slices of the Julibrot, which I define as the slices determined by the Mandelbrot Y-axis and the Julia X-axis. The VB in the formula name stands for Variable Bailout. I recently discovered that a very low bailout radius does strange things in some of the odd planes, particularly in that area known as Seahorse Valley, so I altered my formulas to add an easily changed bailout feature. BTW, I wonder what happened to Elephant Valley at the east end of the Mandelbrot set. It has some very good fractal scenes also, and one almost never hears about it. Maybe elephants are simply too clumsy to be associated with fractals. :-) Whatever the case, today's picture of the cirrus clouds has been posted to: http://home.att.net/~Paul.N.Lee/FotD/FotD.html Until tomorrow then, keep looking up. You might see a UFO; you might see a fractal! Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 19.6 FILE============================================= cirrus { ; 2 minutes at 200mhz, 640x480 reset=1960 type=formula formulafile=cirrus.par formulaname=OblateVB passes=1 center-mag=-1.584890\ 27912513300/+0.01512015871562687/137.8441/1.9206/\ -4.818/3.522 params=0/-1.36818/6/0 float=y maxiter=200000 bailout=100 logmap=yes periodicity=10 colors=000e1Te1Te1Tf1Uf1Uf1Uf1Uf1Vg1Vg1Vg1Vg1Wg1Wh\ 1Wh1Wh1Wh1Xh1Xh1Xi1Xi1Yi1Yi1Yi1Yj1Zj1Zj1Zj1Zk0Yj0Z\ j0_i0_h1`h1ag1bg1bf1ce1de1ed2ec2fc2gb2ha2ha2iZ2jW3\ mT3rQ3wN3zK3zK3zK3zK3zK4zK4zK4zL4zM4zN4zO4zP5zQ5zQ\ 5zP5zO5zN4zN5zN6zO7zO7zO8zO9yOAyOByPCyPCyPDyPEyPFy\ PGyQHyQHyQIxQJxQKxQLxRMxRMxRNxROxRPxRQxSRxSRwSSwST\ wSUwSVwTWwTWwTXwTYwTZwT_wU`vU`vUavUbvUcvUdvVevVevV\ fvVgvVhvViuWjuWjuWkuWluWmuWnuXouXouXpuXquXrtYstZtt\ _tt`utavtbwtcxudxueytfztgzshzsizrjzrkzqlzqmzrnzsoz\ tpzuqzvrzwszxtzyuzzvzzwzzxzzyzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzlXVlWUlWUlVTmVTmU\ SmUSmTRnTRnSRnSQoRQoRPoQPoQOpPOpPNpONpOMqNMqNLqMLr\ MKrLKrLJrKJsKIsJIsJHsIHtIGtHGtGGuFHtGG`2N`2N`2Na2O\ a2Oa2Oa2Oa2Pa2Pb2Pb2Pb2Pb2Qb2Qc2Qc1Qc1Qc1Rc1Rc1Rd1\ Rd1Sd1Sd1Sd1Sd1Se1Te1Te1T } frm:OblateVB {; Jim Muth z=real(pixel)+flip(real(p1)), c=flip(imag(pixel))+imag(p1), a=sqr(p2): z=sqr(z)+c, |z| <= a } END 19.6 FILE===============================================

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Classic FOTD 10-06-00 (A Head of Bubbles)
by Jim Muth 21 Oct '03

21 Oct '03

Do not go to the fractal image of June 2000. Today's version is a slight outzoom of the original image. The color has also been refined. ========================================================== CLASSIC FOTD, June 10, 2000 (Break-away Fractal [6]) Fractal visionaries and enthusiasts: Today's fractal is another surrealistic scene created with one of the MandNewt formulae, which are actually the Ikenaga function in disguise. I chose formula number 1 to explore for today's image, and the formula did not let me down. As is the case with many images created with these formulas, the inside fill has been set to bof60, which has a tendency to create bubbles. The bof61 inside fill also works well with these formulas, as was demonstrated with yesterday's FOTD. The picture itself is another surrealistic one, with a mass of bubbly froth at the bottom and bubbles of assorted sizes and shapes all through the scene. The largest bubble is off-screen, though its lower part fills the upper left of the picture. The intense purple background speaks of infinite depth. I named the picture "A Head of Bubbles" when I noticed the effect of individual bubbles breaking away from the mass of froth. The parameter file takes all of 6-1/2 minutes to render on a P200 machine. If that is too slow, the GIF image file has been posted to Paul Lee's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The fractal weather today was quite warm, but without the oppressiveness we have so much of in this area in the summer. The temperature of 88F (31C) was a bit warmer than the fractal cats would have preferred, but they spent the afternoon on the back porch anyway. My philosophy once again floundered -- I'll try again tomorrow. Until then, take care, and when it's hot, try a cool fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Head_of_Bubbles { ; time=0:06:45.10--SF5 on a P200 reset=2000 type=formula formulafile=mandnewt.frm formulaname=MandNewt01 passes=1 center-mag=0.10382\ /0.313706/13.77989/1/-42.5/-1.2337353361147052e-014 params=-3.979/-3.596/1.305/-2.202/3.594/1.401 float=y maxiter=175 bailout=25 inside=bof60 logmap=yes symmetry=none periodicity=0 colors=000zzzzzzzyyxxyswyouyjsxgqxdpxaox_nwXmwUlwU\ kvUjvUiuUhuUgtUftUesUdsUcrUbrUaqU`qU_pUZpUYoUXnUWm\ UVlUUkTTjSSiRRhQQgPPfOOeNNdMMcLLbKKaJJ`IH_HFZGDYFB\ XEAWD9VC7TB6RA4O930c4zc6zc6zc6zc6zc7zc7zc7zc7zc7zc\ 7zc9zc9zc9zc9zc9zcAzcAzcAzcAzcAzcAzcCzcCzcCzcCzcCz\ cCzcCycCycDycDycDycFx00000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 0000000000000000000000000 } frm:MandNewt01 {; Jim Muth z=c=pixel: a=z^3+(c-1)*z-(p1*c) b=3*z^2+(p2*c-1) z=z-p3*a/b .00005 <= |a| } END 20.0 PAR-FORMULA FILE==================================

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Re: The Julia Rectangle !
by JackOTradez 21 Oct '03

21 Oct '03

Here it is: ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;START PAR;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; start { reset=2002 type=formula formulafile=juliax.par formulaname=test passes=1 corners=-1.6/1.6/-1.2/1.2 params=-1.7435/0/0/0 float=y maxiter=2110000000 fillcolor=0 inside=0 logmap=yes colors=000000000c00zW0zz00k000zc0cc00nG0zW0zz00c000zc0cc00<3>p_0sh0wq0zz\ 0<2>0c0<2>00zK0oc0cc00<9>qb0sf0tj0<3>zz0<3>Cg00c00WC<3>00z<3>W0gc0cc00<2\ 5>vn0wp0wr0<3>zz0<3>aq0Wo0Pl0<3>0c0<3>0OP0KV0Ga<3>00z<3>E0rI0pL0n<3>_0ec\ 0cc00<57>xt0xu0yv0<3>zz0<13>Jj0Gi0Cg0<3>0c0<13>0Cg0Aj08n<2>02w00z10y<21>\ c0c } zoom1 { reset=2002 type=formula formulafile=juliax.par formulaname=test passes=1 corners=-0.5632/0.5632/-0.4224/0.4224 params=-1.7435/0/0/0 float=y maxiter=2110000000 fillcolor=0 inside=0 logmap=3 colors=000000000c00zW0zz00k000zc0cc00nG0zW0zz00c000zc0cc00<3>p_0sh0wq0zz\ 0<2>0c0<2>00zK0oc0cc00<9>qb0sf0tj0<3>zz0<3>Cg00c00WC<3>00z<3>W0gc0cc00<2\ 5>vn0wp0wr0<3>zz0<3>aq0Wo0Pl0<3>0c0<3>0OP0KV0Ga<3>00z<3>E0rI0pL0n<3>_0ec\ 0cc00<57>xt0xu0yv0<3>zz0<13>Jj0Gi0Cg0<3>0c0<13>0Cg0Aj08n<2>02w00z10y<21>\ c0c } zoom2 { reset=2002 type=formula formulafile=juliax.par formulaname=test passes=1 corners=-0.1779712/0.1779712/-0.1334784/0.1334784 params=-1.7435/0/0/0 float=y maxiter=2110000000 fillcolor=0 inside=0 logmap=7 colors=000000000c00zW0zz00k000zc0cc00nG0zW0zz00c000zc0cc00<3>p_0sh0wq0zz\ 0<2>0c0<2>00zK0oc0cc00<9>qb0sf0tj0<3>zz0<3>Cg00c00WC<3>00z<3>W0gc0cc00<2\ 5>vn0wp0wr0<3>zz0<3>aq0Wo0Pl0<3>0c0<3>0OP0KV0Ga<3>00z<3>E0rI0pL0n<3>_0ec\ 0cc00<57>xt0xu0yv0<3>zz0<13>Jj0Gi0Cg0<3>0c0<13>0Cg0Aj08n<2>02w00z10y<21>\ c0c } zoom3 { reset=2002 type=formula formulafile=test.frm formulaname=test passes=1 corners=-0.049831936/0.049831936/-0.037373952/0.037373952 params=-1.7435/0/0/0 float=y maxiter=2110000000 fillcolor=0 inside=0 logmap=28 colors=000000000c00zW0zz00k000zc0cc00nG0zW0zz00c000zc0cc00<3>p_0sh0wq0zz\ 0<2>0c0<2>00zK0oc0cc00<9>qb0sf0tj0<3>zz0<3>Cg00c00WC<3>00z<3>W0gc0cc00<2\ 5>vn0wp0wr0<3>zz0<3>aq0Wo0Pl0<3>0c0<3>0OP0KV0Ga<3>00z<4>I0pL0nP0k<3>c0cc\ 00<57>xt0xu0yv0<3>zz0<13>Jj0Gi0Cg0<3>0c0<13>0Cg0Aj08n<2>02w00z10y<21>c0c } zoom4 { reset=2002 type=formula formulafile=test.frm formulaname=test passes=1 corners=-0.0276739647/0.0285649345/0.0528917631/0.0950709375 params=-1.7435/0/0/0 float=y maxiter=2110000000 fillcolor=0 inside=0 logmap=40 colors=000000000c00zW0zz00k000zc0cc00nG0zW0zz00c000zc0cc00<3>p_0sh0wq0zz\ 0<2>0c0<2>00zK0oc0cc00<9>qb0sf0tj0<3>zz0<3>Cg00c00WC<3>00z<3>W0gc0cc00<2\ 5>vn0wp0wr0<3>zz0<3>aq0Wo0Pl0<3>0c0<3>0OP0KV0Ga<3>00z<4>I0pL0nP0k<3>c0cc\ 00<57>xt0xu0yv0<3>zz0<13>Jj0Gi0Cg0<3>0c0<13>0Cg0Aj08n<2>02w00z10y<21>c0c } zoom5! { reset=2002 type=formula formulafile=test.frm formulaname=test passes=1 corners=-0.00966372122/0.0101323713/0.0664873996/0.081334469 params=-1.7435/0/0/0 float=y maxiter=2110000000 fillcolor=0 inside=0 logmap=62 colors=000000000c00zW0zz00k000zc0cc00nG0zW0zz00c000zc0cc00<3>p_0sh0wq0zz\ 0<2>0c0<2>00zK0oc0cc00<9>qb0sf0tj0<3>zz0<3>Cg00c00WC<3>00z<3>W0gc0cc00<2\ 5>vn0wp0wr0<3>zz0<3>aq0Wo0Pl0<3>0c0<3>0OP0KV0Ga<3>00z<4>I0pL0nP0k<3>c0cc\ 00<57>xt0xu0yv0<3>zz0<13>Jj0Gi0Cg0<3>0c0<13>0Cg0Aj08n<2>02w00z10y<21>c0c } frm:test { ;Julia-X z = pixel: z = z ^ (2.003) + p1 |z| <= (4 + p2) } ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;END PAR;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; Stay Amazed! JoTz

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4D
by cjsonnack＠mmm.com 21 Oct '03

21 Oct '03

Jim Muth wrote: > What does a 4-D hypersphere look like? We shall never know. At least, those of us who are not, in fact, 4-dimensional.... [grin] Hey, whatever happened to that Yale guy?.... -- |_ CJSonnack <Chris(a)Sonnack.com> _____________| How's my programming? | |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL | |_____________________________________________|_______________________|

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Classic FOTD 30-05-00 (Octagonal Star)
by Jim Muth 20 Oct '03

20 Oct '03

CLASSIC FOTD, May 30, 2000 (Octagonal Star [7]) Fractal enthusiasts and visionaries: Distracted as I was by Tippy, the fractal cat, my finger paused a bit too long on the <1> key as I was entering the parameters for today's fractal, causing me to inadvertently enter 111111.... instead of the 11 I had intended as the value of imag(p2). "What the heck," I mumbled as I saw the string of ones. "Let's see what these parameters will do." Substituting a decimal point for the third digit, I let the formula do its thing. As expected, I found that the extra digits have almost no effect on the appearance of the parent fractal. On a whim I set real(p3) to 0.3. The formula then created a grossly oversized and nearly indescribable fractal with grossly underestimated potential. A bit of searching revealed things in the fractal that looked like a space alien's antenna with a bulb on the end. I investigated one of these antenna bulbs. As I went deeper into the bulb, I came to an area of sickle- shaped elements, and soon I found the two symmetrical features that usually mean a midget is hiding there. As today's picture shows, I was once again right. With its star-like coloring and delicate filaments, today's fractal looks pleasing from both near and far, easily deserving its above-average rating of 7. When I saw the eight-pointed star effect, I named the picture "Octagonal Star". Coinciden- tally, the time the parameter file takes to render on a P200 machine is almost exactly 7 minutes. Yes, I realize that fractalists are sometimes very busy people, so the GIF image has been posted to: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The fractal weather today was dry but cloudy and quite cool, with a raw east wind and a temperature of 61F (16C) that kept all but the hardiest picnickers safely indoors. It was a day more typical of those in the Pacific Northwest than those on the Mid-Atlantic coast. The raw weather also kept the fractal cats indoors, where they passed the day eating and sleeping. And now for the bad news . . . yes, I once again failed to philosophize. My humblest apologies to the disappointed and my sincerest empathies to the relieved. But all is not lost, for the longer the philosophy takes to ripen, the better it will be when it's finally ready. So brace yourself for imminent and unexpected philosophical enlightenment. But until that time when the light shines forth, take care and keep those fractals coming. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Octagonal_Star { ; time=0:07:03.15 -- SF5 on a P200 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-15.17590216674/-56.06011507835/3.861277e\ +007/1/142 params=1/1.1/1/11.11111111111111/0.3/0 float=y maxiter=1200 inside=0 logmap=136 periodicity=10 colors=00009D<2>07A079268<3>A45C44E33G33<9>_S5aU5cW5\ <2>ic5ke5kg5<4>UOSRKWNG`<3>A0q<5>VTXYYUaaQ<3>ntDnuDn\ vDmvDowD<2>wxDzyDzyD<3>zvEzuEytExtF<3>qqFopFnoF<6>gk\ HfjHeiH<2>cgHbfHbfIbeI<12>XXKXWKXWKWVKWUKWUK<12>EISC\ HSBGT<3>5CVABW<4>ZQMcTN<2>raVsdYtg`ujbtmatpasqa<26>j\ _Yi_XiZX<3>hWXgWYgVZ<3>fTbfScgRd<3>iOhjOimJjjNkkMl<2\ >lKmmJmkOmiNmgNm<7>iMuiMviMwiMxiLy<9>kKzlKzlKz<3>mJz\ <2>ZJzUPz<3>AOz<11>RMzTLzULz<3>_KzeAzdAz } 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=========================================

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Classic FOTD 30-05-00 (The Omega Point)
by Jim Muth 20 Oct '03

20 Oct '03

CLASSIC FOTD, May 30, 2000 (Octagonal Star [7]) Fractal enthusiasts and visionaries: Distracted as I was by Tippy, the fractal cat, my finger paused a bit too long on the <1> key as I was entering the parameters for today's fractal, causing me to inadvertently enter 111111.... instead of the 11 I had intended as the value of imag(p2). "What the heck," I mumbled as I saw the string of ones. "Let's see what these parameters will do." Substituting a decimal point for the third digit, I let the formula do its thing. As expected, I found that the extra digits have almost no effect on the appearance of the parent fractal. On a whim I set real(p3) to 0.3. The formula then created a grossly oversized and nearly indescribable fractal with grossly underestimated potential. A bit of searching revealed things in the fractal that looked like a space alien's antenna with a bulb on the end. I investigated one of these antenna bulbs. As I went deeper into the bulb, I came to an area of sickle- shaped elements, and soon I found the two symmetrical features that usually mean a midget is hiding there. As today's picture shows, I was once again right. With its star-like coloring and delicate filaments, today's fractal looks pleasing from both near and far, easily deserving its above-average rating of 7. When I saw the eight-pointed star effect, I named the picture "Octagonal Star". Coinciden- tally, the time the parameter file takes to render on a P200 machine is almost exactly 7 minutes. Yes, I realize that fractalists are sometimes very busy people, so the GIF image has been posted to: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The fractal weather today was dry but cloudy and quite cool, with a raw east wind and a temperature of 61F (16C) that kept all but the hardiest picnickers safely indoors. It was a day more typical of those in the Pacific Northwest than those on the Mid-Atlantic coast. The raw weather also kept the fractal cats indoors, where they passed the day eating and sleeping. And now for the bad news . . . yes, I once again failed to philosophize. My humblest apologies to the disappointed and my sincerest empathies to the relieved. But all is not lost, for the longer the philosophy takes to ripen, the better it will be when it's finally ready. So brace yourself for imminent and unexpected philosophical enlightenment. But until that time when the light shines forth, take care and keep those fractals coming. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Octagonal_Star { ; time=0:07:03.15 -- SF5 on a P200 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-15.17590216674/-56.06011507835/3.861277e\ +007/1/142 params=1/1.1/1/11.11111111111111/0.3/0 float=y maxiter=1200 inside=0 logmap=136 periodicity=10 colors=00009D<2>07A079268<3>A45C44E33G33<9>_S5aU5cW5\ <2>ic5ke5kg5<4>UOSRKWNG`<3>A0q<5>VTXYYUaaQ<3>ntDnuDn\ vDmvDowD<2>wxDzyDzyD<3>zvEzuEytExtF<3>qqFopFnoF<6>gk\ HfjHeiH<2>cgHbfHbfIbeI<12>XXKXWKXWKWVKWUKWUK<12>EISC\ HSBGT<3>5CVABW<4>ZQMcTN<2>raVsdYtg`ujbtmatpasqa<26>j\ _Yi_XiZX<3>hWXgWYgVZ<3>fTbfScgRd<3>iOhjOimJjjNkkMl<2\ >lKmmJmkOmiNmgNm<7>iMuiMviMwiMxiLy<9>kKzlKzlKz<3>mJz\ <2>ZJzUPz<3>AOz<11>RMzTLzULz<3>_KzeAzdAz } 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=========================================

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Fractal Creations 2nd Ed.
by George Priest 20 Oct '03

20 Oct '03

Hi: I have "lurking" around the fractint discussion group for some years. (Just at the moment I still can't figure out how to get Fractint to work with Windows XP -- and don't tell me about DOS boot disks or multiple partitions.) Anyway, I have an almost new copy of Fractal Creations 2nd Ed, complete with CD, 3 !/2 " floppy and 3-D glasses that I am willing to sell for $10 plus shipping -- say $5. If anyone is interested, let me know at geopriest(a)raincity.com George Priest

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Re: Fractal Creations
by JackOTradez 19 Oct '03

19 Oct '03

Let the bidding begin! <g> I have Frcatal Creations 2nd ed. CD and I will sell (a copy of) it for $9 plus shipping! Also have Fractals for Windoze (Winfract 18.21, original installation floppy) and old CD's like "FracTools 3.0", "Fractal Generators", "Fractal Frenzy 1 & 2", Fractal Ecstasy". These are early '90's vintage; alot of Lee Skinner and other pix, primitive animations, etc. Serious collectors items. You can still find these floating around at computer shows or bookstores, also online sales if you know where to look ...

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Classic FOTD 17-11-98 (The Omega Point)
by Jim Muth 19 Oct '03

19 Oct '03

FOTD November 17, 1998 (The Omega Point) Fractal visionaries: The weather today was so dull that I can barely remember it. Oh yes, it was partly cloudy with a temperature of 60F 15.5C and a south wind at 12kph. Regardless, it was a perfect day for scrounging in fractal land for that one perfect fractal that might exist among the infinity of infinities of fractals that might exist. Unfortunately, tonight has become totally cloudy, and the meteor storm, if it happens, (which I doubt), will be invisible from fractal central. But I'll be up around 5am just in case a hole opens in the clouds and the meteors are there. The fractal I found was created by the next in my series of 12 MandNewt formulas, MandNewt10. This formula, as well as numbers 11 and 12, has six variable parameters. Since the six parameters are limited to real numbers, the resulting fractals always have X-axis symmetry. In some cases, the extra variable parameters are redundant, simply increasing or decreasing the values of other parameters, but overall the result is totally unpredictable, which is the way I like my fractals. I named the picture "The Omega Point" because as I studied it, I wondered if there could possibly be a last fractal. Actually, that's the way I name most of my fractal pictures -- I stare at them until a name comes into my head. The picture is a lot like my "Fractoland" picture of several days ago, though I'm not blaming this one on Dr. J. The picture has vague buds half obscured by bits and pieces of ectoplasmic fractal material, and areas of chaos offset by organized areas of quasi-order. But this image has at least a hint of order amid the most chaotic disorder. The spiral occupying most of the top third has no corresponding feature in the earlier picture. This spiral reminds me somewhat of the images produced by the Barnsley formulas. The GIF file has been posted to: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> And now I suspect that the honorable thing to do would be to wrap this up and see if I can get it posted. Until next time, when I shall likely be a bit more settled, take care, and remember that no matter how far you search, you will never find the last fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 19.6 PARAMETER-FORMULA FILE============================ The_Omega_Point { ; 16 min on a P200, 640x480x256 reset=1960 type=formula formulafile=mandnewt.frm formulaname=MandNewt10 passes=1 center-mag=-0.7352\ 27/1.28731/1.153329/1/-75/-2.50563458870090017e-014 params=3.524/1.979/-3.263/1.769/0.733/0.736 float=y maxiter=12000 inside=0 logmap=yes periodicity=0 colors=000HELHEMGDNGDOFDPHFRFDPE7ODANC9MB8LABPEATI\ 9XMCWLi_KmZJlYIjXHiWGhVFfUDeSCcRBbQAaP9_O8ZNAYODXP\ FWQHVQKVRMUSOTTQSUTRVVQWXPW_OXaNYcMZfM_hL`jK`lJaoI\ bqHcsHctIdtIdtJetJetJetJetKfuKfuKfuKfuLguLguLguMhu\ MhuMhuMhuNiuNivNivNivOjvOjvOjvOjvPkvPkvPkvQlvQlvQl\ wQlwRmwRmwRmwRmwSnwSnwSnxRmxRlxRlxRkxRkxRjxRjxRixR\ hxRhxRgxRgyRfyRfyReyRdyRdyRcyRcyRbyRbyRayR`yR`yR_y\ R_yRZyRYyRYyRXyRXyRWyRWyRVyRUyRUzRTzRTzRSzRSzRRzRQ\ zRQzRPzRPzROzROzRNzRMyQLyQLyRLyRLySMySMyTMyTMyTMyU\ MyUMyVNyVNyVNyWNyWNzXNzXNzYOzYOzYOzZOzZOz_Oz_Oz`Pz\ `Pz`PzaPzaPzbPzbPzcQzcQzcQzdQzdQzeQzeQzeQzfRzfRzgR\ zgRzhRzhRzhRziSziSzjSzjSzkSzkSzkSzlTzlTzmTzmTzmTzn\ TznTzoUzoUzpUzpUvqQqrNlsJfsFatCXu8Sv4Mu1Nu1Nu1Ov2P\ v2Pv3Qv3Rv4Rv5Sw5Tw6Tw6Uw7Vw8Vx8Wx9Xx9XxAYxAZyBZyC\ _yC_yD`yDayEazEbzFczGczGdzHezHezIfzJgzJgzKhzKizLiz\ LjzMjzMkzNlzOlzOmzPnzPozQ } frm:MandNewt10 {; Jim Muth z=g=pixel, a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), e=real(p3), f=imag(p3): h=z^a+(g-b)*z-g j=c*z^d+g z=z-e*h/j, f <= |h| } END 19.6 PARAMETER-FORMULA FILE==============================

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Classic FOTD 31-03-98 (Symphony in P-Flat)
by Jim Muth 18 Oct '03

18 Oct '03

F.O.T.D., March 31, 1998 (Symphony in P-flat) Fractal visionaries: This first paragraph was written on October 18, 2003. I wonder whatever happened to Doctor J. in the 5-1/2 years since the rest of this discussion appeared. And things are looking good for the resumption of the ongoing FOTD by the end of the month. START MARCH 31, 1998 DISCUSSION=========================== I see that Dr. J is loose again on the internet. I heard his mad-scientist laughter the moment I signed on. I only hope he can keep himself firmly in three-space. We've been losing far too many good fractalists into the fourth dimension lately. As the doctor zipped past my place, he dropped off a fractal that looked like two M-sets, one on top of the other. To view the image properly, I needed my red and blue glasses. Luckily, I found them still tucked inside my "Fractal Creations" book. The glasses showed not two but three M-sets -- a red one that looks like a snowman and two overlapping blue sets. I had several questions to ask, but the doctor flashed away before I had a chance. Today I had planned, I had honestly planned on describing how I stumbled upon what I consider to be one of the most incredible of fractal objects -- the perfect rectangle at Z=0.00019,0.07388 in the Julia set of the Z^2.003+C figure with a starting point of C=-1.7435,0.0. I started out well enough on the article, and had it nearly half finished, when an unexpected rush job arrived that took longer than expected. Rather than rush the article to comple- tion, I decided to postpone it until tomorrow, when I will have time to get it right. But not to disappoint anyone, I have a fractal for today -- an admitted quickie. It looks rather like a Pollock painting, where streaks and splotches of paint are dripped and splashed around the canvas. But this one is a pure fractal. It is a scene in the (-Z)^(-0.95)+C figure, made more presentable by the epsiloncross inside fill, which adds the streaks to the splotches, which are part of the fractal. I named the picture "Symphony in P-flat" because it reminds me of a scene in an old Disney animated musical film. (I think it is the 'After You've Gone' segment of the film 'Make Mine Music'.) The image is sliced in the Parabolic direction. This particular image could really benefit from anti-aliasing to correct the fine lines which have broken into dashes. But even in its imperfect state, it is worth a look. The picture has been posted to: http://home.att.net/~Paul.N.Lee/FotD/FotD.html Tomorrow, I'll tell the tale of the vanishing rectangle -- I really will -- honest! Until then, take care and . . . Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 19.6 PARAMETER-FORMULA FILE=========================== Symphony_in_P-flat { ; 38 seconds at 200mhz reset=1960 type=formula formulafile=slices.frm formulaname=ParabolicMiN passes=1 center-mag=0.0\ 860258/0.0841156/0.8239817/1/-57.5 params=-0.95/\ 0/0/-1/0/0.4 float=y maxiter=252 bailout=25 inside=epsiloncross logmap=yes symmetry=none periodicity=10 colors=000kBXP0mK_JnpEz0z000tzZJI\ bZCfd4J0v0HdGYNVpWmoJkHC5Y9Q3wNYpYfTcBT7VHRV9D\ <2>i6amV4nMInEWkMRmE`T7R<2>i6eRp5<2>hH_eSShKYkDc\ FcCRSObHZBBqP9na7kPzIK8xV7sd6n17E<2>b6a`7OCwjWXi\ 5iMLWU_Jac5d<2>l6hZThzwW<2>qJftjV<2>oGfpsC<2>nIa\ WG89Zi6JJ`N7<2>kA`EMQRGXbBcB2UNab<2>gEhrJ1jobl_e\ mLgXiabWdhJg`Cyafl<2>kFiFN3<2>eA_WOeeFghVdkIgU7L\ <2>i6cvb8B_mPQkaGjczOiYZrGfq`BpQNoGZC4WW5b4kL<2>\ cGcf4c<2>l6hrzPpY_fDfj9hRlyZYsfKnDLmQGkbBjRdgbNh\ 7GLhIqjEnlAk6vMLdU_NaXoZEnZR_bbLfNCb7F0<2>c8ZWdw\ `WseNpjEln7N<2>n6d7SjTHi5Wn<2>cCj0V9HMMYEYdY`hOc\ kFfwOZiH5<2>m8_lJemCgQpiZ`ifLisAyp8q`dG`y5efJjOX\ UcqdNmt4Ur5_p6dpli<2>nGi5ly<2>cGmnfSnUYnIclvu<2>\ nJlECnRAlb8jggjkPiqLLea2QcKBeaT8R<2>mM2<2>9up3i5\ TNHS_QSkZQhYPeXPSIPF3W4M<3>o11Uczn4OgGJiDQ } frm:ParabolicMiN {; Jim Muth b=p1, z=imag(pixel)+p2, c=real(pixel)+p3: z=(-z)^(b)+c, |z| <= 16 } END 19.6 PARAMETER-FORMULA FILE=============================

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Classic FOTD 10-10-99 (Mandelbrot Maestro)
by Jim Muth 17 Oct '03

17 Oct '03

CLASSIC FOTD October 10, 1998 (Mandelbrot Maestro) Fractal visionaries: It was cloudy today here in fractal land, with a few light showers in the evening. The high temperature of 68F 20C was perfect for exploring a hyperfractal, which I did with my Mandel_4-D formula. Every fractal explorer knows that when the starting point of Z is perturbed, the features of the resulting image are distorted. But when the fractal is a four-dimensional Mandelbrot set, the distortion can be downright grotesque, as today's image shows. The mis-shapen object in today's picture is the prominent midget on the negative tail of the 4-D hyper-M-set, viewed in a remote perturbed plane. I have named the picture "Mandelbrot Maestro" because that phrase popped into my head as I studied the image. I can't begin to explain why the image appears as it does. Nor can I explain exactly what the formula does. At times, the fractals drawn by this formula don't make sense, leading me to suspect that some of the images are artifacts. I'll need to do quite a bit of testing before I can add comment lines -- something that I have resolved to start doing with all my formulas. (Nothing is more annoying than having a formula and not knowing how to make it work.) The GIF file of today's quick image has been posted to: http://home.att.net/~Paul.N.Lee/FotD/FotD.html Tomorrow . . . who knows? I'll be here again with another fractal -- that's for sure, but as to what type of fractal it will be -- I won't know until I actually see it. Even then I may not know. So until then, take care, and didn't someone once claim that the fractals of Autumn are the best of the entire year? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 19.6 PARAMETER-FORMULA FILE============================ Mandelbrot_Maestro { ; 25 seconds on a P200 at SF5 reset=1960 type=formula formulafile=jim.frm formulaname=Mandel_4-D center-mag=-1.75909/0.0021\ 9158/69.70197 params=0/0/0/1.137/0.001/0 float=y maxiter=1200 inside=0 logmap=yes periodicity=0 colors=000KYN<8>1u43n7029<3>06H47H<4>TEOYAPbGQg7R\ lISmCTnPUoIVpVWpOXq`YrPZsc_oNzsb_lHgkaekJckZakL_k\ WYkNXkYVkPTkVRkRP<3>kVIkWGlYH<12>hD0<7>4p0<13>l7y\ <3>DRq0_r<7>VA_Z7Yb1X<13>R_MRaMPcO<6>EpWHxa<2>BhZ\ 4f`<12>u9N<2>lTCi_9dd3<12>sg_<15>a38<10>SgUNoMJwF\ <14>ZaV_`W`ZZ<9>bPx<3>lxe<6>ZrmYrnWpl<9>L``<2>GlZ\ KcQNVIfJHy7HdALKDOVLY<3>NWQ } frm:Mandel_4-D {; 4-D Mandelbrot, 8-D Julibrot a=(p1), b=(0,0), d=p2+2: f=sqr(a)-sqr(b)+pixel b=d*a*b+p3 a=f |a|+|b| <16 } END 19.6 PARAMETER-FORMULA FILE==============================

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Classic FOTD 19-05-99 (Bed of Hot Coals)
by Jim Muth 16 Oct '03

16 Oct '03

CLASSIC FOTD May 19, 1999 (Bed of Hot Coals) Fractal enthusiasts: Yesterday's fractal showed a view of the bottomless pit. Today's fractal shows the bed of glowing coals at the bottom of the bottomless pit. Yes, I realize that a bottomless pit has no bottom, but for the sake of convenience, we'll give our pit a bottom. The scene of today's image usually is filled with imps, hopping around on the coals, crying, "ouch!" Unfortunately, none of these unpleasant entities appear in the picture. I named the picture "Bed of Hot Coals" as a description. Don't worry if the first three inches of the picture are featureless. The detail is in the bottom half of the image. The image is actually a zoom into the left edge of yesterday's FOTD. I changed the color palette only slightly, to achieve a more sinister effect in the sky. This scene itself has some interesting zooms in it, so we'll see what tomorrow brings if I decide to go zooming. The parameter file runs in a few minutes; the picture file is posted to: <alt.binaries.pictures.fractals> and to: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> I've noticed that on the UF list, they're discussing whether fractals are art. Having thoroughly thought about the situation, and noting the effort that goes into the creation of some of these images, I can state in no uncertain terms that yes, fractals are indeed art. Whether my fractals are art is another question, however, and one which I have not yet answered. Some of the fractals being posted to ABPF have been achieved only after hours, even days of work. The average length of time I spend working on my images is about 15 minutes, draw time excluded. I doubt if art can be created on such a production line basis. But, art or not, I'll be here again tomorrow with another fractal, perhaps a closer look at today's bed of coals, perhaps a skewed view of a great spiral. And perhaps some philosophy. For now, I'm going to ponder whether the eight diagonals of a tesseract intersect at right angles. (I'll bet not!) Until next time, take care, and be at peace with peace. Jim Muth jamth(a)mindspring.com START 19.6 PARAMETER-FORMULA FILE========================= Bed_of_Hot_Coals { ; 0:05:50.82, p200, SF5 reset=1960 type=formula formulafile=mandnewt.frm formulaname=mandnewt05 function=atanh passes=1 center-mag=2.22365/1.06229/10.4956/1/77.5/-3.77822\ 773067748585e-014 params=1.172/-1.191/0.957/-0.004\ /-4.046/0.798 float=y maxiter=250 inside=bof60 logmap=yes periodicity=10 colors=000zZ9yW9uS9pO8lK8hG8eG8bF8_E7XD7UB7RB7PA7M\ 97K87K77K87KA9KAAKABKACKADKAEKAFKAFKAFKAFKAFKAFKAF\ KAFKAFKAFKAFKAFKAFKAFKAFLAFNAFPAFRAFTAFUAFWAFYAF_A\ F`WIbWHdWHfWGgWGiWFjWFkWEnWEoWDqWDrXBtXBvXAwXAw_Aw\ c9wf9wi8wk8wk8ogGh`M`USUNYQB_RGcSJfXNjaQm`Rj_Si_Tg\ ZUfYVdYWcXXaWY`WZZV_YU`WU`VTaTSbSScQRdPQeNQfMPgKOh\ JOiHNjGNkFMmDJp4Ln8MmBOjGPjJQhMSgQTeTVcXWa_X`bZZf_\ XiaVmbTodRtdRscSrcSrcSqbTpbToaUoaUnaUn`Vn`Vm`Vk`Vk\ _Wj_WjZXjZXiZXhZXgYYgYYfYZfXZeXZdW_dW_cW_bUZdVZcX_\ bY_aZ_`_`_a`Zb`XcaWdaVfaUgbThbSjcRjcQkcPmdOndNodMp\ eLreKsfJtfIufHwgGxgFygEygDzgByhEyiFyiGyjHxjIxkJxkK\ xkLxmNxnOwnPwoQwoRvpSvpTvpUvqWurXusYusZut_tt`tuatu\ bqrdnofknhjjjghkdemaco_`pXZrUWtOVySVuWUrZUnbTjaTj_\ TjZUiYUiWUiVUiUUhSUhRVhPVhOVgNVgLVgKVgJWfHWfGWfFWf\ DWfBWeAWe8We7We6We7Uf8Tf9Rg9QgAOgBNgDLhEKhFIiFHiGF\ iHEiIBjAAjAAjAAjBBjBBjBBj } frm:MandNewt05 {; Jim Muth z=c=fn1(pixel): a=z^2+(c-p1)*z-c b=p2*z^2+c-1 z=z-1*a/b p3 <= |a| } END 19.6 PARAMETER-FORMULA FILE===========================

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Lost
by Brian Rankin 16 Oct '03

16 Oct '03

Help! I have lost my Fractint front end.I would be obliged if anyone could tell me where to find it. Brian

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Classic FOTD 20-04-99 (Hyper-Spherical)
by Jim Muth 15 Oct '03

15 Oct '03

October 15, 2003 This FOTD image and discussion originally appeared on April 20, 1999. I present the image today in an improved version with fine-tuned colors. The discussion has been edited to remove some irrelevant stuff, and a few new comments about the fourth dimension have been added. ======================================================== CLASSIC FOTD April 20, 1999 (Hyper-Spherical) Fractal enthusiasts: What does a 4-D hypersphere look like? We shall never know. Speculation is futile. A hypersphere is not a visual object; it is an abstraction. Trying to visualize a hypersphere is as hopeless as trying to visualize any other abstraction, such as honor. But it is still fun to try to see what a hypersphere would 'look like' if we were four-dimensional beings. Of all the higher-dimensional figures, the hypersphere is the simplest. Any 3-dimensional slice of a hypersphere of any number of dimensions is a 3-D sphere. For example, any 3-D slice of a 4-D hypersphere is a sphere. Any 2-D slice is a circle, and any 2-D slice of a hypersphere of any number of dimensions is a circle. Today's fractal is a revelry of circles, which I assume, though I have not checked, are slices of 4-D hyperspheres. The three-dimensional effect is due entirely to the coloring, to which I devoted an unusual, (for me), amount of time and effort. The image resembles nothing as much as a scene in orbit around a giant planet in some far away galaxy. The entire picture is composed of circles colored to appear as spheres. These circles are arranged into interesting sheets and tendrils, which need investigating. Anyone out there who would like to investigate further, go ahead. I've got too many more fractals waiting, to have time to spend more than one day on a given image. I named the picture "Hyper-Spherical" more out of hope than fact. I hope that these circles are slices of near-perfect 4-D hyperspheres, but I have a strong suspicion that they are not. The GIF file has been posted in all its planetary glory to: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather at fractal central has not changed. Partly cloudy skies with occasional sprinkles of rain and a temperature of 57F 14C made it a chilly spring day, yet a perfect day for finding fractals. I shall now close down the fractal shoppe for another evening, and call it a day. But I'll return tomorrow with more fractal blather. Until then, take care, and keep the fractal faith. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 19.6 PARAMETER-FORMULA FILE========================= Hyper-Spherical { ; time=0:12:57.80--SF5 on a P200 reset=1960 type=formula formulafile=mandnewt.frm formulaname=MandNewt12 passes=1 center-mag=+0.7897\ 05601237999/-0.02843030167377993/477729.2/1/30 params=-4.3808/-0.5139/-1.2595/1.0881/-0.81/2.519 float=y maxiter=250 inside=bof60 logmap=yes periodicity=0 colors=000zzYyxYxuXwqWvmVukUtiTsgSrf\ RqeQpdPocOnbNmaMl`Lk_KjZJiYIhXHgWGfVFeUEdTDcSDbRCa\ QC`PB_OBZNAYMAXL9WK9VJ8UI8TH8SG7RF7QF6PD6OA5N75M98\ LBAK75J66I66H008WT8WT8WT8WT8ZV8`Y8c_8fa8ic7kf7nh7q\ j7tl7vo7yqAwqDurHrrKpsNnsQltTjtWhu_eubcveavh_wkYwn\ WxrTxuRyxPyuMqsIipF`nBTk8Lj9KhAJgBIfCHeCGcDFbEEaFD\ `GCZHCYIBXJAWK9UL8TL7SM6RN5PO4OP3PP4QP6RQ7SQ8TQAUQ\ BVQCWREXRFYRHZRI_RJ`RLaSMbSNcSPdSQeSRfTTgTUhTViTXj\ TYkUZlU`mUanUboUdpUeqVgrVhsVitVkuVlvWmwWoxWpwYmuZk\ t`hrafqccpd`nfZmgWliTjjRilOgmMfoJhpKipLkqMmrNosOps\ PrtQstRrqSqoSplSojSnhSmfSmcSlaSk_SjYSiVShTSgRSfPSe\ MSdKScISbGSbDSaBS`9S_7SZ4SY2SY0SZ1R_1R_1R`2Qa2Qa2Q\ b2Qc2Pd2Pd3Pe3Pf3Of3Og3Oh3Oh4Ni4Nj4Nj4Nk4Ml4Ml5Mm5\ Mn5Lo5Lo5Lp5Lq6Kq6Kr6Ko7Jl7Ji8Ig8Id9Ha9GZAGWAFTBER\ BEOCDLCDIDCJEDKGFKHGLIIMKJNLLOMMOOOPPPQRRRSSSTTSVV\ TWWUXYVZZW_`W`aXbcYcdZdc_dcwTgwSgwRgwQg } frm:MandNewt12 {; Jim Muth z=g=pixel, a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), e=real(p3), f=imag(p3): h=z^a+(g-1)*(z-b) j=c*z^d+g z=z-e*h/(f*j), .0000000000000000000000000000005 <= |h| } END 19.6 PARAMETER-FORMULA FILE===========================

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Classic FOTD 12-03-99 (Edge-on Galaxy)
by Jim Muth 14 Oct '03

14 Oct '03

CLASSIC FOTD March 12, 1999 (Edge-on Galaxy) Fractal enthusiasts: Today was bright and sunny, but chilly here at Fractal Central. The temperature of 41F 5C was perfect for a journey through fractal land. My journey took me to the same area as yesterday's shamrock fractal. I wrote a new formula just for the trip, which will let me view the scene from an entirely new direction. The angle of the slice has been turned -10 degrees from the Rectangular direction toward the Oblate direction, giving the effect of a galaxy seen edge-on through clouds of interstellar dust. I named the picture "Edge-on_Galaxy" as a straightforward description. And yes, once again I have sinned by loading the GIF file into a graphics program for some fine-tuning: The gently illuminated galaxy is visible on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where you will find links to lots of hyper-dimensional stuff, and some pretty far-out hyper-fun-stuff also. I've been busy today, so I'll have to cut the discussion short, but the fractal is good enough to make up for a lack of words. After all, one picture of a three-dimensional object is worth a thousand words, so a picture of a four-dimensional object must be worth a million words. Until tomorrow, take care, and don't get lost in the stars. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 19.6 PARAMETER-FORMULA FILE========================= Edge-on_Galaxy { ; 0:01:43.64--SF5 on a P200 reset=1960 type=formula formulafile=allinone.frm formulaname=multimin-xz-yw-new passes=1 center-mag=+0.05750247255816/+0.00097963198354/204\ .5845/0.04123 params=90/-10/3.5/0/0.03907/-0.28621\ /0.8042/0 float=y maxiter=1200 bailout=25 inside=0 logmap=16 periodicity=10 colors=000RAWQAVPAUOATNASMARLAQLAQKAPJAOIANHAMGALF\ AKEAJD9JB9J89I6BI4BI1BG0BG0BG0BE0BE0BD0BE0BE0BE0BG\ 0BG0BG0BI0BI0BI0BJ0BJ0BJ0BJ0BL0BL0BL0BL0BN0BN0BN1B\ O1BO1BO1BO2BQ2BQ2BQ4BR4BR4BR6BT6BT6BT6BT8BV8BV8BV9\ BX9BX9BX9BXBBYBBYBBYDB_DB_DB_DB_E9aE9aE9aG9bG9bG9b\ I9dI9dI9dI9dJ9fJ9fJ9fL9gL9gL9gL9gN9iN9iN9iO9kO9kO9\ kO9kQ9lQ9lQ9lR9nR9nR9nT9pT9pT9pT9pV9qV9qV9qX9sX9sX\ 9sY9tY9tY9tY9t_9w_9w_9wYDt_9w_8xa6za4za1zb0zb0za0z\ a0zb0zb0zb0zd0zd0zd0zd0zd0zf1zf1zf2zf2zf2zg4zg4zg4\ zg6zi6zi8zi8zi8zi9zk9zkBzkBzkDzkDzlEzlEzlEzlGxnGxn\ GxnIxnIxnJxpJxpJxpLwpLwpNwpNwqOwqOwqOwsQwsQtsQtsRt\ sRttTttTttVttVttVswXswXswYswYsxYsx_sx_sxaqxaqzaqzb\ qzbqzdqzdqzdqzfpzfpzgpzgpzgpzipzipzkpzknzlnzlnzlnz\ nnznnzpnzpnzplzqlzqlzslzslztlztlztlzwkzwkzxkzxkzxk\ zzkzzkzzkzxlzxlzwlzwlzwlzwnzwnzxpzzqzzszztzzwzzxzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:multimin-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 19.6 PARAMETER-FORMULA FILE===========================

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Classic FOTD 17-02-99 (A Little Lotus)
by JimMuth＠aol.com 13 Oct '03

13 Oct '03

FOTD February 17, 1999, (A Little Lotus) Fractal visionaries: It was a bright and sunny day here at the Fractal Place -- unusually warm for winter, but pleasant nonetheless. The temperature of 64F 18C was perfect for hunting fractals, and as you might expect, I hunted. Yesterday's FOTD was a bit disappointing, so I decided to post an extra impressive fractal as today's FOTD. The workhorse MandelbrotMix4 formula once again did its job when I needed it, turning up today's lotus-like picture after only 15 minutes of searching. The scene I stumbled upon resembles an unfolding lotus blossom, so I named it "A Little Lotus". The parameter file runs slow, but as always, the GIF file of the image has been posted to: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Now, I must make a confession. I hate to disappoint my philosophy lovers, but I've got no words of wisdom today. I've been irritable all day from a job that went sour, and it's hard to philosophize when you're in a bad mood. Tomorrow is another day, however, and it will bring another fractal. It might even bring some babble, so check then to see. Until next time, take care, and don't stare too long at any one fractal. They do strange things if they're stared at too intensely for too long a time. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 19.6 PARAMETER-FORMULA FILE============================ A_Little_Lotus { ; 21 min on a P200 SF5 reset=1960 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-1.43928832160053900/+0.04139571017709617\ /1.414159e+010 params=100/0.9/101/-1.1/-0.985/100 float=y maxiter=12000 bailout=25 inside=0 logmap=361 symmetry=xaxis periodicity=12 colors=000jT0jT0iT0gT0fT0dT0cT0aT0`T0_T0YT0XT0TT0Q\ T0ST0QT0PT0QT0ST0QT0TT0SV0SV0VV0TX0TX0VX0VX0TY0XY0\ VY0VV0YV0YT0YS0_S0_Q0_O0cP0cO0dO0dM0dL0dJ0gJ0gI0gG\ 0iG0iF0iD0mF0mC0mA0oC3oA3o93rA7r97r77u70r77o69m6Dm\ 6Gi6Mg1Og1Td1Yc1``1dc3mc1rc3yd4zc4zc6zd7zf9zgCziFz\ lGzmIzoLzpMzrPzsQzuTzuVyxYyx_xycxzfxzfxycuxasu_ru_\ rrXooVmoTmmTmiPiiPiiMigMidJgdJgcIg`Ig`Fg_FdXCdXCdX\ 9dT9cQ7cQ7cP4cL4_J1_G1YD0XC0VAiu0ez0az0Yz0Ux0Qr0Mm\ 0Ig0Ec0Aa0E_0Ia0Mc0Qe1Tg1Wi4Yk4Zm9_o9aqCcmCdmDdoDf\ oGgrGirJjuJluMmxMoxPpyPryTrzTuzVvzXxzYyz_yz`zz`zzd\ zzdzzgzzgzzizzjzzmzzmzzpzzpzzuzzuzzxzzxzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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 19.6 PARAMETER-FORMULA FILE==============================

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Classic FOTD 23-12-98 (Ceremonial Radical)
by Jim Muth 12 Oct '03

12 Oct '03

CLASSIC FOTD December 23, 1998 (Ceremonial Radical) Fractal visionaries: Today seemed a lot more like winter here at fractal central. The afternoon temperature of 28F -2C and forecast of snow for tomorrow made it perfect for a fractal hunt. I hunted in the MandelbrotMix7 formula, experimenting with the parameters in a whimiscal manner to see what I might find. What I found was today's image, a strange fractal with a ceremonial aura about it. I named the picture "Ceremonial Radical" because of the effect of deep symbolism in the image. As I understand it, a radical is almost the same as a bud, but differs from a bud in that the word "radical" refers to the entire set of features connected with a bud, such as sub-buds, stars, filaments, etc. In today's picture, the radical is the bud at lower center, along with all the associated debris. Toward the top of the picture lies a very distorted M-set, with its period-2 bud larger than its main bay. Today's GIF file, (a small one), has been posted to: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Tomorrow, I'll return with more wonders from the world of fractals, and maybe a fractal limerick or two. Until then, take care, be cynical if you wish, and be true to your fractals if you want them to be true to you. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 19.6 PARAMETER-FORMULA FILE============================ Ceremonial_Radical { ; 0:05:37.79 on a P200 SF5 reset=1960 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=2.87321/-9.76996e-015/0.259034/1/-90 params=10/0.5/-10/0.5001/1150/0 float=y maxiter=1200 inside=0 logmap=yes periodicity=10 colors=000M5EL5FK5GI5HH5IG5JF5KE5LD5MB5NA5O95P85Q7\ 6R67SP6XH5XS5aU7`VA_XC_YEZ_HY`JXbMWcOVeQVfTUhVTiXS\ k_RlaRncQogPqhOrmNtmMuqMwrLxrKxtKwsJwsJwrIwrIvrHvq\ HvqGupGupFuoFtoEtoEtnDtnDsmCsmCslCqkEpjFohHngImeJl\ dLkaMjaNiZOhZQgWRfZSgWThZUiYVjZWk_Xl`YmaZnb_oc`pda\ qe`rf_sgZthYuiWvjVwkUxlTymSznRzoQzpPzqPzrQzsQztQzu\ RzvRzwRzxSzySzzTzzTzzTzzTzzUzzUzzUzzVzzVzzVzzWzzWz\ zWzzXzzXzz`zzczzgzzkzzozzrzzvzznzzfzzZzzRzzSzzSzzT\ zzUzzVzzVzzWzzXzzYzzYzzZzz_zz`zz`zzazzbzzczzczzdzz\ ezzfzzfzzgzzczz_zzXzzTzzPzzLzzQzzUzzZzzbzzgzzkzzPz\ z2zz4zz6zz8zzAzzCzzEzzGzzIzzKzzMzzOzzQzzSzzUzzSzzQ\ zzOzzMzzKzzIzzGzzEzzCzzAzz8zz6zz4zz7zz9zzCzsFzsIzs\ KztNztQztSztVzuYzu_zubzzdzzgzzizzhzzgzzfzzfzzezzdz\ zczzdzzfzzgzzhzzhzzizzizzjzzkzzkzzlzzmzzmzznzzAzzc\ zzUzzJzzLzzLzzKzzKzzKzzKzzJzzJzzJzzJzzIzzIzzIzzHzz\ HzzHzzHzzGzzGzzGzzGzzFzzF } 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 19.6 PARAMETER-FORMULA FILE==============================

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Classic FOTD 21-12-97 (Lost Midget)
by Jim Muth 11 Oct '03

11 Oct '03

Classic F.O.T.D. December 21, 1997 (Lost Midget) Fractal visionaries: Happy Solstice! This, after all, is what the season is really about. In the Northern Hemisphere it's the shortest day of the year; in the Southern Hemisphere it's the longest day of the year; at the equator it's just another 12-hour day; while at the North Pole it's the middle of the six-month-long night, and at the South Pole it's high noon of the six-month-long day. Here at coordinates 39.20 north 76.30 west, the sun sets at 4:45pm, which is not too bad when one considers places like Norway and Sweden, which receive almost no sunlight at all at this time of year. But the shortage of sunlight certainly does not imply a shortage of fractals. Today's fractal is ample proof of this. I've named it "The Lost Midget" because, like yesterday's FOTD, (which BTW was wrongly dated 19-12), it illustrates one of those obscure midgets that instead of actually existing, has merely a tendency to exist. I chose this particular midget because it best illustrates the effect of a ghostly something that is not really there. The formula is a generalized one of the form, (Z^n+C)+(C^n+Z). It is one of an experimental series that I worked up a few months back and then laid aside. I've actually got versions of this formula that draw all six perpendicular planes. (I do this with most all my formulas.) Some of the odd planes of this series are most unusual, so expect to be seeing more of them in the near future. The image has been posted at 640x480 resolution to Paul's web site at: http://home.att.net/~Paul.N.Lee/FotD/FotD.html Tomorrow will bring a longer (or shorter) day and a new fractal. At this time, I can't say what I'll decide on, but what ever it is, it will be interesting. So until then, take care and never choose a fractal when you play charade. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE====================================== lostmidg { ; 0:01:14.20 SF5 on a P200 reset=1960 type=formula formulafile=test.frm formulaname=MandelbrotZC passes=1 symmetry=xaxis center-mag=-0.601331/1.52656e-016/31.61269 params=1.26/0/0.5/-2/0.5/1 float=y maxiter=100 bailout=25 inside=bof60 logmap=yes periodicity=10 colors=000i`2Uc3TAmLIQYA_THROQJzKBuCAzU0wHSzm0VQ\ WzUyKZetLBkKB_F8QB5KA50hz<6>0hzcA8SN6Hb4MQ6RD8WA\ A_ACkAXwAp3D0aH4<2>RBwSU3NJhKRVHZHKeYmkosA1YAIMA\ _JHPGUEKAnSAFLH9hUAT`6ScULeGQLlMTXI_IlkAVh6BgTCf\ KDfBCKGGAyFAeERMXb5YA2RD3KS3EAGECBES7JT2HY3Fb3JL\ AZEUSOLLYC6`8<2>Ce45XlAaQZGE3A19AaCKKD_5UZcOaRJd\ FpZUXbGOiQJgE9RpCZSqYCVA0MAAKC8IM6GX45dj<2>CfExA\ 2MQ3IZ30cC7e7vADQCSMNJIXBIjFaZU<2>Kd90BG<2>BZ64A\ m7Aa9IQCVEcACRO7ZDT6_M9bFCd9sAL0gSLAzIDfGSNDCJES\ BmaC<2>Ne5IJHGVAKQ7VA8MH5_A7SB5LR4PLeJWMek46GwkA\ SVQFBR6CV5DZ4Eb3DE0<2>E_34Xo<2>CdFSexKiR<2>Ff9LP\ yDTdEYSEbFGPgFVUE`GEJq<2>E`FocnXeRyA4iD3US38CuAN\ bCXLqVcjQt_WbPaLHRIGVEFZAEb6FFvETV`J8<2>J`4NhA\ <2>Gf4UAzMOXsRy<2>ObHAA`CEKyNtaXU8KBBW7Je6Gf4WMy\ <2>IaHkWa0F37T3dK1<2>Ka3cGyRUWiAwpAxfAiXGWNUH } frm:MandelbrotZC {; Jim Muth z=p1, c=pixel: z=real(p2)*(z^imag(p2)+c)+real(p3)*(c^imag(p3)+z), |z| <= 100 } END PARAMETER FILE====================================

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Re: Classic FOTD ??-??-???? (Star for the Ages [8])
by Jim Muth 10 Oct '03

10 Oct '03

At 11:53 AM 10/10/03 -0500, Paul Lee wrote: >I just realised this was the Classic image you >re-posted just seven days ago. It must be one >of your most favorite of all time. :-) Actually, today's image is not identical to the 'Zodiac' image. Today's image has had its contrast enhanced in a separate graphics program. An A-B comparison will show the improvement. When I posted today's image, I didn't realize that I was re-posting an image that I had posted only a week ago. Things have been pretty hectic around here lately. When I found the image just lying around in a spare GIF directory, I souped it up and decided to use it. Jim M.

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Multifractal_9
by Albrecht.Niekamp＠t-online.de 10 Oct '03

10 Oct '03

Hi, the title of the first image is taken from James Taylors first album, which came out 1966. Greetings, Al. ----------------------------------start-frm----------------------------- FRM:Multifractal_9 { ; Albrecht Niekamp 170903 ;p1 (spider)julia-seed ;real(p2) 5digits : (1)shape (2)outside (3)inside1 (4)inside2 (5)inside3 ; 0_off 1_secant 2_mand 3_bees 4_jul 5_m_mods 6_phoen 7_newt 8_spider ; input2 : 2digits_many-mods 2digits_phoenix 2digits_spider ; 5digits_reset : 0_no 1_z-reset 2_iter-reset 3_both +5_warp ;imag(p2)(-) 5digits_colour(bailout) number ; input2 : 4digits(-)_mand/jul 2digits_secant 4digits_bees ;real(p3) 2digits_newt 4digits_colour1, 5digits_colour2 5digits_colour3 ;imag(p3) shape : factor (fn1), 5digits_colour4 5digits_colour5 ;real(p4) outside: factor (fn2), 4+1digits_bord-out 4digits+fract_bord-in ;imag(p4) inside1: maxit1, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor1 (fn2) 4digits+fract_border1 ;real(p5) inside2: maxit2, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor2 (fn3) 4digits+fract_border2 ;imag(p5) inside3: maxit3, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor3 (fn4) 4digits+fract_border3 ;fn(1) shared by many-mods+bees ; da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=d3==0 vb=d>5 sc=d==2 mo=d==6 px=d==7 ab=px+(d==3)+(d==5)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 sc1=d==2 mo1=d==6 px1=d==7 v1m=mo1+px1 v1j=d>7 dd1=v1j+(d==4)+(d==5) ab1=px1+(d==3)+(d==5)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 sc2=d==2 mo2=d==6 px2=d==7 v2m=mo2+px2 v2j=d>7 dd2=v2j+(d==4)+(d==5) ab2=px2+(d==3)+(d==5)+(d==9) d=trunc(dd/10) ex3=d>1 sc3=d==2 mo3=d==6 px3=d==7 v3m=mo3+px3 v3j=d>7 dd3=v3j+(d==4)+(d==5) ab3=px3+(d==3)+(d==5)+(d==9) d=dd-d*10 ex4=d>1 sc4=d==2 mo4=d==6 px4=d==7 v4m=mo4+px4 v4j=d>7 dd4=v4j+(d==4)+(d==5) ab4=px4+(d==3)+(d==5)+(d==9) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex1+ex0+ex2+ex3+ex4 ; d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 ; d=imag(p3) sfac=trunc(d) da=(d-sfac)*10000000000 ba4=trunc(da/100000) ba5=da-ba4*100000 ; d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) ; d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=d==3 fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=d==3 fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 ; d=imag(p5) mi3=trunc(d) da=(d-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=d==3 fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 ; if (d4) z=0 if (vb) if (mo) c=0.4*log(sqr(pixel^mm)) else c=pixel z=pixel endif else c=pixel z=pixel*sc endif else c=p1 z=pixel endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else z=pixel cb=p9*u c=p1*u p=pp*u endif tt=tt-1+ex0 endif elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(pixel^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(pixel^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(pixel^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(pixel^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Qusinewton Pusk s Istv n z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+ph-0.5*zold ;Phoenix Mike Wareman zold=z z=z1 else z2=fn1(z)+c ;Many_mods Linda Allison z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z ;Julia Pusk s Istv n z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) z2=z*z ;Mandel Pusk s Istv n z=z2*z2+p6*z2+c-p0 else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba } ----------------------------start-par------------------------------------- The_original {;flying_machine ; Time 3.54.24.45 ; Albrecht Niekamp Oct, 03 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_9 function=sin/exp/exp/sin passes=t center-mag=+0.69407468245339080/+0.03415551174862821/115.2977/0.5977/-92\ .5000000000000284/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/21225.32565788021/15234.0\ 506030602/152048.0404808048/384.1604894048/384.00482000595/256.100768300\ 1/512.1007683001/768.1007683001 float=y maxiter=3072 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=2000QY<10>09C08A068<2>022000211<21>icNkeOmfP<3>unTwpVxqWzsX<25>CB\ 7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<11>LLLNNNPPPQQQSS\ SUUU<6>fffgggiiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0cq0es<3>0kz\ <13>0R_ } Madhouse { ; Time 3.25.34.35 ; Albrecht Niekamp Oct, 03 ; reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_9 function=sin/sin/exp/sin passes=t center-mag=+0.80170883016743030/-0.00197191029829151/36192.88/1/-159.999\ 999999981441/-1.69965014285011762e-011 params=-0.05825983458967864/0.3785210730307932/21222.32595705021/15423.0\ 506030602/51024.02048000094/384.0449690484/384.0242000145/256.1007683001\ /512.1007683001/768.1007683001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200012<24>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<21>icNkeOmfP<3\ >unTwpVxqWzsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>00\ 0<21>bbbdddfffgggiiijjj<3>qqqsssqqq<24>BBB999777555444222000 } The_magic_mirror { ; Time 3.14.24.15 ; Albrecht Niekamp Oct, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_9 function=sin/sin/exp/sin passes=t center-mag=+0.80171328060885840/-0.00196810603325942/1070795/1/-159.9999\ 99995678252/-3.12983081118822781e-009 params=-0.05825983458967864/0.3785210730307932/21222.32595705021/15423.0\ 506030602/51024.02048000094/384.0449690484/384.0242000145/256.1007683001\ /512.1007683001/768.1007683001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200012<24>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<21>icNkeOmfP<3\ >unTwpVxqWzsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>00\ 0<21>bbbdddfffgggiiijjj<3>qqqsssqqq<24>BBB999777555444222000 } -----------------------------------------end--------------------------------

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Classic FOTD ??-??-???? (Star for the Ages [8])
by Jim Muth 10 Oct '03

10 Oct '03

CLASSIC FOTD -- ??????? ??, ???? (Rating 8) Fractal visionaries and enthusiasts: Today's fractal image is a lost blast from the past, which originally appeared as a FOTD several years ago. The problem is that I have lost track of the original discussion that goes with it, as well as the date on which it originally appeared. This is the same problem that still plagues my long-awaited but never- delivered FOTD-CD. Since the image really is quite striking, and I have lost track of the original name, I gave it the new name "Star for the Ages". The rating of an excellent 8 makes the 14-minute render time barely worth the effort. And as always, the finished GIF image is available on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather has been uneventful here at Fractal Central the past few days. The fractal cats have reasonably well behaved. The work backlog is still shrinking, and all else is well. Until tomorrow's Classic FOTD, take care. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Star_for_the_Ages { ; time=0:14:50.67 SF5 on a p200 reset=1960 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+1.66407211226380200/+0.392889263279063\ 20/2.145788e+007/1/-5/1.95473841280158211e-008 params=0.01/100/-100/1/-0.9897/0 float=y maxiter=12000 inside=0 logmap=267 periodicity=10 colors=00002G04A06A06C06E06G06J06L06N06P06R06T06V0\ 6X06Z06`06b04d04e04g04i04k04m04o04o04o04o04o04m04m\ 02m02m22k22k42k42k62i62i60i80i80gA0gA0gJCoTLubXzke\ zuqzzzzzxzxvzuuzsqzoozmmzikzgizdgzbezZbzX`zTZzRXzN\ VzLTzHRzGPzCLzAJz6Hz4Gz0Ex0Cx0Av06v04u02u00s04u08v\ 0Az4EzAHzGLzLPzRTzVVz`Zzebzzezzizzmzzozzszzzzzszzq\ zzokzoZumXkmTbkRRkNHiL8iH0gG0gE2eA4e86d68d2Ab0Cb0E\ b0G`0H`0JZ0LZ0NX0PX0NZ0J`0H`0Gb0Cd6AeC6gH4gN2iT0kX\ 0mb0mg0om0qs0sx0uz0uz0vz0xz0vz0uz8szHqzTozbmzmkzvi\ zzgxzevzduzduzbszdszeqzgqziozkozkmzkkzkkzkizkizkgz\ kgzkezkezkdzkdzkbzkbzk`zk`zkZzkXzkXzkXzkXzkXzkXzkX\ zkXzkXzkXzkXzkXzkXzkXzkXzkXzkXzkXzkXzkXzkXzkXzkVzk\ VzkVzkVzkVzkVzkVzkVzkVzkVzkVzkVzkVzkVzkVzkVzkVzkVz\ kVzkVzkVzkVzkVzkVzkVzkVzkVzkVzkVzkVzkVzkVzkVzkVzkV\ zkVzkVzkVzkVzkVzkTzkTzkTzkTzkTzkTzkTzkTzkTzkTzkTzk\ TzkTzkTzkTzkTzkTzkTzkTzkT } 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 2

Re: Classic FOTD 01-01-98 (Projective Plane)
by Jim Muth 10 Oct '03

10 Oct '03

At 11:23 AM 10/7/03 -0500, you wrote: Paul Lee wrote: >> Classic F.O.T.D., January 01, 1998 (Projective Plane) > >Actually, The above date and fractal name did not originally get used >together many years ago on the "Fractal-Art" List. > >Though I am sure this was an accidental mistake by Jim, I would hate to >see this List end up like a couple of others I know of, where the >participants try to alter history whenever they wish. ;-} Lee is right; history is safe. I made a mistake -- most likely the first of many. The 'Projective Plane' fractal appeared on Jan. 6, 1998. The fractal of 01-01-98 was named "Snub-Nosed Midget", an image that I considered but did not use. Jim M.

3 3

Re: Minibrots anf the FPU
by Kenneth Lifvenborg 09 Oct '03

09 Oct '03

Thanks to those that answered my question! My faith in the Universe have been completely restored and I can sleep better at night ;-) Regards Kenneth Lifvenborg _________________________________________________________________ The new MSN 8: advanced junk mail protection and 2 months FREE* http://join.msn.com/?page=features/junkmail

2 1

Minibrots and the FPU
by Kenneth Lifvenborg 09 Oct '03

09 Oct '03

I just scanned the sci.fractals newsgroup for the past few weeks and found this post from Brian Quincy Hutchings <QncyMI(a)netscape.net>, dated 19 september 2003 23:27: <snip> but folks should know that the "universality of the M-set," that is the recurrence of "mini-bugs" or cardioids, at every level of "magnification," is just an artifact of the floating-point ops (IEEE-755, -855, I think). this was (really/partially) confirmed by monsieur M, when he glroriously begged my (only) technical question at a talk for a "general audience." <snip> Is this just some "besserwisser"-talk or might it imply that images containing minibrots/midgets (and there certainly are a *lot* of those on the Net and in the litterature) are just artifacts from some weird bug in the floating-point algorithms? The fact that the main cardoid itself stems from a very simple formula make it seem, if not probable so at least possible, that some oddities in the FPU could produce unexpected results. I find this a bit disturbing. Could anyone please care to comment? Regards Kenneth Lifvenborg _________________________________________________________________ The new MSN 8: advanced junk mail protection and 2 months FREE* http://join.msn.com/?page=features/junkmail

4 4

Classic FOTD 20-03-2000 (Midget Inferno [7]))
by Jim Muth 09 Oct '03

09 Oct '03

FOTD, March 20, 2000 (Midget Inferno [7]) Fractal enthusiasts and visionaries: It's been a rather exciting day here at Fractal Central, with a hostage standoff situation in progress only 2 miles (3km) away. But that has had no effect on the fractals, which once again appeared almost by magic, as though nothing had happened. To create today's image, I entered some of my more bizarre parameters into the M-Mix4 formula, finally finding the interes- ting fractal that results when 1/Z is added to 666*Z^666 before adding C. I chose the number 666 because that number is consi- dered apocalyptic in some circles, and I enjoy defying danger. Today's FOTD is another of those unlikely images, since one would suppose that 666 parts of Z^666 would simply obliterate one measly part of 1/Z, resulting in a boring open circle with 665 tiny identical bays. In the world of fractals however, things are seldom as one would suppose, and instead of the boring circle, the expression fills the screen with an interes- ting fractal. I named the picture "Midget Inferno" after deciding on the dark red and black color scheme for the scene, which gives the impression of lurid flashes of red breaking through billowing clouds of black smoke. The parameter file takes 4 minutes to render. The GIF image has been posted as always to: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The fractal weather today was raw. Heavy clouds off the ocean, and a chilly wind of 42 degrees F (5.5 degrees C) made condi- tions too unpleasant for the cats to venture out of doors. They passed the day instead in frustrated comfort, stretched in front of their favorite radiator. As for the philosophy of the day -- it's still inside me, where there are lots of thoughts that I haven't had a chance to compose. But in a day of two I'll have the ideas hatched and ready to propose on the philofractal list. So keep tuned to that list. You wouldn't want to miss the enlightenment, nor would you want to miss your chance to correct a mistaken wannabe philosopher. Until tomorrow, take care, and save the best fractal until last. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Midget_Inferno { ; time=0:04:00.30 SF5 on a P200 reset=2000 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.18405946781424860/+0.120523122844577\ 40/8.7115e+008/1/-117.499 params=1/-1/666/666/0/0 float=y maxiter=2500 inside=0 logmap=77 periodicity=10 colors=000701A03E03H05K05N05Q15U17V17Y38Z38`58a58d\ 7Ae7Ag7Ai8Aj8BlABmABoABpADrBDsDEuDEwEExGEyJHzMGzPG\ zRGySEyVEyWExYExZEx_Dw`DwaBwcBudBueBugAwhAwiAxj8xk\ 8yl8zl0zl1zl5zm8zoDzpGzpKyqNxrQwsSurWtrWsrWrrWqsVp\ sVosVmsVlsVksUjsUisUhsUgsUisUjsUkuZktWktUksRkrPkqM\ kpJkpGkoDkmAio7jo7km7lm7mm7om7pl7ql7rl7sk7tk7uk7wk\ 7xj7yj7zj7zi7zi7zi7zi7zh7zh7zh7zh7zg7zg7zg7zg7ze7z\ e7ze7ze7ze7zgAzhDziGzkJzlMzmPzoRzpUzqWzrZzs`ztczue\ zxizwhzugzueztdztczsazr`zr_zqZzpYzpWzoVzoVzmUzlSzl\ RzkQzjPzjNziMyiKyhJxgHxgGweEudDtdBtcAsc8sa7r`5t_3u\ Y0tZ1s_3q`7pa8ocAmdBkeEjgGihHhiJejMdkNclPamQ_oSZpU\ YqVWrWVsYUtZSu`QwaPxcGzeHzeJzeMzeNyePyeQxeRxeSweVw\ eWudYudZtd_td`sdcsddrderdgqdipdjpdkpdlodmodomdsldu\ odspdrodpmdol`lkQqhEoiGljJilKgmNdoPapRZrSWsVUtWRuY\ Nx_Ky`HzcEzdBze5zh8zgBzgEzeHzeKzdNzdQzcSzcVzaYzagz\ NdzMazJ_zHYzEVzDSzAQz8Nz5 } 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

Fractal Creations CD
by Tim Wegner 09 Oct '03

09 Oct '03

I got an email from someone who bought Fractal Creations 2nd Edition (FC2E) that had no CD. I offerred to make him a copy if he sent me a stamped, self-addressed envelop with a blank CD. I extend the same offer to anyone else. Email me and I will send you my address. Hmm, actually, Fractint has my correct mailing address, so you don't need to email me. I would not object to posting an ISO image of the FC2E CD somewhere. I have the rights to it. If someone has the bandwidth to do that, let me know. I have a rather uninspired web site running on a machine in my home office, and the download speed would be my 128kb upload, so that would not be a good option. Tim

1 0

re Classic FOTD September 28, 1997 (Pollock)
by cjsonnack＠mmm.com 08 Oct '03

08 Oct '03

Jim Muth wrote: > Today's prize-winner fractal is named in honor of that not quite > so famous American abstract artist, J. Pollock. SciAm did an article recently about him and his work. Researchers analysed his paintings and discovered they were highly fractal in nature (containing self-similar detail at multiple levels). They derived a "fractal number" based on the painting details and found that number approaching "more perfect" fractality as Pollock's work evolved. -- |_ CJSonnack <Chris(a)Sonnack.com> _____________| How's my programming? | |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL | |_____________________________________________|_______________________|

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Classic FOTD 01-01-98 (Snub-Nosed Midget)
by Jim Muth 08 Oct '03

08 Oct '03

FOTD October 08, 2003 Fractal visionaries: This short introduction is being written the morning of October 8, 2003. After the mini-flap over the 'snub-nosed midget' fractal that actually appeared on January 01, 1998, I decided it best that I actually present the little fellow so that he might be honestly judged on his own worth. It's good that Paul (it was not Lee, as I mistaken wrote yesterday) noticed the error. If he had not, the snub-nosed fellow might never have had his second moment of glory. :-) As for the present-day situation here at Fractal Central, the work backup is slowly clearing, (down to 4 days), the cats are still well, and if all goes well, the ongoing FOTD will resume toward the end of this month. START ORIGINAL DISCUSSION============================== F.O.T.D., January 01, 1998 (Snub-nosed Midget) After yesterday's cosmic fractal, today's must be considered a minor interlude. It is a picture of a lopsided little midget that looks just as exhausted as I feel after last evening. And no wonder I'm exhausted -- I just got through the last day of another entire year. We begin the third-from-last year of the 20th century with a picture of a midget with a nose problem. I named the picture "Snub Nosed Midget" but this little midget is more than snub- nosed, it's actually coming apart at the seams, filled as it is with more holes than a swiss cheese. The formula mixes various portions of the Z^2, Z^-5 and Z^-3 Mandeloids, and slices the figure in the vicinity of a critical point. The finished image has been posted to Paul's web site at: http://home.att.net/~Paul.N.Lee/FotD/FotD.html Tomorrow, I'll have more energy for a longer commentary and hopefully a better fractal. Until then, take care and keep the faith in your fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER-FORMULA FILE============================= Snub_Nosed_Midget { ; 2 min on P200 640x480 reset=1960 type=formula formulafile=test.frm formulaname=3wayMandelbrot passes=t center-mag=-0.471598/1.82755/3.053522/1/-29.999 params=-1/-5/0.1/-3/-1.3321721988/0 float=y maxiter=1800 bailout=25 inside=0 logmap=yes symmetry=xaxis periodicity=10 colors=00024F<4>79G8AG9BIABKDBL<2>ICQJCSKCULCVMC\ X<10>ZEn<8>USCUT8VV9<19>fqAfrAgqD<18>jct<3>sea\ <10>kvVkxUjyUizTizTn`I<13>mosmpvmqxmrzmszmtzgkq\ <2>SLC<21>RffRfgSch<9>TCl<13>WJp<5>McxKfzJjz<3>D\ wzBsq<2>8gC<17>Rpo<16>xRozPozOozMozLoxRm<4>Vsdpz\ u`zfMzT<7>QyNQyMQyLRxLRxKSxJ<4>TwGZsPdpX } frm:3wayMandelbrot {; Jim Muth z=p3, g=pixel, a=real(p1), b=imag(p1), c=real(p2), d=imag(p2): z=(a*z^b)+(c*z^d)+(.3*(sqr(z)))+g, |z| <= 100 } END PARAMETER-FORMULA FILE==================================

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Classic FOTD 01-01-98 (Projective Plane)
by Jim Muth 07 Oct '03

07 Oct '03

Classic F.O.T.D., January 01, 1998 (Projective Plane) Fractal visionaries: The world of higher dimensions is filled with objects which are impossible in our three-space, and can be represented here in only a distorted way. The Klein Bottle is one such object. In three dimensions it appears as a closed figure which intersects itself and joins itself in such a manner that despite having no breaks it has only one side. The inside is also the outside. But this is a distortion of the true object, which can exist only in spaces of four or more dimensions. In four dimensions, the Klein Bottle is constructed by taking a rubber sheet, curling it and connecting one pair of edges so that a tube results, then bending the tube and joining the open ends into a doughnut shaped object. But before joining the edges, and with no cutting, the tube is given a half-twist and turned inside- out, so that without self-intersection, the resulting doughnut- shaped object has only one side. Its inside is also its outside. The Klein Bottle is difficult enough to visualize, but the Projective Plane is even more difficult. In fact it is difficult to even describe. In this case, the sheet of rubber is given a half-twist into a kind of Moebius Strip tube before being curled and given a second twist before the open ends are joined to each other, forming the Projective Plane. In this case, even a distorted model is nearly impossible in three-space. Well, if an accurate model of a Projective Plane is impossible in three dimensions, one could never hope to illustrate the monster on a two-dimensional screen. I named today's fractal "Projective Plane" only because that's what I thought of when I saw the image. Actually, it is a picture of a curious feature that appears at Z=0.00019,0.07388 C=-1.7435,0.0 in the Z^2.003 Julibrot figure. This object is extremely thin and exists only very near the Julia orientation, where it appears as a near- perfect rectangle. To create today's image, I gave the object a 2-degree double rotation from the Julia orientation, which distorted the rectangle into the curved shape in the picture. A little playing with the colors produced the effect of a flying sheet of rubber. The flying plane has landed at Paul's web site at: http://home.att.net/~Paul.N.Lee/FotD/FotD.html Tomorrow, I'll have another interesting FOTD. At this time I have no idea what it will be, but something will turn up -- as it always does. Until then, take care, and keep finding those fractal gems. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER-FORMULA FILE================================ Projective_Plane { ; 3-1/2 min on a P200 at SF5 reset=1960 type=formula formulafile=multirot.frm formulaname=multi20031 function=flip/ident/ident\ /flip passes=1 center-mag=-0.00037327503160875/\ +0.00003799627771399/514.8005/1/25 params=88/88/0.00022/0.0755/-1.74308/0 float=y maxiter=1800 bailout=25 inside=253 logmap=yes symmetry=none periodicity=10 colors=000QVZ<2>PXZ\ PYZP_Z<7>PlZPnZRt_<4>PmZPkZOhZ<6>MTZMRZMQZ<12>I9\ ZI8ZJ6a<19>I8OI8NH9KH9IH9HH9IH9IH9HH9FH9FH9H<11>\ HA9HA9JCB<2>OIGQJHRMJ<7>dgVejWgkY<3>nncooeqnf<3>\ wshxuixwjyylyzm<4>zwizvhzugzugztgzthzshzsh<10>pl\ `ol_mkZ<7>YfTWfSVdR<3>RZOQXNPYN<6>IUHHTGGUG<3>I_\ IJ`IJ`I<38>asSXrT<19>stPttPvvJvuM<3>oqWmpZmqZ<3>\ moZnoZopZskZwzZzwZzwZ } frm:multi20031 {; Jim Muth, best=ifif, fiif, fifi, iffi a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2, c=cos(b)*fn3(real(pixel))+cos(a)*fn4(imag(pixel))+p3: z=z^2.003+c, |z| <= 100 } END PARAMETER-FORMULA FILE==================================

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Classic FOTD 22-11-97 (Budrise)
by Jim Muth 06 Oct '03

06 Oct '03

F.O.T.D., November 22, 1997 (Budrise) Fractal visionaries: How can I describe today's fractal? Well, to begin, I'll let my imagination run wild. (It won't be difficult; that's my usual mental state.) :^) Picture yourself alone at night on an alien beach, standing under a sky filled with strange constellations. In the darkness you can hear the alien surf washing gently up the sands and swishing back out. Out on the methane ocean, strange lights are gently blinking on and off. You have no idea what they are -- this world is supposed to be uninhabited. In the distance to your right, a barely discernible glow like that of a city below the horizon reveals where methane ends and sky begins. Perhaps this planet is not deserted. But as you watch and wonder, the glow increases and spreads, until at last, in its undiminished splendor, its radiance piercing the high clouds, accompanied by the opening of "Thus Spake Zarathustra" the great cosmic bud rises into the sky. Day has come and you are still alone, but those dots that were lights blinking in the night still mar the horizon. . . . OK, so I exaggerated a little! Perhaps today's fractal isn't quite that spectacular, but it's still a striking one, and I feel it's good enough to make it as the FOTD for 22-11. When I saw this image, a sunrise, or budrise in this case, was my first and only impression. The image is a scene in the Z^24-(1.1*Z) figure, sliced halfway between the Mandelbrot and Oblate directions. It is another example of an order-2 object where none should appear. I had intended to post a different formula today, but this particular fractal so struck me that I felt it must be shown at once. And so here it is -- my FOTD for 22-11 -- not my best, but not my worst either. The finished image, which takes 6 minutes on an 80486-DX4 at 100mhz, is posted to Paul's web site at: http://home.att.net/~Paul.N.Lee/FotD/FotD.html Tomorrow, if I find no more irresistable images in the M-O rotation, I'll post an image from the M-R rotation. Until then, take care and put your best fractal forward. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE================================== budrise { ; 55 seconds on a P200--SF5 reset=1960 type=formula formulafile=minusrot.frm formulaname=M-O-rotation passes=t center-mag=1.26462/-3.33067e-016/4.372549/1.454/-90 params=24/44.5/0/0/0/0 float=y maxiter=1200 bailout=100 inside=253 logmap=yes periodicity=10 colors=000A00PF0UF0XG0aE0aI0`H0RG67CL7CN8DN<2>7C\ R6CP<2>8BKEBHKBFJACJ9AJ87H64J75K75H85<2>LC5MD5MD\ 5LE5<2>NE5NF5MF5<25>vL6<29>lbhkcjlckmdloel<6>tao\ paor`o<36>rJzrJzrKx<13>rWjqXiqYhpZgo_f<13>ekTelS\ dmRdmQenP<3>frLfsKgrK<28>et9gz2<4>cmIbzMbzPayS`v\ V_vX<8>deZdcZccX<12>hadzwP7V`7U` } frm:M-O-rotation {; Jim Muth ; real(p1)=power of Z, imag(p1)=rotation angle ; p2=parallel planes, p3=rotation point a=real(p1), b=imag(p1)+.0000000000001, z=sin(b*.01745329251994)*real(pixel)+p2, c=cos(b*.01745329251994)*real(pixel)\ +flip(imag(pixel))+p3: z=z^a-(1.1*z)+c, |z| <=25 } END PARAMETER FILE====================================

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Re: Fractint and IEEE
by Raymond Filiatreault 06 Oct '03

06 Oct '03

>Intel(-type) Processors IIRC use 80 bit FP numbers for internal >calculations and do a conversion back to 64 bit when saving the results >to registers. If by registers, you mean the regular (non-FPU registers) this is correct. However the FPU register stack maintains values in 80 bit form exclusively, and these values CAN be copied to memory intact as 80 bit values. Parts of both statements may be right or wrong. The FPU internal computing registers are 80-bits but it also has a few 16-bit registers for various functions. One of them is the Control Word register in which 2 of the 16 bits are used for Precision Control and define how the results will be rounded after an instruction is performed. The choices are 32-bit, 64-bit or 80-bit. Depending on your OS, those bits may be set initially to 64-bit mode when a program first starts (such as under Windows). If those bits are not reset to get 80-bit precision, all results get rounded to the 64-bit precision when "saving the results to registers" although all computations are performed with 80 bits. The FPU cannot save any data directly to the regular non-FPU registers (and they're still only 32-bit registers in most computers). But, yes the FPU can copy 80-bit values to memory intact as long as the Precision Control has been set accordingly. However, if you store intermediate results as 64-bit values, you immediately waste the higher precision of the 80-bit computations. Raymond _________________________________________________________________ Help STOP SPAM with the new MSN 8 and get 2 months FREE* http://join.msn.com/?page=features/junkmail

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Re: Fractint Hack
by JackOTradez 05 Oct '03

05 Oct '03

Tim - you mentioned: "Once I did a huge hack of fractint for Lee Skinner in which I changed nearly all "double" types to "long double" so Lee could squeeze out another couple of orders of magnitude of precision for a very deep zoom (but not quite arbitrary precision) image he was working on. " Can I get a copy of that? JoTz

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Re: Floating Point, 64 bit, 80 bit and beyond
by Jim White 05 Oct '03

05 Oct '03

I've done a lot of fractal programming in Visual Basic, and have built an engine which runs Fractint-compatible formulae in Windows. The speed of modern PC's makes the slightly slower calculation times less inconvenient, and I don't have to worry about video drivers. Using VB's "Double" data type gave me the standard 64-bit FP calculation mode. When I learned that most FPU's today can do 80-bit mode, I was disappointed that VB doesn't support this type. I converted my engine to PowerBasic, a VB-like 3rd-party compiler that offers a data type called "Ext", which is the 80-bit extended FP. PowerBasic also lets you create DLL's which you can't do in VB, so I was able to easily replace the VB engine with the PB version, retaining my VB front-end. Of course, 80-bit is only a marginal improvement over 64-bit, with just a few extra digits of accuracy. Of the extra 16 bits, it seems that only 10 are given to the mantissa, the other 6 being given to extending the exponent (as far as I can tell). I've been looking at arbitrary-precision options over the last few months. I'm very interested in the public domain library GMP (Gnu Multiple Precision) which can be built in optimised form for specific CPU's, e.g. Pentium2, Pentium4, i386 etc ... The "primitives" (fundamental operations like add, multiply) can be performed very fast, much faster than generic/portable libraries. Deploying GMP to use with fractals under Windows has proved to be tricky, as GMP is mostly used in Unix environments, but I've managed to overcome these problems and now have a GMP DLL I can use. Soon I hope to be able to do some comparative time tests to see how GMP performs "in the field" - ie. with a deep-zoom fractal calculation. Regards Jim White ________________________________________________________________________ Want to chat instantly with your online friends? Get the FREE Yahoo! Messenger http://mail.messenger.yahoo.co.uk

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Classic FOTD 19-06-97 (Prophet)
by Jim Muth 05 Oct '03

05 Oct '03

Fractal of the Day, June 19, 1997 Fractal visionaries: Every once in a while there comes a fractal picture that fairly shouts its name. Today's image is one of those. Despite the abysmal initial coloring, the moment I saw the image, with its stylized figure standing on a mountain top, showering blessings, I knew it could be named nothing but "prophet". It took only a carefully selected palette to bring the prophet to life. The formula is one of my failed efforts. But though the formula doesn't give me exactly what I was after, it does draw some very interesting images, which have earned it a place in my permanent formula file. Probably half the formulas in my collection were failures when I first tried them. But success can sometimes come from failure, and unless a formula draws nothing but a blank screen, I almost never give up on it until I have tried a wide variety of parameters. My current effort to draw all the oblique and skew planes in the julibrot figure is producing an unusually rich variety of formulas and images. For tomorrow's fractal, I'm going to wing it. Maybe I'll post another of my lucky accident fractals; maybe one of my older gems. But whatever it turns out to be, it will be interesting. Today's image has been solemnly posted to Paul's web site at: <> for the convenience of those who can't tie up their machines. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START COMBINED FILE FOR 19.6================================ prophet { ; 22 seconds at 200mhz, 640x480 reset=1960 type=formula formulafile=jim.frm formulaname=Test1XY passes=1 center-mag=2.66454e-0\ 15/-1.31262/0.2554581 params=0/0.5/0.5/0/-2/0 float=y maxiter=1000 bailout=100 inside=bof60 logmap=yes symmetry=yaxis periodicity=10 colors=00000000BFBDFFEGLGIQHKRJLSKNTMOUNQVPRXQTYSU\ ZTW_VX`WZaY`bZcc`fdbieclfeogfqhhtiiwjkzklzmlzmlzll\ zllzlmzkmzkmzzzzyyzxxywwxvvwuuvttusstrrsqqrpppoonn\ nlmnjlnhknfjndinchncgobfoaeo`do_coZboZaoYaoYaoX`oX\ `oW_oW_oV_oVZoUZoUZpTYpTYpSXpSYpRYpRXpQXpPXpOXpOXp\ OXpPXpPWpPWpPWpPWpPWpQWpQVpQVpQVpQVpRVpRVpRVpRUpRU\ pRUpSUpSUpSUpSUpSTpTTpTTpTTpTTpTTpTSpUSpUSpUSpUSpU\ SpVSpVRpVRpVRpVRpVRpWRpWQpWQpWQpWQpXQpXQpXQpXPpXPp\ XPpYPpYPpYPpYPpYOpZOpZOpZOpZOpZOpZNp_Np_Np_Np_NpZM\ pZMpYLpYLpYKoXKoXJoXJoWIoWIoWHoVHnVGnVGnUFnUFnUEnT\ EnTDmTDmSCmSCmSBmSAmR9mR7mR5mQ3mQ1mQ0mP0mP0lO0lO0k\ O0kN0jN0jN0iM0iM0hM0hL0gL0gL0fK0fL0eK0eJ0dI0dH0cG0\ bF0aE0`D0_C0ZB0YA0X80W60V40U20T00S00R00Q00P00O00N0\ 0M00L00K00J00I00H00G00F00E00D00C00B00A009008007006\ 00500400300200100000000000000000000000000000000000\ 0000000000000000000000000 } frm:Test1XY { z=real(pixel)+(p1*(imag(pixel)))+flip(real(p2)), c=imag(pixel)+(p1*(real(pixel)))+flip(imag(p2)): z=z^p3+c, |z| <= 16 } END COMBINED FILE===========================================

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Fractint and IEEE
by Tim Wegner 04 Oct '03

04 Oct '03

One little addendum to an earlier message. It may actually be false that Fractint uses IEEE math. In some modes, fractint uses 80 bit "IEEE-like" numbers. I'm not an IEEE math expert, but I'm not entirely sure that 80 bit numbers as used in an Intel Floating Point Unit are legal "IEEE" (though they are very "IEEE-like"). Fractal types in fractint that are implemented 100% in assembler use pure 80 bit floating point math. In other modes implemented primarily in C, Fractint does an odd mixture - the 64 bit double precision numbers used to implement double types are IEEE, but these are converted to 80 bits briefly when passed to the math coprocessor. In my workplace (NASA) this mixed precision behavior on the Intel platform has caused some problems we don't get on machines that use pure IEEE 64 bit doubles consistently. None of this affects my negative critique of the statement that minbrots are an artifact of IEEE math. That claim is pure unadulterated hogwash. Tim

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On vacation
by Scott D. Boyd 04 Oct '03

04 Oct '03

List members and FOTD enthusiasts: I will be out of town Monday - Wednesday, Oct. 6th - Oct. 8th, so I will not be posting Jim Muth's FOTD's during that time. They will be posted when i return on Thursday the 9th. Scott ------- sdboyd56(a)swbell.net http://sdboyd.dyndns.org/~sdboyd/ ------------------------------------------------------------ No Microsoft or other proprietary products were used in the creation of this email.

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Classic FOTD September 28, 1997 (Pollock)
by Jim Muth 04 Oct '03

04 Oct '03

F.O.T.D., September 28, 1997 (Pollock) Fractal visionaries: Today's prize-winner fractal is named in honor of that not quite so famous American abstract artist, J. Pollock. The resemblance to the paint drippings which made him almost famous is apparent. I achieved such an effect by taking a nondescript Rectangular plane fractal and redoing it with the inside fill set to epsilon cross. I'm not sure how this option achieves its effects. I think it colors the image according to whether the points' orbits come closest to the real or imag axis. Until recently I had never used this option, considering such a fancy fill method artificial, but I have now had second thoughts about fractals. There is no such thing as a "natural" or "pure" fractal other than the bare formula. And since a natural frac- tal doesn't exist, it makes no sense to try to maintain fractal purity. And since I no longer must try to keep my fractals pure, I will be able to use the entire range of Fractint's coloring options without compunction. For best effect, today's fractal should be drawn at a minimum resolution of 1024x768, to prevent the streaks of paint from breaking up. The finished image is available at: http://home.att.net/~Paul.N.Lee/FotD/FotD.html Until tomorrow then, may your fractals be infinitely beautiful. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 19.6 FILE============================================= pollock { ; 17 seconds on a P200--SF5 reset=1960 type=formula formulafile=jim.frm formulaname=Rectangular passes=1 center-mag=-7.\ 77156e-016/-2.05391e-015/1.369962/0.6701 params=0.42/0.33 float=y maxiter=500 bailout=100 inside=epsiloncross logmap=yes symmetry=origin periodicity=10 colors=000Wgq00ZTal<4>LN_000HHVGETEBQzsfz0dD8O\ <6>ObZm``db_Xd_KhZ<6>q`dg9z<3>rVhu_dve_vjWgEJnRM\ ucPvoSenU3yL<9>gYkHRiOSjYFK<12>BQiGBN<4>9Up8Yv4r\ N5l`6fn7`zHdvRhqQ_A`np<5>`hd`gb`fa`e`<12>`ZTUZE\ <8>mZugrnkhtklzmgznbz<2>rQusLsv8y<7>nd_Dyz<9>Spf\ <9>OfiOeiPbe<2>NgqMhuNmzMkz<5>LaoL`mLZj<5>KPZCQW\ <10>XKYTDl<6>aQNcOH<12>Xa`XbaWed<4>UrqBkzFmz<4>Y\ vraxpgzqfzp<3>bwoavnatn<4>XolZrm<7>Tbl`pyZmvXjs } frm:Rectangular {; Jim Muth z=flip(real(pixel))+real(p1), c=flip(imag(pixel))+imag(p1): z=sqr(z)+c, |z| <= 36 } END 19.6 FILE===============================================

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Classic FOTD 11-08-99 (Zodiac)
by Jim Muth 03 Oct '03

03 Oct '03

FOTD August 11, 1999 (Zodiac) Fractal enthusiasts and visionaries: I named today's fractal picture "Zodiac" not because of its appearance, but rather because I was wishing that I could be somewhere along the path of the solar eclipse. But the eclipse is in Europe and Asia, and I'm stuck here on the East coast of North America. Curiously enough though, if the path of totality were extended beyond the sunrise line, it would cross Maryland. As it is, we will see 20 percent of the sun obscured at sunrise. But alas, we will not even see that tiny event, for it will be overcast at sunrise. While I'm bemoaning our bad luck, I'll remind the fractal fans of the world that today's fractal is not a bad one. The midget is part of the fractal that results when a large amount of Z is subtracted from a little Z^100 and the difference multiplied by a factor of 0.0103. The parameter file is slow, so downloading the image file is strongly recommended. The image file can be found posted to: <alt.binaries.pictures.fractals> and to: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The always unimportant weather was partly cloudy and quite a bit warmer. The midday temperature of 88F (31C) was perfect for fractals of all ages, both liberal and conservative. And don't ask what a liberal fractal is. If you're not totally confused by this time, check here again next time, which will be in 24 hours plus or minus 1-1/2 hours. You'll be totally and absolutely confused if you do. Until then, take care of your pet fractal, and if you have no pet fractal, get one immediately. They work wonders for high blood pressure. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 19.6 PAR-FORMULA FILE================================ Zodiac { ; t=0:13:12.57 on a p233, 640x480 reset=1960 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+1.664072112263802/+0.3928892632790632/2.\ 145788e+007/1/-5 params=0.01/100/-100/1/-0.9897/0 float=y maxiter=12000 bailout=25 inside=0 logmap=267 symmetry=none periodicity=10 colors=000DGNCHKBIK<6>6IS6IT7IU<10>CHdCHeDHeDHe<16>K\ Fa<5>mkw<28>6Fg<10>`Ztm`u<3>zgyzkzzgrwfkrecmeX<6>EaN\ <13>SW4<18>2ju<8>oajn`io_hp_hqZg<3>ubevcewcdwcc<13>w\ cXwcWwcWwcW<78>wcU } 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 19.6 PAR-FORMULA FILE==================================

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Re: Suggestions?
by JackOTradez 03 Oct '03

03 Oct '03

Folks, this discussion is amusing me. You are approaching it from the wrong angle. Fractint is still the BEST of the fractal programs, but it is a 16 bit DOS app and you are trying to get it to work in a 32 (soon to be 64) bit WinDoZe world. Forget it! You will frustrate yourself into a padded cell! There are 2 ways to deal with this. 1) Set up a dual boot with your WinXP; run Fractint in Win9X or native DOS. FORGET WinXP! 2) Best way: Get an old system, load DOS or Win9X on it, and dedicate it to Fractint. No problems, no hassles. I use my P4-2GHz / WinXP system for all my "real" work, internet, coding, graphics, video/multimedia, etc. I have 2 older systems, P3-733 and P2-300. I have DOS on these and they are dedicated 24/7 to Fractint. All is perfect. I then just transfer the GIF files to the P4/XP system for further manipulation / videos etc. (no floppy, use a USB flash drive!) You can buy P2 and P3 systems for around $100 now, even cheaper, at computer shows and some mail-order places. What's the problem? Why try messin' with XP and video drivers? A wise man sayeth: when there are more than one solutions to a problem, the simplest is best. Don't have Win9X installation CD? You can get these now dirt cheap also online or at computer shows. I have the original DOS 6.22 installation floppies; there are 3; less than 5 Meg total. If there is enuf interest, I can post them on my web site for download. JoTz

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A Few Comments on the Number 666
by mdoctorow＠comcast.net 03 Oct '03

03 Oct '03

>From Osher Doctorow Ph.D. I am glad to notice the heavy volume of replies to my Feigenbaum Constant and Weak Force posting, although it is amusing to notice that they mostly concern my comment that I'd forgotten what 666 means. I hadn't been reading the replies because I'd been watching the California Recall Election for Governor here in California, which may explain why I had trouble recalling what 666 means (?). Actually, I looked up 666 as internet keywords ("The number 666") after seeing the replies and apparently in Revelation verse 18 Chapter 13 the Number of the Beast 666 is mentioned, which is taken to mean the Devil. Also there are some hysterically funny jokes at geocities.com about 666, including extremely high precision 666.0000... and so on. Is there anything that one can learn about fractals or chaos from 666 aside from Jerry Iuliano's and my and your interesting comments? Well, this got me to thinking after reading the comments and looking up the sites mentioned: what exactly was 666 doing in the Gospel or New Testament? According to one site, 6 + 6 + 6 = 18, which is the verse in which it appears, and chapter 13 is supposed to represent death because of the 13 traitors, etc. Well, what if 666 was put into chapter 13 verse 18 by whoever wrote that verse knowing that 6 + 6 + 6 = 18? What would be the purpose of this? Let's put on our Fractal Thinking Caps (FTCs, which also stands for Federal Trade Commission incidentally), and think about this. Whoever wrote that wanted to point out that Armageddon was coming. I suppose that a visitor from Outer Space looking at the ensuing history of humanity would tend to agree, although not quite in the literal sense. But what better way for the writer of ch. 13 verse 18 to emphasize the importance of his/her verse and chapter than by a mystical emotional number which succeeding generations would remember more than the usual warnings of future doom? This moves us into the rather non-mainstream (if not dubious) field of historical reconstruction, but wait! There's more. What would give a scholar whose main literary interests had been the Old Testament an interest in 666? According to one of the sites, this was related to the worth of the gifts received by King Solomon from Egypt (I think via Queen Sheba). So it started in the Old Testament. According to this interpretation, it was simply appropriated into the New Testament. This isn't the first such case where Old Testament ideas were used in the New Testament. But what does King Solomon have to do with anything in Armaggedon? Well, Queen Sheba was so to speak his downfall (well, in a sense - I suppose that Bill Clinton would have other comments on that). His people had been slaves in Egypt. Also, King Solomon was the smartest King of Israel. To my recollection, he was into numerology in addition and was stated to have "spoken with animals". This would appeal to New Testament writers and scholars probably. Ladies and Gentlemen, what we may have here is a number 666 that represents not the Devil but Number Theory - the birth of Number Theory which led to fractals and chaos and to where we are today (give or take some problems off the internet). As for the member of Fractint who has the social security number with 666 in it, the person is not the Devil but a prospective assistant Moderator of Fracint! I've forgotten his/her name, but I'll look it up as soon as there is another pause in the California gubernatorial race. Osher Doctorow

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Re: 666 and all that
by Jim White 02 Oct '03

02 Oct '03

May I offer a little poem I've constructed on this subject? ===================================================== At the bottom of the input screen are inputs for Fractint's "pieces" layering Julia sets in the x-y plane and continuously varying c Once at the full level the decay period starts and the volume dies down If your "corners" choice is symmetrical, Fractint - downright cosmic! ===================================================== It has a reasonable degree of ambience, I suggest. But the words are not mine - each of the 4 lines was found in FRACTINT.DOC, and each line has a numerological value of ....... guess what? Now, any suggestions for what other text I might scan? Mischievously yours Jim White ________________________________________________________________________ Want to chat instantly with your online friends? Get the FREE Yahoo! Messenger http://mail.messenger.yahoo.co.uk

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Mini-Brots
by cjsonnack＠mmm.com 02 Oct '03

02 Oct '03

Kenneth Lifvenborg wrote: >> <snip> >> but folks should know that the "universality of the M-set," >> that is the recurrence of "mini-bugs" or cardioids, >> at every level of "magnification," is just an artifact >> of the floating-point ops (IEEE-755, -855, I think). >> <snip> > > I find this a bit disturbing. Could anyone please care to comment? (DISCLAIMER: Not An Expert) Doesn't FractInt use integer math? If you find buds at the upper integer levels, doesn't that suggest they continue on down? Has anyone ever dove deep into the Mbrot using infinite precision numbers? Probably slow, but--hey--it'd be like the old days of FractInt.... -- |_ CJSonnack <Chris(a)Sonnack.com> _____________| How's my programming? | |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL | |_____________________________________________|_______________________|

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PHILOFRACTAL
by cjsonnack＠mmm.com 02 Oct '03

02 Oct '03

Yale Landsberg wrote: > ...and all I seem to get is your cool and amazing fractals and -- > your pleasant commentaries on the weather and what is happening in > your life. Did something happen to the original intent of the > list, or are you sailing under a false flag? A question I've posed a few times myself, as either there aren't many people reading this list, or there are and most of them are just reading--not participating. There are a few regulars you can count on, though. I've always thought debate a vital part of philosophy, so it's a little disappointing. It may also be that there just isn't that much philosophical "meat" to fractals. -- |_ CJSonnack <Chris(a)Sonnack.com> _____________| How's my programming? | |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL | |_____________________________________________|_______________________|

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Classic FOTD 05-07-99 (A New Angle)
by Jim Muth 02 Oct '03

02 Oct '03

FOTD July 05, 1999 (A New Angle) (c) Fractal enthusiasts, lurkers and visionaries: As I write this FOTD, I can look through the fractal shoppe window and see three separate fireworks displays in progress around the city. And the weather is also hot as a firecracker. Once again the predicted showers failed to appear, but the heat did not fail. It is getting ever more oppressive. The temperature of 99F (37C) was great for nothing but fractals. Tomorrow is due to be even hotter, so I suppose tomorrow will also be good for nothing. Today's picture is a new view of yesterday's cubic midget. It is actually the same scene of the Julibrot sliced in a different direction. The midget itself lies buried near the center of the frame. It's quite stretched and a bit hard to find. At this angle, which is close to halfway between the Parabolic and Oblate directions, the surrounding pattern undergoes a strange transformation. We can see the nine elements converging on the midget, but before they can trifurcate into 27 elements, they get cut off, and form some rather interesting configura- tions. (The 27-element convergence never appears.) I named the picture "A New Angle" to bring out the fact that it is a different aspect of yesterday's image. Yes, I did give the image a boost in a graphics program, but not enough to damage its purity. It's a very fast fractal, so it might be quicker to run the parameter file than to download the JPEG image file from: <alt.binaries.pictures.fractals> or from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Since I've already exceeded my speculative philosophical quota for the day in earlier letters, I'll add nothing at this time. But I will be here again tomorrow with another fractal, which easily could be another view of the same scene. I also could easily erupt into more philosophy, (if my ramblings qualify as such). Check then to see what happens. Until then, take care, and I've yet to see the first fractal fireworks display. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 19.6 PAR-FORMULA FILE================================ A_New_Angle { ; 0:00:33.06 on a p233, 640x480 reset=1960 type=formula formulafile=multmult.frm formulaname=multirot03-XZ-YW passes=1 center-mag=+0.00000000000052113/-0.00000000000074647\ /1.844175e+010/72.885/0/-34.92 params=-46.895/5.599/\ 0.5388592866040914/0.6163082906621036/0.53885928660\ 40914/0.6163082906621036 float=y maxiter=2000 bailout=25 inside=0 logmap=75 symmetry=none periodicity=10 colors=000600000000102706F3CL9HQFNYLR\ cQXiX`pafvgkzkoxiksffoccl`_gYXcVS_SOXOLSLHOIEJF9GC5C\ 92760430990<2>IM8MQBPVES_HVcK_iNamPdrSgvWlzZ<2>uzfpz\ kmznjyqgutcpx`lyYgyVcyT`yTYyTVy<2>SOySLyQIy<3>P7yP4y\ P3yO7yOCyMGxMLwLPuLStLXqJ`oJdnIilImkIpiGukGykGzkGzkD\ zhCxfAse9pc7lb6g_4dZ3`X0XW0TU0PR0LP0IO0DN09L06K0LI0_\ I0lH0zH0zH0zI3zK7zKCvLGrLMmNQiNVfO_aOcYPiTPmPRrLRvGS\ zDScVBIl0``KrPfoTcmXb<4>fjWdmUarS<2>YzO<2>TzKSzIPzKM\ zKJxLGrLFmNCiN9cO6_O3VP1PP0LR0GR0AS06S01S0AU4IWDQXLY\ ZTf_`m`gubcoe`ifXdhT_iPTkMPlIJnFFoA9q73r30t00u00w40x\ A0yG3yM7ySCy_IydMy<2>v_yr`ym`xi`tdao`aiXaeSc`OcXJcSG\ dRDfRCgP9iP7jP4lO3mO0mN0oN0pN0rL0sL0uK0vK0vK0jh3`yFg\ xPor_vkizedzbaz`_y_VyZSxWPvULvSIuRFsOAsN7rL4pK0pH0oF\ 0mE0mC0rE0vF0yH6dkJ_fXTciO_vIXzDUyFZpGbiIf`JkTLoLMtD\ Mx9_u4jr0vq6pnCjlGdkM_iJ00D00 } frm:multirot03-XZ-YW {; 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)+p2, c=e*imag(pixel)+p3: z=z*z*z+c, |z| <= 36 } END 19.6 PAR-FORMULA FILE==================================

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Classic FOTD 05-02-00 (Art Nouveau Midget [7])
by Jim Muth 01 Oct '03

01 Oct '03

Classic FOTD, February 05, 2000 (Art Nouveau Midget) Fractal enthusiasts and visionaries: I named today's fractal picture "Art Nouveau Midget" because it reminds me of the curvilinear art style that was popular around the turn of the last century. It is the third in the present series of spectacular midgets. How long can I keep the streak going? I haven't the slightest idea, since the quality of the FOTD images is largely a matter of good luck in searching. The formula behind the image is Z^(-1.05)-Z^(1.05)+C, an expression that I entered on a whim and examined with more intuition than logic. The parameter file runs in under four minutes -- still slow enough to make the download preferable. That download can be found at: <alt.binaries.pictures.fractals> and at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Happy downloading . . . The fractal weather today was cloudy with off and on flurries of snow, amounting to about 1cm. The temperature of 36F kept the cats indoors, feeling sulky. Our friend Percy Smedley is still puzzling over that four-dimen- sional figure painted into the surface volume of his west wall. The object, if that word can be applied to a 4-D thing, is the fourth of the six regular 4-D polytopes. The monstrous thing consists of 24 octahedral cells, 96 triangular faces, 96 edges and 24 vertices. The three dimensional projection, which resembles an octahedron filled with a network of distorted octahedra, is too complex to describe in detail. To form the figure, a hypercube must be inscribed in a hypersphere, and then the centers of the eight cubical cells of the hypercube must be projected onto the hypersphere. The 16 vertices of the hypercube plus the projections of the centers of the eight cells of the hypercube form a network of 24 points on the hypersphere. These 24 points are the vertices of the 24-tope, the icosatetratope, the fourth of the six regular 4-D hypersolid polytopes. Curiously, this method also produces a regular figure in two- dimensional space, where it results in an octagon, but in three- dimensional space as well as all spaces higher than four, the figure that results is not regular. Having decorated four walls of his room, Percy is still not yet finished, for he has two more walls to decorate -- the in wall and the out wall. He will decorate his in wall with a picture of a hecatonicosatope, which I will make a brave but futile effort to describe next time. Until that next time, take care, and don't try to visualize the fourth dimension -- it's not a visual thing. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Art_Nouveau_Midget { ; time=0:04:31.38 SF5 on P200 ; Version 2000 Patchlevel 6 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-3.415040480289464/-2.498805152893876/240\ 7.815/1/-127.499 params=1/-1.05/-1/1.05/0/1000 float=y maxiter=2500 bailout=25 inside=0 logmap=55 symmetry=none periodicity=10 colors=000szm<6>QZpMVpIRp<3>2Cq<3>e5Lo3Dx25<6>_73W83\ T93<3>FB3<3>Q90OF3<3>J_CIeEHjHGqJFzLFqJFlHFeFFVE<2>F\ 99<15>ma7pc7rd7<3>zk7<16>IUGGTGDSH<3>3OI<10>Z_Wa`Xda\ Z<3>oeb<3>hi_fj_dkZclZalY_mYYlX<2>TcV<3>McTLcTJcSHcS\ GcREcRCeQBfQ<2>CkLDmJDmm<3>EbmF`mFYmFWmGTn<2>GMwHNz<\ 15>MPzMQzMQz<2>NQzNQzPPz<12>nIzpIzrHztHzvGzxGzyHz<4>\ zJzzJzzJzzKzzKz<5>zPzzQzzRzzSzzTz<37>zUz } 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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Re: [Fractint] Video drivers
by Russell Walsmith 01 Oct '03

01 Oct '03

I have XP pro on a laptop and XP Home on my current desktop and I've yet to see any difference in perfomance in regards to display. My 'default' display mode is shift/F7 (i.e., 1024x768 with 256 colors); what happens, Marty, when you try that? Russ -- --------- Original Message --------- DATE: Tue, 30 Sep 2003 00:39:54 From: Alex Dukay <alexdukay(a)rogers.com> To: Fractint and General Fractals Discussion <fractint(a)mailman.xmission.com> Cc: >Marty, >I'm running Widows XP Home on a Dell laptop (Inspiron 8200) with an Nvidia >card. And to my amazement Fractint runs in high resolution mode...I'm no >expert but I would bet it could be XP pro - try the home version. Perhaps >others have other solutions. >Alex > > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >

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FOTD 30-09-03 (The Sun and Moon [7])
by Jim Muth 30 Sep '03

30 Sep '03

FOTD -- September 30, 2003 (Rating 7) Fractal visionaries and enthusiasts: Having found, or rather created, a spare moment, I used that time to find a very slow fractal, which I could let develop on my fractal machine while I accomplished other things on my other machines. The fractal took almost 3 hours to complete, and when it was finished, I named it "The Sun and Moon". I can give no reason for choosing such a name. Perhaps someone viewing the image can supply a reason. The parent fractal is an oversized something, too distorted to be called a Mandeloid, which consists of little more than two prominent valleys. Today's image is located rather deep in the larger valley. This valley must be of the 'Seahorse' variety, because the midget I found in it resembles 'Seahorse Valley' midgets more than 'Elephant Valley' midgets. When all was said and done, I rated the image at a 7. But even a 7-rated image is not worth a wait of almost 3 hours. So I recommend downloading the image from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Things are coming along reasonably smoothly here at F.C. By working long days, I am getting the old work out a little faster than new work is coming in. And if the present trend continues, things will eventually get caught up. It is far too early to say when 'eventually' will arrive. Monday was a fine early Autumn day here at Fractal Central, with lots of sun and a crisp temperature of 66F 19C. The fractal cats enjoyed themselves in the yard for two hours in the afternoon, and settled for the evening without a treat of tuna. As for me, I still have enough work backed up to keep the 12-hour days going for another week or two. But the backlog will 'eventually' be cleared and the daily FOTD will resume. Until next new FOTD, whenever that is, take care, and keep checking those old classic FOTD images. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Sun_and_Moon { ; time=2:55:18.39--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-2.99293075927805800/+0.248764115526592\ 00/733067.4/1/-135/-8.75853476550725318e-009 params=1.3/0.9/-1.3/-0.9/0/0 float=y maxiter=42000 inside=0 logmap=3014 periodicity=10 colors=000i`Uj`Tl`Sm`Ro`Qp`QeVGWQ6XP7YP8ZO9_OA`NBa\ NCaMDbMEcLFdLGeLHfKIgKJgJKhJLiIMjINkHOlHPlHQeKMZMJ\ SOFMRCFT88V52X25Z58_8B`ADaDGcGJdILeLOfORhQTiTWjVZk\ Y`l`cnbfoehphkqjnsmptpsurvvuxwwvvtturruoptmntjmshk\ reircgq`eqZdpWboU`oRZnPXnMVmKUlHSlFQkCOkAMj7Lj5OiB\ RiHUiNWhTZhYahccgifgoigukgzmXhoNSqDBnFElHGjJIhLKeN\ McOOaQQ_SSYUUVWWTYYRZ`P`bMbdKdfIfhGhjEilBkn9mp7or5\ qt3rv3qs3qq3qo3qm3qk3pi3pg3pe3pc3pa3p_3oY3oW3oU3oS\ 3oQ3oO3nM3nK3nI3nG3nE3nC6kD8iEAgFCeFEbGG`HIZIKXIMU\ JOSKQQKTOLVMMXJNZHN`FObDPdAQf8Qh6Rj4Sl2Sm4Qm6Pm8Om\ ANmCMmELmGKmIJmKImMHmOFmQEmSDmUCmWBmYAm_9ma8mc7me6\ mg5ke4jd4hc4gb4fa4d_4cZ4aY4`X4_W4YV4XT3VS3UR5TQARP\ FQOKOMPNLUMKZKJcJIhIHmMFrQDwTBzSFzRKwQMmPOcOQVNRSM\ SPLTMKUKJWHIXEHYBG_9IaAKcALeBNgBPiCQkCSmDToDVqEXsE\ YuF_wFayGbzGdzHezHczJazL`zMZzOXzQWzRUzTSzVRzWPzYNz\ _Mz`KzbIzdHzebzXdzWezVgzV } 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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The Feigenbaum Constant and the Weak Nuclear Force
by Bill Jemison 29 Sep '03

29 Sep '03

Lee, Lots of nice images in that gallery! I particularly liked "I'll Bite" and, if I remember correctly, "Bon Voyage" (or whatever the name of the one with the "ship" in it is). Great stuff! Bill

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Classic FOTD 31-12-97 (Galaxia)
by Jim Muth 29 Sep '03

29 Sep '03

Classic FOTD, December 31, 1997 (Galaxia) Fractal visionaries: (This discussion, as will be all Classic FOTD discussions, was written on the date in the subject line.) Today's fractal is the final one I'll post this year, so I wanted it to be a good one. But being very busy today, I had no time to find a new one. As a result, I went to my collection of fractals and pulled out one that had been lying dormant and unappreciated for several months. After a few quick minor changes to the color palette, I renamed it "Galaxia", and here it is. I think it's acceptable. The image is actually the Z^500 Mandeloid, turned inside-out, and with the number of arms reduced to two. The soft halo represents the combined glow of billions of stars, while the foreground could well be the ring of cosmic dust that exists in the galactic plane. The completed image has been posted to Paul's web site at: http://home.att.net/~Paul.N.Lee/FotD/FotD.html I must run now, so that's it for today. But tomorrow, I'll be here again with another wonder-fractal. Until then, take care and Happy New Fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START FILE================================================== galaxia { ; 40 seconds on a P200 -- SF5 reset=1960 type=formula formulafile=jim.frm formulaname=JimsCompMand center-mag=-4.61853e-01\ 4/2.57017e-014/0.04201427/1/-37.5 params=500/0/-501/0/30000/0 float=y maxiter=1200 bailout=25 inside=bof60 logmap=yes periodicity=10 colors=00INFaICSKEULDYMDZND_ODaPEbQEcQEdREfSEgTEhU\ EiVEjWFlXFmYFnZFo_Fp`Fr`FsaFtbGucGwdGxeGyfGzgHzhHz\ iHzjHzkHzlHzmHznHzpEzoFznGzmIzlJzkKzjLziMzhOzgPzfQ\ zeRzdSzcTzbVzaWz`Xz_YzZZzY`zXazWbzVczUdzTfzSgzRhzQ\ izPjzOkzNmzMnzLozJqzKpzLpzLozMozMnzNnzNmzOmzOlzPlz\ eboeboeboebodbodbodbodbodbodbodbocbocbocbocbocbocb\ ocbocbobbobbobbobbobbobbobboaboaboaboaboaboaboabo`\ bo`bo`bo`bo`boaanabnabo`co`co`do`dp_ep_ep_fp_fq_gq\ ZgqZhqZhrZirYirYjsYjsYksYksXltXltXmtXmtWnuWnuWouWo\ uWpvVpvVqvVqwVrwUrwUswUsxUtxUtxTuxTuyTvyTvySwySwzS\ xzSyzRyzRzzRzzRzzTzzRzzQyzPxzOwzNvzMuzLtzKszJszIrz\ HqzGpzFozEnzDmzClzBkz9kzAjzAjzAizBizBhzBhzBgzBgzCf\ zCfzCezCezCdzCdzDczDczDbzDbzDazEazE`zE`zE_yE_yE_xF\ ZxFZwFYwFYvGXvGXuGWuGWtGVtGVsHUrHUrHTqHTqHSpHSpIRo\ IRnIQnIQmIPlIPkJOjJOiJNhJMgJLfJKeIJdHIcGHbFGaEF`DE\ _DDYCCWCBUCASB9QB8OA7MA6K } frm:JimsCompMand {; Jim Muth z=c=pixel: z=z^p1*(c^p2)+c, |z| <= p3+100 } END COMBINED FILE===========================================

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Re: 666 Meaning
by JackOTradez 29 Sep '03

29 Sep '03

Although not wishing to continue the divergence from the normal subject, I wish to point out something here; I have always had a mystical interest in numbers, numerical ratios, numerology, etc. Some write this off as para-science nonsense, but I believe many of the keys to the Universe are hidden in numbers. As The Angel Gabriel told the children during a recent visit to Earth: "Study your math - it's the key to the Universe". The prevalance of numbers like the Golden Ratio and Feigenbaum constants has always fascinated me. I for one, believe the entire Universe is a Fractal, a Chaotic ("complex") System on an infinite scale that even it's very Creator can not predict with 100% accuracy; that then would be the whole point of existence - an experiment. Each of us are infinitesimal parts of an infinite chaotic system; what we do in our lives may be insignificant now, but may have ultimately major consequences in the far future. Sort of like very small changes affecting weather prediction over time (think Lorenz). The so-called "prophesies" are necessarily vague and not exactly predictive - they can't be. They are the equivalent of our weather predictions for next week - it may be close, but there is always uncertainty and intrinsic error. Consider this: Assign a number to every letter of the alphabet, 1 thru 26 multiplied by 6. Thus A=6, C=18, M=78, etc. all the way thru. Spell the word COMPUTER. Add it up. "Let he who hath wisdom understand ..." It is 666. "But that is only in English" you may argue. Well, have you seen technical papers in other languages? Certain words in English are ubiquitous in all languages, simply because they or what they mean were discovered, or are a product of, America, and there were or are no analogous words in that native language. It is strange to see a paper with Asian characters writing, and English words like "computer" peppered here and there! Computer=Antichrist? Could be. See Revelation 13:15-18. "And he had power to give life unto the image of the beast, that the image of the beast should speak ..." Artificial Intelligence? Robotics? Speach recognition, processing? Artificial speach? All these things exist today, if in rudimentary form, but how about a few years from now? A super-computer that is genuinely intelligent, (self-aware?) and can speak can not be too far off. "And he causeth all ... to receive a mark in their right hand or forehead ..." , "And that no man may buy or sell that he have that mark ... or the name or number of the beast ..." We have had credit cards for a long time, with the advent of chips in cards in recent years, the move to a cashless society has been predicted for some time - it may be very soon. We already implant microchips in pets to track them; some are seriously suggesting doing it to people. The technology is already here, all that stands in the way is politics (for now). First convicts and criminals, then the rest of us. It is also being seriously suggested that microdevices be implanted in people at birth, and upgraded ("flashed") over time in life to contain all info about that person, identification, life, medical, finances, occupation, everything. Also it would be used for commerce and financial transactions - eliminating both cash and credit cards! There was a chilling article on this in one of the cyber magazines recently (WIRED I think). You just wave your arm in front of the scanner ... Sounds good for convenience and security, but ... Thus a person without this chip ("mark of the beast") would not be able to function in society. Those who control the chips (computers and their operators in the central govt) would in effect totally control all of us and our lives. "And he causeth all ..." Something to panic about as a new week begins. But remember, as prophesies go, these are things that may come to pass, not necessarily will come to pass ... BTW, some of my new fractal animations are kick-A! Stay Amazed. JoTz

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Please lets move the political commentary
by Tim Wegner 28 Sep '03

28 Sep '03

There are many other lists for politics. Tim

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Re: The California Gubernatorial Campaign...
by Jim Muth 28 Sep '03

28 Sep '03

At 08:21 AM 9/28/03 +0000, Osher Doctorow wrote: <snipped> >2. Ethnic prejudice only works from majority to minority, not in the reverse >direction if we are to believe the current Recall speeches and actions. It gets worse than this. Here in Baltimore, a group that comprises 65 percent of the total population is called a minority group. And speaking of philosophical things, I heard people on the radio seriously talking about bringing a class-action law suit against God for sending the hurricane that caused the power outages and the inconvenience of no lights or TV for 5 days. As God's representatives, and because God would not be expected to appear in person, the churches would pay the awards. Too bad this is not connected to fractals and I have no time to continue. But sometimes I wonder whether 1+1 really does equal 2. Jim M.

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[Fractint] A Controlled Growth Mandelbrot Riccati Equation of the Universe
by mdoctorow＠comcast.net 28 Sep '03

28 Sep '03

>From Osher Doctorow Ph.D. The renowned Professor Peebles of Princeton University in 1993 or 1994 devoted a few pages of his volume on Astrophysics to showing that a fractal model of the Universe appeared to disagree with various radiation results under the most common model. However, since the Universe now appears to be divided into Rare Event/Process, Fairly Frequent Event/Process, and Very Frequent Event/Process regimes or parts, which were not considered in Peebles' work, it's probably time to look at fractal and chaotic models of the Universe again. The Mandelbrot set in polar coordinates has cardioids of type: 1) r = a1(1 - cos(u)) where r can be intuitively thought of for our purposes as the distance from the origin or pole to a point on the cardioid and u is the angle which r regarded as a line segment makes with the positive x-axis or polar axis. I don't know how familiar the different members of Fractint are with calculus, so I'll assume that nobody knows calculus and just gives the result from calculus, letting v be the velocity or speed of u with respect to time at each instant of time and a be its acceleration with regard to time, and "speed of r" refers to its speed of change in time, etc.: 2) speed of r = a1vsin(u) 3) acceleration of r = a1asin(u) + a1(v)^2 cos(u) Here adjacent letters mean multiplication, so for example a1vsin(u) means a1 times v times sin(u), and ^2 means square so that (v)^2 is the speed squared. There is a space between (v)^2 and cos(u) to make reading easier, but they're actually multiplied. Equation (3) is a Riccati differential equation growth control type equation in v. Nowdays, most people learn sine and cosine functions in algebra courses already, so if anybody isn't familiar with them, just look up keywords like graphs of trigonometric functions on the internet. They're basically up and down wavy lines like hills followed by valleys followed by hills followed by valleys followed etc. I'm going to ignore the third dimension of space and concentrate on a two- dimensional model for simplicity, although a "round cardioid" in 3-dimensional space may be more applicable to the universe. The above equations tell us that the main results of astrophysics and cosmology such as the expanding universe and the recently (as geological time goes so to speak) accelerating universe can be modelled by the above equations provided that the velocities and accelerations of the angle u are properly chosen in certain parts or intervals of time. For much of the history of the Universe, there doesn't have to be much "control" of v or a, but periodically sine and cosine (abbreviated sin( ), cos( )) graphs become negative, and since two negatives multiplied make a positive, in those intervals of time v and/or a has to be made negative. This doesn't mean that the Universe slows down or decelerates, only that the angle u with which it traces out a cardioid in the Mandelbrot set decreases or decelerates in time. A slight problem concerns the interpretation of r as both the line segment from the pole to the cardioid and the interpretation of r as the "principal radius" of the Universe or for short the radius of the Universe. We could make r ultimately extremely large by choosing a1 in r = a1(1 - cos(u)) to be very large - far larger than we're likely to observe with current astronomical technology. Some people might argue that a1 should change in time, at least a little over long intervals, and in that case we get what might be called a time- generalized cardioid. So in a sense we can have our Chaos and eat it too. :>) Osher Doctorow

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Classic FOTD 29-04-97 (Monster)
by Jim Muth 28 Sep '03

28 Sep '03

Fractal of the day, April 29, 1997 Fractal visionaries: Today's fractal is something a little different. It is a warped Mandelbrot created from the basic Mandel formula in Fractint, and colored using the ranges feature. There are only 10 colors in the entire picture, but those ten colors had to be carefully adjusted to create the three-dimensional effect of the foreground monster arms covering and enveloping the blue remains of the classic Mandelbrot set. I have always been fascinated by the way perturbed points, no matter where they start, if they don't escape first, eventually settle into the same orbits as points that start at 0,0, giving a ghostly background image in the high iteration range. The effect is almost one of independent but overlapping fractals, as this picture, which has been posted to ABPF, illustrates. Jim Muth jamth(a)mindspring.com START PAR FILE=================================================== monster { ; Draw time 2 minutes on a P200 reset=1950 type=mandel passes=1 center-mag=-0.25810954616588430/+0.6410480167014\ 6280/76.36852 params=0.777/-0.555 float=y maxiter=32500 bailout=100 inside=0 logmap=yes symmetry=none periodicity=25 ranges=0/-1/300/600/1000/1600/2400/3600/500\ 0/10000/32500 colors=000N9D`OKPTsPVz0cp0ew0iz0mz`\ kzYmwVpzSPRPSVMWYr0s`IiSzN<5>KbZyx2<2>TdT9Id<5>IX\ `oUH<5>RYWNZZHRH<2>JXWyiQ<4>Q__vzd<2>TeaUeZSc_Qb_\ gbY<2>ZNW<4>hL9dgS2Z7<2>f11<3>PbaXMNSRSNVXGhXHdZI\ a_IbR<5>J_ZJZ_LKL<6>JYZjUh<2>QYba6J<5>LVZdDw<5>MW\ cEFDHPPGeb<5>J_`ScG<6>KZZbRe<3>NYaYKp<6>KYb1`D7_L\ DZTjYN<3>OZZV3T<6>KV_MT9U`iyR_jU`XX`eQX<5>MY`vuC\ <5>OaYrVs<6>NZba69SLN4Lf9QdEVbC2X<3>IT`cYDLV1<5>\ JZWYum<6>K`a1I_<4>GX`pCW_OZZVD<5>LZYBT8<2>HYUez1\ UlJT57<6>KWYhrBWhOgOk<6>MYa } END PAR FILE====================================================

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[Fractint] Has the California Gubernatorial Campaign Any Lessons for Fractint?
by mdoctorow＠comcast.net 28 Sep '03

28 Sep '03

>From Osher Doctorow Ph.D. A member of Fractint (whose name I can't reveal) has asked me whether the California Gubernatorial Recall Campaign has any lessons for Fractint. Here are a few. 1. In USA politics, it's apparently worse for an excellent actor to ask for questions in advance of a debate than for a Governor and Lieutenant Governor who are poor actors to put the State into catastrophic financial disaster. 2. Ethnic prejudice only works from majority to minority, not in the reverse direction if we are to believe the current Recall speeches and actions. 3. Indian gambling casinos in California have apparently decided to choose Bustamante with enormous donations because Spain originally conquered the Indians. 4. Kennedy relatives are only good if they move to the left; their right-sided profiles apparently don't stand up as well in the public image. 5. If you watch your numbers carefully, you too may invest in an Indian Gambling Casino and thereby become President (or at least Governor). Osher Doctorow

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A (Mathematical) Biology Archive at the Los Alamos arXiv
by mdoctorow＠comcast.net 28 Sep '03

28 Sep '03

>From Osher Doctorow Ph.D. The Los Alamos arXiv:gr-qc, arXiv:astro-ph, etc., are Archives on the internet of preprints in mathematics and physics mostly, but they have just added arXiv:q-bio.QM, a Mathematical Biology Archive that remarkably goes back from September of this year quite a few years backward. Two papers of this September (both September 16, 2003) might be of interest to members of Fractint: "Multi-Stability in Monotone Input/Output Systems" arXiv:q- bio.QM/0309002 and "Monotone control systems," same place/0309001, both by authors David Angeli of U. Florence, Italy, and Eduardo D. Sontag of Rutgers University. I will simply mention for now that monotonicity is a rather interesting property that seems to be related to growth-expansion-contraction rather than constancy or cyclic behavior as I've developed them in my postings and elsewhere in Rare Event Theory/Geometric Physics. The authors don't use any of my explicit ideas, but we seem to be going in somewhat similar directions in some ways. Osher Doctorow Ph.D.

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Still on IFS...
by Andrew Coppin 27 Sep '03

27 Sep '03

http://mathworld.wolfram.com/BarnsleysFern.html Does anyone know of a good interactive IFS editor? I found a copy of F-Design, but eeeek! That thing is SO not fun to use... Any URLs? Thanks. Andrew.

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Re: [Fractint] The Feigenbaum Constant and the Weak Nuclear Force
by JackOTradez 27 Sep '03

27 Sep '03

You say: " I seem to have forgotten what the 666 represents " Let me enlighten you. There is a number. It is the number of a man. He shall be the AntiChrist. Let all who have wisdom understand. His number shall be 666. Find him. Hunt him down. Kill him!

3 4

Classic FOTD 09-04-98 (Pink Midget)
by Jim Muth 27 Sep '03

27 Sep '03

F.O.T.D., April 09, 1998 (Pink Midget) Fractal visionaries: I had planned on discussing in today's FOTD the ultimate ques- tion of life, and the way it relates to the realm of fractal geometry. But I just couldn't muster the proper degree of profundity that one must feel before tackling such a life- altering topic. So instead, I dredged up a picture of a baby Mandelbrot. The guilty formula is my MandelbrotMix4, which automatically calculates a critical point of the formula and sets that value as the starting point of Z. The actual equation being iterated is (4*Z^3)+(2*Z)+C. These values draw a small Mandelbrot set rotated 90 degrees, with a curious tail dropping down from the cleft of East (Elephant) Valley, which has now become a South Valley. The main Mandelbrot figure is fairly conventional, but the East Valley tail is filled with cut-off bits and pieces that demand further investigation. Only a slight magnification is needed to reveal the tell-tale patterns that lead to hidden midgets. At first glance, today's image appears to have come from a spiral in Elephant Valley itself. A quick examination, how- ever, will show that the pattern around the midget is more delicate, with more fine, hairline detail than that which appears around the midgets in Elephant Valley. Also, the features are broken rather than connected, as they are in the valley. I gave the image a pastel-like palette of colors, which empha- sizes the more delicate nature of this midget. The tendrils curving away from the central midget are themselves filled with midgets, but alas, these midgets are beyond the reach of conven- tional DP math. (Hint, hint . . . Fractint developers, wouldn't it be great if arbitrary precision math could be applied to formula type fractals?) Today's harmless little midget has been posted to the usual sites -- alt.fractals.pictures and alt.binaries.pictures.fractals It is also available at Paul Lee's web site at: http://home.att.net/~Paul.N.Lee/FotD/FotD.html and Scott's site at: http://sdboyd.dyndns.org/~sdboyd/fotd/index.html Tomorrow, I might gather my profundity and discuss the ultimate question of life, or then again, I might blather on about some- thing of little consequence, but whatever I do, I will have another fractal ready and waiting. Until then, take care, and the next time you see a fractal, view it with reverence, for that fractal might encode the answer to the riddle of the universe. Jim Muth jamth(a)mindspring.com START 19.6 PARAMETER-FORMULA FILE=========================== Pink_Midget { ; 7min on a P200, SF5 reset=1960 type=formula formulafile=apr-98.par formulaname=MandelbrotMix4 passes=1 function=ident center-mag=-0.00218445795113323/-0.2346673882601\ 9790/9.192243e+010/1/-160/1.5611329691467279e-005 params=4/3/2/1/0/0 float=y maxiter=6000 bailout=9 inside=0 logmap=123 colors=00016727929A2CB2EC2FD\ 3HF3IG3KH3LI3MJ4NL4OM4PN4QO4SP4SQ4SR5TT5TU5TV9VX\ DXZHZaL`cPbeUehYhlbkognrlqupsxstxutyuqvuottlrukq\ ujpvhnvgmwflxckxajyZhyXgzVfzUewUbuU`rUYoVVmUTjUQ\ gTNeTLbRI`OGYMDVJATH8QG5OF3PE4QD5SE6TF7VG8WH9YIA\ ZJB_KC_LD`PE_TFbVFcXFeYFe_FV`FVaFVbFVcFVcFTdEReD\ PfCOfBMhALjAJl9Hm8Fp7Dr6Cs6Au59w47w35w24v2KncQam\ VQxO9xOCvOEsNHqNJnNMlNPjNRgNUeMWbMZ`M`YMcWMfUMhR\ LkPLmMLpKFeOWV_bLia5obAobFocKpcOpdTpeYpebpfgpflq\ gpqguqhzqcvn_qjVmgRhdMdaI_YDWV9WSEXZI`dMdkQhqRco\ R_lSVjSRgTMeTHbUD`U8YU4WT3UT3TS3SS3RR3QR3PQ3OQ3N\ P2MP2LO2KO2JN2IN2HM2GM2FM2EN4FO6FO7FP9FQGFRIFSKF\ SMFTOFUQFVSFVUFWWFXXFYZFY`FZbF_dF`fF`hFajFblFcnF\ cqFbrJ`sO_tSYuXXv`VwdUxiSymUymVymXymZym`ylaylcyl\ eylgylhzljzllzlnzlozlqzkszkuzkvzkxzkuzlrzmoznlzo\ izofzpczq`zrXzsUztRzuOzvLzvIzwFzxCzyEzyGzyIzyKzy\ MzxOzxQzxSzxEzz0zz0zz1zz1zz } 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 19.6 PARAMETER-FORMULA FILE=============================

2 1

Multifractal_9
by Albrecht.Niekamp＠t-online.de 27 Sep '03

27 Sep '03

Hi, have you ever seen a circular shaped Julia, even the spirals consist of circular structures ? Or an inverted Mandel, which means the "lake" in fact is outside ? Fractal greetings, Al --------------------------------start-frm-------------------------------- FRM:Multifractal_9 { ; Albrecht Niekamp 170903 ;p1 (spider)julia-seed ;real(p2) 5digits : (1)shape (2)outside (3)inside1 (4)inside2 (5)inside3 ; 0_off 1_secant 2_mand 3_bees 4_jul 5_m_mods 6_phoen 7_newt 8_spider ; input2 : 2digits_many-mods 2digits_phoenix 2digits_spider ; 5digits_reset : 0_no 1_z-reset 2_iter-reset 3_both +5_warp ;imag(p2)(-) 5digits_colour(bailout) number ; input2 : 4digits(-)_mand/jul 2digits_secant 4digits_bees ;real(p3) 2digits_newt 4digits_colour1, 5digits_colour2 5digits_colour3 ;imag(p3) shape : factor (fn1), 5digits_colour4 5digits_colour5 ;real(p4) outside: factor (fn2), 4+1digits_bord-out 4digits+fract_bord-in ;imag(p4) inside1: maxit1, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor1 (fn2) 4digits+fract_border1 ;real(p5) inside2: maxit2, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor2 (fn3) 4digits+fract_border2 ;imag(p5) inside3: maxit3, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor3 (fn4) 4digits+fract_border3 ;fn(1) shared by many-mods+bees ; da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=d3==0 vb=d>5 sc=d==2 mo=d==6 px=d==7 ab=px+(d==3)+(d==5)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 sc1=d==2 mo1=d==6 px1=d==7 v1m=mo1+px1 v1j=d>7 dd1=v1j+(d==4)+(d==5) ab1=px1+(d==3)+(d==5)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 sc2=d==2 mo2=d==6 px2=d==7 v2m=mo2+px2 v2j=d>7 dd2=v2j+(d==4)+(d==5) ab2=px2+(d==3)+(d==5)+(d==9) d=trunc(dd/10) ex3=d>1 sc3=d==2 mo3=d==6 px3=d==7 v3m=mo3+px3 v3j=d>7 dd3=v3j+(d==4)+(d==5) ab3=px3+(d==3)+(d==5)+(d==9) d=dd-d*10 ex4=d>1 sc4=d==2 mo4=d==6 px4=d==7 v4m=mo4+px4 v4j=d>7 dd4=v4j+(d==4)+(d==5) ab4=px4+(d==3)+(d==5)+(d==9) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex1+ex0+ex2+ex3+ex4 ; d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 ; d=imag(p3) sfac=trunc(d) da=(d-sfac)*10000000000 ba4=trunc(da/100000) ba5=da-ba4*100000 ; d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) ; d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=d==3 fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=d==3 fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 ; d=imag(p5) mi3=trunc(d) da=(d-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=d==3 fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 ; if (d4) z=0 if (vb) if (mo) c=0.4*log(sqr(pixel^mm)) else c=pixel z=pixel endif else c=pixel z=pixel*sc endif else c=p1 z=pixel endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else z=pixel cb=p9*u c=p1*u p=pp*u endif tt=tt-1+ex0 endif elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(pixel^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(pixel^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(pixel^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(pixel^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Qusinewton Pusk s Istv n z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+ph-0.5*zold ;Phoenix Mike Wareman zold=z z=z1 else z2=fn1(z)+c ;Many_mods Linda Allison z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z ;Julia Pusk s Istv n z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) z2=z*z ;Mandel Pusk s Istv n z=z2*z2+p6*z2+c-p0 else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba } ----------------------------------start-par------------------------------- Fullmoon { ; Time 0.29.11.30 ; Albrecht Niekamp Sep, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_9 function=sin/cosxx/cos/exp passes=t center-mag=+0.50651979529167650/-0.61792919511027970/1102.367/1/142.2060\ 56268235727/8.22999403236879257e-006 params=-0.02237006744590594/-0.07473982970671712/20684.64575300005/11541\ .0608020602/80148.03072420481/17384.2204812048/384.00240000045/128.30076\ 80000451/256.300768002431/512.2007680082311 float=y maxiter=3072 inside=maxiter outside=tdis logmap=9 periodicity=0 rseed=-2436 colors=200034<23>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<13>UQFWSGYTH<3\ >e`LgbMidN<3>qjRslSunT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25\ >C00A00800<3>000<23>eeegggiiijjjlllnnn<2>sss<25>BBB999777<2>222000012 } Inversion { ;Time 1.52.59.62 ;Albrecht Niekamp Sep, 03 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_9 function=sin/exp/exp/sin passes=t center-mag=+0.79641132292408450/-0.00131969871981132/2017.308/1/-170.000\ 000000001194/-3.61272123328149064e-012 params=-0.05825983458967864/0.3785210730307932/21222.32595700021/25143.0\ 506030602/51024.02048000094/384.01048089094/384.00048000545/256.10076830\ 01/512.1007683001/768.1007683001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200444<19>bbbdddfffgggiiijjj<3>qqqsssqqq<24>BBB999777<2>222000012\ <24>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<21>icNkeOmfP<3>unTwpVxqWzsX\ <25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000222 } Three_rivers { ; Time 0.57.54.48 ; Albrecht Niekamp Sep, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_9 function=sin/cosxx/cos/exp passes=t center-mag=+0.51651583292708940/-0.60133383907525690/1107.555/1/142.2060\ 56268216969/8.2300112836941608e-006 params=-0.02122867519150365/-0.06936307870723595/20684.64575300005/11321\ .0608020602/80148.03072420481/17384.2204812048/384.00240000045/128.30076\ 80000451/256.300768002431/512.2007680082311 float=y maxiter=3072 inside=maxiter outside=tdis logmap=9 periodicity=0 rseed=-2436 colors=200068<21>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<13>UQFWSGYTH<3\ >e`LgbMidN<3>qjRslSunT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25\ >C00A00800<3>000<23>eeegggiiijjjlllnnn<2>sss<25>BBB999777<2>222000012034\ 056 } Juliversum { ; Time 0.45.00.97 ; Albrecht Niekamp Sep, 03 ; Version 2002 Patchlevel 5 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_9 function=sin/cosxx/cos/exp passes=t center-mag=+0.50651979529167650/-0.61792919511027970/55.37774/1/142.2060\ 56268212706/8.23001490952990356e-006 params=-0.02122867519150365/-0.06936307870723595/20684.64575300005/11321\ .0608020602/80148.03072420481/17384.2204812048/384.00240000045/128.30076\ 80000451/256.300768002431/512.2007680082311 float=y maxiter=3072 inside=maxiter outside=tdis logmap=9 periodicity=0 rseed=-2436 colors=200034<23>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<13>UQFWSGYTH<3\ >e`LgbMidN<3>qjRslSunT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25\ >C00A00800<3>000<25>iiijjjlll<3>sss<25>BBB999777<2>222000012 } Loop_the_loop { ; 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[Fractint] Summary of Cardioid-Cycloid-Epicycloid-Hypocycloid Relationships
by mdoctorow＠comcast.net 27 Sep '03

27 Sep '03

>From Osher Doctorow Ph.D. To summarize the relationships between/among cardioids, cycloids, epicycloids, and hypocycloids, after correcting my confusion of cardioid and cycloid, here is the story. All of these are curves generated by rolling circles. While cycloids are generated only by one rolling circle (being the slowly oscillating path traced out by a point on the circumference of a circle that rolls without slipping along a straight line in one direction, cardioids are special cases of epicycloids. Epicycloids are similarly generated by one circle rolling over a second fixed circle on the outside of the latter - the point of tangency (touching) traces out an epicycloid, and for epicycloids the rolling circle is smaller than or equal to the other circle in radius. When the radii are equal, it's called a cardioid. The hypocycloid is like the epicycloid but with the smaller circle rolling inside the fixed larger one. The cardioid has one cusp, the nephroid is like the cardioid except that it has 3 equally spaced cusps, and the ranunculoid is like the others but has 5 equally spaced cusps. The cycloid, epicycloid, and hypocycloid have the following respective equations: 1) x = a(t - sin(t)) y = a(1 - cos(t)) 2) x = (a + b)cos(t) - bcos[(a + b)t/b] y = (a + b)sin(t) - bsin[(a + b)t/b] 3) x = (a - b)cos(t) + bcos[(a - b)t/b] y = (a - b)sin(t) - bsin[(a - b)t/b] The cardioid is the second case when a = b, which results in: 4) x = 2acos(t) - acos(2t) y = 2asin(t) - asin(2t) Osher Doctorow Ph.D.

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Oops!
by mdoctorow＠comcast.net 27 Sep '03

27 Sep '03

>From Osher Doctorow Ph.D. I've confused the cardioid and the cycloid in my last posting and I may have done it previously too. The cardioid is: 1) r = a(1 - cos(u)) nsofar as it is represented by the Mandelbrot cardioids, while the cycloid is: 2) x = a(t - sin(t)) y = a(1 - cos(t)) Although y and r look similar, they're very different curves because of the x equation in (2). The same restrictions and considerations apply as I stated in my last posting since the forms of the equations are so similar. In general, one should be very careful with a closed curve like a cardioid or circle or ellipse or a closed surface like a sphere or ellipsoid in not regarding it as a growth-expansion-contraction object except in very special conditions or for very special reasons, because being closed (an object moving along it returns to its original position and repeats its path in finite time), its equation is cyclic unless it taken as purely a spatial equation - and in the latter case, an additional equation has to be hypothesized to give its time variation. Osher Doctorow Ph.D.

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Coordinate-Dependent Growth Difficulties
by mdoctorow＠comcast.net 27 Sep '03

27 Sep '03

>From Osher Doctorow Ph.D. The equations dy/dt = ky, dy/dt = ky(1 - y) or ky(k2 - y), dy/dz = f(z) + g(z)y + h(z)y^2 and the latter similarly for y^3 in an added term are the "standard" growth equations provided that z can be regarded as a non-oscillating function of time. If z were to oscillate so much that it cancelled out the growth efect of y or time, then it would defeat the intuitive idea of growth-expansion- contraction which is not rapidly oscillating (back-and-forth) increase and decrease although that could belong to some different theory. It is possible for things to expand during "youth" and contract during "old age", but oscillating quantities of usual trigonometric type (sin(t), cos(t), etc.) are generally found in science and mathematics to characterize rapid rather than long-term change at least as we intuitively understand that as human beings. Another type of problem, though sometimes interacting with the previous one, occurs when equations change very much during transformations to polar or spherical or cylindrical coordinates (other coordinates won't be considered here). In that case, as long as the above types of equations work in one coordinate system (Cartesian or rectangular being the most common one, which is the ordinary one used in Euclidean Space), that is fine. With "extended" growth equations that involve cardioids or equations of type dy/dt = k/y or dy/dt = sqrt(1 - y) or sqrt(y), this may fail because the main coordinate system may be polar or spherical or cylindrical in which trigonometric oscillating functions like sin(t), cos(t), etc., are the main type in these coordinates. For example, one of the simplest equations of a circle is in polar coordinates: 1) r = asin(u) where u is the polar angle. Unless we restrict u to be between 0 and 2pi, this oscillates too much. Even with such a restriction, there would have to a very good physical or biological and mathematical reason for making that restriction, and this is generally unlikely since there is so much difference between the restricted and the unrestricted cases. The cardioid which is so important to the Mandelbrot set suffers from this difficulty. In polar coordinates it is of form: 2) r = a(1 - cos(u)) In parametric coordinates, it has the form (with sine and cosine possibly changed to cosine and sine respectively, etc.): 3) x = a(t - sin(t)) y = a(1 - cos(t)) which repeats its graph every 2api intervals from 0 onward on the x axis. In my opinion, we are justified in restricting the interval of t or u to be only one of those intervals, which eliminates the oscillation, but only because the Mandelbrot set is critical to fractals and chaos. Even here, there is a question of whether u or t is taken to be time or not. If it is time, then we are asserting that the physical object - for example, the Universe as a whole - is drawing out a cardioid in spacetime, not just in space. This may or may not be what we want to theorize. If u or t is NOT time but some spatial angle only, then we are not even talking about growth as expansion-contraction in time. We would then have to separately hypothesize how the Mandelbrot set or its cardioids change in time, and this is an entirely different question. Osher Doctorow Ph.D.

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Classic FOTD 27-08-97 (S_Curve)
by Jim Muth 27 Sep '03

27 Sep '03

F.O.T.D., August 27, 1997 (s_curve) Fractal visionaries: (Originally posted on the Fractal Art list.) While the debate about whether to organize or not to organize grows in intensity, I stand on the sidelines, contentedly continuing to search for fractal images. I am pretty much neutral on the idea of a fractal artists' guild. Belonging to such a group would give a certain legitimacy to our fractal art field, but I doubt if such a group would suddenly open the general public's eyes to the wonderful things that numbers can do. All too many people disengage their brains when they encounter art. They judge a painting's worth by how photographically realistic it is, a novel by how sensational it is, and a piece of music by the immediate catchiness of the major scale melody or else by the volume of the percussion. This natural human aversion to intellectual effort is in my opinion the chief impediment to the wide acceptance of fractal art, and indeed, to the acceptance of all abstract art. I have been a member of a similar group, the Graphic Artists' Guild, for several years. And to be honest, the greatest effect the guild has had in my life to this point has been when I wrote the checks for the membership fee. If a fractal guild were formed, I would consider the membership fee and what the group might accomplish, before making my decision about joining. My fractal today, as promised yesterday, is a figure I discovered in the Julia plane of the (-Z)^1.007 mandeloid. It's incredible that an exponent so close to unity could produce an image with as much detail as in today's fractal. But here it is, in all its spiral glory. The image will soon be available at: http://home.att.net/~Paul.N.Lee/FotD/FotD.html and at: http://sdboyd.dyndns.org/~sdboyd/fotd/index.html Tomorrow will be my last FOTD until I return from a well- deserved vacation on September 8. I will try to make it a good one, but my good intentions sometimes are not fulfilled. So check then to see what fractal turns up. Jim Muth jamth(a)mindspring.com START 19.6 FILE============================================= s_curve { ; 8 minutes on a P200 SF5 reset=1960 type=formula formulafile=jim.frm formulaname=JulibrotInvZ passes=1 center-mag=0.986183/0.601218/0.7013364/0.7171/90 params=1.007/0/2/1.3/0/0 float=y maxiter=10000 bailout=100 inside=0 logmap=yes symmetry=xaxis periodicity=10 colors=000JTqBFC<12>B32<30>akealf\ `kZ_jRZjJ<42>g`ug`ufat<34>TfnTfnUgm<41>qnm<7>19t\ <28>tP9<2>2vc<27>zna<7>IXw<4>JUr } frm:JulibrotInvZ {; Jim Muth ; Draws oblique slices of order n inverse Julibrot Figure ; P1 defines power of Z, P2 determines center of slice ; P3 determines angle of slice z=pixel, c=p2+(pixel*p3): z=(-z)^p1+c, |z| <= 100 } END 19.6 FILE===============================================

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The "bug "is not a bug!!! Is not! Is not!
by Tim Wegner 26 Sep '03

26 Sep '03

OK folks, listen up. :-) For you Fractint is a fractal program, for me it is the World's Best Quick And Dirty Reference to Complex Transcendental Functions. Press F1, go to "Fractals and the PC", and navigate down to trig identities. I put these in the help because I went through a LOT of books finding these and wanted to collect them all in one place in order to code them up. Some books are too simple and so don't have the formulas, and other more advanced books are too abstract and so don't have them either. The formula for the complex power is as follows: z^w = e^(w*log(z)) (here"^" is ASCII text shorthand for exponentiation, in this case z^w means "raise the complex number z to the power of the complex number w") where: e^(x+iy) = (e^x) (cos(y) + i sin(y)) and log(x+iy) = (1/2)log(x^2 + y^2) + i(atan(y/x) + 2kPi) for k = 0, -1, 1, -2, 2, ... (The log function refers to log base e, or ln. The expression atan(y/x) is an angle between -pi and pi in the quadrant containing (x,y) implemented in C as the atan2() function.) The point of these formulae from a programmer's perspective is that they define the complex valued power function in terms of the real versions of e^x, log(x), sin(x), and cos(x) that are available to the C programmer. The interesting and important thing here is that the value of the complex log is not unique. There are infinitely many different values, with the imaginary members. Put another way: the complex log is not single valued. Let's look at the log. In the "bug" illustration, the complex argument is: (-5.0, 0.0) The assembler log function gives: (1.6094379124341,-3.141592653589793) Coding by hand in C gives: (1.6094379124341, 3.141592653589793) BOTH ANSWERS ARE RIGHT!!! The imaginary parts differ by 2*PI, which is acceptable. What actually causes this is that the log implementation normalizes the result to a particular 2*PI segment. Jim's fatal mistake was when he assumed that given a = 1, b = -5, g = 1, h = -1, j = 1/6, that (-a*b*g*h) is -5. Yes, it's very close to -5 in the actual computer calculation, but "close" wins only in horseshoes. The problem is that the complex logarithm of (-5,0) has an imaginary part exactly on the logarithm software implementation's boundary of 2*PI normalization (namely PI). So if the calculation (-a*b*g*h) drops a bit here or adds a bit there, even a bit of the lowest significance, it can change the imaginary component from ~ PI to ~ -PI. I leave it to the reader to plug both these logarithm values into the rest of the formula for the exponential power, and see that the result is (1.132467200411351, -0.653830243005915) in the one case and (1.132467200411351,+0.653830243005915) in the other, as Jim discovered. Here's the main point - a recurring theme in trying to create fractals with complex transcendental functions. The complex power function x^y is discontinuous because of the ambiguity in the many- valued complex log. Each decision to normalize the log to a particular 2*PI interval in an effort to define a single-valued function creates a discontinuous tear in the result in a different way. The "bug" Jim found had values right on the boundary of the tear, so that tiny perturbations and rearrangements of the code pushed the calculation over the edge of the discontinuity. Fractint is cleared of the unjust accusation! The verdict: INNOCENT! All is well with the fractal world :-) One single absolute truth of the universe is thus upheld again. It is this: There are NO software bugs, ONLY USER ERRORS!!! (Sorry Jim ... -no, not *really* sorry, I lied :-) I suggest the future Fractal of the Day explore a fractal based on a discontinuous complex transcendental function in such a way that the fractal itself has visually manifest tears. There are several examples in Fractal Creations, and I am sure many of the artists here, including the honorable Mr. Muth, know of or can discover examples. Tim Wegner

2 1

FOTD 24-09-03 (Sir Fractal Galahad [7])
by Jim Muth 25 Sep '03

25 Sep '03

FOTD -- September 24, 2003 (Rating 7) Fractal visionaries and enthusiasts: It's been six days since the last FOTD. This does not mean that I am losing my enthusiasm for the FOTD. The reason for the delay is that we had a hurricane here at Fractal Central, and the resulting power failure lasted almost 6 days. This was bad enough, but the work, which was quite a bit behind to start, got much farther behind during the time I could not work on it. I am now so far behind that I am in danger of losing customers due to my inability to deliver their jobs on time. As a result, this will be the last FOTD discussion until I catch up my other work, a task that will take at least several weeks, and possibly over a month of 12 hour days. I must work these hours until the pile of 'work to be done', which now holds over one week's work, has been reduced to a manageable size. In the meantime, I will continue to monitor the Fractint and Philofrac- tal lists. When I find the time, I will inject a few brief com- ments. It will be up to the lurkers to keep the lists alive and active for the duration. As a matter of curiosity, my e-mail box held 1181 letters when I checked it for the first time in 6 days. Most of them were junk, which together took almost 2 hours to download. The most curious letter informed me in broken english that I had been identified as a money launderer, and for some strange reason, requested my credit card number. I replied that I always launder my money. I use mild detergent and luke-warm water. Hot water makes the colors fade. ;-) ;-) Today's quickie fractal subtracts 1.11 parts of (1/Z) from Z^(1.11), then adds C. The parent fractal is a distorted M-set rotated -90 degrees, with a curving tail extending from its East Valley, which in this case is on the northeast side of the main bay. The scene is located at the end of a broad irregularly curving area of chaos on the main bay side of the northwest branch of the Seahorse Valley of the parent M-set. I named it "Sir Fractal Galahad". I have no idea what Sir Galahad has to do with fractals -- the name simply sounds noble in a comical way. And the picture looks good, honestly earning its rating of a 7. The render time of 7 minutes is short enough to be reasonable. The download, which is available on the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> is even more reasonable. The fractal cats had perhaps the best time of their lives in the 6 days since the last FOTD was posted. As I predicted, the only casualties the big blow brought to Fractal Central were a 6-day power outage and a yard of broken tree branches. The dynamic cats watched from their window shelf with interest last Thursday night as the wind roared, trees fell, and the sky was illumina- ted by the blue flashes of falling power lines and the distant pops of blowing transformers. When the next day arrived, the cats were ready for a full day's romp in the yard, which, with nothing but clean-up to do, I was able to give them. Since then, the weather has been much better, the only exception being a heavy rain that brought more flooding to the area early Tuesday morning. The cats have had 5 full days in the outdoors with me there to watch over them, making them perhaps the two happiest cats in the world. But it's very disconcerting to have so much backed-up design work waiting to be finished. And with an additional pile of storm- associated stuff likely to come in, I'm not as happy as the cats. I guess that, like the linemen of the local electric company, I'll be working 12 and 14-hour days. I'll be doing it until I clear away enough backed-up work to resume the FOTD in a relaxed manner. Until next time and next FOTD, whenever that is, take care, and see you for certain in the relatively near but not immediate future. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ SirFractalGalahad { ; time=0:07:35.70--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+0.15079637605670420/-1.480224054715044\ 00/5.344319e+009/1/144.999982895458032/9.399329566\ 45073148e-006 params=1/1.11/-1.11/-1/0/0 float=y maxiter=1200 inside=0 logmap=144 periodicity=10 colors=000WNFXPBYR8ZT4_V1YX5WZ9UaDScHRfLPhPNkSLmWK\ p_IrcGugEwkDynfHjdKkcNlaPm`Sn_VoYXpX_qWarVbnVckVdg\ VddVe`VfYUfUUgRUhNUqKUnGUlDUjASd9Q_8OV7NPALKFJFKIA\ PHDUGGZFJcEMhDPmCSsCUzBXoAZf9aY8cPHNcOMZUMV_MRfMMr\ MIwMErNHmOKgONcPQ`PTXQWTRZQRaMSdJSgFTjCTmEWiFYeG_b\ HaZJcVKeSLgOMiKNkHziJrhKmgLhfMcdOZcPUbQPaRK`SFZUEY\ VDXWCWXCVYFUXHTWKTVMSUPSTRRSURRWQQZQP`POcPNeOMgOMh\ HMjGSkFXlEamDgnCloCqe6rW1rX1pX1oX1mX1lX1jY1iY1gY1f\ Y1dY1cY1bW4`U6ZS9XQBWOEUNGSLIQJLPHNNFQLDSJCUIEPFGL\ CIG9KC6KIEKFCKCAK98K66K45L77M98MC9NEBNHCOJDPMFPOGQ\ RHQTJRWKSYLS`NTbOTdPS_ORVOQROPYZOdiNjsNktNltNltNmt\ NntNntNotNotLnuKmuJluIkuHjuFivEhvDgvCfvBev9dw8cw7b\ w6bw5cw8dsBepDfmGgjJhfLicOj`QkYOlRMmLKnEIo8Gp2Jq8M\ rEPsJStPVuVYv_`webxjdziezhgzghzfjzekzdlzdjzchzcfzb\ dzbbzb`za_zaYz`Wz`Uz`Sz_Qz_Pz_Mz5Jz4Gz4Hz9IzDJzHSz\ T`zcVzhQzmSzlSzTTzPUzMVzI } 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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Multifractal_9
by Albrecht.Niekamp＠t-online.de 25 Sep '03

25 Sep '03

Hi, the image is the message. Fractal greetings, Al. --------------------------------start-frm-------------------------------- FRM:Multifractal_9 { ; Albrecht Niekamp 170903 ;p1 (spider)julia-seed ;real(p2) 5digits : (1)shape (2)outside (3)inside1 (4)inside2 (5)inside3 ; 0_off 1_secant 2_mand 3_bees 4_jul 5_m_mods 6_phoen 7_newt 8_spider ; input2 : 2digits_many-mods 2digits_phoenix 2digits_spider ; 5digits_reset : 0_no 1_z-reset 2_iter-reset 3_both +5_warp ;imag(p2)(-) 5digits_colour(bailout) number ; input2 : 4digits(-)_mand/jul 2digits_secant 4digits_bees ;real(p3) 2digits_newt 4digits_colour1, 5digits_colour2 5digits_colour3 ;imag(p3) shape : factor (fn1), 5digits_colour4 5digits_colour5 ;real(p4) outside: factor (fn2), 4+1digits_bord-out 4digits+fract_bord-in ;imag(p4) inside1: maxit1, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor1 (fn2) 4digits+fract_border1 ;real(p5) inside2: maxit2, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor2 (fn3) 4digits+fract_border2 ;imag(p5) inside3: maxit3, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor3 (fn4) 4digits+fract_border3 ;fn(1) shared by many-mods+bees ; da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=d3==0 vb=d>5 sc=d==2 mo=d==6 px=d==7 ab=px+(d==3)+(d==5)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 sc1=d==2 mo1=d==6 px1=d==7 v1m=mo1+px1 v1j=d>7 dd1=v1j+(d==4)+(d==5) ab1=px1+(d==3)+(d==5)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 sc2=d==2 mo2=d==6 px2=d==7 v2m=mo2+px2 v2j=d>7 dd2=v2j+(d==4)+(d==5) ab2=px2+(d==3)+(d==5)+(d==9) d=trunc(dd/10) ex3=d>1 sc3=d==2 mo3=d==6 px3=d==7 v3m=mo3+px3 v3j=d>7 dd3=v3j+(d==4)+(d==5) ab3=px3+(d==3)+(d==5)+(d==9) d=dd-d*10 ex4=d>1 sc4=d==2 mo4=d==6 px4=d==7 v4m=mo4+px4 v4j=d>7 dd4=v4j+(d==4)+(d==5) ab4=px4+(d==3)+(d==5)+(d==9) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex1+ex0+ex2+ex3+ex4 ; d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 ; d=imag(p3) sfac=trunc(d) da=(d-sfac)*10000000000 ba4=trunc(da/100000) ba5=da-ba4*100000 ; d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) ; d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=d==3 fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=d==3 fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 ; d=imag(p5) mi3=trunc(d) da=(d-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=d==3 fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 ; if (d4) z=0 if (vb) if (mo) c=0.4*log(sqr(pixel^mm)) else c=pixel z=pixel endif else c=pixel z=pixel*sc endif else c=p1 z=pixel endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else z=pixel cb=p9*u c=p1*u p=pp*u endif tt=tt-1+ex0 endif elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(pixel^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(pixel^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(pixel^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(pixel^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Qusinewton Pusk s Istv n z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+ph-0.5*zold ;Phoenix Mike Wareman zold=z z=z1 else z2=fn1(z)+c ;Many_mods Linda Allison z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z ;Julia Pusk s Istv n z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) z2=z*z ;Mandel Pusk s Istv n z=z2*z2+p6*z2+c-p0 else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba } ----------------------------------start-par------------------------------- Phoenix { ; Time 2.56.13.76 ; Albrecht Niekamp Sep, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_9 function=sin/exp/exp/sin passes=t center-mag=0.739239/0.000686676/19.29681/1/-90/-1.23373533611470521e-014 params=-0.05825983458967864/0.3785210730307932/21227.32595788025/15234.0\ 506030602/152048.0404808048/384.1604894048/384.00482000595/256.100768300\ 1/512.1007683001/768.1007683001 float=y maxiter=3072 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=2000QY<10>09C08A068<2>022000211<21>icNkeOmfP<3>unTwpVxqWzsX<25>CB\ 7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<11>LLLNNNPPPQQQSS\ SUUU<6>fffgggiiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0cq0es<3>0kz\ <13>0R_ } ---------------------------------end----------------------------------------

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Re: [Fractint] FOTD 24-09-03 (Sir Fractal Galahad [7])
by Jim Muth 25 Sep '03

25 Sep '03

At 08:26 PM 9/24/03 -1000, David Jones wrote: >My wife got one informing her that our credit card had >been charged $284 for downloading child pornography, >and they needed our credit card info to reverse the >charge. . . . I received one of these child pornography letters about two weeks ago. I think it was from the same sender. It was immediately apparent that the letter was a scam. How did the sender know it was *my* card that had been charged without already having the number? And why was the letter not addressed to me personally? Also, the letter was in 'html' format, formatted to look like an advertisement. Very unconvincing for such a serious thing, yet these schemes must work or else so many people would not be trying them. BTW, I am thinking of re-posting some old FOTD's from the early days of 5 and 6 years ago to keep the lists active while I am catching up my other work. Does anyone on the list object to seeing some images and discussions that were originally posted in 1997 and 1998? Jim M.

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[Fractint] The Feigenbaum Constant and the Weak Nuclear Force etc. via Jerry
by mdoctorow＠comcast.net 25 Sep '03

25 Sep '03

>From Osher Doctorow Ph.D. Jerry Iuliano send me a new posting today by email on Brun's constant (B), the Omega-2 constant (OM) of elliptic curves, and the fine structure constant a (em). In my notation: 1) (B^12)/[100(OM^(OM))] = sqrt(1/a(em)) In his previous posting, he pointed out that the Weak Nuclear Force G(w) or Fermi-coupling charge = .000011664 is obtained from: 2) (emev/pmev)/(10F) = G(w) where F is the Feigenbaum constant and emev/pmev is the electron-proton energy ratio. He also pointed out in his previous posting that the strong force coupling constant a(s) is given by: 3) a(s) = (omega-2 ^ omega-2)/(.37)^2 if I haven't made any typos (one problem is that he omits parentheses fairly often) in multiplication-division. Since the weak nuclear force is related to radioactive decay, definitely a growth-expansion-contraction process (with the emphasis on contraction of material), while the strong nuclear force binds quarks including protons and enutrons together in opposition to the electromagnetic proton-proton repulsion, the appearance of the Feigenbaum constant is encouraging from my post on its appearance in Mandelbrot successive cardioid subcircle area ratios. The strong nuclear force turns out to be related to the electromagnetic force (both in terms of coupling constants a(s), a(em) respectively) by: 4) ((666/(omega-2^a(s)) - 1)/100 = a(em) I seem to have forgotten what the 666 represents. In any case, the fundamental forces of elementary particle physics appear to be closely related to fractal, chaos, and growth parameters. Osher Doctorow Ph.D.

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Call for FOTD fill-ins!
by Tony (Anthony) Hanmer 25 Sep '03

25 Sep '03

Greetings all, Jim Muth - sounds like you've really got your hands full for the next long while! I really apreciate your daily explorations into fractals - they've become something of a fix for me. But of course life throws the occasional fly into the ointment, beyond our control. I suggest that this may be a critical time for the Fractint forum, the expected month-long absence of FOTDs. Rather than it drying up almost entirely, how about all of the rest of us digging out OUR favourite fractals and posting them? Preferably new work, but not only. There are so many other fractal types which rarely get any action anymore. An impromptu competition? No limit to the number of entries. Here's one of mine, a variation on the famous Dragon Curve rendered as an IFS. The accompanying IFS entry must be cut and pasted into any existing .ifs file, and then the par will run. Dragon_Curve_Var01 { ; SOME good work takes a little time! ; Version 2002 Patchlevel 5 reset=2002 type=ifs ifsfile=dcs01.ifs ifs=dc022b6c passes=1 center-mag=0.370231/4.5196/0.203252 params=0 maxiter=50000 sound=off colors=KAw006<3>00800900A<9>K04M04O03<2>U01W00W00<\ 10>d00e00f00<14>u70v70w80x80z90<79>zm0zm0zn0<43>zx\ 0zy0zy0zy0zy0<68>zzz } DC022b6c {; Tony Hanmer 3/2002, Designed with Brazil: DC variation 0.3535534 0.3535534 0.3535534 0.3535534 -3.5251263 4.9362330 -0.1428571 0.4999245 -0.4999245 0.4999245 0.4999245 0.1356225 2.4994715 0.4901932 -0.4999245 -0.4999245 0.4999245 -0.4999245 4.2405285 7.4996225 0.4901932 0.001 0 0 0.5 5.586 2.284 0.0098068 0.5 0 0 0.001 -3 1.057 0.0098068 } _________________________________________________________________ Add photos to your e-mail with MSN 8. Get 2 months FREE*. http://join.msn.com/?page=features/featuredemail

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[Fractint] Deeper Signifance of Cardioids, Light, Springs, Electromagnetics
by mdoctorow＠comcast.net 24 Sep '03

24 Sep '03

>From Osher Doctorow Ph.D. Following up further on Jerry Iuliano's email (see my previous posting), we find that cardioids and their more general relatives epicycloids relate strongly to optics and curve minimization (and thereby to calculus of variations which in turn relates to general relativity and quantum gravity and many other branches of physics) via such things as caustics, diacaustics, the brachistochrone problem (most rapid travel of a point acted upon only by gravity between two different fixed points), light sources at infinity (Huygens), nephroids, etc. I will let readers who are interested look these up as keywords on the internet and simply mention that when a circle of radius b rolls around a fixed circle of radius a (without slipping), a point on the first circle traces out an epicycloid, and when a = b it traces out a cycloid. How this relates to growth and expansion-contraction could well be regarded as a fascinating open problem. I want to spend the rest of this posting dealing with a rather curious "counterexample" that seems to go against the general idea of growth equations for Rare Events, namely the electromechanical analogy. Basically, a simple system of masses or weights with springs and friction acted upon by a force (simple problems in mechanical vibrations) is completely analogous to a simple electrical system (simple circuit) with a resistor and a capacitor and inductor and source of voltage, with mass ("weight" near the Earth) corresponding to inductance L, damping or friction corresponding to resistance R, spring constant ("springiness" vs "stiffness") corresponding to 1/capacitance = 1/C, impressed force F corresponding to source of voltage E(t) that depends on time t. The equation for the circuit, with Q being electrical charge, is: 1) LDtt(Q) + RDt(Q) + (1/C)Q = E(t) were Dtt(Q) is the acceleration of charge with respect to time, Dt(Q) is the velocity or speed of charge (called the current) with respect to time. Solutions of differential equations like (1), called linear differential equations of the second order, are sums of real and complex exponentials, or in real terms simple sums of exponentials and trigonometric sine and cosine functions with possibly some simple multiplication of exponential and sine or cosine factors. Those are familiar from growth expansion-contraction problems tat I have discussed except for the trigonometric functions. If we write Dt(Q) as I, the current, then Dtt(Q) is the change of current, which we can write as Dt(I), so that if the (1/C)Q term is absent we have an equation of growth in I type. Even if the LDtt(Q) term is absent, we have an equation of growth in Q. What makes equation (1) NOT a growth equation in general is the case where all the terms are not 0 except possibly for E(t). Yet the special cases where one term or two are zero other than E(t) indicate that growth is not entirely unrelated to mechanical vibrations and electrical circuits. What relates growth to mechanical vibrations and electrical circuits at a deep level is WAVES and their simulation. In mechanics, these are Vibrations. In electricity, these are Electromagnetic Waves. Waves tend to go outward from a source, although electrical or electromagnetic circuits tend to "capture" this behavior so that they travel instead circularly or rectangularly or perpendicular to these directions. When growth is "captured", it stops being similar to expansion-contraction as my previous postings have described the latter two and instead either becomes fixed (unchanging) or keeps repeating or oscillating (up and down, etc.) although sometimes the oscillations die down if the voltage source E(t) dies down for example or alternatively is 0 to begin with. This is somewhat similar to the case when planets orbit around stars or the Sun as opposed to comets or asteroids which pass by and never return (although some do return in larger orbits). I pointed out in an earlier posting that growth-expansion-contraction is typical or radiation from a source, biology, the expansion of the universe, development of galaxies (spherical to elliptical, etc.), condensation as from water to ice or gases (water vapor) to liquids (water), consciousness- perception-human memory. But we see that although the early Universe was expanding in growth, later on parts of it became attracted in cyclical and orbiting or oscillating ways to other parts, and we call this the Matter- Dominated Era as opposed to the earlier Radiation-Dominated Era. Radiation still exists to considerable extent in the Matter-Dominated Era, but some of it is "captured" by Matter and near Matter. We see that in Black Holes including photospheres also. We see that in NASA's recent finding of heat-light-to-sound- wave conversion in the Perseus cluster of galaxies which retains instead of diffuses heat outside the cluster. Rare Events are least "oscillating" or repeating - intuitively, if they repeat exactly at fixed intervals, their probabilities could no longer be less than .05 because they are perfectly certain to occur at those intervals or points in time. One could extend probability to include rarity of occurrence even if it is deterministically predictable, but I think that would be a different type of situation and I don't deal with that in my present work. Fairly Frequent Events do, however, begin to have a closer relationship to determinstic predictability because of processes similar to such repeats or oscillations that return to their original states or positions in some way. This is an explanation of why Bayesian (Conditional) Probability-Statistics or BCP, which involves division of probabilities to indicate dependencies, has been roughly fairly successful in Mainstream Fairly Frequent Event Probability- Statistics but not in applications to Rare Events usually. Very Frequent Events, such as random bombardment by molecules on dust particles, curiously enough have an intermediate status between Rare and Fairly Frequent Events/Processes, because there is so much contact between matter and radiation that there is "over-kill" - you can never tell when something will bombard you, so to speak, and these events are called Independent. With Fairly Frequent Events, there is typically only dependence on the immediately preceding Event so to speak - Markov Chains perfectly illustrate that, and have resemblance to Independent Events in that Markov Chains depend on only one preceding Event whereas Independent Events depend on NO preceding events. Very Frequent Events depend on either ALL or INFINITELY MANY preceding events, so that while more "random" in this sense than Independent Events, they also have some more predictability than Markov Chains since more past things are being simultaneously taken into consideration. It is sometimes claimed that Markov Chains do take more than the immediately past Event into consideration, but they do that by one-step-at-a-time paths like checkers or chess or event ants touching one other ant at a time in sequence rather than being simultaneously influenced by more than the immediately past Event. So when Markov Chains are used in Very Rare Event situations, they tend to go astray. Osher Doctorow Ph.D.

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An Email From Jerry Iuliano
by mdoctorow＠comcast.net 24 Sep '03

24 Sep '03

>From Osher Doctorow Ph.D. Jerry Iuliano, whose email is JerryIuliano(a)aol.com, posted some very interesting comments to me today on the subject Omega-2 constant and TOE. Jerry is far more familiar with number theory and numerical constants than I am, and he is interested in (and has been pursuing for a long time) both a unified theory of fundamental forces in physics and Fermat's Last Theorem. At a number of points in my theorizing when I have touched on matters related to numerical constants of considerable importance, Jerry has emailed me with extremely valuable ideas, some of which I have pursued and some of which I wished that I had. As a Non-Mainstreamer myself for a long time, I can say with little doubt that Jerry is even more Non-Mainstream than I am in his particular fields - he isn't embarrassed at pointing out Ancient Egyptian and Biblical references to or occurrences of various number constants, while I tend to look over my shoulder in embarrassment at those points at least when discussing them on scientific-mathematical forums. Jerry's posting concerned the Omega-2 and Omega-One Constants and Transformations, but he mentioned their tie-in with Weierstrass Elliptic Functions which are involved in Fermat's Last Theorem's proof and which in turn tie in with Fibonacci numbers which are of considerable interest in plant growth and other contexts. I looked up Jerry's references to Wolfram and Eric Weisstein's World of Mathematics, and reviewed some characteristics of the Weierstrass Elliptic Function that now take on a new significance for me at least. Letting r(z) be the Weierstrass Elliptic Function in my terminology, one of the most remarkable equations is: 1) r'^2(z) = 4r^3(z) - g2r(z) - g3 where g2 and g3 are elliptic invariants which, in the equianharmonic case, are respectively 0 and 1. Readers will recognize the growth equations in (1) except that with r' as dr/dz, r'^2(z) is used instead of r'(z) as in typical growth equations and the cube of r is one degree higher than in most growth equations for the relevant function taking the place of r. The Weierstrass elliptic curve modular form is equivalent to the "golden number" of ellptic modular forms, this number being the Omega-One constant which is (1/2)w2(1 + isqrt(3)) where w2 is called the Omega-Two constant defined by the value 1.529954037... according to Jerry. If we follow up the Golden Mean or Golden Ratio Phi, for example in the Eric Weisstein source mentioned, it turns out to be the limit lim Fn/Fn-1 of successive Fibonacci numbers as n --> infinity, but the latter ratio Fn/Fn-1 also measures fractions of turns between succesive leaves on stalks of various plants in botany. Fn itself turns out to be of considerable interest in biological growth - for example, it is the number of pairs of rabbits n months after a single pair begins breeding if newly born bunnies are assumed to start breeding when 2 months old. Phi turns out to be the most irrational number because of its continued fraction representation entirely by ones. Osher Doctorow Ph.D.

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I'm back online -- FOTD coming soon
by Jim Muth 23 Sep '03

23 Sep '03

There is good news and bad news from F.C. The good news is that the power is back on and Fractal central survived the hurricane with nothing more than the expected power failure. The FOTD for September 24 will appear in a few hours. The bad news is that the work has fallen so far behind that I will need to suspend further FOTD's until I get caught up. More details in the upcoming FOTD. Jim M.

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[Fractint] Is the Cardioid-like Heart Surface related to Big Bangs and Black Holes?
by mdoctorow＠comcast.net 23 Sep '03

23 Sep '03

>From Osher Doctorow The 3-dimensional generalization of a cardioid is something like G. Taubin's (IBM Thomas J. Watson Center, Yorktown Heights, N.Y.) Heart Surface in his "An accurate algorithm for rasterizing algebraic curves and surfaces," IEEE Graphics Appl. 14, 14-23, 1994. Rasterizing is representing or converting graphical information into or with pixels. The equation of the Heart Surface, which looks like a 3-dimensional cardioid with a cusplike part of the surface on top (in the positive z direction), is the sextic equation: 1) [x^2 + ((3/2)y)^2 + z^2 - 1]^3 - x^2 z^3 - [(3/2)y]^2 z^3/20 = 0 If we use spherical coordinates after changing (3/2)y to a new y coordinate which could be labelled y' (not the derivative of y!), we get an expression for Dz(rho) where rho is the spherical radius coordinate whose square is x^2 + y'^2 + z^2 which resembles the last derivative for the cardioid in the previous posting. In other words, Dz(rho) is an expression with (rho - 1)^2 in the denominator. Mathematical physicists are immediately reminded of a black hole singularity in this context, especially with a chaotic Heart Surface. Although there were various theoretical reasons for various quantum theorists to consider that the Big Bang was not exactly a black hole, quantum theorists have not exactly kept up with analysis of Existence and Change in their own field, and if we add the fact that a similarity to a black hole doesn't imply that something is exactly a black hole, there is plenty of room for theorizing. A Big Bang and a Singularity are rather odd events even for Growth Events/Processes. Most Growth is not Big Bang type or Singularity type, and the fact that division is involved for cardioids and Heart Surfaces suggests that a major split has occurred between additive-subtractive Growth as in exponential and logistic and Riccati differential equations, on the one hand and chaotic-related Mandelbrot and Heart Surface growth with division, on the other hand. This division corresponds to a division between Rare Events and Fairly Frequent Events - Rare Events involve additive-subtractive Growth, Fairly Frequent Events involve division-multiplication in or out of Growth although division is primary. Very Frequent Events appear to be on the borderline between Rare and Fairly Frequent Events with regard to Growth. If you follow most of my postings to various cited places over the past few years, including some publications, you'll probably understand this most rapidly. Also look at researchmathematics(a)yahogroups.com. (Some of my postings have a remarkable tendency to disappear after several years - for example, I posted to anzap-l (an applied probability forum/mailing list in New Zealand-Australia) for several years, only to have the list owner close down the list with the rather cryptic remark which in essence amounted to the list not going in the directed that he had wanted (whatever that was - I'm still not clear about it). Superstringtheory.com is currently closed in the main forum on Strings/M Theory- Duality to which I had posted for quite a long time, apparently due to a deliberate virus by somebody.) Speaking of viruses, there is an indication that Rare Event Growth, which is the most important type of Growth except possibly for Singularities, is more Lifelike than Deathlike or Virus-like. A good model for Rare Event Change and Existence, in other words, is certain lifelike processes and events such as Knowledge (or Knowledge-Information), Perception, Memory, Consciousness. The other types of Change and Existence appear to bring in the Deathlike or Virus- like or Singularity-like regimes, and to be associated with events whose probabilities are greater than .05. The intuitive concept of an "over- bombarded" Existence with higher frequency Events/Processes in central to this. It isn't Knowledge that is the culprit at least in its simple expressions, but more like Complication and perhaps even Imitation and Mediocrity. Are Fractals and Chaos then signs of the breakdown of "beneficial" Change and Existence? We always assumed that Chaos at least involves the breakdown of predictability, but I emphasized the difference between Knowledge as Semantics or Meaning and "Information" as Syntactics or Form of messages. In some sense, becoming less predictable increases Information and Entropy but decreases Knowledge as Semantics or Meaning. To understand the Meaning of something is closely related to our ability to predict something. Rare Events seem to increase in Knowledge, whereas more common Events seem to increase in Entropy and Information. So in a deep sense, Existence and Change near the Big Bang involved a clash between Meaning and Form. The Mandelbrot and Julia sets demarcate the boundaries between the two pairs of clashing tendencies, Meaning vs Form, Existence vs Change. Existence and Change seem to be more compatible in Growth than Meaning and Form, Semantics and Syntactics. Osher Doctorow Ph.D.

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Mandelbroat Set Chaotic Existence 2
by mdoctorow＠comcast.net 22 Sep '03

22 Sep '03

>From Osher Doctorow Ph.D. >From r = a(1 - cos(u)), we get alternatively to the last posting: 1) dr/du = asin(u) Since sin^2(u) = 1 - cos^(u) and from the first equation cos(u) = 1 - r/a, we get: 2) dr/du = asin(u) = sqrt(1 - (1 - r/a)^2) when we're in the first and third quadrants, and the minus sign goes in front of sqrt in the second and fourth quadrants. Since discontinuities occur for simple real-valued functions mainly of types y = 1/(polynomial function of x), y = log(x), and y = sqrt(x) at x = 0 or x = root of polynomial (x = 0 for polynomial = x, etc.), we see that the discontinuity in the Mandelbroit Cardioids of the previous posting are not simply "removable singularities" or irrelevant as they might be considered in complex analysis, quite important. The Mandelbroit Cardioids are characterized in terms of Existence among the various types of Existence discussed by infinities or discontinuities - not at all points, but at some points (often only one). Osher Doctorow Ph.D.

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Re: Centre de Gravité
by JackOTradez 22 Sep '03

22 Sep '03

Some good info on this at: http://www.mrob.com/pub/muency/centerofgravity.html Check it out. Nice site too, lotsa math and stuff. JoTz

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Mandelbrot Set Growth and Existence via Cardioids
by mdoctorow＠comcast.net 22 Sep '03

22 Sep '03

>From Osher Doctorow Ph.D. The Mandelbrot Set from a computational viewpoint involves following orbits of 0 like 0, c, c^2 + c, (c^2 + c)^2, ..., where c is a complex number of form c1 + ic2 where i = sqrt(-1) and only those c orbits which never exceed 2 in modulus or absolute value are in the Mandelbrot set. However, the Mandelbrot set is from another viewpoint a bunch of cardioids that are smaller and smaller, where a cardoid is a heart-shaped object which looks like a circle but has a sharp bend on "top" (or on its side depending on whether it is sideways) where the heart bends inward. The equation of a cardioid is simplest in polar coordinates, where any of the Mandelbrot cardioids in particular have equations of form: 1) r = a(1 - cos(u)) where r is the distance from the origin to the cardioid (the radius or length of radial vector) and u is the angle that r makes with the positive x axis or "pole". The pair (r, u), often written (r, theta) where theta looks like a zero with a horizontal slash through its center, is called the polar coordinates of a point on the cardioid, and there is also a Cartesian or rectangular coordinates given by: 2) (x, y) = (rcos(u), rsin(u)) Let's multiply both sides of (1) by r, obtaining: 3) r^2 = ar - arcos(u) It is always the case that r^2 = x^2 + y^2 and rcos(u) = x, so we can write this as: 4) r^2 = ar - ax Let's calculate the partial derivative of r with respect to x, Dx(r), with u held constant. Actually, there is no explicit u in (4), but just in case we use the notation Dx(r) which is the "derivative of r with respect to x holding u constant". Those who are familiar with calculus can follow the following derivation, while others can just accept the final result below. We get (by implicit differentiation): 5) 2rDx(r) = aDx(r) - a and algebraically this gives us the final result: 6) Dx(r) = a/(a - 2r) Although this is not one of the usual growth equations dy/dt = ky, dy/dt = ky (1 - y), dy/dz = f(z) + g(z)y + h(z)y^2, it has the form dy/dz = a/(a - 2y) if u is held constant. By comparison with the other equations, it is recognizable as a somewhat rarer type of Growth Equation. If we had 2r = a or r = a/2, the denominator of (6) would be 0, which is not allowed in mathematics, but which would signify infinitely large value of Dx(r). Thus, the Mandelbrot set's cardioid(s) are the first growth equations which we have examined which are potentially "explosive" in a sense. Of course, the presence of z^2 in the orbits is another clue, as is the fact that replacing r^2 by x^2 + y^2 in (4) results in: 7) x^2 + y^2 = ar - ax which can be used to solve for r as a quadratic or bilinear/affine polynomial in x and y. The type of Existence expressed by the right-hand-side of (6) can be distinguished from ordinary Geometric Existence by referring to it as Potentially Infinite/Explosive Geometric Existence, or more simply by Chaotic- Fractal Existence or an example of the latter. Osher Doctorow Ph.D.

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FOTD 13-09-03 (Elephant Spiral [7])
by Jim Muth 21 Sep '03

21 Sep '03

FOTD -- September 13, 2003 (Rating 7) Fractal visionaries and enthusiasts: Today we recreate the same parent Julibrot that held yesterday's image, but we slice it at one of its other two critical points. This point is entered as the real(p5) parameter. The Mandeloid that this point draws is shaped quite like the parent Mandeloid of yesterday's image, with the exception that, unlike yester- day's parent, today's has an East Valley. Today's image is located on the south shore of the East Valley of its parent, in a cut-off island located quite deep in an elephant-trunk spiral. The image consists of cut-off combina- tions of elephant-like features and spirals. These features inspired the name. Something about the image pleases me. Maybe the image is not as pretentious as some of my FOTD images, maybe it gives a stronger impression of being a real object, but whatever he reason, I have rated it at an above-average 7. The rating of 7 makes the slow render time of 54 minutes less extravagant. But those who would rather have no extravagance at all in their fractals may see the image by downloading it from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The rain set in just after noon here at Fractal Central on Friday, and the temperature reached only a chilly 64F 18C. The cats managed an hour or so of outdoor time before the rain began, so they were not too irate when they were forced onto the porch and then indoors. When they came inside, a tuna treat kept them happy. But it's raining again this morning, and due to continue almost all day. How will the dynamic duo adjust? Check back in 24 hours to see. Until then, take care, and those with fractals in their days live longer and happier lives. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Elephant_Spiral { ; time=0:54:36.47--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix3a function=ident passes=1 center-mag=+1.19654217940102500/-0.000107572576658\ 21/2.017302e+012/0.9999/-165.009901528464155/0.001\ 66372648813901958 params=-1/2/0.5/4/0.25/6/0.125/8\ /-0.78036013139/0 float=y maxiter=3600 inside=0 logmap=656 periodicity=10 mathtolerance=/1 colors=000lWAkY6j_9iaBhcDgeFfgHeiJdkLcmNbpPaqR`rT_\ sVZtXZuZVq_Sn_Pk_Mh_Id_Fa_CZ_9W_HYaO_cW`dbbfjcgqei\ xfjbhpIjvRplZubXr`Wp_UnZTlYRjWQhVPfUNdTMbRK`QJZPIX\ OHZMG_LFaKEbJDdICeHBgFAhE9jD8kC7mB6nABjDGfGKbIPZLT\ VNVWOWXOXYPYZP__Q``QaaQbbRdcRedSfeSgcSabQWYOQTMLPL\ FLJ9HH4DG4AI47J59I6AH7BG8CF8DE9EDAFCKGBPHB0U2eZidc\ cdhZckUcmPamS_mUZmWXmYWo_UqaTscRsePrhOqjMplLpnJopI\ nrKmtPhvUhVZjUcZThOSmCRn1Qm3Tm4Wl5Zl6ak7dk8gj9ijAl\ iBoiCrhDuhExhFzgDugCpgBkgAgg9bg8Yg7Ug6Pg5Kg4GcAH_F\ IWKJSPJOUKKZLGcMChMBgNBfOBeOBdPBcPBbQBaRB`RB_SBZSB\ YTBXUBWUBVVBVVETTHSSJRRMQQOPPROOTNMWMLYLK`KJbJIeIH\ gHGcIH`IIYIIUIJRIJOIKLIKHILEILBIM8IMGKJOMGWODcQBkS\ 8sU5zW3wY2rZ2o_2na2mb2lc1ke1jf1ig1hh1tjSqiRniQkiPh\ iOeiNbhM_hLXhKUhJRhIOgHLgGIgFFgEDgEMiEVkEcmEloEhpD\ dpCaqCYqBVqBRrAOrAKs9Hs9Ds8At8Fu7Kv7Pw8Ux8Zy8cz9hz\ 9mz9rz9wzAzzAzzAzzOzzJzzF } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 09-09-03 (Smokey-Joe Midget [6])
by Jim Muth 21 Sep '03

21 Sep '03

FOTD -- September 09, 2003 (Rating 6) Fractal visionaries and enthusiasts: Long ago, there was a coal-burning ferry that plied the Chesapeake Bay, ferrying cars from Baltimore on the western shore to Love Point on the eastern shore. The boat was named 'Smokey Joe' because its whereabouts could always be determined by the plume of smoke that constantly rose from its smokestack. The ferry was in operation many years, but went out of service when the bridge across the bay opened. I came on the scene too late to ride the ferry, but my father often told of the times he had ridden it on his way to a special fishing spot, the location of which he never made clear. He described how the plume of smoke from its stack could be seen coming long before the boat itself became visible. I never saw the boat in operation, but in my imagination I often tried to picture the smoky ferry moving across the water, trailing its smoke behind it. For some reason, today's image reminds me of the plume of smoke that I never saw in person. The image is named "Smokey-Joe Midget" in honor of that never- seen but much-imagined ferry. The formula combines Z^(-8.8) with 8 times as much Z^(-0.88) and adds (1/C) instead of C. The resulting parent fractal is one of those indescribable things that result when two negative powers of Z are mixed -- a fractal with more valleys than a penguin has feathers. Today's scene is located at the point where one of these valleys splits into two separate valleys. The basic scene with outside=iter was acceptable enough, but I tried the other outside fills before deciding to evaporate the entire scene. None of the other outside options made an image that was worth the effort. Then I evaporated the scene by raising the escape radius to one-googol, and applied the various inside options to the blank screen that resulted. The 'bof61' option worked best, so that's the one I used. The end result rates a 6 -- not outstanding, but at least a little above average. The render time of 8-3/4 minutes is acceptable, but the image may be seen far more quickly by downloading it, already rendered, from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Monday ended in a satisfactory manner here at Fractal Central, with contented cats and up-to-date work. True, the clouds thickened as the afternoon progressed, but no rain fell, and the temperature of 79F 26C kept things comfortable for the cats. Today is starting the same as yesterday. I hope for another good day. Until 24 hours from now, when the next FOTD appears, take care, and don't get spammed. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Smokey-Joe_Midget { ; time=0:08:46.90--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+2.52482220888604100/-0.244198577126244\ 40/794648.8/1/-5/-9.42602412651316612e-008 params=1/-8.800000000000001/8/-0.88/-0.93/1e+100 float=y maxiter=750 inside=bof61 periodicity=10 colors=000i6si6sg7rg7pf7oi6pf7oc9m`AlYCjXCjTDiQFgO\ GfMGfJIdGJcDLaAM`9M`6O_3PY0QX0QX0SV0TT0VS0XQ0VS0VS\ 0VT0VT0VV0VV0VX0VX0VY1VY3V_4V_6V_7V`9V`AVaCVaDVcFV\ cGVdIVdJVfLVfMVfOTgPTgQTiSTiTTjVTjXTlYTl_Tm`TmaToc\ TodTofTpgTpiTrjTrlTsmTsoTupTurTvsTvuTvvXsvYpv_mv`j\ vaivcfvdcvf`vgYviXvjTvlQvmOvoLvpJvrGvsDvuAvv9po6lg\ 3g`0cT0_O0VG0Q90M10I00G00G00F10F40F60D70D91CC3CD6C\ F7AGAAJC9LF9MG9OICPLDQOFSQGTTITXJV_LXaMYcOYfP_iQ`l\ SaoTcrVcuXdvYfy_gz`gzaizchzdlzZjzcizagz`fz_dvYarX`\ mT_iSYdQX`PTVOSQMQMJPIIMDGL9FJ4DI0CG0PDDaCToAjz9zy\ CzvDzsFzpGzmJzjLzgMzdOzaPz_SzXTzTVzQXzOYzL`zIazFcz\ CdzAfzOdm`cYmaIz`1z`0zc0zf0zi0zl0yo0vr0ss0pv0my0jz\ 0gz0dz1cz1jzIrzXyzlzzzzzvzzsyvoxplujisddp_aoTYlOVj\ ISiGTgFTfDVdCVcAXa9X`7Y_6YY4_X4_V3`T1`S0aQ0aP0cO0c\ M0dL0dJ0fJ0fP0gLYCVVGcTLlQPuPTv0zu0zs0zs0zr1zr1zp1\ zp3zo3zo3zm3yl4xl4xj4vj6u } 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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Existence, Change, and Mandelbrot Set Area
by mdoctorow＠comcast.net 21 Sep '03

21 Sep '03

>From Osher Doctorow Ph.D. mdoctorow(a)comcast.net I posted yesterday to geometry-research in the Math Forum (which can be accessed by keywords Math Forum or geometry-research or geometry- research(a)forum.swarthmore.edu) the posting "Geometric Existence" which basically strongly indicates that for growth-expansion-contraction processes and events, including optimally controlled processes and events, Geometric Existence is the Inverse or Opposite (in a certain sense) of Geometric Change. This explains the exponential bacteria growth and radioactive decay equations, the logistic population growth equation in a limited-supply environment, and the Riccati optimal controlled growth equations, and much more. For those who know Calculus (not required to roughly understand these things) or Differential Equations (similarly), Geometric Change is the Derivative, while Geometric Existence is the Integral, under growth scenarios. For those who don't know Calculus, it turns out that lengths, areas, and volumes are direct expressions of Geometric Existence under growth situations. Hence, the area of the Mandelbrot Set becomes of critical importance. Robert P. Munafo, 2000 Aug 31 in "Center of Gravity, Mu-Ency at MROB," www.mrob.com/pub/muency/centerofgravity.html, also stated to be from Munafo's Mandelbrot Set Glossary and Encyclopedia, 1987-2003, points out that the Center of Gravity of the Mandelbrot Set is obtained similarly to calculating the area of the Mandelbrot Set, and is very closely approximated by: 1) (ln(3) - 1/3)^Feig1 where Feig1 is the first Feigenbaum constant, equal to .28676 82633 82935 02685 29586... However, the first Feigenbaum constant is the (limiting) ratio between the areas of each circular region (main regions in a sense) and the next smaller one in moving to the left from the origin in the Mandelbrot set. Although it may be premature of conclude that we understand this, it seems as though Geometric Existence is central to Chaos and thereby to Fractals. I would guess that the Universe in its formation was on the borderline of Chaos if not in Chaos, and that this was an expression of the nature of its early Geometric Existence and also Geometric Change (expansion, etc.). Osher Doctorow Ph.D.

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Re: [Fractint] [Fwd: Undelivered Mail Returned to Sender]
by Jim Muth 20 Sep '03

20 Sep '03

At 11:23 PM 9/17/03 -0700, Kevin Sexton wrote: >hmm why would I get this, after my message went through? >Return-Path: <MAILER-DAEMON(a)arkion.es> <rest of bounced letter snipped> It's a mystery. I've been getting similar returns for about 2 weeks. It rather looks like one of the list addresses is no longer valid and the mail is bouncing back to the individual senders rather than the list itself. Jim (now watch this bounce back) Muth

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[Fractint] Growth Equations from Lorentz Contraction of Special Relativity
by mdoctorow＠comcast.net 18 Sep '03

18 Sep '03

>From Osher Doctorow Ph.D. The gamma or beta factor of Special Relativity or its inverse is given by: 1) b = sqrt(1 - v^2/c^2) Since 1 = 1^2, this motivates the idea of an ellipse via: 2) (r/ro)^2 = (definition) b^2 = 1 - v^2/c^2 which is the ellipse: 3) r^2/ro^2 + v^2/c^2 = 1 The simplest differential equation which can be derived from this is obtained by setting: 4) v^2 = 1 +/- d(r^2)/dt The positive sign results in the solution: 5) r^2 = exp(k1)exp(-t/ro^2) where k1 is the constant of integration. The negative sign results in the solution: 6) r^2 = exp(k1)exp(t/ro^2) Thus, we obtain either exponential growth/expansion or exponential contraction with time. Since v is more or less unrestricted, r could be related to a macroscopic or microscopic radius or length including a principal radius of the Universe. Interestingly, (6) appears to permit acceleration of the Universe by implicit differentiation, although it doesn't require it. Osher Doctorow Ph.D.

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FOTD 18-09-03 (Image of Staghorns [5])
by Jim Muth 18 Sep '03

18 Sep '03

FOTD -- September 18, 2003 (Rating 5) Fractal visionaries and enthusiasts: I have very little time for a fractal discussion today. I want to get as far ahead as possible in my regular work in case a power failure happens. Power failures are the one predicted thing that usually does happen here at F.C. when the weather acts up. As for that weather, it is not looking too bad. We can survive 35 to 40mph winds with gusts over 50mph (80kph), and 3 inches (7.5cm) of rain. The threat of tornadoes has been removed from the local forecast, though it still exists for areas well south and east of here. For today's image I turned to the manzpower formula and the Mandeloid that results when the formula Z^(2.002)+C is iterated. I went to the area just east of the largest midget and examined the rail-like chaos that lies between the two main branches of the negative stem, which has split into fragments. Midgets are very numerous in this area, though they all look pretty much the same. I named today's image "Image of Staghorns". At one time, the image reminded me of staghorns, or stagantlers, (but 'horns' sounds better). I can no longer see much of a resemblance, but the name remains. Since the image is a routine one, found and colored with almost no effort, I could rate it only a 5. But it is very fast, and worth the two minutes required to render it from the parameter file. Those who would rather not render may download the finished GIF image from the internet at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Perfect weather here at Fractal Central once again produced perfect cats on Wednesday. Sunny skies, light winds, and a temperature of 79F 26C kept them so happy that their customary evening treat of tuna was not needed. Today however is starting far more threatening, with leaden skies, winds already picking up, and a tropical storm on the way. To see how the dynamic duo pulls through the mini-tempest, check back here tomorrow. As for me, I have finished all the preparations I am going to make, which involved 5-minutes of work to take in the lawn furniture. So until next time, take care, and I see no cause for alarm. (Of course, I could always be wrong.) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Image_of_Staghorns { ; time=0:02:07.65--SF5 on a P200 reset=2002 type=manzpower passes=1 center-mag=-1.6\ 71974101237228/+0.00065516117700869/700556.1/1/-87\ .5/2.35157879280301074e-010 params=0/0/2.002/0 float=y maxiter=600 bailout=9 inside=0 logmap=49 periodicity=10 colors=00078S8AV8BX8D_9Ea9Gd9IgAJiA\ LlAMnBOqBPsBRvBSxBLlBEaB7RB1GI2OP2WW3cb3ki3rj6nj9j\ jCgjEcjH_jKXjMTkPPkSMkVIkXEk_Bkb7kd4ohErkOunYxqfwr\ fwsfvsfvtfvufuufuvfuwftwftxftyfsyfszfszftwctuats_t\ qXtoVtlTtjQthOtfMtdKrfJqhJpjIolImnHlpHkrGjtGhiEgZD\ fOCeDBd2A`ELXPVU_dT`fT`gT`hS`iSajSalRamRanRboQbpQb\ rQbsPctPcuPcvPcwNcvLcvKcvIcuGcuFcuDctBctAct8cs6cs5\ cs6`t7Zt8Xt9VtASuBQuCOuDMuEKuFHvGFvHDvIBvJ9vL8uM7t\ N7tO6sP6sQ5rS4qT4qU3pV3pW2oX2ogISqX4rU3sS2tP2uM1uK\ 1rO6oSAlVEjZIgaMdeQahU_lYXoaUseSviUuhWthYsg_rg`qfb\ pfdpefoehndimdkmcmmcombpmblm`im_fmZcmY`mXXmWUmVRmU\ OmSLmRHmQEmPBmO8mN5mM2mLDmLNmLYmLgmLqmLomOmmRkmTim\ WgmYen`dobbpe`qhZrjXsmVtoTurSvthwnxxhuydrzapzZmzVk\ zShzPezLczI`zFZzCXzEVzGTzIRzKPzMUzQZzUczYhzamzerzi\ wzmrzinzeizaezY`zUXzQTzMdzCpz2MzrJzjGzbEzVBzN8zF6z\ 78zB9zEAzHCzKDzNEzQGzTHzWIzZKzaLzdMzg7zQ } END PARAMETER FILE=========================================

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[Fwd: Undelivered Mail Returned to Sender]
by Kevin Sexton 18 Sep '03

18 Sep '03

hmm why would I get this, after my message went through?

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A Mandelbrot-Feigenbaum-Similarity Insight Into Growth
by mdoctorow＠comcast.net 18 Sep '03

18 Sep '03

>From Osher Doctorow Ph.D. We are coming to a rather curious juncture in fractals and chaos research related to interdisciplinary growth processes. The good news is that we are making headway into interdisciplinary equations (logistic types especially), into dimensional analysis and its generalization Lie groups of point transformations and dimensionless ratios related to growth involving radiation (which expands from a source) and logistic and even exponential growth constants, and we are pushing our way into different phases including a more and more plausible superluminal phase. The bad news is that we still don't have a handle on growth in respect to expansion-contraction. One possible solution is to change our focus from expansion to contraction in an effort to understand similarity (e.g., self-similarity). Fractals have this tendency to create similar but smaller geometric objects on smaller and smaller scales, but it is difficult to find an equation form of this because of the difficulty of nth iterations or recursions or compositions. However, in geometry similar objects tend to have constant ratios at least in pairs of similar objects. The difficulty occurs in the fact that in a long sequence of similar objects, the ratios of sizes may changed for one constant to a different one and on and on. The Mandelbrot set give us a remarkable clue. It turns out that the sequence of disks as we proceed along the main direction of the Mandelbrot set (along the negative real axis from the origin) approaches a constant in their ratios of diameters, the Feigenbaum number, approximately 4.669 or 4.669201660910.... In mathematical language, with dn the diameter of the nthdisk (n = 1, 2, 3, ...), we have: 1) lim dn-1/dn = 4.669 approximately where the limit is as n approaches infinity (increases without bound). We can obtain a rate of contraction roughly analogous to the rates of expansion that we've been discussing logistically. This would be approximated by: 2) rate of contraction = lim (dn+1 - dn)/(dn+1) = lim (dn+1 - dn+1/4.7)/dn+1 = 1 - 1/4.7 where the Feigenbaum number 4.669 has been rounded off to approximately 4.7 Osher Doctorow Ph.D.

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Re: [Fractint] FOTD 16-09-03 (FMOD Mandeloid [5])
by Jim Muth 18 Sep '03

18 Sep '03

At 09:53 PM 9/16/03 -0700, John Wilson wrote: >Ah, now I understand! Jim, what you call a basement, >(which is perennially full of water), we other folk >call "a WELL"! > >John W. It was a paradoxical situation, being located 50 feet below the top of a 250-foot hill and having a wet basement. Fortunately, the problem has been solved for over a year. The culprit was, and probably still is, a partially blocked basement drain pipe. Normally, the pipe worked as it should and drained away any water that happened to get onto the floor. But in very heavy rain, the drain backed up into the basement, sometimes leaving 4 inches of water. I solved the problem by driving a wooden plug into the drain. I have no idea where the backed-up water goes nowadays. It's not my problem. BTW, the hurricane watch for the local area has just been changed to a storm watch, so the fractals should continue uninterrupted. Jim M.

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FOTD 17-09-03 (A Sparkling Midget [6])
by Jim Muth 17 Sep '03

17 Sep '03

FOTD -- September 17, 2003 (Rating 6) Fractal visionaries and enthusiasts: This morning at Fractal Central features a plethora of junk e-mail and media hype. One of the junk e-mails actually had a subject line that got me to open it. The line was 'you left your umbrella'. Since I recently lost an umbrella, I thought the letter was from some good samaritan who had found it and wanted to return it. I never stopped to wonder how the sender had known not only the person who had left the 4-dollar umbrella, but his e-mail address as well. When I opened the e-mail, I saw the usual gibberish that results when an html document is opened in text mode. I have yet to fathom what a lost umbrella has to do with selling a low-interest loan. Then there is the current local weather forecast, which has a hurricane watch in effect for Thursday and calls for winds of 35-40mph. Hurricane winds start at 75mph. I could see a storm warning, but a hurricane watch . . .? I guess a hurricane situation is remotely possible. The local TV outlets have of course gone into overdrive. By Friday morning, when the storm has just passed its mini-peak, they will probably be frantically searching for a fallen tree and showing rain water flowing down the gutters. So much for the local nonsense. Today's image was created by combining decreasing portions of Z^2, Z^3, Z^4 and Z^5. The resulting Julibrot figure was then sliced at a minor critical point, which drew a tiny Mandelbrot set located well off to the west of the default screen. This M-set is rotated 180 degrees and is surrounded by tiny dots, each of which contains a universe of M-sets. These M-sets are unusual in that they have basically no patterns around them, but are surrounded instead by flat iteration bands containing sparse clouds of star-like points. I have named today's image "A Sparkling Midget" because it is surrounded by little other than widely scattered stars. The coloring was done using the usual equal-iteration bands method. The other outside coloring options give more detail to the image. In fact, some of them give too much detail, but I wanted to show the basic star-like blandness of today's scene, so I chose the standard outside=iter option. The image rates a 6, which is not bad for such a bland picture. It renders in 3 minutes, which is even better. Best of all, it downloads in one minute or so from . . . <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather remained perfect throughout the day here at Fractal Central on Tuesday. Not a single cloud was seen all day, the wind was light, and the temperature reached 77F 25C. The dynamic fractal cats made the most of the perfection by spending several hours in the yard. At the end of the day, no tuna was needed. Today is starting perfect once again, but that hurricane is still lurking in the vicinity. Stay tuned to see what develops in the next few days. Until tomorrow's FOTD, take care, and try to be at ease when nature misbehaves. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Sparkling_Midget { ; time=0:03:19.93--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix3a function=ident passes=1 center-mag=-16.27242179554596000/-0.06293582629549\ 968/4.17399e+010/1/25/-0.000463342159198340542 params=1/2/-0.67/3/0.33/4/0.17/5/-2.73312824662175\ /0 float=y maxiter=255 inside=0 periodicity=10 colors=000clsaot`sn_viF5oH4iJ3cL2YN1SO0MS8RWFV_MZb\ Tbf`gjgknnoqus4REAVIFYML`QQcUWgY`jafmekphdijYckRYl\ LSmEMn7Go1Ap5Dj96MCCPGJPKMONOMRRMVUPYYSa`VedYki`rp\ czzemsfllfkggjagicghWhg_hf0hvJRfw0Cq6GkBKjGOiLShQW\ gVZf_U6AW4SY3hdJTzYEyXGeWIbVJ`ULYTMVSOTRPTKRTDTT6V\ T0Wa4ci7kqAroDswGzmJulMugWvcdvZmvVvvNloGbi9Tc2JYUM\ KtP7jV8``8Rf9Hl97r9JlIVfRf`_qWgWUoBSwARm9Qd8PW7ON6\ NE6N5CRDIVLOYTM`RLbPKdNJfLIhJHjHGlFFnEOcJWTNcISk8W\ fIKbS9SXDI`HKaMLaRNaWOa`_U`kN`wG`uKcsNeqQgoTimWkkZ\ mjaoacgTe`KgTBiM2kF5lJ7lN9mRBmVDnZFnbIm`Ll_OkZRjXU\ iWXhVZhUWdRUaPRZMPWKMSIKPFHMDFJBKIGPILTIPYIUbIZfIb\ cGZ`FWYDSVCPUEVTF`SGfRHkZKYfNKnQ7jUCgXHc_M`cRXfWUi\ `RldtNZsQ`rSbqUcpWeoYfL0rJ9sIItGRuF_uDhvCqwBywGvuK\ ssOpqSmoWjm_gkcdieefgfdigakh_lhY`WOPJFTOMXTT_YZcbe\ ggljlrimqinqhnphopgpogpoemidkcbhYafT_cNZaHXZBWX6WW\ 7WW7WW7WW8WW8WW8WW9WW9WW9 } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] FTOD cd question
by RENRAD1＠aol.com 17 Sep '03

17 Sep '03

In a message dated 9/16/03 9:43:45 PM Pacific Daylight Time, jamth(a)mindspring.com writes: << As soon as I organize the files, the CD will be ready to go, but from the way things are going, I cannot say when that will be. Jim M. >> Great!! I'm very happy not to have simply missed it; this was never intended to "jog your elbow" but just a check to see if I had let it slip by me. Thank you for your quick reply! I learn something every time I get the chance to fall into the FOTDs for a bit, thank you for persevering in the explorations and publishing them Cheers, pete (renrad1)

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Re: [Fractint] FOTD 16-09-03 (FMOD Mandeloid [5])
by Jim Muth 17 Sep '03

17 Sep '03

At 07:14 PM 9/16/03 +0100, John Lewis wrote: >I suppose that if the media are over-zealous like >this, it stops them getting sued! Or else, if some >one sues them because the disaster has not happened, >it will be cheaper. True. And the over-zealous reporting also increases ratings. >I hope you and your family (including the cats) will >be alright. I think we will be. The current forecast is for winds of 40-60mph, which should do no more than scattered damage that is not too severe. We are near the top of a hill, so flooding should not be a problem. Jim M.

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Re: [Fractint] FTOD cd question
by Jim Muth 17 Sep '03

17 Sep '03

At 07:56 PM 9/16/03 EDT, Renrad wrote: >Hallo, Listers, >i miss so many of the emails that i'm afraid i may >have missed something about the status of the >Fractal of the Day cd that was in progress. Is that >still in the works? You have not missed the CD. It is still 'in the works'. The delay is because I have been very busy lately with my regular work and the ongoing FOTD. The problem is that the almost 2000 images are not connected to their discussions and even I have forgotten some of the cryptic 8-letter DOS names I gave to the image files. As soon as I organize the files, the CD will be ready to go, but from the way things are going, I cannot say when that will be. Jim M.

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FTOD cd question
by RENRAD1＠aol.com 16 Sep '03

16 Sep '03

Hallo, Listers, i miss so many of the emails that i'm afraid i may have missed something about the status of the Fractal of the Day cd that was in progress. Is that still in the works? thank you for your time, ~ren

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FOTD 16-09-03 (FMOD Mandeloid [5])
by Jim Muth 16 Sep '03

16 Sep '03

FOTD -- September 16, 2003 (Rating 5) Fractal visionaries and enthusiasts: Well, here we go again. Thanks to the over-zealous media, the local area is near a state of panic about the catastrophic hurricane that is supposedly headed directly this way and due to strike Thursday or Friday. Both the Maryland and Baltimore emergency centers have been activated. The local stores are totally sold out of batteries as people buy 20 and 30 at a time to keep their flashlights lit during the week without power that is probably not coming. Panicky residents are emptying the home-supply stores of plywood to board up their windows against the hurricane winds that are probably not coming. Canned goods and toilet tissue are flying off the grocery store shelves, but I am doing little but watching. I have seen these false alarms often enough to feel reasonably certain that we will have no hurricane and very possibly not even a storm. But the devilish side of me still takes wicked delight in seeing the weather people, TV news people, emergency officials, and the general public make fools of themselves preparing for something that will not happen. One of these days I may be wrong, one of these days I may be sorry that I did not prepare, but in over 40 years that day has yet to arrive, and I have saved probably thousands of dollars. (BTW, I do not recommend my reckless approach to others.) Being involved with the media hype, I spent little time in fractal land yesterday, but I did manage to find a fractal in the figure that results when negative portions of Z and Z^3 are combined. This parent fractal resembles an angel, much as the parent of yesterday's image did, though today's angel has fewer wings and a far less impressive halo. Today's image is located at the edge of one of the many needle- like valleys in its parent fractal. I named it "FMOD Mandeloid" as a description and also because I put no effort into finding a better name. As the name implies, the image was colored with the outside=fmod option. When the time came to rate the image, I could give it no more than a 5. A fractal that has so little effort put into it can hardly be considered above average. The render time of 21 minutes is a bit slow for an image of average quality. Downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> is recommended. The weather Monday here at Fractal Central featured showers and heavy thunder-storms. The heaviest rains missed F.C., but with near an inch (2cm) of rain, it was wet enough to keep the dynamic fractal cats confined to the indoors for the day, unable to enjoy the temperature of 79F 26C. They eased their frustra- tion by burying their noses in the tuna that appeared several times in their food dishes. Today is starting very sunny and pleasantly cool. It looks like a perfect day coming. I must finish a bit of design work and finish thinking about the non-preparations for the big hurricane that most likely will never arrive. Until next time, take care, and doctors might bury their mistakes, but weather people put them on the front page. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ FMOD_Mandeloid { ; time=0:21:37.56--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.1575059159887838/+0.1602162344426152\ /46574.45/1/35/-1.0622669411e-011 params=-1/1/-1/3\ /0/0 float=y maxiter=12000 inside=0 proximity=0.5 outside=fmod periodicity=10 colors=000G`7I`8Ka9Ma9ObAQcBScCUdCWdDYeE`fFbfFdgGf\ gHhhIjiIliJnjKpjLrkLtlMvlNxmOzmOylPylQylQykRykRykS\ yjSyjTyjTyiUyiUyiVyhVyhWyhWyhXygXygYygYxfZxfZxf_xe\ _xe`xe`xdaxdaxdbxdbxccxcdxcdxbexbexbfxafxagxagw`hw\ `hw`iw_iw_jw_jw_kwZkwZlwZlwYmwYmwYnwXnwXowXowWpwWp\ wWqzYtxXrwWqvWouVntVmsUkrTjqThpSgoSfnRdlQckQbjP`iP\ _hOYgOXfNWeMUdMTcLRbLQ`KP_JNZJMYILXIJWHIVGGUGFTFES\ FCREBQF8QEAQEBQEDQEEQEFQEHQEIQEJQELQEMQENQEPQEQQER\ QETQEUQEVQDXQDYQDZQD`QDaQDbQDdQDeQDfQDhQDiQDjQDlQD\ mQDnQDpQDqT1xR7uQDrPJoOPlNViM`fLfcKl`JrYGxUIwWJvYL\ uZMt`OsaPrcRqdSpfUogVniXmjYll_km`jobipdhrehtehsdgs\ cfrbepado`cn_blZakY`jX_hWZgVYfUXdTWcSVbRU`QT_PSZOR\ XNQWNPWMOVMNVMMVMLVLLVLKVLJVLJUKJUKIUKIUKIUJHUJHUJ\ HTJGTJGTIGTIFTIFTIFTHESHESHESHDSGDSGDSGCSGCSFCRFBR\ FBRFBRFAREAREARE9Q5bU4dZ5cW5bU5bR6aP6aN6`K7`I7_F7_\ D8ZB8Z88Y65X38Y4AZ5CZ6E_6 } 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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[Fractint] A Superluminal-Subluminal-Growth Tie-In With NASA Results
by mdoctorow＠comcast.net 15 Sep '03

15 Sep '03

>From Osher Doctorow Ph.D. NASA at http://science.nasa.gov/headlines/y2003/09sep_blackholesounds.htm reports in "Black hole sound waves," Sept. 9, 2003 (the story can probably be accessed by the title as keywords if you have any problem with the http) that the following (in my words) seems to be roughly occurring in galaxy clusters to explain why they have so much hot gas and so little cool gas. Heat and light appears to be transformed into sound waves in vast cavities extending away from central black holes (in particular the Perseus cluster 250 million light years from Earth studied by the Institute of Astronomy in Cambridge, England, in coordination with NASA), and the sound waves then dissipate in the cluster gas to keep the gas warm. In fact, the deepest sound "note" ever detected in the Universe (57 octaves lower than middle-C in music, as compared with a typical piano that only contains about 7 octaves) has been detected by them coming from the Perseus cluster and its supermassive black hole. Readers who've been following my development of logistic growth equations here and on researchmathematics(a)yahoogroups.com (a moderated group) may be aware of my recent posting isolating the "momentum kernels" mv and v of the superluminal and subluminal logistic models respectively: 1) d(mv)/dt = kmv(1 - mv) 2) d(v)/dt = k1v(1 - v) Alternatively to (2), velocity or speed v could be replaced by kv where k1 is a constant usually having magnitude 1 but dimension that of mass which might be approximated by sqrt(1 - v1^2/c^) times a constant very close to the speed of light c and where v1 is a constant speed near but below the speed of light. In the second site above I isolated the superluminal/subluminal ratios: 3) mv/v 4) mv/(k1v) where the first has dimension of mass and the second is dimensionless since the mass and speed dimensions cancel. Now consider this equation, where speed v is written u and s is the speed of sound and m is mass: 5) (u/s)(s/c)(c/(mu))(mu/(uk1)) = 1/k1 This is a simple algebaic identity, but (u/s) is the well known Mach Number (Mach for short here) in dimensional analysis, mu/(k1u) is my superluminal/subluminal ratio which I abbreviate as SupSub here, and I will refer to s/c as PERSEUS because of the NASA results that relate sound to heat and light. So (5) becomes: 6) Mach * PERSEUS * (c/(mu))* SupSub = 1/k1 and where * is just multiplication of real numbers. Surely c/(mu) can't be important? On the contrary, it is the partial "reflection" of mu/u (ratio of superluminal momentum to subluminal "momentum" with constant mass) into the ratio of light speed ("light momentum" with the mass replaced by 1 since photons are supposed to have mass zero) to superluminal momentum. We could credit the NASA results (although not their theories, which didn't notice this) with Mach and PERSEUS dimensionless ratios, but logistic growth definitely gets credit for SupSub and c/(mu) (the first dimensionless, the second dimensional with dimension of mass to the negative 1 exponent). Equation (6) can be used by itself even though it is only an identity, but it also has a second use: it tells us the importance of the four ratios which can be used either separately or in combination in astrophysical and cosmological and various mathematical physics or theoretical physics problems. Since growth via the logistic equations and fractals and chaos are so interrelated, we seem to have entered a new "dimension" of applications of fractals and chaos. Osher Doctorow Ph.D.

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FOTD 15-09-03 (Slinky [8])
by Jim Muth 15 Sep '03

15 Sep '03

FOTD -- September 15, 2003 (Rating 8) Fractal visionaries and enthusiasts: All the talk today in the F.C. area today is about a hurricane that appears headed directly this way. Nothing has happened yet, but by Thursday it could be a different story. We'll see how things work out. The parent fractal of today's 8-rated image was created by combining one negative portion of Z with one negative portion of Z^4. It resembles an angel, complete with wings and a halo that is divided into two parts. Today's image lies in the narrow isthmus that separates the two halves of the halo. Much of the image consists of 'inside' material made visible by the 'fmod' inside fill option. This effect of this inside fill reminds me of those toys which consist of nothing more than a large floppy spring that can do things like walk down stairs. I named the image "Slinky" accordingly. The render time of 24 minutes is a bit slow, but the image is worth it. The fastest to see the image is to download it in completed form from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather Sunday was actually quite pleasant here at Fractal Central, with partly cloudy skies and a temperature of 81F 27C. The cats made up their differences overnight and spent a pleasant afternoon in the yard, enjoying the pleasant condi- tions. It remains to be seen how they can handle a hurricane. I've got a bit of work to finish before I can enjoy pleasant conditions, and the way to finish is to start. So until next time, take care, and don't get caught with your fractals down. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Slinky { ; time=0:24:19.09--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.20033578028784250/+0.346991742483397\ 9/1139769 params=-1/1/-1/4/0/0 float=y maxiter=1200 inside=fmod periodicity=10 colors=000RUKRTKQRKPQLOOLONLNLLMKLLILKHLKFLJEMICMH\ BMH9MG8MF6ME5ME4MD5LD6LD7KD8KD8JD9JDAJDBIDCIDCHDDH\ DEHDFGDFGDGFDHFDIEDJEDJEDKDDLDDMCDMCCNCCOBCPBCQACQ\ ACRACS9CT9CU8CU8CV7CW7CX7CX6CY6CZ5C_5C`5C`4Ca4Cb3C\ c3Cc3Fd5Hd6Jd7Ld9NdAPdBReDTeEVeFXeHZeI`eJadIacIbcI\ bbIcbIcaIdaId`Ie`Ie_If_IfZIgZIgYIgXHhXHhWHiWHiVHjV\ HjUHkUHkTHlTHlSHmSHmRHnRHnQGnPGoPGoOGpOGpNGqNGqMGr\ MGrLGsLGsKGtKGtJGuIFtJGtKHtLHtMItNIsOJsPKsQKsRLsSL\ rTMrUNrVNrWOrXOqYPqZPq_Qq_Rq`RpaSpbSpcTpdUpeUofVog\ VohWoiWojXnkYnlYnmZnnZno_mp`mq`mramsamtbmsbkhckgck\ fdkedkdekcekbekafk`gk_gkZgkYgkXhkWhkVikUikUhkThjTh\ iTghTfgTefTdeTcdTbcTabT`aT_`TZ_TYZTXYTWXTVWTUVTTUT\ STTRSTQRTOQTNPTMOTLNTKMTJLTIKTHJSGIRFHQEGQDFQCEQBD\ QACQ9BQ8AQ79Q68Q56P28Q49R6BT8CV9EXBFZDH`EIbGKdILfJ\ NhLOjNPlOPmOPmOOnOOoPNoPNpPMqPMrPMrPLsPLtPKtPKuPKv\ PJwPJwPIxPIyPHzOIyPIyQIyR } 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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Dyson Ring
by Tony (Anthony) Hanmer 15 Sep '03

15 Sep '03

(At least that's what I think it's called. One of the things science fiction has suggested - a ring built around a star instead of a planet orbiting it.) Hi everyone, A par based on Jim Muth's recent FOTD, "Strawberry Fields". Colouring based on a skydye map. Hope you like it. I've rated it an 8 because I was quite pleased with it. Tony Hanmer Tbilisi, Republic of Georgia Dyson_Ring { ; (8) time=0:14:39.46--1.2k x 1.6k, P1300 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=fotd.par formulaname=mandelbrotmix3a function=ident passes=1 center-mag=-1.22979885859737000/+0.002659402810015\ 19/2.461643e+010/1/-125.000103338542431/2.38398470\ 682396613e-005 params=-1/2/0.5/4/0.25/6/0.125/8/0/0 float=y maxiter=1500 inside=0 outside=fmod periodicity=10 sound=off colors=000zH0<3>z60z30z00<8>e1Ab1B`1C<3>R1HO2JN2I<\ 8>917816615<2>201000101<14>B08C09D09<7>J1EK1FL1F<2\ >O2IO2JN2K<23>51q41r31t<2>11x00z01y<22>0jb0la0n`<3\ >0vX<3>0qQ0oO0mN<9>0S80Q70N50L40J20G0<9>1601501401\ 30120110<2>403503504604705<14>I1DJ1EK1E<3>N1HO2IO2\ J<8>h19k18m17<3>w12z00z20<17>zk0zm0zp0<3>zz0<15>zJ\ 0 } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } _________________________________________________________________ STOP MORE SPAM with the new MSN 8 and get 2 months FREE* http://join.msn.com/?page=features/junkmail

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Posting Questions:
by Kent Watring 14 Sep '03

14 Sep '03

Is this where I ask fracint questions?

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FOTD 14-09-03 (The Whole Seahorse [5])
by Jim Muth 14 Sep '03

14 Sep '03

FOTD -- September 14, 2003 (Rating 5) Fractal visionaries and enthusiasts: I am constantly fascinated by the concept of the fourth spatial dimension. Even though four-dimensional space and objects are not visual things, I want to know what a 4-D object looks like when seen all together at a single moment, and not as a 3-D object changing shape over a period of time. I want to see an object with a three-dimensional surface. (The very idea seems absurd.) I want to see an entire plane of a hypersphere remain fixed in position, with every point rotating on itself as the hypersphere rotates. I want to see a hyper- sphere in a state of double rotation, where only the single point at the center remains fixed, while all other points trace out the circular spirals known as surfaces of double revolution. I want to look at the night sky and see not a flat surface with stars scattered over it, but a solid three-dimensional surface with stars embedded all through it. I want to be on the ocean and see the sphere of the horizon surrounding me in all direc- tions including the directions we would call up and down. And finally, I want to see the Z^2+C Julibrot in its full 4-D glory, with its arms shooting off to infinity. There are these things and so much more that I would like to see, but alas, I never will see them, for my visual perception is limited to three dimensions. I know that 4-D objects are possible because I can create them at will in my computer and examine any section I choose. As an example, I have created for today's FOTD the 4-D object known as Seahorse Valley. As I said, Seahorse Valley is a four-dimensional object, and as such can be examined from many impossible-to-visualize angles, one of which is today's image. The outer border of today's fractal is in the shape of the familiar Julia set with a C-value of -0.75,0. This is not unexpected, since the view is turned only one degree from the Julia orientation toward the Oblate orientation. But the interior of the fractal is filled with strange features unseen in either Mandelbrot or Julia sets. This stuff filling the interior of the fractal is an entirely new view of Seahorse Valley. I named the image "The Whole Seahorse" because it shows more of the Valley than can ever be seen in the M-set alone. The narrow straight line cutting down the center of the outer fractal is actually a side view of the two branches of Seahorse Valley coming together. The extreme maxiter of 1,500,000 is needed to close the gap between the two branches because, from this angle, the branches of the valley have been magnified 57 times. The orbits of the points in this area are so close to periodic that the periodicity checking must be turned off to avoid false calculation terminations. Combined with the extreme maxiter of many of the parts of the image, this results in a very slow image, which takes just under an hour to render on my machine. Considering the slowness of the image and the fact that I have posted several similar images in the past, I could rate today's image no higher than an average 5. But it is still an interes- ting image with coloring that is not bad, and the completed GIF image will be ready for download from the FOTD web sites within the hour. The URL for Paul's site is: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's site is at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The temperature reached 75F 24C on Saturday here at F.C., but the rain and showers continued all day The cats made a brave effort to remain in a good mood, but late in the afternoon their frustration got the better of them and a squabble broke out over something minor. They did a lot of yelling and tail thrashing under the dining room table. A few blows were thrown, but no damage was done, and the dynamic duo ended the day eating tuna and sulking at each other. Had it not been for the excitement among the duo, the day would have been uneventful. Today is starting sunnier, but lots of clouds are around and there is still a chance of rain. Only time will tell how it will go. I plan on another uneventful day, which might or might not happen. Until next time, take care, and be of stout spirit and slim body. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Whole_Seahorse { ; time=0:59:42.90--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip passes=1 center-mag=-7.77156e-016/4.996e-016/0.986\ 1933/1/-35/3.88578058618804789e-016 params=89/90/2\ /0/0/0/-0.75/0 float=y maxiter=1500000 inside=0 logmap=yes periodicity=0 colors=00092F85H87J7AL7CN6FO6HQ6KS5MU5PV4RX4UZ4W`3\ Zb3`c2ce2eg2hi1jj1ml0nn0op0pq5qoArnCslDtjEuhFvfGwd\ HxbIy`JzZKzXLzVMzTNzROzPPzNQyLRwJSuHTsFVqFUoEUmEUk\ EUiEUgEUeDUcDTaDT_DTYDTWDTUCTSCTQCTOCSMCSKCSIBSGBS\ EBSCBSABS0B76YB7`E7cI8eL8hP8kS9mW9pZ9sbAueAxhAzgBx\ gBvfBtfBsfBqeBoeCndCldCjdCicCgcCebCcbDbbD`aDZaDY`D\ W`DU`DTaEVbFWbGXcHYdIZdJ_eK`eLafMbgNcgOdhPeiQfiRgj\ ShjTikUjlVklWlmWmlXnmXomXpmXqnXrnXsnXtnXuoXvoXwoXx\ pXypXzpXzrWzpXzoXznXylXxkXwjXuhXsgXqfXodXmcXkbWi`V\ g_UeZTcXSaWR_VQYTPWSOURNSSNQTOQUPSVQTWRVXSWYTYZTZ_\ U``VaaVcbVdcVfdVgeUifUjgUlhUmiUojUpkUrlUsYVeKWT0XA\ 6WGCVMIUSOTYTTcSVeSWgSYiSZkR`mRaoRcqRdsSdxReuQerPf\ oOflNgiNggMhdLhaKiZJiWIjTIjRHkOGkLFlIElFElDDdMCXVB\ PcBIlCMjCPhDSfDVdEYbE``EdZFgXFjVGmTGpRGsPIsQKsQMsS\ OsUQsWSsYTt_UuaVvcWweWxgXyiYzk_zmazoczqezsgzuizvkz\ wmzxozyqzzszzuzzwzzwzzwzz } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================

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Sample of eturned mail
by Jim Muth 12 Sep '03

12 Sep '03

Here is a sample of the continuing returned mail from the Fractint list. I have no idea of what is being returned. I have been receiving the identical letter every day for several days. Does anyone out there know anything about what is going on? Jim M. START RETURNED LETTER-------------------------------- Return-Path: <MAILER-DAEMON(a)arkion.es> From: "Mail Delivery System" <MAILER-DAEMON(a)arkion.es> To: "Jim Muth" <jamth(a)mindspring.com> Subject: Undelivered Mail Returned to Sender Date: Wed, 10 Sep 2003 17:00:55 +0200 X-MSMail-Priority: Normal Importance: Normal X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 This is the Postfix program at host smtp-01.servidoresdns.net I'm sorry to have to inform you that the message returned below could not be delivered to one or more destinations. For further assistance, please send mail to <postmaster> If you do so, please include this problem report. You can delete your own text from the message returned below. The Postfix program <fractint(a)mailman.xmission.com>: host 217.76.128.71[217.76.128.71] said: 550 unknown user <fractint(a)mailman.xmission.com> (in reply to RCPT TO command) Attachment Converted: C:\MIND\EUDORA\DOWNLOAD\Deliver1.dat START ATTACHMENT--------------------------------------- Reporting-MTA: dns; smtp-01.servidoresdns.net Arrival-Date: Wed,10 Sep 2003 16:59:48 +0200 (CEST) Final-Recipient: rfc822; fractint(a)mailman.xmission.com Action: failed Status: 5.0.0 Diagnostic-Code: X-Postfix; host 217.76.128.71[217.76.128.71] said: 550 unknown user <fractint(a)mailman.xmission.com> (in reply to RCPT TO command) END ATTACHMENT-------------------------------------

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Re: [Fractint] Limitations...
by Tony (Anthony) Hanmer 12 Sep '03

12 Sep '03

Hi Gerald, Yes, I'm the Anthony Hanmer who posted some L-systems a long while ago. Thank you for answering my questions. Actually, of the 4 limitations I mentioned, the ones concerning maximum number of entries in a single .ifs or .ls file are the least important for me. I CAN always split up large files into smaller ones, and this is in fact what I have already done, so no worries. I was more hoping to have the other 2 limits removed - those on LS string length (160 characters) and IFS object number (32). But again, these are not limits which really threaten or even prevent my main work - at the moment. However, if Fractint is moving out of its format into somthing less restricted in the future, I ask that all 4 of these limitations be remembered and removed - IF that is possible. If not, life goes on and it's STILL the best fractal programme around! Tony Hanmer _________________________________________________________________ MSN 8 with e-mail virus protection service: 2 months FREE* http://join.msn.com/?page=features/virus

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FOTD 12-09-03 (Strawberry Fields [6])
by Jim Muth 12 Sep '03

12 Sep '03

FOTD -- September 12, 2003 (Rating 6) Fractal visionaries and enthusiasts: Today is starting on an up note: there were less than 100 spam e-mails in my emailbox when I checked a while ago. But at the same time, there is a down note. I have not yet received that apology from the administrator, if one exists, of the fracpro- grammers list that I am waiting for before I re-subscribe. No matter, there is no noticeable decrease in the number of letters I am receiving from the list. More ominously, I am starting to receive returned mail from the Fractint list that I never sent out. Since I have no sneaky viruses or worms in my system that could send out e-mail without my knowledge, and I never use the programs that get infected by these critters, we'll see where this 'returned mail' leads. Now on to the fractal for today. Today's image is named "Strawberry Fields" not because I like the music of the Beatles, which I rather do, but because the phrase simply came into my head while I studied the image in search of a name. I guess the pinkish terraces inspired the name. The parent fractal is a distorted Mandeloid with no East Valley, lying in the proper orientation, with X-axis symmetry. Unlike the classic M-set however, the parts of this Mandeloid are not connected, and it is surrounded by a cloud of tiny isolated midgets, every one of which, with the exception of its mirror image, is different. The formula subtracts Z^2 from lesser portions of Z^4, Z^6, and Z^8. This combination produces a fractal with three critical points, one of which is located at Z=0,0. The remaining two critical points, around Z=+-0.77, produce nearly but not exactly identical Mandeloids, which might hold some interesting scenes and might be worth investigation. The largest satellite midget of today's parent fractal is located on the negative X-axis. Curiously, this midget is rotated 180 degrees, so that its East Valley is on its west side. Today's scene is found near a larger midget in the interior of the north branch of the Seahorse Valley of the very large satellite midget. My standard rendering method, where the outside=iter, produces a fair enough image, but the outside=tdis option that I used does a little better. When rating the image, I felt a bit more satisfied with it than usual, and gave it a rating of a 6. The parameter file's render time of 14-1/2 minutes is slow. Downloading the completed image from one of the FOTD web sites is fast. Those sites are: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Sunny skies, gentle breezes, low humidity, and a temperature of 79F 26C made the cats very happy again on Thursday. They spent the entire afternoon in the yard, romping and resting. In fact, they have been getting so much quality time in the yard this past week that they actually seem to be growing bored with it. Perhaps the rain that is forecast for later this afternoon and over the week-end will give them reason to appreciate days such as yesterday. As for me -- I must finish a pile of work before I can appre- ciate anything, so until next time, take care, and when life serves up a lemon, make lemonade and then blow your top. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Strawberry_Fields { ; time=0:14:35.73--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix3a function=ident passes=1 center-mag=-1.22979885859737000/+0.002659402810015\ 19/2.341307e+010/1/-125/0.00485842217789580338 params=-1/2/0.5/4/0.25/6/0.125/8/0/0 float=y maxiter=1500 inside=0 outside=tdis periodicity=10 colors=000Cgg8fk4fnAblF_jLXhQUfWQe`NcfKakH_pEZ_AUJ\ 6P33LLEQaPVbOXbNZcN`cMbdMddLfeLheKjfJlfJngIpgIrhHt\ hHviGxiGzjJyjMxjPwjSvjVujYtj`tkcskfrkiqklpkookrnku\ nVykWvlXtlXqlYolYmlZjlZhl_el_cl`al`ZlaXlaVl_cjYkhN\ WgCHf22eqtEopFnmGmiHlfIkbJj_KiWLhTLdQJaNIZKHWHGSEF\ PBEM8DJ6CG6AD68A66864FA6LE8RIAXMCbPEhTGnXIt`KzcLvd\ MrdNndNjeOfeObePZeQWfQSfROfRKfSGgTCgT8gU5gU9cWC`XF\ XYIU_LQ`ONaRJcUGdXDebBbhA`n8Zt7Xz6VqEPiLJaSD`TI`UM\ `VR_WV_X__Xceubdr`cpZbnYalW`jV_hTZfRYcQXaOW_NVYLUW\ JTUISSGSQFUVDVZBWbAXf8Zj6_n5`r3av2KVT24sDGgNSXXcMf\ oBdmIclObkUaj_`ie_hkZgqYfwWuKZoJaiIdcHgYHjSGmMFpGE\ rBEdAMSAUFA`zbpvYgsT_oORlJJUG9CD0DI5DN9DSDDWID`MDe\ QDiUKoOQtIWyDQxHLxKGxNIyLJyKKzILzHMzGTwG_tGeqGlnGs\ kGyhGBMgGQaLUWQYQUaLHb7T`HdZRpY_oTaoOcoJenEgn9in4k\ dCnWJpNQsEXu5cwD`nLZfSWY_UQgRHnP9`bNNo_OUkO8vH6XB4\ 7ABE9HL8OS7UZ6`e5fkLh_Hhc } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END 20.0 PAR-FORMULA FILE==================================

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Limitations...
by Tony (Anthony) Hanmer 11 Sep '03

11 Sep '03

I have been experimenting much with IFS and L-system types in Fractint - though I'm afraid my findings are not yet ready for release. There are several limitations I have come up against, and I wonder if they might be removed in the next release of Fractint - I think they are all no longer necessary with the general speed and power of computers nowadays: In both IFS and L-system types, a ceiling on the number of entries allowed in their respective files (*.ifs and *.ls) - 2000 and 1000 items respectively, if memory serves; In IFS types, a limit of 32 pieces making a specified IFS; In L-system types, a limit of 160 characters per line. Might these constraints please be removed? Thank you, Tony Hanmer _________________________________________________________________ The new MSN 8: smart spam protection and 2 months FREE* http://join.msn.com/?page=features/junkmail

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FOTD 11-09-03 (The Fractal Sieve [5])
by Jim Muth 11 Sep '03

11 Sep '03

FOTD -- September 11, 2003 (Rating 5) Fractal visionaries and enthusiasts: I feel strangely down this morning, and I don't know why. True, it's the second anniversary of 9-11-01, and the TV is filled with memorial ceremonies, but I have known the day was coming for a long time. Then there's the work, which has been heavier than usual over the past few weeks, cutting into my fractal exploration time. But more work means more income, so that's not really cause for the blues. Or maybe it's a touch of clinical depression, some brain chemicals not doing what they should. (As cognitive scientists tell us, emotions are caused by chemical activity in the brain.) Could it be sadness because summer is nearly over? I doubt it, since Autumn is one of my favorite times of year. Maybe it's a touch of mid-life crisis, the realization that the time of life has arrived when I must stop asking 'what will I do with my life' and start asking 'what did I do with my life'. But I have never been concerned with growing older -- it happens to everyone. Or could it simply be boredom, my reaction to things going well for a change, and the lack of excitement this smoothness implies? Most likely it's a combination of all of these. Whatever it is, I'll get over it. Today's image is part of the fractal that results when 6 parts of Z^(-1.6) are mixed with Z^(-6.1) before (1/C) is added. This parent fractal is beyond description. When studying today's image, which is located in a valley of its parent, I thought of how good a sieve it would make. I named the image "The Fractal Sieve". I gave little thought to its worth. The rating of an average 5 was chosen because it cannot be too far from the rating I would have chosen if I had given it more thought. The render time of 22 minutes is too slow for such a generic image. For speedier viewing, go to Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> and download the finished GIF file from there. Wednesday was once again a perfect day here at Fractal Central. The sky was sunny and the temperature reached 77F 25C. The cats were perfect also. All this perfection leaves little to write about. Today is showing all signs of being another perfect day. Why then do I feel strangely down? Until tomorrow's FOTD, take care, and keep that chin up. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Fractal_Sieve { ; time=0:22:24.26--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.30641156973805700/-0.190506442327136\ 80/3.935643e+012/0.9998/9.9808/0.03407448068099558 params=6/-1.6/1/-6.1/0/0 float=y maxiter=1500 inside=0 mathtolerance=/1 logmap=376 periodicity=10 colors=000M0zM0zM0zM2zMOzMPzMUzMVvM_tMZrMgpMjnaokM\ tjcueMxgKvgItjGrjBpk9nk7kn4jn0ep0cp0ar0Zr0Xt0Vt0Tv\ 0Qw0Rv0Tx0Vx0Xz7ZzDZzIazOczVezagzejzkjzrkzvnzznzzr\ zzqzznzzkzzjxvgtrepncjpaeeZZiXVXVRaTKORGWO9GM4SI0B\ K0DM0GM0IO0KR0MR0OT0RV0TV0VX0XZ0ZZ0aa0a_0aa0gW0cD0\ aT0ZG0XP0VI0TK0RM0OM0KO0IO0GR0DR0BT09V07V04X00X00Z\ 00a00a00c00c00e00c00e00e00e00g00g00g00g00j00j00j00\ k00k00k00k00n00n02n00r02n07k09g0De0Ga9KZGOVORTVVOc\ XMjaIrgBzcGxaIvXMtVOrRTpOVpKZnIakDejBgg7kg4ne0rc0t\ a0xZ0zZ0zX0zV0zT0zR0zR0zM0zK2vG9pDIkBRe7XZ4eT0nM0t\ I0rG0rG0rW2rD2rc4pB7p99p99p7Bp7Dn4Gn4Gn2In2Kn0Mk0M\ k0Ok0Rk0Tk0Te0VZ0XT0XM0ZG0a90a20c00c20Z70V90RD0MG0\ KK0GM4BR97VD2XI0aM0cR0gV0jZ0ea0aa7XaITcTRcaMckIevD\ ez4gzBezGezMezRezXevaergcnkcjrccvcZzcVzcRzcMzaOzZR\ zXTzVVzTXzRZzOZzMazKczIezGgzDjzBkz9kz7nz4pz2rz0tz0\ vz0vz0jz0Zz0Oz0Dz0zz0zz0z } 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 10-09-03 (Mystic Mandel Vision [5])
by Jim Muth 10 Sep '03

10 Sep '03

FOTD -- September 10, 2003 (Rating 5) Fractal visionaries and enthusiasts: It appears the booming design business is having an effect on the quality of the FOTD. For about two weeks I have been unusually busy, and the FOTD fractals have suffered from a lack of attention. I'm not sure whether this is good news or bad, but I would rather concern myself about a less-than-great FOTD than a lack of money. The only thing I am certain of is that the FOTD will continue appearing almost every day for the foreseeable future. Today's image of a midget surrounded by a brightly glowing aura was created by mixing various portions of Z^2, Z^3, Z^4 and Z^5. I named it "Mystic Mandel Vision" because it reminds me of something a meditating mystic with an interest in fractals might see in his mind while he meditates. This particular mystic vision is of only average quality, and it rates only an average 5. It deserves nothing more. Mystical visions are true, though they are not real in the generally accepted sense of the word. The same is true of fractals. Much can be learned through mystical visions; much can be learned through fractals. Much of what is learned through both means has no apparent practical value. Today's image requires 27 minutes to render on my tired machine, which is almost 10 years old and still humming. The image downloads in far less time from the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> With a temperature of 75F 24C and lots of sun, the day remained perfect from noon until night on Tuesday here at F.C., as did the fractal cats. Even the work went well. There is no cause for complaint. Today is starting the same. It's almost too good to be true, so check the next FOTD to see what goes wrong. Until that next FOTD appears in 24 hours, take care, and who says there's a Murphy's law? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ MysticMandelVision { ; time=0:27:24.69--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix3a function=ident passes=1 center-mag=+0.43234523371375270/+0.001248383281929\ 91/1.149306e+008/1/30/-1.61624185861242164e-007 params=1/2/-0.2/3/0.03/4/-0.03/5/0/0 float=y maxiter=2400 inside=0 logmap=186 periodicity=10 colors=00086TA6UC6WE6XG6ZI6_K6aM6bO6dQ6eS6gU6hW6jY\ 6k_6ma6nW9gQBaKEVFGPJHTNIXRJ`VKdZLhbLlcKneIpfHrqMb\ qMbjI_dFXYBUS8RL4OF1LE3PE5SD7VD9ZDBaCDdCFhCHkBJnBL\ rANuAPxARz9Tz9Vz9XzBYzDZzF_zG`zIazNbzRczVezYgz`jzc\ lzemzgnziozkqzmrzhqzcpzZozUnzTmzRlzQkzPkzNkzMkzKkz\ JkzIkzGkzFkzEkzHfwKarNXmQShTOcWJZZEUa9Pd4Kg0Ff2If3\ Lf4Oe5Qe6Te7We8Yg8Wi8VeCTbGR_KQXOOUSMRWLTUOUTRWSUX\ QXZP__Ob`MegFsbLhcKkeInfHq_KfgMZgJi2dz6bz9`zCZzFXz\ JVzMTzPRySPxWNwZLvaJudHtcURcUWcU_cUccUgaUkdWocUedW\ WdYYd__ea`ecbecdecffcgfcifckfcmgcngcpgcrecafcefcig\ clgcpccctciqckocmlcoicqhctfcugctgctgctgctgcsgcsgcs\ BcqEcrGcrIcrKcrMcrPcrRczTczVczXcz_czaczcczeczKczMc\ zOczQczSczUczWczXczZcz`czbczdczfczSczUczVczWczYczZ\ cz_czaczbczcczeczfczPczRczTczVczXczZcz`czbczdczfcz\ BczGczKczOczSczWcz_czcczQczSczUczWczYczZczSczUczXc\ zZcz`czbczdczfczUczIcz6cz } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 08-09-03 (Trying Again [6])
by Jim Muth 08 Sep '03

08 Sep '03

FOTD -- September 08, 2003 (Rating 6) Fractal visionaries and enthusiasts: The later than usual FOTD is a result of a heavier than usual work load earlier today. Sometimes in life the unexpected happens. This is true not only in the fields of fractals, relativity and Q.M., but in ordinary chemistry as well. I still remember the day in high-school physics lab when the instructor produced a sealed tube contain- ing a clear liquid. (I don't think it was water. It might have been CO-2.) He then asked the class what they thought would happen when he heated the tube. Most said that the liquid would boil away. Remembering that increasing the pressure raises the boiling point, I said that the amount of liquid in the tube would grow smaller, evaporating away without boiling until the last drop evaporated from the bottom of the tube. What actually happened surprised even me. As the instructor heated the tube, the surface of the liquid filling the lower part of the tube soon grew vague. It became blurred and wavy. The whole tube looked like it held liquids of two different densities, which were mixing together. And then the optical effects were gone. The instructor said the tube was now filled with only high-pressure gas. Neither I nor anyone else in the class had expected this to happen. The instructor had just demonstrated the critical temperature and pressure of whatever liquid was in the tube, the temperature above which the substance would be in the form of gas regardless of the pressure applied to it. Today's fractal demonstrates what happens when 0.2 part of Z^3 is subtracted from Z^2. The resulting M-set has strange things happening along the X-axis east of East Valley. Today's image lies in a shallow spiral rather deep in East Valley. I once again colored the outside with the 'fmod' option, and named the image "Trying Again". It's better than yesterday's effort, but still nothing to brag about. The rating of 6 is appropriate. The render time of 54 minutes however is excessive for such an image. The best way of viewing the scene is to download the finished GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Sunday was another perfect day here at Fractal Central, both with the weather and with the cats. The sunny skies and temperature of 81F 27C could not possibly be bettered. Cats that behave like angels for an entire day cannot be bettered either. Days like this come only once or twice a year, and we made the most of it while it lasted. Except for more clouds, today is again almost perfect. Could three perfect days in a row be possible? The cats are currently enjoying the yard, so check back in 24 hours to find out how the rest of the day goes. Until then, take care, and maintain that sense of wonder. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Trying_Again { ; time=0:54:00.04--SF5 on a p200 reset=2002 type=formula formulafile=slices.frm formulaname=MandelbrotMix2way passes=1 center-mag=+0.28383179310875450/+0.000005192775516\ 76/5.640753e+009/1/90/3.88578058618804789e-016 params=1/2/-0.2/3 float=y maxiter=2800 inside=0 proximity=0.085 outside=fmod periodicity=10 colors=0006VL6UK3TJ3SI3RH3QG0PFphlshkshkshkthithit\ hivhgvhgvfgvfgxfexfexfezfczfczfczfczfazfazfazf`zf`\ zf`zhazf`zf`zf`zf`zf`zf`zf`ydZydZxdZwdZvdZudZtdZsc\ WtcWqcWpcWocWncWmcWlbVkbVjbVibVhbVgbVfbVeaTdaTcaTb\ `Ta`T``T__TZZRY_RXZRWZRVZRUYRTYRSYORYOQXOPXOOXONWO\ MWOLWMKVMJVMIVMHUMGUMFUMETKDTKCTKBSKASKBSKCRMDRKDS\ KDSKDTIDTIDUIDUIDVGDVGDWGDWDDXDDXDDYDDYBDZBDZBD_BD\ _9D`9B`9Ba6Ba6Bb6Bb6Bc3Bc3Bd3Bd3Be0Be09f09f09g09g0\ 9h09h09i09i09j09j06k06k06l06l06m06m06n06n06o06o03p\ 03p03q03q03r03r03s03s03t03t00u03u03v03v03w03w06x06\ x06y06y06z09z09z09z09z09z0Bz3Bz6Bz6Bz9Bz9DzBDzBDzD\ DzGDzGGzIGzIGzKGzMGzMIzOIzOIzRIzTIzTKzVKzVKzWKzZKz\ ZMz`MzaMzcMzeMzgOzhOziOzjOzkOzlRzmRznRzoRzpRzqTzsT\ zuTzwTzyTzzTzzRzyRzwRzuOzsOzqOzpOyoMxnMwmMvlMukKtj\ KsiKrhKqgIpfIoeIndImcGlbGkaGj`Gi_DhZDgYDfXDeWBdVBc\ UBbTBaS9`R9_Q9ZP9YO6XN6WM } frm:MandelbrotMix2way {; Jim Muth z=0,0, c=pixel, 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==================================

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FOTD 07-09-03 (A No-Repeat Fractal [4])
by Jim Muth 07 Sep '03

07 Sep '03

FOTD -- September 07, 2003 (Rating 4) Fractal visionaries and enthusiasts: I must be developing amnesia. When I checked my e-mail box this morning I found about a dozen letters from different people telling me that I was great last night but could still use some improvement. Then there were four more people who had seen my profile online and wanted to meet me. There were four who had met me in a chat room. I had three letters that gave the information I had requested. And several letters simply said something like 'hey' or 'hi' or 'how're ya', or 'Jane told me you are too small', or the most mysterious of all -- 'dgins hebs oihndy fgotushn eod'. Finally, I wonder why the billing depart- ment at Mindspring wanted me to re-submit my credit card number to confirm that the number is correct. The number has been working as it should for 7 years. What has me worried is that I have no memory of being with twelve different people in one night, or of having my profile online. I have totally forgotten visiting any chat rooms, and I don't remember requesting any information. I have no memory at all of those many people who sent me greetings. I also wonder who this Jane is who thinks I am too small. My height is just about average. As for that message in a foreign language -- it might be important, but I can't read it. Finally, I wonder why my latest credit card statement shows a balance of $8,758.63, when last month it was $176.53 and I paid that in full and have charged nothing since then. (The first paragraph is true; the second is frivolous. Every few weeks I need a short rant about spam...) ...especially when the FOTD doesn't turn out too well. For today's image I tried the same trick that worked so well in yesterday's image. But it didn't work at all in today's image. I named the image A No-Repeat Fractal" because it's apparently impossible to repeat the same trick and get an equally fine result. I rated the image at a meager 4. The image was generated with the MandelbrotMix3a formula, which does nothing but permit 4 different exponents of Z to be combined in different portions, and permits the initial value of Z to be adjusted to a critical value of the formula. In today's case, zero is a critical value, so the (p5) parameter remains at zero. The biggest drawback is the time required to render the image -- over one hour on my machine. I strongly recommend giving Paul and Scott time to generate the image and post it to their web sites before going there to download the image. Paul's site is found at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's is at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Near-perfct weather prevailed once again Saturday here at Fractal Central. The bright sun, dry grass and temperature of 79F 26C produced near-perfect cats. They had such a pleasant day in the yard that by the time they came in, they wanted to do nothing but grab a few bites of food and fall asleep. If they were still kittens, I would say they are at their best behavior when they are sleeping, but now that they are fully mature, they sleep far too much for sleep to be considered their best behavior. Today looks to be a repeat of yesterday, so I expect we'll do it all again. The duo is already romping in the yard. I'll be back in 24 hours with a new and fresh fractal, not another inferior imitation. Until then, take care, and be peaceful. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_NoRepeat_Fractal { ; time=1:08:11.40--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix3a function=ident passes=1 center-mag=+0.92952219950070970/+0.209587282531303\ 70/1.545435e+009 params=-2/2/1/3/0.5/4/0.25/5/0/0 float=y maxiter=1200 inside=fmod proximity=0.15 outside=tdis logmap=yes periodicity=10 colors=000Zah_eg_if`meaqdatdbpbcmadi`efZfbYg_XhXWi\ TUjQTkMSlJQmFPnCOn9NoFQpLTqQVrWYs`_q_`pZaoYbnXcmWd\ lVekUfjTfiSghRhgQifPjeOkdNlcMmbLmYJ`THOPFCXGHcGMjH\ RqHWxH`ySUzbNzmHvkGsjGphGmgGjeGgdGccG`aGY`GVZGSYGP\ XGRUETSDVPBXNAZK8`I7aF5bD4cA2d81e60e74e78f8Bg8Fi9J\ i9MkAQlAUmBXnB`pCdqCgUPpUPpUPp6ay9bwBcvEduGdtJerLf\ qOfpQgoThmVhlYik_jjajiajhajhcljenkfplhrmjtngXyhZti\ `pjbljcgkeclg_lhWmjRnlNonJooEpqAqs6qt2fkEWbQLUaBLl\ HMnMMoRMpWMr`MsfNtkNvpNwuNxzNy_mrRYnIJj94gCBiEHkGN\ mJToLZqNdrGei9e`2eS4dR5cR6bR7aR8aQ9`QA_QBZQCZQASR8\ LR7FR58R42R57S5BT5GU6KV6PW6TX7XY7aZ7e_8j`8na8rbEse\ JthOujUumZvocwrhwtetqbqo`nlYkjVigTfeQcbN``LYYIWWFT\ TDQRANO7KM5IKirIirLirN8EQ9DSACVBAXC9_D8aE7dF6fJEdM\ LcQSaTZ`XeZ_lYcsWfzVawTYtSUqQQnPMkNIhMEeKAbJBaKBaK\ BaKBaLBaLBaLBaLCaMCaMCaMCaNCaNCaNCaNEcTFdYHebIggKh\ lLiqMjvNciOXXWNlXRkYVjYYi } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END 20.0 PAR-FORMULA FILE==================================

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[Fractint] Linked Logistic System Across Fractals, Chaos, Physics, Biology
by mdoctorow＠comcast.net 07 Sep '03

07 Sep '03

>From Osher Doctorow Ph.D. I meant to put this same subject heading on my last posting a few minutes ago, but I forgot to put a subject heading on the posting. There is one typo in the posting: the last expression should read 1/[v(1 - v)] = 1/v) + 1/(1 - v) instead of reading v(1 - v) = (1/v) + 1/(1 - v). For those who deleted the previous posting because it had no subject heading, it turns out that if, instead of taking force as the time rate of change of momentum as it has been taken since Sir Isaac Newton in the later 1700s, one takes force as proportional to the time rate of change of "logistic momentum" mv (1 - v) where m is mass and v is speed or velocity, then if the proportionality is written F = kmv(1 - v), the higher or stronger the proportionality is, that is to say the larger k > 0 is, the closer v is to 1/2 for mass approximately constant. However, 1/2 is halfway between a speed of 0 ("at rest" condition) and the speed of light which is taken as 1 (ignoring superluminal speeds here). This enables us to solve the linked logistic system: 1) dv1/dt = k1v1(1 - v1) + k2v2(1 - v2) dv2/dt = k3v1(1 - v1) + k4v2(1 - v2) since with v1 approximately 1/2, we can use partial fractions to obtain an exact solution for v2 because 1/[v(1 - v)] = 1/v + 1/(1 - v) for any v. The linked logistic system (1) was first introduced by James W. Bruno and me and Chris Kappner in a 1981 publication in population growth/migration, and reflects the interrelated effects of the two populations on each other and slightly modifies the Lotka-Volterra predator-prey equations. The latter are useful when the environment contains competitors and limitations on growth (scarcity, etc.). We did not apply the equations (1) at that time to physics or analyze the case of v1 = 1/2. I introduced the equations (1) today on stardrive1(a)yahoogroups.com to model an Alcubierre-like warp drive in space travel with v1 the rear speed and v2 the front speed of the craft which (curiously enough) are different in the Alcubierre type scenarios. Osher Doctorow Ph.D.

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by mdoctorow＠comcast.net 07 Sep '03

07 Sep '03

>From Osher Doctorow Ph.D. We get closer to the relationship between chaos/fractals and physics and biology by considering the linked logistic system: 1) dv1/dt = k1v1(1 - v1) + k2v2(1 - v2) dv2/dt = k3v1(1 - v1) + k3v2(1 - v2) which is a modification of the predator-pret Lotka predator-prey equations in which two speeds (2-population growth speeds) v1 and v2 are interlinked logistically with each other. James E. Bruno and I and Chris Kappner in 1981 did some publications on this and related systems in population growth/migration, but we didn't explore the physics picture or even the equations beyond the particular empirical problem studied there. The equation (1) has arisen again, this time when I introduced it today in stardrive1(a)yahoogroups.com to model a 2-velocity spacetime warp star drive of the Alcubierre-related type. What I want to emphasize here is one of the strangest outcomes of the use of equations (1) in physics. Here is the basic result: PRINCIPLE OF SPEED 1/2. The speed 1/2, on a scale from speed 0 to the speed of light taken as 1 (here I'm not considering possible superluminal speeds), is not only the average between these two extremes but is also the speed at which Force becomes very highly proportional to the time rate of change of "logistic momentum" which has the form mv(1 - v). We know since Sir Isaac Newton's time in the late 1700s that force is the time rate of change of momentum, but "logistic momentum" is more realistically the growth-related analog of momentum. For those who know calculus (for others, just notice that dv/dt cancels in the second equation below if it isn't 0 and then solve algebraically for v), force F = kd[mv(1 - v)]/dt and approximating m by a constant and incorporating it into k leads to (using the same constant k) dv/dt = kdv/dt - 2kvdv/dt which has the solution v = (1/2) - [1/(2k)] and for k very large this is close to (1/2) and gets closer the larger k is. Now if we approximate v1 in (1) by (1/2), it becomes a simple matter to solve system (1) by the same method as solving the logistic equation, that is to say by partial fractions noting that 1[v(1 - v)] = 1/v + 1/(1 - v). The logistic system of course is central to chaos and fractals and environment- limited growth in its discretized (and non-discretized) version and so on. Osher Doctorow Ph.D.

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FOTD 06-09-03 (Mandelbrot Feathers [9])
by Jim Muth 06 Sep '03

06 Sep '03

FOTD -- September 06, 2003 (Rating 9) Fractal visionaries and enthusiasts: A FOTD fractal with a rating of 9 is rare indeed, but today we have found one. It is a scene in the fractal that results when Z^(1.1) is subtracted from (1/Z) and (1/C) is added. This parent fractal consists of two large Mandeloids surrounded by scattered fractal debris. Today's scene is located at the point where a continuous filament breaks up into a series of disconnected bits. The scene is unusual in that nearly all the outside rendering options work well with it. I happened to choose the 'fmod' option with a proximity of 3, though I could just as well have chosen the 'summ' or the 'imag' options, or any of the others. It's just an easy scene from which to get a good fractal. When I was studying the image in search of a name, I thought of ostrich feathers and found the name "Mandelbrot Feathers". I was undecided as to whether the image rates an 8 or a 9. But since I have had a run of sub-par images lately, I decided on a rating of an exceptional 9, which might be stretching it a bit. But regardless, the image is still well above average. The image also benefits from a relatively fast render time of 7 minutes. And as always, the completed GIF image is posted on the internet at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Take a trip to one of the sites. You will not regret the journey. With mostly sunny skies, a high temperature of 77F 25C, and no rain, Friday was a near perfect day here at Fractal Central. The fractal cats took full advantage of the perfection by enjoying the yard from 11am until evening. They were near perfect angels, the only imperfection coming when Tippy returned with a burdock burr stuck in his tail. The burr was easily removed and the day ended peacefully with the duo's noses in their food dishes. Today is starting even more perfect. Since perfection cannot be improved upon, I hope for a repeat of Friday. To see if my ex- pectations are fulfilled, check back in 24 hours. Until then, take care, and unless I am mistaken, burdock burrs gave the inventor the idea for Velcro. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ MandelbrotFeathers { ; time=0:07:07.54--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=-0.16918139027290410/+0.463847222461736\ 50/6.731712e+011/1/90/3.88578058618804789e-016 params=1/-1/-1/1.1/0/525/0/0 float=y maxiter=900 inside=0 proximity=3 outside=fmod periodicity=10 colors=000NYNNTGON9OI3LN6JR9HWBF_EDcGE_IEXJETKEQLE\ MNFJQFFTFCVF8XF5_F2bG3`G4XH4UH5PI6MI6IZHNoRUnUTmWT\ lYTk_TjaTicTheTghTfjTelTdnTcpTbrTatTcqVdoXflYgj_ig\ `jeblbcm`enZgpWhqUjsRktPmvMnwKpxIqMhAPdCT`DVQHURHS\ TGRUGQWGPXGNZGM_FLaFJbFIcFHeFFfEEhEDiEBkEAlE9nD7oD\ 6qD5rD4sD6rE7rE9qEAqECqFDpFEpFGoFHoGJoGKnGLnGNnHOm\ HQmHRlHSlHUlIVkIXkIYjI_jJ`jJaiJciJdiKfhKghKhgKjgLk\ gLmfLnfLofLneMmdMlcMlbMkaMj`Mj_NiZNhYNhXNgWNfVNfUN\ eTOdSOdROcQObPObOOaNO`MP`LP_KPZJPZIPYHPXGPXFQWEQVD\ QVCQUBQTAQTAQUBRVCSWDSWETXETYFUZGUZHV_HV`IWaJWaKXb\ LYcLYdMZdNZeO_fO_gP`gQ`hRaiRajSbjTckUclVdmVdmWenXe\ oYfpYfpZgq_gr`hsaisaitbjucjvdkvdkwelxflygmygmxhnxh\ nxhoxhoxhoxhpxipxiqxiqxiqxirxirxirwjswjswjtwjtwjtw\ juwkuwkvwkvwkvwkwwkwwkwuiuthtsgsrfrqeqpdpoconbnmal\ l`kk_jjZiiYhhXggVffUeeTcdSbcRabQ`aP__OZZNYYMXXLWWK\ UVJTUISSVUPaZNhcLngMh`McU } frm:MandelbrotMix2 {; 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)+(p4)), 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 05-09-03 (A Very Deep Midget [5])
by Jim Muth 05 Sep '03

05 Sep '03

FOTD -- September 05, 2003 (Rating 5) Fractal visionaries and enthusiasts: The work was still hectic here at Fractal Central on Thursday, but things calmed enough in the afternoon for me to post a short reply to the list and find an 'automatic' fractal in the Mandelbrot set. Today's image takes us where many have ventured previously -- to the tip of the negative stem of the Mandelbrot set. And when I say the tip, I mean the tip. The magnitude of the image is 3x10^58, and there are 29 consecutive 9's following the 1 and the decimal point in the X-coordinate of the scene. Since the cut-off point is set to 2, today's image is almost exactly on the cut-off point. The rays radiating from the central midget are a direct result of its being so close to the cut-off point. The image rates only a 5, held down by the hackneyed nature of the area in which it lies. Fresher scenes might be found at the tips of some of the other filaments, especially near the cut-off points. I named the image "A Very Deep Midget" as a description. It is certainly a fair name, because, unless I am mistaken, the scene is the second deepest of all the FOTD images. The render time of 19 minutes is quite fast for such a high magnitude image calculated with arbitrary precision math. The X-axis symmetry helps a lot here. Whether the result is worth the wait is open to individual opinion. My opinion is that a more reasonable method of viewing the scene would be to download it from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Though the temperature on Wednesday reached a very comfortable 77F 25C, it was another disappointing day for the cats here at fractal headquarters. The sprinkles that fell off and on through the entire day culminated in a torrential downpour at 7pm, accompanied by thunder. But by that time the cats had already given up all hope of outdoor fun and satisfied them- selves with a tuna treat. When an even stronger storm arrived around midnight, they watched the rain cautiously, until a close lightning strike and a loud bang of thunder sent them scurrying for cover. Thursday began with steady rain, which ended at midday, leaving the skies leaden gray for the rest of the day. The temperature of 75F 24C was fair enough, but fractal cats need dry grass in which to romp, so more tuna was needed. Today is starting much better. It is sunny, cool and dry. Can the dynamic duo actually have a good day after a long string of bad ones? Check back tomorrow to see. As for me, the load of work is still heavy, so I'd best get busy. Until tomorrow, take care, and keep your spirits up when the rain comes down. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Very_Deep_Midget { ; time=0:19:23.10--SF5 on a p200 reset=2002 type=mandel passes=1 center-mag=-1.9999\ 99999999999999999999999997080345601743762432509639\ 57868601/-1.6623896e-61/3.139258e+058 params=0/0 float=y maxiter=1500 inside=0 symmetry=xaxis periodicity=10 colors=000iHpmEorBnv8mvMgvZbvkXvxSp\ lWka_eQc`FgW4k`9adESiAGn75q3GlCMgKSYSYR`cLhiEpo8pu\ DoiHkiKk7MmDPqJRtPTyUhxFxr0vkCqcOe_TibXmg`qfdhda`Y\ ZTUWLATD1RM6OVBMjGKtLIzYGaN89517746874993AC2BE8EFD\ HGJKHONITQJZTKcWLhZLeVQcRV`N_ZKdWGiUCnR8sP5xHYyYdR\ dTPkINP_K2qI7jMCdPHZSMSVRMYWG``AcfDdlFeqHekNaeSY_X\ VUaROfNIkKHfNGaPFXRFSTENVDIXDEZkEUfCYbB`ZAcV9fQ7iM\ 6lI5oE4rCBnBIjAPf9Wb8bZ6dS4eM3gF1h90i37aMDVcJOuQHd\ XBPb9Vh7_n6dt4iy3nd7qLBt1Fw6MpATiE_bJfXNmQRtJVzDPq\ NKhWF`eASn5Kw7Il8Ha9FRAEGBD5DG6EI6FK7GM7HO8IQ8HRBH\ SEHTHHUKHVNKSNMPNPMNRKNTHNWENYBN_9NfT_`PWWLSRHOMDK\ H9GC5C71969H6GO5NW5Vb4aj4hq4oxBmtIlqPknVjkahhhgeof\ bue_tiXsmUsqStlOugKvbGwZCxU8yP4zL1pW3fe4Xo6Oy7AkoB\ UYnhTVTMl6vb8kUA`KCQLpcHbWEQOc3GU7GKAG5sY8YPkwYakT\ T_PKOKzvwNm8KcAHVCEMEmzVUaNgOaRIRtxqdhdQTSFBHDCGeD\ pQDYn`9`TCOLEZksv2kZ8WaDTVDPODMHDJdKr107 } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD 03-09-03 (Spiral [3])
by Jim Muth 04 Sep '03

04 Sep '03

At 06:24 PM 9/3/03 -0700, John Wilson wrote: >Hey, I didn't *state* that 7-armed spirals were rare! >I *asked* if this were so. My fault. I was rushed. I should have taken time to check exactly what you had said. >Since you were able to produce one on demand, I guess >the answer is that they are *not* rare. A spiral of any number of arms can be produced on demand. >My 7up, however is a much nicer spiral, with another >somewhat intriguing feature...I thought. If I back >away some distance from my screen, I see that the sub- >elements of the slowly spiralling arms form another >spiral...a much faster spiral, (shorter pitch). It's a fine spiral. In no way did I intend to criticize it or the formula that created it. >Something that was discussed in Philofractal back in >May and June...I have been surprised by the lack of >comment in "Scientific American" regarding the multiple >universe article by Max Tegmark. Well a few letters >have finally surfaced. It was my own belief that this >whole thing was built upon flawed reasoning which led >to paradox. I never saw a paradox. I saw a hypothesis which is so vast as to be almost mystical. It is not surprising that the more rational thinkers would search for flaws in the reasoning. >One reader pointed out an omission in the boundless >possibilities suggested by Tegmark...a theism. I guess >that this reader is thinking along the same lines that I >followed; "Space appears to be infinite in size. If >so, then somewhere out there, everything possible becomes >real, no matter how improbable it is". Therefore there's >a universe somewhere which is built and managed by "God". In fact, if Tegmark's theory is true, there are an infinity of such universes. In an infinite sub-set of these, the creating God is hidden. In another sub-set, God can be openly seen doing his divine work. And there are an infinity of other universes such as materialists consider ours to be -- accidents that by the unlikeliest of chance came into existence with parameters balanced just right to make the development of conscious intelligent life possible. Since, in our universe, God cannot be seen doing his divine work, our universe must be of the first or last variety. And now the question becomes, what of the multiverse that holds all these infinite universes -- does it have a God who created and is watching over it? If so, that God is also God of the subset universes and their lesser Gods, and even the accidental universes with no lesser Gods still have that greater God in the higher world. God just won't go away. Jim M.

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No FOTD for 04-09-03
by Jim Muth 04 Sep '03

04 Sep '03

Fractal fans: Rather than post another FOTD image with compromised quality, I will post no FOTD today, September 04. I must get the work backlog caught up before I can concentrate on fractals. The FOTD will resume on September 05. Jim M.

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FOTD 03-09-03 (Spiral [3])
by Jim Muth 04 Sep '03

04 Sep '03

FOTD -- September 03, 2003 (Rating 3) Fractal visionaries and enthusiasts: When I opened my e-mail box this morning, I found, among all the offers of more length, a letter informing me that I had just won 13-million dollars, or was it euros, in the European Lottery. This is strange, since I never bought a ticket. But I'm not questioning that aspect. The letter then asked for my bank account number so that the money I had won could be deposited in my account. I replied, requesting that the lottery commission send a check instead. As soon as the check arrives, I shall retire and devote the rest of my days to exploring the world of fractals. I wonder how long it will be before the check arrives. As for today's fractal, it is worth about as much as I am going to be enriched by winning a lottery I never entered. (Could anyone be gullible enough to actually reply to such letters?) I gave today's image a courteous rating of a 3. Actually, it might be closer to a 2. The image is so poor because I had no time to work on it. An unexpected rush job came in on Monday and kept me busy until after midnight. I'm still not quite caught up. Having no time to find a new fractal, I turned to one I generated yesterday, when I saw a message on the Fractint list that 7-armed spirals are a rarity in fractals. I had not realized that such spirals were rare, and to see if this were so, I went to a period-7 bud of the Mandelbrot set and drew the Julia set of that area. Then, for a bit of added interest, I double rotated the image 0.1 degree from the julia direction and got my 7-armed spiral, with a vague hint of Mandelbrot buds in the background. The picture had potential, but then the work came in and I had no time to color it properly. I leave the colors as they were when I had to stop working on it. I named the image "Spiral", and used it as FOTD for today. I might have done better not having a FOTD for today at all, but having gone this far, I am not going to scrap it now. The render time of 18 minutes is too slow for such a question- able image. I advise downloading the finished GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The Tuesday temperature of 84F 29C here at Fractal Central was fair enough, but there was little sun. The occasional sprinlkes of rain were not enough to wet a person, but made the grass too wet for the sensitive paws of the dynamic cats. As a result, they had a bad day and needed their evening treat of tuna to restore their good moods. Today is starting cloudy, cool, foggy, drizzly, with occasional sprinkles of rain. It is sure to be another bad day for the duo. For me, I've still got that left-over work to catch up on. So until next FOTD, take care, and don't get twisted up in an endless spiral. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Spiral { ; time=0:18:49.82--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip passes=1 center-mag=-0.344854/0.856196/4.523577/1/\ 70/-5.05012698326368081e-014 params=89.9/89.9/2/0/\ 0/0/0.36837/0.14068 float=y maxiter=50000 inside=0 logmap=yes periodicity=10 colors=000UFAUPAUFAUPAUFAUQAUFAUQAUGAUUAUJAUXAULAU\ ZAUNAUaAUOAUbAUPAUdAUQAUeAURAUcAUSAUbAUTBUaCUUDU`E\ UVFU_GUWHUZIUXJUYKUYMUZNUZOUZPUZQUZRUZSVZTWZUXZVYZ\ WZZX_ZY`ZZaZ_bZ`cZ`dZ_eZ_f_ZgZZh_YiZYj_XkZXl_WmZWm\ _VlZVl_UlZTk_TkZSj_SjZRj_RiZQi`QiZPh`PhZOg`OgZNg`M\ fZMf`LeZLeaKe_KdaJd`JcbIc`IccHbaHbdGacGaeFadE`fE`f\ D_fD_fC_fCZfBZfBYfAYfAYf9Xf9Xf8Yg7Xf8Xf9Xe9XeAXdAX\ dBXdBXcCXcCXbDXbDXbEXaEXaFX`FX`GX`GX_HX_IXZJXZKXZL\ XYMXYNXXOXXPXXQXWRXWSXVTXVUXVVXUWXUXXTYXTZXT_XS`XS\ aXRbXRcXRdXQeXQfXPgXPhXPiXOjXOkXNlXNmXNmXMmXMmXLmX\ LmXLmXKmXKmXJmXJmXJmXImXImXHmXHmXHmXGmXGmXFmXFmXFm\ XEmXEmXDmXDmS8mVBmXDmZFm`HmbJmdLmfNmhPmiQmjRmjRnjR\ ojRpjRqjRrkRskRtkRukRvkRwkRxlRylRzlRzlRzlSzlSzlSzm\ SzmSzmSzmSzmSzmSznSznSznSznSznSznSznSzoSzoTzoTzpUz\ pVzpVzqWzqWzqXzrYzrYzrZzsZzs_zs`zt`ztaztazsbzrbzrb\ zqczqczpczpdzodzndznezmez } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================

2 1

The Hyper-Logistic Equation
by mdoctorow＠comcast.net 03 Sep '03

03 Sep '03

>From Osher Doctorow Ph.D. The logistic equation is in calculus terminology: 1) dx/dt = c1x(c2 - x) where c1, c2 > 0. When x and t are taken to be in the interval [0, 1] (as for example when x is taken to be a percentage of the population), then c2 can be replaced by 1: 2) dx/dt = c1x(1 - x) This is in fact the usual Rare Event scenario on [0, 1] scales. To extend and generalize the logistic equation, which is very useful for biological growth, to growth in physics and psychology and astrophysics and so on, the simplest general way would be to replace (2) by: 3) dx/dt = c1xf(x, t)(h(x, t) - xg(x, t)) where f(x, t) and g(x, t and h(x, t) are functions that depend on x and t. The case where f(x, t) = g(x, t) = h(x, t) = 1 is the ordinary logistic equation. Since x is some arbitrary variable that grows and/or contracts, why not replace x in a particular scenario by dx/dt? Then we get: 4) d^2x/dt^2 = c1(dx/dt)f(x, t)[h(x, t) - dx/dt g(x, t)] Since the equation has both enough dx/dt's and even has a second derivative d^2x/dt^2, the next simplest choice for f(x, t), h(x, t), and g(x, t) would be either a constant or a linear function of x or a linear function of t. In the bracket, RET tells us that the form of a difference suggests that one term is causal and the other is caused (with probability), so since having t or x in both terms would factor them out into f(x, t), the simplest case is to assign x to one of the two terms in the brackets and t to the other. At this stage, let us compare this picture in (4) with the difference k3 from xp and Et in quantum theory, remembering that xp = k1, Et = k2, xp - Et = k1 - k2 and we define k3 = k1 - k2: 5) mx(dx/dt) - (1/2)m(dx/dt)^2 t = k3 which factors to: 6) m(dx/dt)[x - (1/2)dx/dt] = k3 Equations (4) and (6) are identical except for k3 and d^2x/dt^2 if we set the constant m = f(x, y) and h(x, t) = x and g(x, t) = (1/2)t. This is one of the two ways that we wanted to select h and g (we could have put t and x in opposite terms) except for the constant 1/2, and it is certainly satisfactory to have f as a constant m. We also have the added "bonus" that either space (x) exerts a probable causal influence on time t or vice versa. What do we do about k3 versus d^2x/dt^2, or using differential operator notation, Dtt(x)? It certainly is not unimaginable that the acceleration Dtt (x) of x is constant. It is roughly similar to a constant applied force. We could propose to generalize the resulting equation beyond constant accelerations and just consider that constant k3 holds in certain scenarios, but like special relativity we might as well begin with something constant. So we have another way of deriving a very general "hyper-logistic" equation of growth across several domains. Osher Doctorow Ph.D.

1 0

Geometric Physics and Growth
by mdoctorow＠comcast.net 02 Sep '03

02 Sep '03

>From Osher Doctorow Ph.D. The simplest population growth equation is one that works for bacteria: 1) dx/dt = kx where k > 0. The simplest population decay equation is one that works for radioactive decay: 2) dx/dt = -kx (k > 0) The first has an exponential solution x(t) = x(0)exp(kt), the second a negative exponential solution x(t) = x(0)exp(-kt) I remarked some years ago that Logic-Based-Probability (LBP) and Rare Event Theory proceed somewhat differently from Category Theory, which latter is a branch of very advanced Algebra pioneered by Saunders MacLane and William Lawvere in which the "composition" operation is the main operation. For example, suppose that y = exp(t) and z = y^2, then y o z is the composition of y and z and is equal to exp(y^2), so y o z tells you to put z inside the parentheses of exp(t) instead of t (where y is exp(t)). In LBP and RET and Geometric Physics, we're mostly interested in much simpler operations. For example, we use y * z which is simply (exp(t))*(y^2) where * is just ordinary multiplication. Or we use y + z which is exp(t) + y^2. Since dx/dt is the instantaneous speed or velocity (rate of change of x as t changes), let's write it as an Operator Dt(x): 3) Dt(x) = dx/dt or more generally: 4) Dt(f(x)) = df(x)/dt Since dx/dt = kx is the simplest growth equation, our orientation toward multiplication rather than composition would suggest looking at: 5) Ut(x) = kx 6) Vt(x) = 1/(kx) because: 7) Ut(x) * Vt(x) = 1 so that Vt(x) is a multiplicative inverse of Ut(x). Now let's go one step further and define: 8) W(x, t) = 2x/t which has both a numerator and denominator variable of its arguments. So this leads us to: 9) dx/dt = 2x/t The solution of (9) is rather simple because dx/x = 2dt/t when integrated on both sides leads to log(x) = 2log(t) + c so taking exponentials to both sides leads to x = x(0)t^2. However, keep track of the inequality: 10) dx/dt < 2x/t while I remark about the Heisenberg Uncertainty Principles (HUPs) in the form: 11) U(x)U(p) > = h/(2pi) 12) U(E)U(t) > = h/(2pi) where x is position or distance/displacement (from the origin), p is momentum, E is energy, t is time, and this time U( ) means "Uncertainty of" or "Uncertainty in," so that U(x) means "uncertainty in x". If speeds are not too close to that of light and also potential or potential energy is small, we have approximately: 13) p = mv 14) E = (1/2)mv^2 where v is velocity or speed. In most applications in physics, for example to cosmology and quantum entanglement, a rather curious "oversight" is made - instead of using U( ) in (12), as in U(x), the origin variable is really used, that is to say x. For example, when physicists say that high energy forces act for short times or low energy forces act for long times or that the vacuum seethes with particle- antiparticle pairs coming into existence because short distances are associated with high momenta, they are using (for the latter) xp > h/(2pi) and for the former Et > h/(2pi) and not uncertainties. What happens if we replace U(E) by E, U(x) by x, U(v) by v, U(t) by t in equations (11) and (12)? We get: 15) x(mv) > h/(2pi) 16) (1/2)mv^2 t > h/(2pi) Now it's common to replace the inequalities in the last two equations by equalities and in that case we do have a choice of selecting slightly different quantities from h/(2pi) on the right hand sides. Let's call them constants k1 and k2 respectively: 17) xmv = k1 18) (1/2)mv^2 t = k2 Then we have, by subtracting (18) from (17) and defining k3 = k1 - k2: 19) xmv - (1/2)mv^2 t = k1 - k2 = k3 = mv(x - (1/2)vt) = k3 and therefore if (1/2)vt < x or v = dx/dt < 2x/t, then for nonnegative v the expression equal to k3 will be nonnegative. Readers will recognize this expression from the previous postings. Why would we want k3 to be nonnegative? Well, in RET and LBP and Geometric Physics, the probable influence of x on y can only be calculated if x - y is nonnegative, that is to say y < = x. So if k3 in (19) is nonnegative, then x influences t in x - (1/2)vt. I'll try to continue this shortly. Osher Doctorow

1 0

Multifractal_9
by Albrecht.Niekamp＠t-online.de 02 Sep '03

02 Sep '03

Hi, here are two images I found today. The spiral is the most unusual one Iïve ever seen. Fractal greetings, Al ------------------------------start-frm------------------------------------ FRM:Multifractal_9 { ; Albrecht Niekamp 280803 ;p1 (spider)julia-seed ;real(p2) 5digits : (1)shape (2)outside (3)inside1 (4)inside2 (5)inside3 ; 0_off 1_secant 2_mand 3_bees 4_jul 5_m_mods 6_phoen 7_newt 8_spider ; input2 : 2digits_many-mods 2digits_phoenix 2digits_spider ; 5digits_reset : 0_no 1_z-reset 2_iter-reset 3_both +5_warp ;imag(p2)(-) 5digits_colour(bailout) number ; input2 : 4digits(-)_mand/jul 2digits_secant 4digits_bees ;real(p3) 2digits_newt 4digits_colour1, 5digits_colour2 5digits_colour3 ;imag(p3) shape : factor (fn1), 5digits_colour4 5digits_colour5 ;real(p4) outside: factor (fn2), 4+1digits_bord-out 4digits+fract_bord-in ;imag(p4) inside1: maxit1, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor1 (fn2) 4digits+fract_border1 ;real(p5) inside2: maxit2, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor2 (fn3) 4digits+fract_border2 ;imag(p5) inside3: maxit3, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor3 (fn4) 4digits+fract_border3 ;fn(1) shared by many-mods+bees ; da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=(d3==0) vb=d>5 ab=(d==3)+(d==5)+(d==7)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 v1m=(d==6)+(d==7) v1j=d>7 dd1=(d==4)+(d==5)+v1j ab1=(d==3)+(d==5)+(d==7)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 v2m=(d==6)+(d==7) v2j=d>7 dd2=(d==4)+(d==5)+v2j ab2=(d==3)+(d==5)+(d==7)+(d==9) d=trunc(dd/10) ex3=d>1 v3m=(d==6)+(d==7) v3j=d>7 dd3=(d==4)+(d==5)+v3j ab3=(d==3)+(d==5)+(d==7)+(d==9) d=dd-d*10 ex4=d>1 v4m=(d==6)+(d==7) v4j=d>7 dd4=(d==4)+(d==5)+v4j ab4=(d==3)+(d==5)+(d==7)+(d==9) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex0+ex1+ex2+ex3+ex4 ; d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 ; d=imag(p3) sfac=trunc(d) da=(d-sfac)*10000000000 ba4=trunc(da/100000) ba5=da-ba4*100000 ; d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) ; d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=(d==3) fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=(d==3) fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 ; d=imag(p5) mi3=trunc(d) da=(d-mi3)*10000000000 d=trunc(da/1000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=(d==3) fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 ; mo=vb>ab mo1=v1m>ab1 mo2=v2m>ab2 mo3=v3m>ab3 mo4=v4m>ab4 ; sc=((ab+vb)==0) sc1=((ab1+v1m)==0) sc2=((ab2+v2m)==0) sc3=((ab3+v3m)==0) sc4=((ab4+v4m)==0) ; px=((ab+vb)==2) px1=((ab1+v1m)==2) px2=((ab2+v2m)==2) px3=((ab3+v3m)==2) px4=((ab4+v4m)==2) ; if (d4) z=0 if (vb) if (mo) c=0.4*log(sqr(pixel^mm)) else c=pixel z=pixel endif else c=pixel z=pixel*sc endif else c=p1 z=pixel endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else z=pixel cb=p9*u c=p1*u p=pp*u endif endif tt=tt-1+ex0 elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(pixel^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(pixel^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(pixel^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(pixel^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Qusinewton Pusk s Istv n z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+ph-0.5*zold ;Phoenix Mike Wareman zold=z z=z1 else z2=fn1(z)+c ;Many_mods Linda Allison z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z ;Julia Pusk s Istv n z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) z2=z*z ;Mandel Pusk s Istv n z=z2*z2+p6*z2+c-p0 else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba } ---------------------------------------start-par------------------------- The_spiral { ; Time 0.32.55.43 ; Albrecht Niekamp Sep,03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_9 function=cos/sin/sin/sin passes=t center-mag=-0.00487064/-0.193521/10.41667/1/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/31687.32595705005/15243.0\ 506030602/52048.0408808896/384.1688690886/384.00782000645/128.1007683333\ 1/256.10076833331/384.10076833331 float=y maxiter=3072 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=2000HM<4>09C08A068<2>022000211<21>icNkeOmfP<3>unTwpVxqWzsX<25>CB7\ A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<23>eeegggiiijjjlll\ nnn<2>sss<25>BBB999777<2>222000022<24>0bo0cq0es<3>0kz<19>0IO } Ornaments { ; in a golden frame ; Albrecht Niekamp Sep,03 ; Time 0.14.13.16 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_9 function=cos/sin/sin/sin passes=t center-mag=-0.6404/-2.22045e-016/0.6666667/1/-90/3.88578058618804789e-01\ 6 params=-0.05825983458967864/0.3785210730307932/31687.32595705005/15243.0\ 506030602/52048.0408808896/384.1688690886/384.00782000645/128.1007683333\ 1/256.10076833331/384.10076833331 float=y maxiter=3072 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=200DDC<3>554443221000<25>0bn0cp0er<3>0ky<25>09B089067<2>021000210\ <21>icMkeNmfO<3>unSwpUxqVzsW<25>CB6A95874653442220000400<23>o00q00s00<3>\ z00<25>C00A00800<3>000<2>554776998BBACCB<16>eedggfiihjjillknnm<2>ssr<23>\ EED } ------------------------------------------end-------------------------------

2 1

Geometric Physics and Julia Sets
by mdoctorow＠comcast.net 02 Sep '03

02 Sep '03

>From Osher Doctorow Ph.D. Readers may recall some of my contributions on Logic-Based Probability- Statistics (LBP) and Logical-Experimental Unification Theory (LEUT) and Rare Event Theory (RET) from some years back. My published paper in B. N. Kursunuglu et. al. Quantum Gravity, Generalized Theory of Gravitation, and Superstring Theory-Based Unification, Kluwer: N.Y. 2000, 89-97, is a good presentation of some of this from the viewpoint of LEUT. Some good recent work of mine is on www.researchmathematics@yahoogroups.com (a moderated forum), geometry-research(a)forum.swarthmore.edu which can also be accessed via www.mathforum.com, http://www.superstringtheory.com/forum in the String/M Theory - Duality subforum of their Forum section, Stardrive1(a)yahoogroups.com. Geometric Physics uses not only the 11 fundamental elements which I mentioned last time (Expansion, Contraction, Knowledge as Semantics, Information as Syntactics, Transmission, Rarity, Non-Rarity, inside, outside, potential, actual), but also two very powerful interdisciplinary relationships: A. The cross-discipline expression 1 + y - x for y < = x and usually x and y between 0 and 1 inclusive. In probability-statistics, this is the probable influence of x on y for Rare Events. In fuzzy multivalued logics (FMLs), this is implication (x-->y) such that x implies y for Lukaciewicz and Rational Pavelka FMLs which describe Rare Events. In proximity-geometry-topology, this is p1(x, y) or pn(x, y) for n = 2, 3, 4, ..., where pn(x, y) is the proximity or "nearness" of n-dimensional point or vector x to point y from the viewpoint of x (a one-sided "nearness") for Rare Events. B. The cross-discipline relationships between Expansion and Contraction. These cross the expansion of the Universe as a whole, biological growth and expansion- contraction, expansion-contraction of human (and perhaps animal) consciousness, expansion-contraction in fractals and chaos, self-similarity in dimensional analysis, expansion of radiation from a source, "implosion" or collapse of black holes, expansion of quantum entanglement, and even evolution of galaxies and organic memory materials including plastics. I want to begin here with a rather curious real-valued rather than complex- valued expression which comes from Geometric Physics including both quantum theory and general relativity: 1) dx/dt < 2x/t where dx/dt is the calculus derivative or instantaneous rate of change of x (say a spatial direction) with t (which we'll take as time). In order to x to exert probable influence on t in BOTH a certain quantum and a certain general relativisic (macroscopic) scenario, equation (1) must hold. For those who don't feel comfortable with their calculus or need refreshing in it, dx/dt is the speed of x for x a real variable representing position in space along a straight line or axis - not the average speed of elementary algebra but the instantaneous speed at time t, which is often indicated by writing x as x(t) to mean "x at time t exactly" (not x times t). Readers may find some interest in exploring (1) for the parabolas t = x^2, x = t^2, the ellipse (x^2/a^2) + (t^2/b^2) = 1, the exponential t = t(0)exp(kx), the exponential x = x(0)exp(kt). It turns out that equation (1) is best satisfied for t = x^2 with fewest restrictions, which from the equation t = x^2 brings to our attention the fact that dt/dx, which is 2x, is one way of measuring the SENSITIVITY of t to a change in x. When dt/dx is large, then dx'dt is small if it exists, which relates to (1). I'll try to continue shortly. Osher Doctorow Ph.D.

1 0

FOTD 02-09-03 (Brave Little Midget [6])
by Jim Muth 02 Sep '03

02 Sep '03

FOTD -- September 02, 2003 (Rating 6) Fractal visionaries and enthusiasts: When I wrote yesterday's discussion, I was in a mood of disap- pointment over the things that might have been accomplished in outer space in my lifetime, but were never even tried. Last evening, to remind myself of what might have been, I played an old video tape I recorded almost 20 years ago of a TV presenta- tion of Ray Bradbury's collection of short stories known as "The Martian Chronicles". These stories, which were written mostly in the late 1940's and early 1950's tell the story of the human colonization of Mars and the inadvertent destruction of the already-dying race that had inhabited Mars for apparently millions of years. I'll not go into the plot, which is well known, but I must comment on the time frame in which the Martian Chronicle stories are supposed to take place. Apparently, in 1950, Ray Bradbury, who mellows his fantasy with healthy skepticism, considered it quite believable to write about men from Earth walking on Mars in the year 2003. Well, it is now the year 2003. Where are the men walking on Mars? And what does this failure bode for all the future achievements, which according to sci-tech enthusiasts, science and technology are supposed to bring us? One thing that will certainly be with us in the future is fractals. Today's image is but the smallest example. The parent of today's fractal is an almost-perfect classic M-set rotated about 10 degrees. The set is almost perfect because the exponent of Z is 2.01 rather than 2. The true M-set, with its whole-number exponent, would not rotate when calculated with the MandelbrotBC1 formula. Mandeloids in this range hold interesting new features along the negative X-axis, where a prominent split develops. The MandelbrotBC1 formula rotates these near-whole-number Mandeloids in a controlled manner, so that the split can intersect any desired part of the almost-perfect set. In today's case, which uses the default values and rotation, the split intersects the southern branch of Seahorse Valley, and wreaks its havoc there. The character of the Valley has totally changed. The familiar features are gone. All the features in the vicinity of the great split have split again and again into tiny fragments, until little remains of the original appearance of the area. Yet despite the overall chaos, many midgets remain virtually intact, acting as centers of attraction for the new features emerging from the chaos. Today's image shows one of these brave little midgets holding its place even while the world around it is falling apart. In honor of its valor, I have named the image "Brave Little Midget". The circular holes surrounding the midget are permanent features that do not fill in with higher iterations. Nothing at all like them appears in the classic Seahorse Valley. And look closely at the arrangement of features around the midget. You will notice that it is not quite symmetrical, and does not quite fall into the 2-4-8... series of the classic M-set. The midget in today's image may be brave, but its effort has cost its appearance. I could rate the image no higher than a 6, which is not bad, but still only the slightest above average. The render time of 15 minutes can be avoided as always by down- loading the completed GIF image from the internet at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> As I expected, it never rained here at Fractal Central during the day on Monday, and the dynamic cats had another happy afternoon in the yard. True, a thunder-storm did arise at 9pm, but that was after dark, when the day had ended. The tempera- ture of 88F 31C was uncomfortable for people, but within the comfort range of fractal cats. Today brings another forecast of thunder. It remains to be seen what will actually happen. One thing certain to happen is that the work which needs to be done will be done by day's end. And when the work is out of the way, I will try to find a fractal worthy of a rating of at least a 7. To see if I succeed, check back here in 24 hours. Until then, take care, and see what lies beyond the next iteration. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ BraveLittleMidget { ; time=0:15:10.06--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=recip passes=1 center-mag=-0.79333921686891930/+0.011042202099867\ 17/3.308758e+007/1/-60/7.13843934817270931e-007 params=2.01/0/0/0 float=y maxiter=2100 inside=0 logmap=276 periodicity=10 colors=000ThmSglRfkQejPdiOccNaXM`RLZKKYEJW7JV1PZ6V\ bB`fGeiLkmQqqVyuZvt_st`ptamsbksbhscerdbre_rfYqfVqg\ SqhPpiMpjKpjLlfLicLf_LcXL`TLYQMUNMRJMOGMLCMI9MF6TO\ 5ZX5ee4km4jk7ij9hiCggEgfHfeJecMdbOcaRc`TbZVaYY`X__\ Vb_UdZTgYRiXQlWPnWOp_NobNoeNohNnlMnoMnrMmuMmzKrxMm\ vNitOerPapRYnSUlTPjULhWHfXDdY9bZ5a_1bZ3bZ4cY5cY6cX\ 7dX8dW9dWAeVBeVDfUEfUFfTGgTHgSIgSJhRKhRLkSLhRMfRNd\ RObRO`RPZRQXRRVRRTRSRRTPRTNRULRVJRWHRWFRXDRYBRZ9RZ\ 7R_5R`1Nc3R`4UY6XV7`T8cQAfNBiKCmIEpFFsCGvAIs9Jp9Kn\ 9Lk8Ni8Of8Pd8Qa7S_7TX7UV7VS6WP6YN6ZK5_I5`F5cD5hA4m\ 84r54w34z53r63m83h93cB3_C3_D3ZF3YG3XI3WJ3VK3UM3TN3\ SP3RQ3TP2RR3QS4PT4OU5MW5LX6KY6JZ7H`7Ga8Fb8Ec9Dd9Eb\ CFaEF`HGZJHYMHXOIWRJUTJUWKUYKU_LUbMUdMUgNUiOUlOUnP\ UqQUsQUvRUxRUzSUuTUqUWlVYhV_dWa_XcWYeRYgNZiJ_kE`mA\ Zo7`q6bs6du5fv5hw5ix4ky4mz4oz3qz3rz3dzRSzmTznUzoVz\ oWzpXzqYzqZzr_zsezKazRZzY } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(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==================================

1 0

Re: Virii, Worms, and other Seeds of Evolutionary CHAOS
by JackOTradez 01 Sep '03

01 Sep '03

Folks - lose the blame game attitude and stay friends! I do not have anti-virus on any of my systems, and I have never been hit. (Cause I'm smart with these things.) However, my Parents' PC (where I have been visiting for the past week) DID get slammed by 2 of these beasties. I spent the better part of a day cleaning out the system, repairing and restoring it. This was particularly infuriating to me cause I was using their system to access my email while away. DOZENS of my emails were infected, but Mr. Norton caught them. They apparently opened an infected email from one of their friends / family and unknowingly cut the beasties lose on another system. (not Norton protected). Not everyone is a Cyber-Wiz Dude. System and Server Administrators can not be expected to be 100% foolproof. Having some experience there, I know how tough it is just to keep things running smooth when all is ok! Give 'em a break! Flies and rats do not cause garbage, guns do not cause crime, spoons did not make Rosie fat, and System Administrators do not cause spam and email virii! The fault is 100% with the authors of these toxic codes, and the email spammers. WHEN will enough be enough!? This is costing billions of dollars to an economy struggling to recover, and is especislly irritating to unemployed like me trying to find a constructive job! What needs to be done is this - hunt down and find one of these bastards, and nail him hard! It may be a teenage punk dork with pierced tounge, earrings, tatoos, clothing 10 sizes too big, who can't find a date, but so what! Give him 20 to life and let him get deliverance in the slammer! This is criminal trerrorism and should be dealt with as such. How 'bout a Federal task force, like the "Untouchables" during prohibition? Computer Gurus with an Axe in one hand and an automatic weapon in the other - Raid the spammers' and tear them up! Raid the home of the virus author, smash it all up, drag him away in chains never to see the light of day again! Confiscate all material and financial assets to the State. (Hey Echelon - are you listening? I'm willing to volunteer for this ...)

6 10

FOTD 01-09-03 (Fractal Honeycomb [6])
by Jim Muth 01 Sep '03

01 Sep '03

FOTD -- September 01, 2003 (Rating 6) Fractal visionaries and enthusiasts: I am sometimes accused of being irrational and against science. Well, some of my world views are irrational, but I am certainly not against science. I am rather disappointed with science, and particularly with technology, however -- not with the scientific way of doing things but with the way science and technology have been applied. Thirty-four years ago, when I was still a young man, we landed the first men on the moon -- probably the greatest human achievement that will happen in my entire lifetime. And we did it with 40-year-old technology. The future looked bright back then. I fully expected to see colonies soon established on the moon, Mars, and perhaps some of the large moons of the outer planets. But something went wrong. Instead of pressing onward, we slipped backward into the space shuttle program. Instead of exploring the solar system, we would continue orbiting earth in circles that go nowhere. When it was proposed, the shuttle program was supposed to bring unlimited benefits to mankind. Other than the Hubble telescope, which has brought some spectacular pictures, but probably could have been equalled by a properly designed ground-based system if the effort had been made, I can see little if any benefit to humanity that has come from over 20 years of circling the earth in these oversized space craft. And I have yet to hear of any real benefits that will come from the over-priced space station the shuttles are building and supplying. When deep space was within our grasp, we turned our backs on it, and turned instead to a glittery vehicle that makes a lot of noise and a lot of news but does nothing of importance that I can see. Most of the useful artificial satellites in orbit were launched by inexpensive expendable rockets, which never make the news unless one happens to fail. The question remains: why did we forget the solar system and devote our energies to orbiting the earth? Are we afraid? Was the reason financial? Did a single person make the decision? Are we being controlled by a vast conspiracy of the huge multi- national corporations? One of the least likely explanations I have seen is that, because we cannot restrain our tendencies to violence, we were ordered to stop venturing beyond the immediate vicinity of earth by the Galactic Federation, an alliance of the various advanced civilizations that inhabit our galaxy. It sounds laughable, but hey, it's as logical as any other reason I have heard. Well, it now looks as though I should think of freezing my body or start hoping for reincarnation if I plan on seeing mankind explore even the solar system, much less the galaxy. Yes, some- times I do get a bit testy with the way we are wasting our resources on this planet. But I can hardly be blamed. Today's fractal, direct from the deepest, most abstract space in existence, vaguely reminds be of a honeycomb. And so I named it "Fractal Honeycomb". It is a scene in the fractal that results when 0.2 parts of Z^3 are added to Z^2. The terraced amber parts of the image are inside stuff rendered by the 'fmod' inside option. The rating of a slightly above average 6 seems appropriate; the render time of 21 minutes seems slow. Relief may be found at the FOTD web sites, where the completed GIF image is posted. Those sites are at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> As I expected, the rain forecasted by the experts failed to appear on Sunday just as it had failed to appear the day before. In the 79F 26C air, the cats had a pleasant day. Rain is forecast again today, and though the sky now appears more threatening, I won't believe it will rain until rain is actually falling. The cats hope the experts are wrong again. It's labor day here in the USA -- the day on which no one does labor. And to celebrate the occasion, I will do absolutely nothing. Fractals are not labor however, and by the time tomorrow arrives, I will have the next fractal ready. Until then, take care, and avoid fractal dead-ends. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Honeycomb { ; time=0:21:34.38--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=t center-mag=-2.8414007179238/+0.031120296275605/1.4\ 565e+010 params=1/2/0.2/3/0/0 float=y maxiter=1200 inside=fmod proximity=0.0275 periodicity=10 colors=000OmRMpPLoOLnOLnOKmOKmOKlOJlOJkOJjNIjNIiNI\ iNHhNHhNHgNHgNKfQNfSQfVSfXVcWX`WZYW`WWbTWdQWfNVhLV\ jIVlFVnCVpEVlGWhIWeKWaMWZOXVQXSSXOUXKZXHcYDhYAmY6r\ Y3vYPz`jybksckndkiekdfkZgkUhkPikKjkFkjGljHljIljIli\ JliKmiLmiLmhMmhNmhOnhOngPngQngRngRnkUloXjr_hvbfyde\ nh`dkWVnSKrNAuI0xE2wH4vK6uN8tQAsSCrVDqYFp`HobJneLm\ hNlkOlmLekI_iFUgCNe9Hc6Ba35_49`5Da6Hb7Lb8Pc9Td9XdA\ `eBdfChgDlgEphFtiFwiMthTrh_phfnhllhfme`nbWo_QpXKqU\ FrR9sO4sL6pM8mM9jNBhNCeOEbOF`OHcGJf9Kh2WP4UQ5SQ6QQ\ 6PQ7NQ7LQ8KR8IR9GR9FRADRABRBARBETCHUDLVEOWERXFVYGY\ ZH`_Hd`IgaJjbJfVLbNO_GQEKSGNTHPUJRVKTWMVXNXYfFkhIj\ iKjkMjlOinQioSiqUhrWhtYhu_htXdsVasTZrRWrPSqNPqLMpI\ JoGGoECnC9nA6m83m60i93fB6bE9_GBWJETLHPOKMQMNXHOcCN\ cBNcBNcBNcBNcBNcBKc`HZlG`vGZsGXpFVlFTiFQfEObEM_EKX\ DITDFQDDNCBJC9GC7DC5AE4BG4BJ5CL5CN5DP5DQ5DS5EU5EW7\ FYAF_DGbGGcJGgMFkPFmSFpVE } 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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Multifractal_9
by Albrecht.Niekamp＠t-online.de 01 Sep '03

01 Sep '03

Hi, this (probably) is the final stage of Multifractal. There will be an update if a bug is detected or if I find something which must be included or changed. One essential is still missing, and somehow I literally squeezed it in: separate coloring of each channel. It simply adds a new dimension. To see what I mean check Cottoncandyland. I named it after that beautiful ELVIS song and for me it is a step further to fractal art. The input really is simple: As first input, real(p2) you just type the number of the colour to use for each channel. The colour (bailout) values supply a progressive compression if used in their order, or a progressive expansion vv if counted down. They also can be set according to the needs of the frm which is used for the concerned channel. The many_mods frm always needs the highest value as this will increase complexity. Defining an inside image by the borders is a tricky business as no autoswitch to the next channel is performed, which is the case with iteration defined channels. So if only the channel number is checked during the iterations this will cause the iteration to hang to the border defined channel if the conditions for activation are not met. In that case none of the following channels will be executed. To avoid this channel1 switches off if maxiter1 is reached, even if it is not active. With one testing image this meant about 25% less calculation time. House_of_the_helmets of the last submission (a reproduction is included) needs about 5 min less, inspite of 8 new inputs (p4/2giga at 1600/1200). If this is understood, it should be clear that channel3 (inside1) can be borderdefined only if a previous switch is performed. This means channel1, which applies the warpeffect to the basic shape must be checked (real(p2) second input, last 5 digits. The first of them must read 5 or 7 if an iter reset is required). Consequently, if channel3 is iteration defined channel4 can be border defined. Type the numbers in brackets (7 or 8) to use maxiter and bordervalues simultaneously. Channel2 (outside) must remain bothways defined as two border values, in and out, are used and an iteration switch would have to imply switching on and off and that actually would cause a slow down. The images: Cottoncandyland should be your first choice, check it out. The Galleries image shows a border defined mandel as inside2, which nicely fits into the iteration frontiers. Although itïs a mandel there is no mandel shape, maybe youïll find one on deep zooming, I have not checked. Mandelcross is an overnight fractal (4.5hours). Itïs so slow due to two iteration resets and a very high iteration level at all pixels. The special thing about this one (except the coloring) is that the m_m structures, which usually build circles now support the mandel shape. Multifractal has gone a long way, from the initial experiments (Mandelmania) to a definetly (within the Fractint limitations) usable product. In my first comment I said itïs a new country to explore and thatïs what I did. I learned a lot of things and still do. Jim, youïre wondering about my motivation - is there a better one then this? Fractal greetings, Al ------------------------------start-frm------------------------------------ FRM:Multifractal_9 { ; Albrecht Niekamp 280803 ;p1 (spider)julia-seed ;real(p2) 5digits : (1)shape (2)outside (3)inside1 (4)inside2 (5)inside3 ; 0_off 1_secant 2_mand 3_bees 4_jul 5_m_mods 6_phoen 7_newt 8_spider ; input2 : 2digits_many-mods 2digits_phoenix 2digits_spider ; 5digits_reset : 0_no 1_z-reset 2_iter-reset 3_both +5_warp ;imag(p2)(-) 5digits_colour(bailout) number ; input2 : 4digits(-)_mand/jul 2digits_secant 4digits_bees ;real(p3) 2digits_newt 4digits_colour1, 5digits_colour2 5digits_colour3 ;imag(p3) shape : factor (fn1), 5digits_colour4 5digits_colour5 ;real(p4) outside: factor (fn2), 4+1digits_bord-out 4digits+fract_bord-in ;imag(p4) inside1: maxit1, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor1 (fn2) 4digits+fract_border1 ;real(p5) inside2: maxit2, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor2 (fn3) 4digits+fract_border2 ;imag(p5) inside3: maxit3, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor3 (fn4) 4digits+fract_border3 ;fn(1) shared by many-mods+bees ; da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=(d3==0) vb=d>5 ab=(d==3)+(d==5)+(d==7)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 v1m=(d==6)+(d==7) v1j=d>7 dd1=(d==4)+(d==5)+v1j ab1=(d==3)+(d==5)+(d==7)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 v2m=(d==6)+(d==7) v2j=d>7 dd2=(d==4)+(d==5)+v2j ab2=(d==3)+(d==5)+(d==7)+(d==9) d=trunc(dd/10) ex3=d>1 v3m=(d==6)+(d==7) v3j=d>7 dd3=(d==4)+(d==5)+v3j ab3=(d==3)+(d==5)+(d==7)+(d==9) d=dd-d*10 ex4=d>1 v4m=(d==6)+(d==7) v4j=d>7 dd4=(d==4)+(d==5)+v4j ab4=(d==3)+(d==5)+(d==7)+(d==9) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex0+ex1+ex2+ex3+ex4 ; d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 ; d=imag(p3) sfac=trunc(d) da=(d-sfac)*10000000000 ba4=trunc(da/100000) ba5=da-ba4*100000 ; d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) ; d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=(d==3) fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=(d==3) fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 ; d=imag(p5) mi3=trunc(d) da=(d-mi3)*10000000000 d=trunc(da/1000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=(d==3) fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 ; mo=vb>ab mo1=v1m>ab1 mo2=v2m>ab2 mo3=v3m>ab3 mo4=v4m>ab4 ; sc=((ab+vb)==0) sc1=((ab1+v1m)==0) sc2=((ab2+v2m)==0) sc3=((ab3+v3m)==0) sc4=((ab4+v4m)==0) ; px=((ab+vb)==2) px1=((ab1+v1m)==2) px2=((ab2+v2m)==2) px3=((ab3+v3m)==2) px4=((ab4+v4m)==2) ; if (d4) z=0 if (vb) if (mo) c=0.4*log(sqr(pixel^mm)) else c=pixel z=pixel endif else c=pixel z=pixel*sc endif else c=p1 z=pixel endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else z=pixel cb=p9*u c=p1*u p=pp*u endif endif tt=tt-1+ex0 elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(pixel^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(pixel^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(pixel^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(pixel^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Qusinewton Pusk s Istv n z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+ph-0.5*zold ;Phoenix Mike Wareman zold=z z=z1 else z2=fn1(z)+c ;Many_mods Linda Allison z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z ;Julia Pusk s Istv n z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) z2=z*z ;Mandel Pusk s Istv n z=z2*z2+p6*z2+c-p0 else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba } ---------------------------------------start-par------------------------- Galleries { ; Albrecht Niekamp Aug,03 ; Time 0.37.33.93 ; ; ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_9 function=sin/exp/exp/sin passes=t center-mag=0.332423/0.00308737/1.230666/1/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/21222.32595705/15243.0506\ 030602/152048.0404808048/384.1604894048/384.00482000595/256.100768999990\ 1/384.8007680096201/512.1007689999901 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200RRR<8>fffgggiiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0cq\ 0es<3>0kz<25>09C08A068<2>022000211<21>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A96\ 875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<13>PPP } Cottoncandyland { ; Time 1.49.41.94 ; Albrecht Niekamp Aug,03 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_9 function=sin/exp/exp/sin passes=t center-mag=-0.319529/0.0030641/4.851655/1/-90/-1.23373533611470521e-014 params=-0.05825983458967864/0.3785210730307932/21225.64595788025/14235.0\ 506030602/152048.0404808048/384.1604894048/384.00482000595/256.100768300\ 1/512.1007683001/768.1007683001 float=y maxiter=3072 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=200RRR<8>fffgggiiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0cq\ 0es<3>0kz<25>09C08A068<2>022000211<21>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A96\ 875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<13>PPP } The_mandelcross { ; Time 4.21.19.14 ; Albrecht Niekamp Aug,03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_9 function=sin/exp/exp/sin passes=t center-mag=-0.42439526335446220/+0.00009247620495413/171.1872/1/-90/-1.2\ 3373533611470521e-014 params=-0.05825983458967864/0.3785210730307932/21225.64595788025/14235.0\ 506030602/152048.0404808048/384.1604894048/384.00482000595/256.100768300\ 1/512.1007683001/768.1007683001 float=y maxiter=3072 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=200EEE<3>777555444222000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000\ 211<21>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00\ <25>C00A00800<3>000<11>LLLNNNPPPQQQSSSUUU<6>fffgggiiijjjlll<3>sss<22>GGG } House_of_the { ; Helmets ; Time 2.27.56.08 ; Albrecht Niekamp Aug,03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_9 function=sin/exp/exp/sin passes=t center-mag=0.332423/0.00308737/1.230666/1/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/21222.32595700021/12115.0\ 506030602/152048.0409608192/384.1609649094/384.00482000595/256.100768300\ 01/512.10076830001/768.10076830001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200999<20>iiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0cq0es<3\ >0kz<25>09C08A068<2>022000211<21>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A96875<3\ >000400<23>o00q00s00<3>z00<25>C00A00800<3>000<3>777 }

1 0

FOTD 31-08-03 (The Tiny Crowd [5])
by Jim Muth 31 Aug '03

31 Aug '03

FOTD -- August 31, 2003 (Rating 5) Fractal visionaries and enthusiasts: Take 5/1000 part of Z^1000 and subtract Z from it before adding C, and you get an empty circle with a circumference that resembles a fine-tooth saw. A very tiny valley exists where the X-axis intersects the positive side of this saw-like border. Today's scene is located in a spiral that lies on the southern shore of this valley. I have named the image "Fractal Fern-Forest". One of the earlier attempts at coloring gave the impression of a forest floor covered with ferns. I did not save the color map because I wanted something better, but nothing better ever turned up, and I am stuck with today's inferior color palette. Only the name remains to indicate what might have been. And the rating of an average 5 reminds me to save color palettes that appear all right but easy to improve upon. All the detail in the image is natural high-iteration stuff. The image is a totally traditional one, with a blank black inside and an outside of equal-iteration bands. When it comes to fractals, I am a traditionalist. When it comes to the philosophy of existence, I am a non-tradi- tionalist, but we will not go into that aspect at this time. It is time to post today's FOTD, which renders in 16 minutes. The image can be viewed in far less time by downloading it from the web sites of Paul or Scott at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Other than being rather warm, with a temperature of 93F 34C, Saturday was a near perfect day here at Fractal Central. The weather experts were warning of rain all day, but their warnings were another false alarm. No rain fell to spoil the cats' sunny afternoon in the yard. When evening came, a cool north breeze arose to comfortably end one of the best days the fractal duo has had in several weeks. And I saved a can of tuna. Today once again brings a forecast of rain. It is starting partly cloudy, but after all the empty warnings of yesterday, I feel that a dry and comfortably cool day can be expected. As is apparent, I have little confidence in the ability of the weather forecasters to accurately forecast weather. The chance of the next FOTD appearing in 24 hours is 99.99 percent. The chance it will rate higher than a 5 is 55 percent. The chance I will have a good day is 80 percent. The chance that this is the end of today's FOTD is 100 percent. Until next time, take care, and if I could turn on precognition at will, I would be the world's best forecaster. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal-FernForest { ; time=0:16:29.48--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+1.99617324961325700/-0.000000334263081\ 95/8.949466e+009/1/27.4998800176821874/3.186600636\ 06257538e-005 params=0.005/1000/-1/1/0/0 float=y maxiter=2000 inside=0 logmap=227 periodicity=10 colors=000MIcMJdMKeNMfNNgNPhNQiORjOTjOUkPWlPXmPYnQ\ _oQ_pQ`pR`qR`rRasSatSbuSbvSbvRatR`rQ_pQZnPYlPXjOWh\ OVfOUeNTcNSaMR_MQYLPWLOUKNSKMQKLPJKNJJLIIJIHHHGFHF\ DOEBRD9WD8cM9gU9ja9mj9rr9wz9zwCzuEwrHrpJmmMhkOchQ_\ fTUcVTaYRZ_PXbNUdLRgMSfMSfMSfMSfMTfMTeMTeMTeMUeMUe\ NUeNUdNUdNVdNVdNVdNVdNWcNWcNWcNWcOXcOXbOXbOXbOXbOY\ bOYbOYaOYaOZaPZaPZaPZaP_`P_`P_`P_`P_`P`_P`_P`_Q`_Q\ a_Qa_QaZQaZQbZQbZQbZQbZQbYRcYRcYRcYRcYRdXRdXRdXRdX\ ReXReXReWSeWSeWUfWZfWciWhnVmvVruVrqVmkVhkWciVZhVUf\ VSdVScVSbVS`VS_VS_VS_VR`VRaVRaVRbVRcVRcURbURbURbUR\ aUQaUQaUQ`UQ`UQ`UQ_UQ_UQ_UQZUQZUPZTPZTPYTPYTPYTPXT\ PXTPXTPWTPWTOWTOVTOVTOVTOUTOUTOUUOUVOTWOTXNTYNSZNS\ _NS`NRaNRbNRcNQdNQeNQfMRgNQhOQiPPjQPkROlSOmTNnTNoU\ MpVMqWNrXOsYPtZQuZRv_Sw`TxaUybVzcWzdXzdYzcZzb_za`z\ aaz`bz_czZczZczYczXczWczWczVczUczTczTczSczRczQczQc\ zPczOczNczNczMczLczLczLcz } 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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Re: [Fractint] Spelling
by p.hentges＠gmx.net 30 Aug '03

30 Aug '03

Virii is not correct English - according to the Oxford Advanced Learner's Dictionary the plural of virus is simply "viruses". pierre --On 29 August 2003 17:58 -0600 Tim Wegner <twegner(a)swbell.net> wrote: > Paddy wrote: > >> Virii >> Sorry Tim I'm English. > > English??? If you were Roman I would understand! > > Hmm - shouldn't the Latin plural of virus be viri? > > The list administrator is going to get me for being off topic ... > > Tim > -- COMPUTERBILD 15/03: Premium-e-mail-Dienste im Test -------------------------------------------------- 1. GMX TopMail - Platz 1 und Testsieger! 2. GMX ProMail - Platz 2 und Preis-QualitÃ¤tssieger! 3. Arcor - 4. web.de - 5. T-Online - 6. freenet.de - 7. daybyday - 8. e-Post

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Re: Fractint Digest, bounce messages
by Jim Muth 30 Aug '03

30 Aug '03

At 11:43 PM 8/24/03 -0700, Kevin Sexton wrote: >Before you went off on it it might have been better to politely >let the admin know what happened, Yes, this would have been a better response. >maybe it was just a one time thing, email and listservers >aren't infallible. Yes, it could have been a one-time thing. >Sometimes a mail to you bounces through no fault of your own >but an intermediate server problem. It's possible that over the >past 6 years enough emails bounced that they tripped the 'too >many bounces' counter. Not possible. I only lurked on the list. During the 6 years I lurked, I posted maybe 2 or 3 messages to the list >I would have just tried resubscribing and maybe send a mail to >the admin letting them know there was a problem. On most days, I would have done the same. >Mailing lists are set up to automatically bounce bad addresses, >it doesn't matter if it's a large or small list. Yes, it works best this way. >Most unsubscribes are really due to an address no longer >existing. These addresses should be purged from the list. >There will be on any list that has been around a while bounces >that do not result in an automatic unsubscribe. These take the >administrators time to sort through the headers, and figure out >who bounced (it really isn't always easy, the original address >may not be anywhere in the bounce.) Being a list administrator does take some effort. >I manage a small list, around 10 people, I got about 40 >messages in the last year and several bounces per message, and >when I do get a bounce message, I may have to send test >messages to figure out who has a bad address. Then you know the work involved in being the administrator of a mailing list. >It's even possible that someone else subscribed with a bad >mindspring address and the server matched the headers to your >address. Yes, this is a possibility. >Another possibility is someone subscribed with a forwarding >address like you can get at bigfoot.com, and forwarded to >mindspring. If they cancel mindspring, the bounces come from >mindspring, with no clue to it being another address. Yes, this is another possibility. I'm sure there is a simple, easily explained reason why I was unsubscribed. I didn't blow my top because there was no reason; I blew my top because it happened. On most days I would have shrugged it off and resubscribed. It was the line in the notice which said that, before resubscribing, I should solve *my* problem, that set me off. I found the notice just as I finished a 6-hour argument with a customer who insisted that the errors in his job were caused by my incompetence rather than by his inability to accurately communicate instructions by words or fax. I'll settle down in a day or two. Jim M.

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FOTD 30-08-03 (The Tiny Crowd [5])
by Jim Muth 30 Aug '03

30 Aug '03

FOTD -- August 30, 2003 (Rating 5) Fractal visionaries and enthusiasts: When I opened my e-mail box this morning, I noticed a message with some real fractal substance in it from Osher Doctorow on the Fractint list. The message speculates that perhaps the proper application of fractal geometry could clarify some of the seemingly insoluable puzzles of modern physics. I can't quite grasp how fractals could clarify things such as quantum theory, but I have long watched and wondered how such a revolutionary discovery as fractals could find so little practical application and have so little impact on our under- standing of things. It will be interesting to see where, if anywhere, Osher's ideas go. I am still browsing that old physics text book of mine, which was published in the 1880's. At the time, there were many puzzles which have since been explained. To begin, we were seen living on a world hundreds of millions of years old, illuminated by a sun that could have been burning for no more than ten- thousand years. Then there was the problem of the Ether, which everyone knew existed because waves need a medium in which to propagate, but which was impossible to detect and needed to possess some impossible qualities. Finally, there was a very puzzling situation with thermal radiation, which according to classical physics should have been in the form of extreme ultra- violet radiation. These problems were not solved until we went beyond classical physics. The discovery of nuclear energy solved the puzzle of the generation of the sun's heat. The theory of relativity made the Luminiferous Ether unnecessary, and quantum theory explained why hot coals glow orange-red instead of emitting gamma rays. There are puzzles equally as perplexing in the world of physics today. Could fractals point the direction to the solution of these puzzles? Will fractals solve the puzzles, or better yet, make them irrelevant? And 120 years from now, will the idea of quarks and superstrings be considered as quaint as the idea of Luminiferous Ether seems today? Today's fractal is another scene in the Z^3+C Mandeloid. It is located deep in the West Valley, which is a mirror of the East Valley. For a change, today's image was rendered with the out- side set to the 'fmod' option. I named the image "The Tiny Crowd" because it is filled with many cubic midgets. The rating is an average 5. The 19-minute render time is slow, but speed may be found by downloading the finished GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Friday here at Fractal Central was very warm and muggy, with a temperature of 90F 32C and a dew point of 77F 25C. A brief shower in the afternoon cut short the cats' day in the yard almost as soon as it started, leaving them sulky and making a consolation treat of tuna and turkey necessary. They ended the day in resignation. Today is starting warm and muggy again, but there is more sun than yesterday at this time. Whether this bodes good or evil will not be determined until the day has ended. In any case, I shall return in 24 hours with another fractal, this one not in the cubic M-set. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Tiny_Crowd { ; time=0:19:32.77--SF5 on a P200 reset=2002 type=formula formulafile=slices.frm formulaname=MandelbrotCube passes=1 center-mag=-0.\ 3875828936411013/-0.00020565676691499/4.793506e+009 params=0/0/0/0 float=y maxiter=7200 inside=0 proximity=0.015 outside=fmod periodicity=10 colors=0I0zzzzzzzzyzzyzzyzzwzzwzzwyzwyzuwzuwzuuzsu\ zsszsszsqzqqzqoyqoyomwomuoksoksmiqmiomfokflkdjkdhk\ bhibei`di`difefkhdojbsl`woZzqXzsVzuSzwQzzOzzQzyQzw\ SzuSzsVyqVuqXqoXmlZijZbhZZe`Vd`QdbMabE_dAXd4Vf0Tf0\ Tf0Vd0Xd2Xb4_b4_b7a`Ad`CdZCeZEeZHhXKhXKjXMlVOlVQoS\ SoSSqSVqQXsQZuOZuO`wObwMdyMbwHdyMdzOdzQfzVfzXfzZiz\ `izdizfkzikzkkzomzqmzsmzuozyozzozzqzzqzzqzzszzszzs\ zzuzzuzzuzzwzzwzzwzzwzzyzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzwzzuzzqzzozzkzzizzdzzbzzZzzXzzSzzQzzMzzKzz\ EzzCzy7zw4zu0zs0zq0zo0zl0zo0zl0zl0zl0zj0zj0zj0zh0z\ h2zh4ze7yeAueCqdEmdHkeEidKfaMd_Od_QbXS`VV`VXZTZXQ`\ VNdVNfSLiQIkQImOIoMIqKIsKIuHIyEIzEIzCIzAIz7Iz7Iz4I\ z2Iz2Iz7IzAIzEIzHIzKIzOIzQIzVIzXIzZIzbLzdNziQzkTzm\ VzqXzs_zwazydzzezzhyzjyzlwzowztzztzzrwzqsznqzjmzei\ zcfzabzXZzXXyTSwROuPKuIHsICqI7oI4mI0kI0kI0mI0oI0qI\ 0sL0uQ0wT0yX0za0ze0zj0zo0 } frm:MandelbrotCube {; Jim Muth real(c),imag(c) z=p1, c=pixel+p2: z=z*(sqr(z))+c, |z| <= 16 } END 20.0 PAR-FORMULA FILE==================================

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Spelling
by Paddy Duncan 30 Aug '03

30 Aug '03

Virii Sorry Tim I'm English. Paddy Duncan

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Brief Discussion of Fractals on geometry-research
by mdoctorow＠comcast.net 30 Aug '03

30 Aug '03

>From Osher Doctorow Ph.D. I have been developing an expanded theory called Geometric Physics which may lead to a TOE (Theory of Everything). I discussed fractals in connection with this on geometry-research(a)forum.swarthmore.edu (which can also be reached by accessing http://www.mathforum.org) on 28 Aug. 03 at 19:35:07. The good news is that Geometric Physics has a good possibility of moving Fractals to center stage in mathematics, physics, engineering, and Life Sciences (biology, botany, etc.). The bad news is that I don't have the influence to do it. I am a college mathematics teacher/researcher at one or more of California State Universities and Community Colleges, which are way underfunded compared to Research Universities like UCLA or Berkeley, which in turn are underfunded. Hopefully, some members of FractInt will be interested in Geometric Physics and have more influence than me. Geometric Physics is motivated by the paradoxes, anomalies, infinities, and in fact the general lack of interdisciplinary work and open-mindedness to new ideas in physics, engineering, and to a lesser but still real degree mathematics. Basically, I decided to start physics from almost scratch. The one thing I did was concentrate on ideas related to Cosmology and Astrophysics, where the latter is probably the most tolerant of new ideas of any science. Geometric Physics defines the Universe as containing 11 Fundamental Elements: Expansion (E), Contraction (C), Rare or Rarity as in Rare Events/Processes (R), Non-Rarity (N), Knowledge as Semantics or Meaning (K), Information as Syntactics or Form of Messages (I), transmission (T), inside (i), outside (o), potential (p), actual (a). The 11 Fundamental Elements form a language via concatenation, and they can be taken as elements of Fuzzy Multivalued Lukaciewicz or Rational Pavelka Logic with logical implication (x-->y) = 1 + y - x where x, y are elements of the language in quantified form, that is to say with truth values not just 0 or 1 for true or false respectively but any real numbers between 0 and 1 inclusive, and where 0 < = y < = x < = 1 for the non-trivial cases. Michael Barnsley's contraction maps can be used to generate fractals by iterated function systems. By allowing both Expansion and Contraction, including to different degrees or distances and with different speeds in different directions at different times, one can also generate arbitrary curvature of the Universe and hence geometry and General Relativity. Quantum Theory turns out to be contractive and much less restricted than in the Mainstream. Statistical Thermodynamics including in black holes is recovered by laws of both increasing Information and increasing Knowledge with time. Temperature is derived from speeds and velocities averaged in specific circumstances. Not everybody likes the results. I have posted them recently to Researchmathematics(a)yahoogroups.com, http://www.superstringtheory.com/forum, and a few other forums. Loop Theory of Lee Smolin and Abhay Ashtekar and Carlo Rovelli is not in the "cards" with Geometric Physics, but superstringtheory is including M Theory and brane theory and duality theory. General relativity is in the cards, possibly with modifications, but both Quantum Mechanics (QM) and Quantum Field Theory (QFT) undergo many theoretical modifications. This doesn't make many QM and QFT people very happy when they learn about it, especially ones who are committed to Mainstream theories. Osher Doctorow Ph.D.

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Re: [Fractint] FOTD 28-08-03 (Dog-Bone [4])
by Tony (Anthony) Hanmer 29 Aug '03

29 Aug '03

Hi Jim, It's time for me to apalogise for being mostly a lurker on the Fractint list, with little to contribute. I really enjoy your posts - look forward to the daily fractal fix and am rarely at all disappointed, mostly fascinated. Thank you very much and please indeed keep it up! To our intrepid Multifract developer - wow, those long formulae are really masterpieces of evolving creativity, along with the pars you send to provide glimpses into how they work. The annotations to the .frm files also really help. Thank YOU too very much. Maybe the list is in rather a slump. I have not stopped working on L-systems and IFSs - just not posted much for a long time, hoping to refine some work to the point of a mathematical milestone worthy of major attention, though maybe I'm dreaming. LONG LIVE FRACTINT AND ITS PRODUCERS AND EXPLORERS! Tony Hanmer Tbilisi, Republic of Georgia (usually) _________________________________________________________________ Help STOP SPAM with the new MSN 8 and get 2 months FREE* http://join.msn.com/?page=features/junkmail

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FOTD 29-08-03 (Mission Cubical [5])
by Jim Muth 29 Aug '03

29 Aug '03

FOTD -- August 29, 2003 (Rating 5) Fractal visionaries and enthusiasts: I have on my book shelf a 115 year-old text book on the princi- ples of physics, which I found in my father's house a few weeks after he died. I'm not sure how he came upon the book. Most likely, he got it from his father. But it is one of my favorite books to open and browse when I find a few minutes with nothing else to do. The book is fun to read for several reasons. To start, it is interesting to see the accepted beliefs of the 1880's as they were actually taught at the time, and not as they are described by present day writers. Five forms of matter are described -- solid, liquid, gaseous, ultragaseous, (now called plasma), and Etheric. The Luminiferous Ether was still assumed to be the transmission medium of light, but its existence was not naively accepted without question. On almost every page of the chapter on 'Ether waves' a new puzzle is mentioned. Experiments are pointed out that contradict both other experiments and observa- tion. The problem of the nature of the Ether was considered, as the book states, 'the most recondite in physics'. But perhaps what draws me most strongly to the book is the sense of wonder it imparts to simple experiments that today are taken for granted even in high-school physics labs. The 19th century was an age of enthusiasm and discovery. This sense of wonder reminds me of the sense of wonder that surrounded the discovery of fractals, and then all too soon vanished as people grew bored with pretty pictures and turned to more practical things. Today's not-too-practical image is another scene in the Z^3+C Mandeloid. It pictures a cubical midget very close to the north- west shore of the north bay of its parent, in an area where the tendrils have become quite jagged. This is an area where Siegel Disks are found in the corresponding Julia sets, though I doubt that I would know a Siegel Disk if I saw one. After a few minutes thought, I named the image "Mission Cubical". Since there is nothing really out of the ordinary about the image, I could rate it at only a perfectly average 5. The render time of 6 minutes is not too slow, but a more convenient way of viewing the image is to download it from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Thursday was as pleasant a day as might be expected in this part of the world at this time of year. The mostly sunny skies, temperature of 88F 31C and moderate humidity allowed the cats to have a satisfying romp in the yard. And while they were romping, I finished the graphic work without incident. If only all days could be as uneventful . . . But today is starting cloudy with rain forecast, meaning it is unlikely that the day will be as pleasant as yesterday. We won't know for sure until the day has ended however. To see exactly how things work out, check back here in 24 hours. Until then, take care, and be fractally correct in everything you do. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Mission_Cubical { ; time=0:06:33.31--SF5 on a p200 reset=2002 type=formula formulafile=slices.frm formulaname=MandelbrotCube passes=1 center-mag=-0.29534585848656850/+0.690623707339427\ 90/4.225576e+007 params=0/0/0/0 float=y maxiter=5000 inside=0 logmap=400 periodicity=10 colors=0000qw5ow9nwDmwHkwLjwPiwUgwYfwaewecwibwmawk\ `uj`ti_sh_rg_qfZpeZodYncYmbYlaXj`Xi_WhZWgYWfXVeWVd\ VVcUUbTUaST_RTZQTYPSXOSWNRVMRULRTKQSJQRKSRIQQGOQFM\ QDKPBIPAGP8EP6CO5AO38O27O38M39L39J4AI4BG4BF4CD5DC5\ DA5E95F76F66G46H33E16H29J3CM3FO4HQ5KT5NV6QX7T_7Va8\ Yc9`f9chAfjBhmBkoCnqDqtDtvEwxFvxEuxEuxEtxEtxDsxDrx\ DrxDqxDqxCpxCoxCoxCnxBnxBmxBlxBlxBkxAkxAjxAixAix9h\ x9hx9gx9fx9fx8ex8ex8dx8ez5dx8cwAbvCauE`sG`rI_qLZpN\ YnPXmRWlTVmTWkVXiWXgXYfYYdZZb__a`__a`Yb`XcaVdaTebS\ fcQgcOhdMidLjeJkeHlfGmgEngCohBph9qi7rk4ti6sh8sfAre\ BrcDrbFq`Gq_IqYKpXLpWNpUPoTRoRSoQUnOWnNXnLZmK`mI`l\ JamJbmJcmJdmJenJfnJgnJgnJhnJioJjoJkoJloJmoJmpJnpJo\ pJppJqpJrqJsqJsqJtqJuqJvrJwrJxrJyrJyrLxpMxoNxnOxmQ\ xlRxkSxjTxiVxhWxgXxfYxe_xd`xcaxbbxadx`ex_fxZgxYixX\ jxWkxVlxUlzRmxTmwUmvVmuWmtYmsZmr_mq`npbnocnndnmenl\ gnkhnjinijohlogmofnofnofn } frm:MandelbrotCube {; Jim Muth real(c),imag(c) z=p1, c=pixel+p2: z=z*(sqr(z))+c, |z| <= 16 } END 20.0 PAR-FORMULA FILE==================================

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Some list housekeeping
by Tim Wegner 28 Aug '03

28 Aug '03

1. Given the impact on various viruses on the internet in general and folks here in particular, list discussion of trojans and virusus (viri?) here was understandable. Without in any way chastising participants in that discussion here, I'd like to cheerfully suggest we declare viruses and trojans off topic going forward and move on. If you do have any concerns about viruses and this list in particular, or any other list administrative concerns, let me know via private email. I'm not aware that any trojan-laden software made it to the list but it might have - my own software would have killed them so I might not have realized it. 2. Since the Xmission mailman software upgrade, this list has been set to more or less operate on autopilot. This means that the mailman software will unsubscribe you automatically after a certain number of bounces. If this happens, it's not personal, and I have set things so I won't even know. I can change this if it becomes a problem, but believe me, I am very happy about this - I used to process maybe 10 bounced emails a day, and u-n-s-u-b-s-c-r-i-b-e people by hand. If you noticed that you are not getting messages, just go to http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint and re- s-u-b-s-c-r-i-b-e. Thanks to Jim Muth, there's a message from the list most days. 3. I have received several requests to u*n*s*u*b*s*c*r*i*b*e that were sent to the list. Please note that you can uanbscudbesfcgrhiibje yourself using the web interface posted at the bottom of every list message. You don't need to ask to be u!n!s!u!b!s!c!r!i!b!e!d. But of course if you do ask me, I'll do it. Also notice that certain requests won't make it to the list because the words are taboo, even for all powerful list administrators such as myself. I am sure you are all clever enough to figure out what I mean, and can see the devilishly brilliant means I used in this very message to thwart the censoring software! :-) 4. This message was necessarily on topic because I wrote it, but responses to this message are hereby declared off topic. I just love writing that! 5. This message will self-destruct in five seconds ... Tim

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Re: Fractint Digest, bounce messages
by Jim Muth 28 Aug '03

28 Aug '03

At 12:52 AM 8/26/03 -0700, Kevin Sexton wrote: <much cut> >it's not messages posted by you that would have >bounced, but messages sent to you Considering that the list generates one or two messages per month, the bounce limit must have been set incredibly low. More importantly, why was no attempt made to inform me that messages were bouncing? My e-mail address has always worked as it should for everything else. And they had no problem sending the 'unsubscribe' notice to me. (purging invalid addresses) is what the server was trying to do Probably, but check the two letter fragments attached below, which I received from the list on the day before I was unsubscribed. Do you think this could possibly have had anything to do with the event. And if so, could the 'administrator' have taken corrective action if he, she, or it, had been more alert. FIRST LETTER FRAGMENT----------------------------- Originator: <tieu(a)ai.mit.edu> Recipients: <fracprogrammers-list(a)terindell.com> Subject: Your details WARNING: The file document_9446.pif you received was infected with the W32/Sobig.f@MM virus. The file attachment was not successfully cleaned. SECOND LETTER FRAGMENT---------------------------- Originator: <Kilauea9402-46-24955791-0(a)flonetwork.com> Recipients: <fracprogrammers-list(a)terindell.com> Subject: Your details WARNING: The file document_9446.pif you received was infected with the W32/Sobig.f@MM virus. The file attachment was not successfully cleaned. END LETTERS--------------------------------------- I am not defending my loss of temper. Doing so is never the best course of action. I will accept a proper chastising by anyone who has never lost their temper. And I did count to 10. The 'administrator of the fracprogrammers list' was in the unfortunate position of being number 11. Jim (tempest in a teapot) Muth

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FOTD 28-08-03 (Dog-Bone [4])
by Jim Muth 28 Aug '03

28 Aug '03

FOTD -- August 28, 2003 (Rating 4) Fractal visionaries and enthusiasts: This morning, after clearing my e-mail box of the countless (that is 147) spams, viruses, and returned messages that I never sent out, I found three real messages. One is from a known customer who wanted to make a small change in a job I will be working on later today. The second is an unsubscribe request from a member of the fractint list. The third is a reply to the second letter, echoing the unsubscribe request. Since posting a letter to the list and requesting to be unsubscribed is not the proper way to unsubscribe, I feel these two letters were intended to send a message. And the message is "we're tired of all this off-topic blather. Where has the interest in fractals gone"? I often wonder this same thing myself. When, except for the FOTD, the list is blank for days, when a fractal enthusiast devotes weeks of effort writing and refining a great fractal formula, and, except for a few courtesy fractals, the list members basically ignore it, the message I get is, "we're bored with fractals. Let's move on to something else." Then, when we start bickering over things such as internet spam and precogni- tion, topics that I myself introduced, the message becomes even stronger. Maybe we're all bored with fractals. Maybe the fractal thing has run its course. True, over on the UF list, the messages keep pouring in. But the attitude on that list is more 'hey look, I'm an artist' rather than 'hey look at what these numbers do', which was the attitude when I discovered fractals those many years ago. And yes, perhaps boredom is catching. I must admit that after so many years of one new fractal after another, even I find my enthusiasm not quite what it once was. Perhaps this is the reason I was so irritated when I was unsubscribed from the frac- programmers list, which I was hardly aware I was subscribed to. I am not on the verge of giving up on fractals however. I'll keep the FOTD going for the immediate future, and despite broken promises in the past, I soon will post pictures of the fractal cats, who some might believe are imaginary. And that long promised but never delivered FOTD-CD will be ready as soon as I gather the determination to finish it. Now on to today's glorious fractal. Today's image is simply a different view of the cubic midget that appeared in yesterday's image. It is not a Mandelbrot image; it is not a Julia image. Its orientation lies halfway through the double rotation between the parabolic and rectangu- lar directions, therefore it is a random oblique slice of the Z^3+C Julibrot. I named the image "Dog-Bone" because of the bone-shaped area surrounding the hole at the center. I rated it a 4 because I am not quite satisfied with the final result. The render time of 19 minutes may be avoided by downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Wednesday here at Fractal Central was a repeat of the day before. Blue skies in the morning gave way to a period of light rain at midday, followed by hot sun in the afternoon and concluding with a heavy thunder-storm at 7pm. The temperature of 84F 29C was near ideal, but the wet grass kept the dynamic duo confined indoors for most of the day. A tuna treat was once again needed to bring their bad day to an almost-successful conclusion. I do not yet know how my day will go. There is ample work to keep me busy until late afternoon, and unlimited fractals to keep me busy when that work ends. But there is also the unexpected, which could happen at any time, so check back in 24 hours to see how things turn out. Until next time, take care, and keep the fractal faith. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Dog-Bone { ; time=0:19:43.26--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=1 center-mag=+0.00000000000106292/-0.000000000000044\ 97/6.408169e+011/0.02359/2.05162504355810471/-88.5\ 173199499032393 params=45/45/3/0/0.000917145685720\ 2/1.093381655554282/0.0009171456857202/1.093381655\ 554282 float=y maxiter=5000 inside=0 logmap=-675 periodicity=10 colors=0006Ag4Ah2Ah1Ah6AhBAhGAhKAhL\ AfLAdMAbMB`OCZMD_OE_QF`SG`UHaWIaYJb_KbaLbcNZeOVgQR\ iRNkTJmUGoUFqUEqUDrUDsUCtUBuUAuUAtV9tW9tX8tY8sZ7s_\ 7s`6sa6rb5rc5rd5re4rf4qg3qh3qi2qj2pk1pl1pm0pn0po0n\ p4mp7lpAkpDjpGipJhpMgpPfqTeqWdqZcqabqdaqg`qj_qmZpl\ YplXpkXpkWpjVpjVpiUpi7ER8GS9IUAJVBLWCNYDPZEQ_FS`GU\ bHWcIYdJZfK`gLbhMdjNekOglPimQkoRmpSnqTpsUrtVtuXvwW\ uvVuvUuvUuuTuuStuRttRttQttPtsPssOssNsrMsrMsrLsrKrq\ KrqJrqIrpHrpHqpGqoFqoFqoEqnDpnCpnCpmBpmApmBrpApmAn\ k9lh9jf8hc8fa7d_7bX6`V6ZS5XQ0XR5WO9VMEVJIUHMUFRTCV\ SA_S7cR5hQ0gR3fS5eT7dUAdUCcVEbWHaXJ`XL`YO_ZQZ_SY_V\ X`XXaZWbaVbcUceTdhTejSelRfoagEbhBci8dj5ek2fl6fm9fn\ CfoGgpJgqMgrPgsTgtWhuZhvbhwehxhhykaz`VzROzHIz7FzFC\ zN6zT9zUCzUEzUHzVKzVMzVPzWSzWUzWXzX_zXWzTazXfz`kzd\ ozapzgpzlpzqszxpzvnztlzrjzqhzofzmdzkbzj`zhZzfXzdXz\ bVzcTzcRzdPzdNzdLzeJzeHzeGzfEzfCzfAzg8zg } 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==================================

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Re: [Fractint] unsubscribe
by Bnsky67＠aol.com 28 Aug '03

28 Aug '03

Please unsubscribe me from this mailing list. Thank you, bnsky67(a)aol.com

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Fwd: [Fractint] Possible Web server outage Wednesday
by Scott D. Boyd 27 Aug '03

27 Aug '03

Yesterday I said: > So... my Web server here at home, which hosts Jim Muth's FOTD, may be down > on Wednesday, and/or Thursday. So those of you that view the FOTD at my site > may need to go to Paul Lee's site for a day or two. It looks like my electricity, and my Web site will remain on at least for today. We all know how slow insurance companies can be.... Scott -- sdboyd56(a)swbell.net http://sdboyd.dyndns.org --------------------------------------- No Microsoft or other proprietary products were used in the creation of this email.

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FOTD 27-08-03 (An Actual Spiral [6])
by Jim Muth 27 Aug '03

27 Aug '03

FOTD -- August 27, 2003 (Rating 6) Fractal visionaries and enthusiasts: In yesterday's FOTD I stated on a hunch that the valley in which the scene is located contains no spirals. Shortly after I sent off the FOTD, I returned to the valley in question and found, you guessed it, spirals beyond counting. The features in the valley that truly have no analog in the classic M-set are the wedge-shaped areas that appear hanging from everything in sight. And I'm not too sure even of this. Today's image pictures one of the valley's cubic midgets, and as is obvious, the midget is surrounded by a well-defined spiral. In the world of fractals, as in the everyday world of material, one must never make assumptions unless those assumptions are based upon solid evidence. Yesterday, I spoke before I checked; today I admit my error. I have on the shelf across the room an old text book of the principles of physics, which was published in 1884. When I make assumptions that prove to be wrong, I sometimes console myself by opening this book to the lengthy chapter on "ether waves", which we now call electromagnetic radiation. The book was written at a time when the luminiferous ether was still assumed to exist, but experiment after experiment was showing that the ether concept led to unsolvable paradoxes. Today, the contrived explanations and many interpretations that were in favor back then seem almost comical in their implausibil- ity. Not only does the beleaguered scientific doctrine of that long-past period enable me to feel less embarrassed over my own mistakes, but it shows how the efforts of even the most devoted and rational scientists can be frustrated by their refusal to let go of comfortable old beliefs. At the present time, quantum theory is in much the same state as was the ether theory 120 years ago. Competing interpretations abound. The problems with the theory of ether were solved when a genius called Einstein put all the puzzling theories and exper- iments together and came up with the theory of relativity, which immediately solved the paradoxes by showing that they were based on wrong assumptions, and therefore did not really exist. I wonder what genius will solve the present-day quantum paradoxes and open our eyes in much the same way as Einstein did nearly a century ago. Before getting totally sidetracked, I should tell that today's image is one of an actual spiral, and that is what I named it. The rating of a routine 6 seems about right for the scene, which has really nothing unique in it. The render time of 12 minutes is a bit slow for such an image, the likes of which has been seen numerous times before. But this 12 minutes can be cut drastically by downloading the completed GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> If you get no response from Scott's site, try again later. His server may be down temporarily. The Tuesday temperature of 86F 30C was pleasant enough here at Fractal Central, but light rain at midday and a severe wind and rain thunder-squall at 5pm put a damper on the dynamic cats' day in the outdoors. An evening treat was needed to restore their good moods. Tuesday brought no unusually good events for me, but it also brought nothing serious to complain about, so I'll consider it an uneventful day, which is really all one can ask for. We'll try to have another uneventful day today. Until 24 hours from now, take care, and the best is always yet to come. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ An_Actual_Spiral { ; time=0:12:31.93--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip passes=1 center-mag=+0.0009171456857348/+1.0933816\ 55554275/1.554455e+011/1/-19.9998367841645539/-1.6\ 467749071533144e-006 params=0/0/3/0/0/0/0/0 float=y maxiter=3200 inside=0 logmap=538 periodicity=10 colors=000ctzctzctzctzctzctzctzctzctzctzctzctzctzc\ tzctzctzcszcqzcpzclzcizcizcizciz_iz_gzbdzgawl_spXp\ tTlzRizOfzLbzK_zPXzUTzXQz_NzaJzZGxUGtPIsKIqFIpEJnE\ JlDJkDJgDLfDLdBLbBNaBN_BNY9NV9OT9OR9OQ8QO8QN8QL8QN\ 9QN9QNBQNBQNDQNDQNEQOEQOEQOGQOGQOIQOIQOJQQJQQJQQLQ\ QLQQNQQNQQOQQOQRQQRRQRRQRTQRVQRXQRXQTXQT_QT_QTaQTa\ QTdQTdQVfRTdQTfQTfQTfQTfQTfQTgQTgQTiQTkQTlQTnQTpQT\ qQRsQRtQRwQRwQRzQRzQRzQRzQRxORwORtORsORqORpORnOQlO\ QkOQiOQgOQfOQdOQbOQaOQ_OQYOQYQQYRQYTQYVO_XQYYQX_QX\ aQVbQVdQTfQTgQRiQRkQQlQQnQOpQOqRNsRLtRLwRJxRJzRIzR\ IzRGzRGzREzREzRDzQBzRDwTDsVDpXDlYDi_DfbGbfJ_iNXlQT\ pTQsXNw_JzbGzfDzi9zl6zp4zt9zzDzzGzzJzqNziQzaTzTXzL\ _zDbzDfzDizDlz6nq1si0wa0zT0zL0zD0z40z00z20z60z90zB\ 0zE0zI0zL0zO0zR0zV0zX0z_0zb0zf0zi0zl0zp0zq0zt0zx0z\ z0zz0zz1zz1zz1zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0\ zz0zz0zz0zz0zz0zz0zz0zz0z } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================

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Possible Web server outage Wednesday
by Scott D. Boyd 27 Aug '03

27 Aug '03

Hi, High winds this afternoon brought down a rather large tree branch on the corner of my house, and across the power line leading to my house. (I still have power though). The electric company recommends that I have them cut my power before we cut away the branches. So... my Web server here at home, which hosts Jim Muth's FOTD, may be down on Wednesday, and/or Thursday. So those of you that view the FOTD at my site may need to go to Paul Lee's site for a day or two. Scott Boyd -- sdboyd56 at swbell dot net http://sdboyd.dyndns.org --------------------------------------- No Microsoft or other proprietary products were used in the creation of this email.

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FOTD 26-08-03 (Chao-Brot [5])
by Jim Muth 26 Aug '03

26 Aug '03

FOTD -- August 26, 2003 (Rating 5) Fractal visionaries and enthusiasts: Recovery is in progress. With today's image, we raise the FOTD standard to a rating of 5. This is only an average rating, but it is still better than yesterday's rating of an abysmal 3. The scene that earns the rating is that of a cubic midget in the Z^3+C Mandeloid, deep in the valley that splits the top bud. This valley corresponds to nothing in the classic Mandelbrot set, and therefore holds some rather unique features. To begin, it is not infested with those over-rated spirals that for some reason have become so trendy among certain fractal groups. More importantly, at least in today's image, the orientation of the illustrated slice is not in the Mandelbrot direction; it is double rotated half-way toward the Julia direction. (Double rotation is one of those non-visualizable things that can exist only in spaces of more than three dimensions.) >From this angle, all resemblance to the original cubic Mandel- midget is gone. Instead, we find a narrow diagonal slit. The powers-of-three sequence of features surrounding the midget is also gone, replaced by a stretched and disconnected mish-mash of bits and pieces of the original pattern. As we approach the central hole, there seems to be little if any order remaining. This inspired the name Chao-Brot. The render time of over 1/2 hour on my slow machine is admittedly too much for such a mediocre image. The better way of seeing the chaotic scene is to download the finished image from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Monday was fair enough for cats here at Fractal Central, though it was a bit too warm for people. The hot sun and temperature of 88F 31C made outdoor activity seem unpleasantly strenuous unless something like ice-cold lemonade was handy. The cats had an average day in the yard, which for 13-year old ex-tomcats means sleeping. Today is starting cloudy however, and showers are threatening. It remains to be seen how the day will go. The only thing near certain is that the next FOTD will appear in 24 hours. Until then, take care, and be ready for actual up-to-date photographs of the dynamic duo of cats. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Chao-Brot { ; time=0:31:06.70--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=1 center-mag=+0.00000002434646647/-0.000000000003558\ 43/3.165493e+010/1.089e-005/-179.995344305281634/-\ 89.9990143502176352 params=45/45/3/0/1.63489133e-0\ 06/1.08873023204355/1.63489133e-006/1.088730232043\ 55 float=y maxiter=16000 inside=0 periodicity=10 colors=000UgqVfrWdsYbtZau__vaZwbXxcWybTwaQv`Ou_Lt_\ JrZGqYEpXBoX9n`M_cZLln4fj6af7Wc8R_ALXBGTCAQE5MF0JG\ GFKWBOi0Vk7SmDQnJOpPMqVJs`HtfFvlDwrBunGtkKrhPqeTob\ Xn_alXekUijagiiehqchybeu`cr_`oZZlYWiXUfWRcUP`TMYSK\ VRHSQFPPENSEMUDKXDJZCHaCGcFEaHD`KBZMAYP8XR7VU5UW4T\ T9XRD_PHbMLfKPiITl9ah1ie8faFcYM`VTYRZWOaUPcTPfSQhR\ QkQRmPRoQOqSLrTJqSKpSKpRKoRLoQLnQLnQLkSMiUNgWOeXOc\ ZPa`Q_bRYcRWeSUgTSiUQjUOlVMnWKoWLlULiSLfRLcPL`OLYM\ LVLLSJLPILMGLJFKLIKNLJOOJQRJRTITWIUZHWaHXdHZfG_iGa\ lFboFdrFetHbsJ_sLXrMUrORrQOqRLqTIpVFpWCpY9o_6o`3oO\ B_BJLDQUFXaGbiGbhGbhGbhGbgGbgGbgGbfGbfGbfGbeGbeGbe\ F`cE_bDZ`CY_B`ZA_X9ZW8XV7UT6SS5QQ4OP3LO2JM1KL0JK3N\ O6RR9UUCYXF`_HdcKgfNkiQnlTroVurUvsTvsTvtSvtRwuQwuQ\ wuPwvPwvOwwNwwNwwLsrKpnJljHifGebFbZE_VUfNimFjiDjeC\ jaBkY9kV8kR7lN5lJ4lF3lC2h8Hd5Wa2jZ5hW8gTAeQDdNGbKI\ aHL_EOZBQYNolOmmQlnRjoSip } 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==================================

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Re: [Fractint] Re: Fractint Digest, bounce messages
by gnome＠hawaii.rr.com 25 Aug '03

25 Aug '03

>I'm trying out a little app called "Mailwasher" http://www.mailwasher.net >This allows you to look at all the headers in your ISP's server, and decide >whether to accept it, delete it I can do that using Pegasus Mail for Windows. ;-) >or bounce it. Don't use that "feature." The only valid bounce message is the one the sender receives when it connects to your mail server and tries to send the message. At best, any "bounce" message received after the mail has already been delivered goes to a bogus email address. At worst, if the spammer actually used a real address to receive bounces, it confirms that the email address was read by someone. David gnome(a)hawaii.rr.com

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FOTD 25-08-03 (Wooly Mammoths [3])
by Jim Muth 25 Aug '03

25 Aug '03

FOTD -- August 25, 2003 (Rating 3) Fractal visionaries and enthusiasts: Elephants certainly are common in fractals. I run into them everywhere. They are almost as common as spirals and midgets. They exist in both the Mandelbrot and Julia fractals, as well as all the oblique planes in between. They have a connection to the East Valley areas of Mandelbrot Midgets, but not every midget that lies in the East Valley of a larger midget has elephants. Today's image pictures a midget surrounded by 8 elephants. There are an infinity of elephants closer in toward the midget, as well as three of them farther out, but we will concern ourselves only with the 8 clearly visible ones. To make things a bit more interesting, we will call the creatures wooly mammoths instead of elephants, and name the image "Wooly Mammoths". But a clever name cannot turn a poor work of art into a great one, nor can it turn a sub-par fractal into an exceptional one. Today's image earns only a lowly 3. The fault is mine. While working on it, I could find no fractal inspiration at all, and believe it or not, inspiration is a necessary part of great fractal images. The 11-minute render time can be avoided by downloading the completed GIF image from one of the FOTD web sites: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Sunday's weather turned into the best of the month here at Fractal Central, with nothing but sun and a temperature of 79F 26C. Still being a bit irate about Friday's business events, I could not fully appreciate the near-perfection, but the dynamic duo, who never engage in the folly of business, had a gorgeous day, and needed no treats to make them happy. Today means back to work, (as well as back to school), but that is not bad news, for the day could only be better than Friday. I will return for certain in 24 hours with a better fractal, so until then, take care, and count to 10. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Wooly_Mammoths { ; time=0:11:34.37--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.07140706412661836/+2.582655886647872\ 00/3.67779e+010/1/107.50897038509423/0.00495479811\ 651823587 params=5/-0.87/0.7/-8.7/-0.85/525 float=y maxiter=1800 inside=0 logmap=241 periodicity=10 colors=000B5NA5R96V86Z76b67f57j57n3Jr1Vv0ez5awAYvF\ UuJRtONsTJrXGqZJm_MiaPebSbdUZeXVg_ShbOjdKkgHmjDnm9\ oo6kh8gm9dmA`mBYmCUmDRmEUmYXtqYshYr_ZqRZpI_o9_o0Gd\ RJiWLm_NrcPvgSsfVqfYoe`mecjdfhdifdldcoacr_buYbxWbb\ 6Y_8WYAUWCTUERSFPQHOOJMLLKJNJHOHFQFDSEBUC9WA7X9LQD\ YJGkCKz6Nt9OqCPnFQkIRhLSeOTbQT`HMY8GW0A_BDcLGgVJkd\ MonPsxSrwUqvVpuWpuXotZns_ms`mralqckqdjpejofiohhnig\ mjgmkdlgaldZlaWlZTlWQlTNlQXkMfjJpiGyhDxcJwZPvVUvQ_\ uMdtHjtDopFmlHkiJjeLhbNfZOeWQcSSbOU`LWZHXYEZWA`U7b\ T3dR0eQEgOShMeiKsjJaaTKUb2Mk5Oj7Qj9SjBUjDWiGXiIZiK\ `iMbhOdhRehTghVigXkgZmg`ngZofYpeXqeWkfUkfTkgRkhQkh\ OkiNkiTcfZXcdQ`jJYpCWxu8qnEkhJeaO_WTUQZOJcIDhC7mEE\ iFKeGQbHWZJbWKhSLnPMtLNzITyNYxScwXhvanufstkxsptrlp\ qimpfiocen_bmXZmUWmRSmNOmKLmHHmEEmBEmtHmmKmgMmaOmY\ QmVTmRVmOXmK_mHsmgqmdpmbnm_lmXnmTkmVhmXfmZcm`ambZm\ dXme_mgbmiemkhmlkmnGmfCmf } 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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Re: Fractint Digest, bounce messages
by Jim Muth 25 Aug '03

25 Aug '03

At 12:48 PM 8/24/03 -0400, H. Harry wrote: >I suppose that you all might know this, but worms such as >"so-big" "Klez" etc... raid other peoples mailboxes and >send messages to, and apparently FROM those folks... > >So all it takes is some who has (lets say) "Jim Muth" >in their mailbox, and suddenly the virus on kluelessloser's >machine is spamming everyone in the name of Jim Muth... >and they dont even know their machine is infected... >the list bot cannot tell that it is not the REAL Jim Muth, >or his real Domain.... > >I'd agree that it is annoying to have messages bounced back >to you, or get unsubscribed... > >but if I was the list administrator I'm not sure i could tell the >real messages from the spoofed ones... > >so just grin, and bare it ( * ) Ha! You appear to actually be defending the peanut-brained idiot. It is the job of a list administrator to tell the real messages from the fakes. If the administrator in question cannot do this for some reason, then he should resign from his position and turn the job over to someone who can. If no on else is available who will take the job, then there is so little interest that it might be time to kill the list. The fracprogrammers list sends about 1 message per week. This is certainly not too much traffic for a single person to monitor. If the poor wretch truly is unaware of the situation or can do nothing about it, then he should crawl into a corner, stick his thumb in his mouth, start crying, and consider himself unfortunate indeed. And if you are trying to tell me that there may be hundreds of infected computers out there distributing spam and viruses in my name, and the owners of these computers don't even know that their machines are infected, then I would say that the entire internet system is broken, and I had best stop using it until it is fixed. If it can't be fixed, then to hell with technology. We would do better by communicating with mental telepathy, and now is the time to start learning how to do it. (Yes, I am aware of how the various viruses, worms, etc. work. That's why I'm so annoyed.) None of my machines has ever been infected by an electronic virus. And I'm no cyber-genius. I open all my e-mail in text mode. I never open e-mail attachments unless they are obviously legitimate jobs in proper format from known customers. This is very simple. There is no excuse for being infected. I am certainly not going to change my e-mail address after 8 years. In fact, if I am irritated just one more time, I just might quit the internet entirely. I have posted the FOTD nearly every day for the past 6-1/3 years. I have done this because it has been fun. If it stops being fun and becomes an ongoing irritation . . . who knows . . . maybe I'll buy a chicken farm and start raising chickens. Jim M.

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Re: Fractint Digest, bounce messages
by harrybissell 24 Aug '03

24 Aug '03

I suppose that you all might know this, but worms such as "so-big" "Klez" etc... raid other peoples mailboxes and send messages to, and apparently FROM those folks... So all it takes is some who has (lets say) "Jim Muth" in their mailbox, and suddenly the virus on kluelessloser's machine is spamming everyone in the name of Jim Muth... and they dont even know their machine is infected... the list bot cannot tell that it is not the REAL Jim Muth, or his real Domain.... I'd agree that it is annoying to have messages bounced back to you, or get unsubscribed... but if I was the list administrator I'm not sure i could tell the real messages from the spoofed ones... so just grin, and bare it ( * ) (resume lurk) H^) harry

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FOTD 24-08-03 (A Fractal Oddity [4])
by Jim Muth 24 Aug '03

24 Aug '03

FOTD -- August 24, 2003 (Rating 4) Fractal visionaries and enthusiasts: Today's image was found logically and automatically, with almost no intuitive or creative input or inspiration. Thus, it rates only an indistinguished 4. I started with the Mandelbrot set, found a midget in a seven-pointed star on the northwest shore, and rotated the midget through several fourth-dimensional direc- tions until it lost all resemblance to its original appearance. The result appears as today's image, which is named "A Fractal Oddity", mostly because it is sliced at an odd oblique angle through the Julibrot. Any resemblance between today's twisted, stretched hole and a Mandelbrot midget is purely coincidental. But the image does illustrate that the things we call midgets are far more complex than their usually-observed Mandelbrot and Julia aspects would indicate. The low rating of today's image is partly offset by the very fast render time of 2 minutes. And the image is also available on the internet, virus-free, at the web sites of Paul and Scott at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Saturday was one of those rare days in August here at Fractal Central, with deep blue skies, puffy white cumulus clouds, a gentle north wind, a temperature of 82F 28C, and low humidity. The dynamic fractal cats behaved like aging angels, (do angels grow old), romping in the yard and enjoying the near-perfect conditions. At one time Thomas actually chased Tippy up a tree. It's nice to know that the old guy can still climb if he needs to. My own mood was also much improved as I put the annoying graphic work behind me, enjoyed the fine weather, and was kicked off no more mailing lists. Today is starting even better than yesterday. Could it possibly be an even better day? The fractal certainly could be a better one. Check back here in 24 hours to see how things work out. Until then, take care, and enjoy life when things go well, but endure life when they don't. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Fractal_Oddity { ; time=0:02:04.41--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=1 center-mag=-0.00000046122435371/-0.000001676965467\ 04/298743.3/1.0525/89.086483798635598/-64.11303405\ 1931024 params=184/-77/2/0/-0.6704863129/0.4579022\ 548/-0.6704863129/0.4579022548 float=y maxiter=1500 inside=0 logmap=177 symmetry=none periodicity=10 colors=000UNfVOeXPdYQcZRb_Sa`T`aU_bVZcWYdWXeWWeWWf\ VWfUWfTWfSWeSWeRWeQWePWeOWeNWeMWeLWeKWeIWdIWcHWbGW\ aFW`EW`DV_CV_BVZAVY9VXAUWAUVASUARTAQSAPRBPQBOPBNNB\ MMBLLBKKCKJCJICIHCHGCGFCFCAGECFFEFGGFHIFIKEJMEKOEL\ QEMSENUDOWDPXDQZDR`CSbCTdCUfCVhCWjBXlBYnBZpB_qBUkA\ PeAJ`AEVAAPB9QA9QA9RA9RA9R99S99S99T99T89T88U88U88V\ 78V78V78W78W78X68X68X67Y67Y57Z57Z57Z57_47_47`47`46\ Z17`48a68b89cA9dDAeFBfHBgJChLCiODjQDkSElUFmWFnZGo`\ GpbHqdIrfIsiJtkJumKvoLvzKwqKwhKw_KxRKxIKx9Kx0Lw3Mv\ 5Nv7Ou9PuCPtEQtGRsISsLTrNTrPUqRVpTWpWXoYYo_YnaZnd_\ mf`mhaljallbmmcmmdmmdnmenmfnmgomgomhomipmjpmjpmkqm\ lqmmqmmrmnrmormpsmpsmqsmrtmstmstmtumuumvumvumtslsr\ lrqlpplonlnmllllkkkjikhhkggkffkddkcckbbj`aj__jZZjX\ YjWXjVVjTUiSTiRSiPQiOPiNOiMNiNRjNUjNYkNalNemNhmOgn\ OgoPfpPfpQfqQerResResSdtSduTcvTcvUcwUbxVbyVbyWcvXc\ sXcqYcnZckZci_cf_cdYbbXba } 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==================================

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FOTD 23-08-03 (Fractals-101 [3])
by Jim Muth 23 Aug '03

23 Aug '03

FOTD -- August 23, 2003 (Rating 3) Fractal visionaries and enthusiasts: It was a bad day Friday here at Fractal Central, with a broken air-conditioner and complaining customers. I finally got the work problems behind me in the evening, though it was nature that supplied the cool air. Unfortunately, the letter from the fracprogrammers list appeared with its 'you have been unsub- scribed' notice at exactly the right moment to act as the target for the frustration that had been building all day. After my outburst, I settled down and found a fractal. I looked exactly where someone just beginning their exploration in the world of fractals might look -- along the main stem of the Mandelbrot set, deep in the East Valley of the large midget. I did make a slight change however -- I double rotated the scene 45 degrees before starting my exploration. Surprisingly, the rotation makes little difference in the image that appears on the screen, though the larger midget in whose East Valley it appears, as well as the appearance of the M-set itself, have been totally changed. I named the image "Fractals-101", since such images serve as an introduction to the world of fractals. The rating of a below- average 3 might be a bit harsh, but I'm disappointed with myself for blasting the list administrator, who is probably not respon- sible for sending the notice, and I feel I deserve no better a rating. There is certainly nothing lacking with the render time, which at less than 1-1/2 minutes is probably less time than it will take to download the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Friday, with a temperature of 95F 35C, was very hot and humid here at Fractal Center, especially indoors when the cool air stopped working. In the evening, a spectacular but harmless rain and lightning storm arose and cooled things down to 70F 21C. The fractal cats spent the entire afternoon outdoors, lurking in the shade of the holly trees, and venturing inside only when the thunder began. They must have sensed my bad mood. Today promises to be much better. My mood can be only better. The next FOTD, which should also be better, will appear in 24 hours. Until then, take care, and hope for the best. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractals-101 { ; time=0:01:24.75--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip passes=1 center-mag=-2.47457594999916800/0/4.60569\ 6e+007 params=-45/45/2/0/0/0/0/0 float=y maxiter=1800 inside=0 logmap=274 symmetry=xaxis periodicity=10 colors=000eK0fK0gK0hK0iK0jK0kK0lK1kQAgWIc`R_fZWlgT\ qoUtmUvmUxoZzqczshzumzvmzwmzxmzymzzmzzVSbn9lkDciGV\ gKNeNEcQ6`O5YN4VL3TK3pfCqeIrdNsdTtcYuccvbhvbmYdi9e\ eE84rJhR9MyMAVB5AUz5FVbUQTMJJFD976fIBL95dcm8gu6Xf4\ MT2BExWdhOUUGKF8AYWIMLCBA6iqWNRGDDZBc6WleCa88P54C2\ BcGSjeENLLmNF`HAPB5C5Aw75U303j02V01F_rpNSkHL_BEO57\ CqkRc_KRODDC6cZyQNdDBKr_Y_OMICBSHLE8AN6PB3CySyzJzj\ EjV9VF4FgmeX`VMPLBCAfeeWVVLLLAAAdmnsldSOKVrCFR6N2w\ H1hB1U50FybJVJ9_N0RH0IB0950H8DC69846423cCzQ8eD4LkT\ 7_L5OE3C714SZ2IN19BUIcF9K3lSF`SAOI5C9JlZ9OHMZuBHT_\ WhuUytuzaaeJJLqyx_dcIKKH`n8IPR9lKLjEHiMbOXWLgQJqKH\ MYBVc8cl5lw2tz0gRgYepOtyOJuVTq`bmflilveYqXKlP6gHI_\ KTTNcMQcYLmEM`AGP7BC4kC35q0x_0cI0KCusUmENKwBKUCCv8\ Eb4GJXIlOK_GMO8OCgQeTSSEUEFWM7_c5aU3cK1eAqgT_iJIk9\ Imw9oUNqNNseBuL5wA3z72z51z2PzPGzG8z8mzbPzJDzaczpQz\ ZDzH9zM6zG4zB2z5hzXjzPlzH } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================

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Weirdness in v20.02.5?
by David Jones 23 Aug '03

23 Aug '03

I have a Disk 'Video' mode set up as: ,Disk/RAM 'Video',3,0,0,0,11,2048,1536,256 But when I generate fractals using it, they always come out at 1024x768. At the same time, I have a similar mode setup for 2048x2048: AF6,Disk/RAM 'Video',3,0,0,0,11,2048,2048,256 And that one generates a properly-sized image. What am I doing wrong, or is this something in the version of Fractint (20.2.05) that I'm using? David gnome(a)hawaii.rr.com

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Re: You have been removed from the list
by JimMuth＠aol.com 23 Aug '03

23 Aug '03

When I opened my e-mail box 1/2 hour ago, I found the following message from the Fracprogrammers list. This list generates so little traffic that I had almost forgotten that I was sub- scribed. After a long, dragged-out and irritating day, the letter caught me in just the wrong mood, and I am really fuming. This time I shall not count to 10 before posting. BEGIN MESSAGE FRAGMENT FROM FRACPROGRAMMERS LIST============ >Your mail address jamth(a)mindspring.com has been removed from the >fracprogrammers-list(a)terindell.com mailinglist. It generated an >excessive amount of bounced mails. >Before sending in a subscription request to fracprogrammers-list- >request(a)terindell.com again, please ensure that this problem has >been resolved. When in doubt, ask your system administrator or >send mail to "postmaster". END MESSAGE FRAGMENT======================================== System administrator, whoever you are: In reply, I would suggest that you (the 'system administrator'), should resolve *YOUR* problem instead of trying to shuffle the responsibility onto me. Don't try to blame worms or viruses or spammers. Don't say that the message was generated automatical- ly. Don't blame equipment failure. Don't say you are too busy. Making excuses such as these merely confirms your own deficien- cies and justifies my anger. Stand up like a man and accept your responsibility. If the list had been run properly, this would not have happened. I have not posted a message to the fracprogrammers list for several years, though I lurk constantly. A quick search of the meager archives will reveal no messages from me. It is absurd to accuse me of posting through the fracprogrammers list gibberish messages with questionable attachments to non-existent addresses when I have not posted a thing since 1998. By this letter, I do not mean to imply that you are a shamefully poor administrator; I mean to state it outright, with no possibil- ity of being mis-understood. Until you assure me that *you* have solved *your* problem with running the list, I have no intention of re-subscribing. When the problem has been solved, contact me, explain the steps that have been taken, and I might consider re-subscribing. If this letter has offended you, contact me privately and I'll see if I can do anything to help you control your anger. And despite my harsh words, I do sympathize with you, for I do realize how humiliating it is to have one's deficiencies made public. Awaiting your sincere apology and corrective measures: Jim M. (If I'm wrong, I'll say I'm sorry.)

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FOTD 22-08-03 (Only One Surprise [6])
by Jim Muth 22 Aug '03

22 Aug '03

FOTD -- August 22, 2003 (Rating 6) Fractal visionaries and enthusiasts: I heard two interesting rumors yesterday. Rumor number 1 is that Microsoft is using Linux!!! on its web servers to protect them from worms and hacker attacks. Rumor number 2 is that the world of fractals is filled with surprises. I don't know about rumor number 1, but rumor 2 is certainly correct. I have discovered many surprising things in the 16 or so years I have been exploring the fractal world. Fractal trees, one of which appears in today's image, are only one of these surprises. The trees lurk in and near the Julia sets of the Julibrots with an exponent of Z between 1 and 2. The orientation of today's image lies 0.65 degree from the Julia direction, and the expo- nent is 1.5, making the conditions perfect for the generation of fractal trees. Since the 'tree' in today's image is but one of an infinity of similar trees in the vicinity, I named the image "Only One Surprise". I rated the final result at a 6, which is just slightly above average. BTW, perhaps the greatest fractal surprise of all came when I discovered that there are two ways in which the Z^2+C Julibrot can be sliced to give a perfect Mandelbrot set, and the second M-set has twice the area of the more familiar classic set. But that's a story for another day. Right now, it's time to give the good news that today's image renders in less than 3 minutes from the parameter file, and the equally good news that the finished GIF image is available on the W.W.Web at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Typical summer heat and humidity with ample sun and a tempera- ture of 90F 32C gave the fractal duo a pleasant day Thursday in the shadier parts of the yard. By the time the end of the day came, they had worn themselves out, and came indoors to eat with no coaxing. Today promises to be a repeat, with the chance of showers added. We'll see how it goes. It will go well for me if I finish the day's work without any unexpected problems. (Such as a call complaining that I sent a job in CMYK instead of grey scale, from a customer who for some reason could not convert the file.) Regardless of any problems, I shall return in 24 hours with more fractal goodies and a few words of wisdom. Until then, take care, and be advised that one person's wisdom can be another person's kookiness. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Only_One_Surprise { ; time=0:02:41.64--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=multimin-XY-ZW-new function=ident/flip passes=1 center-mag=0.380743/0.154547/41.90764/1/\ -32.5/-1.014e-013 params=89.35/90/1.5/0/-0.6391/0/\ -1.15/0 float=y maxiter=1200 inside=0 periodicity=0 colors=0007An6Ao6Ap5Ap5Aq4Ar4Ar3As2At3As3Ar4Ar4Aq4\ Aq5Ap5Ao6Ao6An6An7Am7Al8Al8Ak8Ak9Aj9Ai9AiAAhAAhBAg\ BAfBAfCAeCAeDAdDAcDAcEAbEAbEBaFC`FD`GE_GF_GGZHHYHI\ YIJXIKXILWJMVJNVJOUKPUKQTLRSLSSLTRMURMVQNWPNXPNYOO\ ZOO_NN`OOaNPbMQcMRdLSeLTfKUgJVhJWiIXjIXkHYlHZmG_mF\ `mFamEbmEcmDdlCelCekBfkBgkAhjAij9ji8ki8li7mh7nh6nh\ 6mg7lf7ke7jd7jc7ib7ha7g`8f_8fZ8eY8dY8cX8cW8bV8aU9`\ T9_S9_R9ZQ9YP9XO9XO9WNAVMAULATKATJASIARHAQGBPFBPEB\ ODBNDBMCBMBBLABK9CJ8CI7CI6CH5CG4CF3CG2DF3CF3CF3CF3\ CF3CF3CF3CF3CE3CE3CE3CE3CE3CE3CE3CE3CD3CD3CD3CD3CD\ 3CD3CD3CD3CC4CC4CC4CC4CC4CC4CC4CC4CB4CB4CB4CB4CB4C\ B4CB4CB4CA4CA4CA4CA4CA4CA4CA4CA4C938A4CA5FA6JA7MA8\ PA9TAAWAB_ACbADe9Cf9Cg9Cg8Ch8Ch8Ci8Ci7Cj7Cj7Ck7Ck6\ Cl6Cm6Cm6Cn5Cn5Co5Co5Cp4Cp4Cq4Cq4Cr3Cs3Cs3Ct3Ct2Cu\ 2Cu2Cv2Cv1Cw1Cw1Cx0Bz1Cx1Dw1Ev1Fu1Gt2Hs2Ir2Jq2Kp2L\ o3Mn3Nm3Ol3Pk3Qj4Ri4Sh4Tg } frm:multimin-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=(-z)^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 21-08-03 (Wicked Screensaver [5])
by Jim Muth 22 Aug '03

22 Aug '03

FOTD -- August 21, 2003 (Rating 5) Fractal visionaries and enthusiasts: WARNING . . . the first four paragraphs are an off-topic rant. Spam is one thing, but when I opened my e-mail box last evening after a 3-day absence, I found over 750 spams, many with a 70KB attachment waiting to be downloaded. Since I have a slow dial-up connection, each attachment takes almost one minute to download. A simple bit of math will show that the total download will take close to 12 hours to complete, and the new junk is arriving almost as fast as I can download it. Needless to say I am rather annoyed. REMAINING 3 PARAGRAPHS OF RANT DELETED . . . I counted to 10. Today's hastily found image combines Z^(-7.7) and Z^(-1.1). Much of the image consists of 'inside' parts made visible by the 'epsiloncross' inside fill. The name, "Wicked Screensaver" was inspired, if it can be called inspiration, by the subject line of many of the spam e-mails. I didn't give much thought to rating the image, so the rating of an average 5 will have to do. The render time of 16 minutes can be cut drastically by letting Paul and Scott render the image and downloading it from their web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> After being indoors for two days, the fractal cats were quite eager for the brief spell in the yard they had when I returned late Wednesday afternoon. They grew grouchy when I brought them in too soon. Since I was already grouchy, we all sulked together. This morning is starting very warm, and my e-mail box is once again stuffed with over 300 worthless letters. While down- loading and deleting, I'll get some real work done on another machine. Until tomorrow, when I may be in a better mood, take care, and don't lose your cool. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Wicked_Screensaver { ; time=0:16:20.31--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-3.706926183106532/+14.67823304557001/4\ 828493 params=-0.3/-7.7/-2.1/-1.1/0/0 float=y maxiter=850 inside=epsiloncross proximity=0.002 logmap=206 periodicity=10 colors=0009LVBMUCNTDOSFPRGQQHRPJSOKSOLTNNUMOVLPWKR\ XJSYITYIVZHW_GX`FZaE_bD`cCacCbdEbdGcdHceJceLdeMdeO\ dfQefRefTbdWefUhhSjjQmlOpnMrpKurIzvFwtGtrHrqIooJmn\ KjlLgkMeiMbhN`fOYePVcQTbRQ`SO_SP`VQaXQbZRcaSccSdeT\ egUfjUglVgnWhqWisXjuXjwYktYkrYloZlmZmjZmh_ne_nc_o`\ `oZ`pW`pUaqRaqPdsPaqNZpMVlKSjJPfHLdGIaEFZDBXB8UA5S\ 97RC8QEAPHBOJDNMEMOGLRHLTJKWKJYMI`NHbPGeQFgSEjTElW\ FkYFj_GiaGhcHgeHfhIejIdlJcnJbpKarK`zJYtK_oLaiMcdNe\ ZOgUPiOQkJRmDSo5Pr8SqBVpEYpH`oKbnNenQhmTklWmlXlkYk\ kZjjZjj_ii`hiahhaghbfgcfgdefddfedefcegbdgbdhaci`cj\ `bi`ch`dg`dg`ef`ee`fe`fd`gc`gc`hb`ia`i``j``j_`kZ`k\ Z`lY`lX`mZWrX`mVeiUieSnaQsYOzTPwUQuURsURqUSoVTmVTk\ VUiVVgWVeWWcWXaWX_XYYXZWXaeUZUXVCJXIZVH_UH_TG_SG_R\ G`QF`PF`OF`NEaMEaLEaKDaJDaICbHCbGCbFBbEBcDBcCAcBAc\ AAcCEaEI_GMZIQXKUVMYUOaSQeQSiPUmNiy0VpMScWOcWJcWFc\ WBcW4en7cW8i69bD9XJ000Pol } 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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Re: [Fractint] FOTD 21-08-03 (Wicked Screensaver [5])
by nick.grasso＠hrads.com 22 Aug '03

22 Aug '03

Jim Muth wrote: >>>Spam is one thing, but when I opened my e-mail box last evening after a 3-day absence, I found over 750 spams, many with a 70KB attachment waiting to be downloaded. Since I have a slow dial-up connection, each attachment takes almost one minute to download.<<< Yeah, this is Blaster worm, or whatever Worm-de-Jour. The company I work for has been getting over 500 a day, but the virus checker on our email server deletes the attachment before it gets to the end user. I would suggest signing up with an ISP that has similar software. Better yet, find an ISP that lets you optionally view your email on the web. That way you can view a list of all your messages on a web site and either read them, or delete them without reading them. You can still use your regular email client. Personally, I think computer users should have to pass a 'drivers license' test before they're allowed on the internet. Nick

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Re: [Fractint] FOTD 21-08-03 (Wicked Screensaver [5])
by Jim Muth 21 Aug '03

21 Aug '03

At 11:14 AM 8/21/03 -0400, Nick wrote: >.... find an ISP that lets you optionally view >your email on the web. That way you can view a >list of all your messages on a web site and either >read them, or delete them without reading them. Apparently Earthlink got the message. The unwanted e-mails abruptly stopped soon after I posted today's FOTD. I have received none since. Jim M.

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FOTD on 3-day Vacation
by JimMuth＠aol.com 18 Aug '03

18 Aug '03

Fractal fans: An unexpected lull in the work has given me a chance to take an unscheduled 3-day vacation. I don't know where I'm going, but wherever it is, I'll be back late Wednesday. The next FOTD will appear on Thursday August 21. Jim M.

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FOTD 17-08-03 (The Supreme Mystery [7])
by JimMuth＠aol.com 17 Aug '03

17 Aug '03

FOTD -- August 17, 2003 (Rating 7) Fractal visionaries and enthusiasts: Today's image takes us to number 4 in my series if 12 MandNewt formulae, all of which are based very loosely on the Ikenaga function. Like most images produced by these formulae, today's consists largely of inside stuff, which in today's case, has been brought to life by the 'zmag' inside fill. I named the image, which resembles a scene on an alien world, "The Supreme Mystery". When I gave it the name, I had no parti- cular mystery in mind, so the viewers may take the image to mean anything they choose. The coloring is about as smooth as is possible to achieve with fractals using the measly 256 colors of the GIF format. It raises the normally 6-rated image to a rating of 7. The bottom 1/4 of the image is almost total black, so be careful not to save the image before it has finished generating. The render time of 8 minutes is acceptable, though stretching things a bit. The most efficient way to view the mystery is to download the completed GIF image from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Saturday started threatening here at Fractal Central, and grew more threatening as the day progressed. The temperature reached 88F 31C, then, just after 3pm, the first thunder-shower struck, with a sudden burst of wind and rain that thoroughly soaked the grass and put a quick end to the fractal cats' day in the yard. Another storm, even heavier than the first, arrived after dark, but by then the cats' moods were already sullen, and the rain made little difference. They ended the day sulking and eating tuna. My day was pleasant enough. I enjoy storms. . . . and fractals. Today is starting much better. There may be hope for happy cats. Until next FOTD, take care, and ponder the unspeakable mysteries of life. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_SupremeMystery { ; time=0:07:46.15--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandNewt04 passes=1 center-mag=0.26686\ 1/0.010155/17.31184/1/-80/-3.77822773067748585e-014 params=7.25463423566393/-5.527127903073214/2.36711\ 935789056/-2.570262764366588/-6.781682790612506/-5\ .718723105563524 float=y maxiter=250 inside=zmag logmap=yes periodicity=0 colors=000PTnQTnRToSUoTUoUVoVVoWVoXWoYWpZWp_Xp`Xpa\ XpaYpbYpbYqcZqcZqdZqd_qe_qe`qf`rf`rgargarharhbricr\ icsjcsjcskcskcslcslcskcrjbqiaph`og_nfZmeYmdXmcWmbV\ maUm`Tm_SmZRmYQmXPmWOmVNmUMmTLmSKmRJmQImPHmOGmNGmM\ GmLGmKGmKGmKGmKGmKGmKGmKGmKGmKGmKGmKGmKGmKGmKGmJae\ JbfJbfJcfJdgJdgJegJfhJfhKghKhiKhiKiiKjjKjjKkjKlkKl\ kKmkKnlKolKolKpmKqmKqmKrnLsnLsnLtoLuoLuoLvpLwpLwpL\ xqLyqLyqLzrLzrLzrLzsLzsLzsOSnPSnQSnFFFWVKVUIVQFWPF\ WPFWPFXPGXPGXPGYOGYOGYOGZOHZOHZOH_NH_NH_NH_NH`NI`M\ I`MIaMIaMIaMIbMJbLJbLJcLJcLJcLJdLKdKKdKKeKKeKKeKKe\ KKbLN`MPZNSXNUWMVWMVWMWWMWWMWVMXVMXVMYVMYVLYULZULZ\ ULZUL_UL_TL`TL`TL`TKaTKaTKaSKbSKbSKcSKcSKcRKdRJdRJ\ dRJeRJeQJfQJfQJfQJgQJgQJgRKhRKhRLhRLhRMhRMhRNhRNhR\ OhROhRPhSPiSQiSQiSRiSRiSSiSSiSTiSTiSUiSUiTVjTVjTWj\ TWjTXjTXjTXjTYjTYjTZjTZjU_kU_kU`kU`kUakUakUbkUbkUc\ kUckUdkVdlVelVelVflVflWf` } frm:MandNewt04 {; Jim Muth z=c=pixel: a=z^3+(c-1)*z-c b=p1*z^2+c-1 z=z-p2*a/b p3 <= |a| } END 20.0 PAR-FORMULA FILE==================================

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FOTD 16-08-03 (Ikenaga Tree [5])
by Jim Muth 16 Aug '03

16 Aug '03

FOTD -- August 16, 2003 (Rating 8) Fractal visionaries and enthusiasts: Today's image takes us back to the mysterious Ikenaga function, which was apparently created for the purpose of generating Fractint fractals, and then forgotten by its author, who, as far has I know, has never been definitely determined. Well, it's not exactly the Ikenaga function, since I have made numerous changes and additions to it, but whatever it is, it was inspired by the IkeNewtMand formula that appears in fractint.frm and was written by Ron Barnett, who states in the formula comments that it is based on the Ikenaga function. Several years ago I wrote a series of 12 formulae that I called 'MandNewt**.' These formulae are based on this mysterious 'Ike' function. Today's image was created with number 6 of the series. This series of formulae creates totally unpredictable images that consist largely of 'inside' parts, and therefore must be rendered with an active inside fill. Today's image uses the bof61 fill. The resemblance to some kind of fantastic tree is striking, and inspired the descriptive name, "Ikenaga Tree". The color palette, which uses only a few of the 256 registers, is a model of getting much from little. The rating of an exceptional 8 is fully justified. The frugal render time of 3 minutes is fast enough for all but the busiest fractalists. Of course, the completed GIF image is available as always on the internet at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Another hot, dry, sunny day on Friday here at Fractal Central gave the dynamic cats ample time in the yard. The temperature reached 93F 34C, but cats are native to northern africa, and can easily endure such mild heat. Their day was quite happy. No treat was needed. Today is promising to be a let-down, with clouds and showers possible. But with any luck at all, the duo will have another satisfactory day. As for me, most of my days are satisfactory, which may be because it takes so little to satisfy me. The next fractal will be along in 24 hours. Until then, take care, and good fractal luck. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Ikenaga_Tree { ; time=0:03:28.39--SF5 on a p200 reset=2002 type=formula formulafile=mandnewt.frm formulaname=MandNewt06 passes=1 center-mag=37.3298\ /-49.3884/0.03536232/1/-30/-2.5056345887009e-014 params=-6.47/-5.23/-1.59/-0.59/1.25/2.08 float=y maxiter=100 inside=bof61 logmap=yes periodicity=0 colors=B00c`d`cgYeiVhlSkoOmpZkZghIog0re2sd4vc7wa8z\ `CzZDzYHzWIzWKwaUaMzYSzTWzOezLczJazJ`zJYwJWpJTkIQh\ IOdILZIIVFHQEDNB00NO`OUeQ`oSexTkzVozYsz`uzcxzizzqz\ zwzzzzzzzzzzyizwVlwJYxBIxFKtIKqLKmOLkSLgVLdYL`aMYd\ MUgMRiMMlOKoOFrOCuO8rY4qe0nm0lu0sk7x`MzP`zDmz0zzDt\ zPmu`hnkaguW`zPVzK`zLdzLizLnzLswLwsLzoMzkMzgMzcMzZ\ MzVMzZIdaDvIKz0Oz8SzIWzR`xZduhhqpllxpizskzqkypkwok\ tmkplkmlkkkkhildhlaglZglWelSdlPclMalKakP`iUZiYZhaY\ ggWgkWeoVesVdxUczSczSazRazRczPczOdzMdxLetKepIgmIgi\ HheFhaDiYCiUAkP8kM8eVAaaCYhDToDYmCcmAgl8kl8ok7si5w\ i4zh2zh2zg0zg0ze0ze0zg0zg2zg4zg7zh8zhAzhDzhFxiHviK\ siLqiMniPkkRhkSekVckW`lYYl`VlaSlcOldLghIalFWpBRtBL\ xBFzB8zB2zB7zBAyBFuFIpJMlNPhQScTWZYZV`cRceLehHilCl\ o5os0ru0ux0vu0vt0vs0vp0vo4vm5vl8wiAwhDwgFwdIwcKwaM\ w`Ox`Px`Rx`Rx`Sz`Sz`Uz`Uz`Vz`Vz`Wz`Wz`Yz`Yz`Zz`Zz`\ `z``z`az`az`cz`czZ`hVZeYa } frm:MandNewt06 {; Jim Muth z=c=(pixel*p1): a=z^3+(c-p2)*z-c b=p3*z^2+c-1 z=z-1*a/b 0.000000000000000000000000000001 <= |a| } END 20.0 PAR-FORMULA FILE==================================

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FOTD 15-08-03 (Dual Pentagons [5])
by JimMuth＠aol.com 15 Aug '03

15 Aug '03

FOTD -- August 15, 2003 (Rating 5) Fractal visionaries and enthusiasts: The world of fractals holds many mysteries that will never be discovered, much less solved. But the mystery of today's image is one that has been discovered and, if I decide it is worth the effort, will be solved. At risk of being considered repetitive, today's image shows what happens to yesterday's image when the angle of the slice is double-rotated merely 0.0000685 of one degree from the Julia orientation. (Double rotation is a motion that can happen only in spaces of four or more dimensions.) When I began the rotation, I expected the octagon that appeared at the center of yesterday's image to become distorted. I did not expect it to break apart into two separate symmetrical holes shaped like near-perfect pentagons. But this is what happened. Now the question arises, which of the two pentagonal holes is a slice of the original rectangle that appears in the Mandelbrot aspect of the scene? And also, what happens to the other hole as we turn toward the Mandel direction? My intuition is that these questions are irrelevant, for there is only a single hole in the four-dimensional Julibrot figure, but this hole is shaped so irregularly that it can be intersec- ted in more than one place by certain slices, such as today's slice. Switching the functions in today's formula shows a very distorted aspect of the hole that would seem to prove this. I named the image "Dual Pentagons". I was ready to rate it at another 8, but then I realized that it is basically the third identical image in a row, and decided that a rating of 5 is more appropriate. Those who enjoy the art side of fractals rather than the math side might be growing a bit bored. Those who are feeling the beginnings of boredom, as well as those who lack the time, may escape the 15-minute wait of rendering the image from the parameter file by downloading the completed GIF image from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> A really unusual thing happened Thursday here at Fractal Central -- for the first time in almost 4 weeks, it did not rain. True, a few showers were in the vicinity, but none reached F.C. The fractal cats, who have made up after yesterday's quarrel, were quite happy, and despite an oppressive temperature of 91F 33C, enjoyed several hours in the yard. Today is due to be a repeat, so I expect a repeat of the cats' good moods. Until next FOTD, take care, and it is sometimes easier to see the light when one is in the dark. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Dual_Pentagons { ; time=0:15:53.78--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=flip/ident passes=1 center-mag=-0.00006842222800720/-0.000036\ 15877643450/1535.55/1/-45/3.88578058618804789e-016 params=90.0000685/89.9999315/2.003/0/0/0/-1.743504\ 25848689/6.977862219e-006 float=y maxiter=7200 inside=0 logmap=641 periodicity=10 colors=000voOtmMrkKpiKngJleJicJfaJd_JaYJZWJWTITRIR\ PIOMILKIIIIEFFGGIHHKJIMKIOMJQNKTOKVQLXRMZTN`UNcWOe\ XPgYPi_Qk`RnbSpcSreTtfUvgUxfXwfZve`vebueetdgtdisdk\ sblqalo`lm_llZljYlhWlfVleUlcTlaSm_RmZQmXOmVNmTMmSL\ mQKmOJmMImLKkOMiQOhSQfUSdWUcYWa_Y_a_ZdaXfcVheUjgSl\ iQnkPpmNrnLwoMtlMqiNneNk_NhVNeRMbNL_JLXFKUBJSCLRDO\ RERQFUQGXPH_PIdOJhOKnNLrNJwOLqNMlMOfMPaLQXLSTKTQKU\ NJWJJXGIYDIXGMWJQVMUUPYUSaTVeSYiR`mO`tRbpUdmXej_gg\ bhdejahkYkmVnnSqpPtqMwsJytGulNrdToXZlPdiHjfApdIocP\ nbWnacm`jm_qlZxl`wjawhbwfcvedvcevafv_guZhuXiuVjuTk\ tSltQmtOntNnkcnbslcrkcqjdpidohengemfelefkdfjcgibgh\ aggeaahXWkRQnMLrGFvB9z64s88iAC`CGSEKKFOIOKGWHEcEDk\ BClEClHBlKBlNAlQAlT9lW9lZ8la8ld7lg7lj6lm6lp6ls9kmC\ jhEibHhYJgTKeOLdJMbENa9O`4Rb7UdAWfDZhG`iJckMemPhoS\ kqVmrYpt`rvcuxfwyhuuetqbsn_rjYqgVpcSo_PmXNlTKkQHjM\ EiIChF9gB6f84eC8eFBmjSnjQ } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 14-08-03 (Mandelbrot Octagon [8])
by Jim Muth 14 Aug '03

14 Aug '03

FOTD -- August 14, 2003 (Rating 8) Fractal visionaries and enthusiasts: The joke of the day is an unusual e-mail from Taiwan that I found when I checked my e-mail box this morning. The sender is having a sale on guano and wanted to know how much I need. The letter closed by telling me that if I did not need guano, to delete the message -- which I did without raising a stink. Today's fractal is also quite unusual, and that's no . . . umm . . . stuff. It is the Julia set of one of those rectangles that appear where the arms branch out in yesterday's image. It is obvious that the Julia set of a Mandelbrot rectangle will be another rectangle . . . at least I thought it was obvious until I actually calculated a Julia set. The Julia set of the Mandelbrot rectangle I chose is not another rectangle; it is an octagon. The figure in which yesterday's rectangles are embedded has also changed. Well, it hasn't actually changed, but rather it looks different when sliced in the Julia direction. It has many more arms, in addition to smaller octagons where the arms branch out. No! Wait a minute! Those are not octagons where the arms branch out; they are rectangles. We have a Julia figure with a large octagon at the center, surrounded by smaller rectangles. Actually, I have seen this doubling before. I once checked the Julia set of the center of a 5-pointed star of the Mandelbrot set and found a 10-pointed star. And as I recall, there were also 20-pointed stars in the vicinity. I don't know if any 16-sided holes lie near today's octagon, but I am certainly going to check. And I wonder what will happen to today's image when I rotate the plane of the slice ever so slightly . . . Some of these questions may be answered by the time the next FOTD appears 24 hours or so from now. I named today's image "Mandelbrot Octagon" for obvious reasons. I rated it at an exceptional 8 mostly because of its mathemati- cal interest. The render time of 17 minutes can be avoided by downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Wednesday started pleasant enough here at Fractal Central, with sun and a temperature of 86F 30C, but at 2pm, a heavy thunder- shower moved in, cutting short the dynamic duo's time in the yard and putting them in a bad mood for the rest of the day. They must have been quite cranky while I was not around, because when I gave them their evening treat of tuna, I noticed a new scratch on Tippy's ear, which means they had had a fight. Thomas looked totally innocent of course. Today is starting in a similar manner. Hopefully, the midday shower will not be repeated, and the cats will have a happy day. For me it will be just another in an unending stream of similar days. Until next time, take care, and be alert for polygons with multiplying sides. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Mandelbrot_Octagon { ; time=0:17:31.33--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip passes=1 center-mag=+0/+0/1878.375/1/-45/3.8857805\ 8618804789e-016 params=90/90/2.003/0/0/0/-1.743504\ 25848689/6.977862219e-006 float=y maxiter=7200 inside=0 logmap=641 periodicity=10 colors=000voOtmMrkKpiKngJleJicJfaJd_JaYJZWJWTITRIR\ PIOMILKIIIIEFFGGIHHKJIMKIOMJQNKTOKVQLXRMZTN`UNcWOe\ XPgYPi_Qk`RnbSpcSreTtfUvgUxfXwfZve`vebueetdgtdisdk\ sblqalo`lm_llZljYlhWlfVleUlcTlaSm_RmZQmXOmVNmTMmSL\ mQKmOJmMImLKkOMiQOhSQfUSdWUcYWa_Y_a_ZdaXfcVheUjgSl\ iQnkPpmNrnLwoMtlMqiNneNk_NhVNeRMbNL_JLXFKUBJSCLRDO\ RERQFUQGXPH_PIdOJhOKnNLrNJwOLqNMlMOfMPaLQXLSTKTQKU\ NJWJJXGIYDIXGMWJQVMUUPYUSaTVeSYiR`mO`tRbpUdmXej_gg\ bhdejahkYkmVnnSqpPtqMwsJytGulNrdToXZlPdiHjfApdIocP\ nbWnacm`jm_qlZxl`wjawhbwfcvedvcevafv_guZhuXiuVjuTk\ tSltQmtOntNnkcnbslcrkcqjdpidohengemfelefkdfjcgibgh\ aggeaahXWkRQnMLrGFvB9z64s88iAC`CGSEKKFOIOKGWHEcEDk\ BClEClHBlKBlNAlQAlT9lW9lZ8la8ld7lg7lj6lm6lp6ls9kmC\ jhEibHhYJgTKeOLdJMbENa9O`4Rb7UdAWfDZhG`iJckMemPhoS\ kqVmrYpt`rvcuxfwyhuuetqbsn_rjYqgVpcSo_PmXNlTKkQHjM\ EiIChF9gB6f84eC8eFBmjSnjQ } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================

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re: FOTD 13-08-03 (Mandelbrot Object [8])
by Programmer Dude 13 Aug '03

13 Aug '03

Jim Muth: > I find my fractals; Albrecht creates his. Which method is the > better way of working with fractals? Asking such a question is > like asking whether fractals are art. It is up to each > individual to decide. I would have said it was more like asking if it's better to fly in a plane or eat chocolate ice cream.... I.e., an *utterly* meaningless question with no sensible answer. What makes you think the concept of "better" applies? -- |_ CJSonnack <Chris(a)Sonnack.com> _____________| How's my programming? | |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL | |_____________________________________________|_______________________|

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FOTD 13-08-03 (Mandelbrot Object [8])
by Jim Muth 13 Aug '03

13 Aug '03

FOTD -- August 13, 2003 (Rating 8) Fractal visionaries and enthusiasts: While assembling the parameter section of today's FOTD, I noticed my humble MandelbrotN formula. I saw all four lines of it -- about as short and simple a formula that could produce a fractal. Then I brought up Albrecht's latest Multifractal formula -- a work of fractal-programming genius, a mini-program with hundreds of lines that took many days of labor to develop, and still may not be finished. The two formulas illustrate two different approaches to the art of fractaling. I find my fractals; Albrecht creates his. Which method is the better way of working with fractals? Asking such a question is like asking whether fractals are art. It is up to each individual to decide. In my long fractal career I have written thousands of short, simple formulas, most of which took less that 1/2 hour to complete and have long since been filed away and forgotten. I could never imagine myself working weeks or months on a single formula, even if I did have a clear idea of where I was going. But why should I need to, when nearly every fractal created by every formula contains infinite surprises? Today's image rates an 8. One point of this rating is due to the surprising nature of the image. Until I found it, I had assumed that the near-perfect rectangles such as I used to create yesterday's 'Space Station' image exist only in the Julia plane of the Z^2.003+C Mandeloid. I should have known better. Yesterday, while searching the area of the Julia rectangle in the Mandelbrot direction, I found many small figures like the larger Julia figure that holds the rectangle. I found no midgets, but most surprising, I found that the small figures hold near-perfect empty rectangles where the arms branch out. To see some empty rectangles in their natural surroundings, toggle today's image of one of these small figures in and out of color-cycling mode and watch for the areas that blink. Clearly, I have much more exploring to do in this area. To begin, I must find those elusive Mandelbrot midgets. And if the figures with their rectangles are present in both the Julia and Mandelbrot directions, they should be present in the odd and oblique Julibrot directions also. I gave little thought to the naming of the image. "Mandelbrot Object" was as good a name as I could come up with. But the name is a perfect description of the surprising nature of the scene. The render time of 15 minutes is starting to border on the excessive. Relief in the form of the completed GIF image is available on the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Tuesday was actually a pleasant day here at Fractal Central. The temperature reached 86F 30C, the humidity was bearable, and the heavy rain storms that broke out in the afternoon stayed well west of us, leaving the F.C. area with a partly cloudy day and happy cats. If tomorrow's FOTD is as surprising as today's, I'll be happy. If it's not, I'll still be happy. Until next time, take care, and life is just a happy procession of fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Mandelbrot_Object { ; time=0:15:38.35--SF5 on a p200 reset=2002 type=formula formulafile=slices.frm formulaname=MandelbrotN passes=1 center-mag=-1.74350425707497900/+0.000006977798978\ 60/4.029834e+008 params=2.003/0/0/0/0/0 float=y maxiter=7200 inside=0 logmap=644 periodicity=10 colors=000404601700900A00C00D00F00G00I00J01L01M01O\ 13P33Q33S44T44V64X76Y76_96`97aA7cC7dC9fD9dA6gD9iGC\ jJFlMImPJoSMpVPsYSu`TvcXxf_yiazlczofzrizulzxmzzpzz\ szzvzzxzzvxxvprvilvafuVauOXuGQu9Ls1Fs09s04s06o07j4\ 9gAAcFC_LDXQFSXGOYFP`GLcIIdJFgLAiM7lO4mO1jS7iXDf`J\ ddPaiV`m_YrdXvjTzpSzvPzzOzzLzzJzzGxzFrzCmzAiz7cz6_\ z3Vz1Pz0Lz0Gz0Az06z01z00z00z03z06z39z7CzAFyFIvILuM\ OsPQrTToXXm`_lcaigdgjgfojdrmavp`ys_zvXzyVzzTzzSzrV\ zgXzXYzM_z9azC`xF`uG`sJ`pL`mO`lP`iS`fV`cX`a_`_``Xc\ `YiXVd`SadQ_gOXlLSoJPsGMvDJzCGz9Cu77l63c40V30M10D3\ 0I40L61O74Q97TAAXCD_DGaFJdGMgIPjJSmLVpMYsMYtOXuPWr\ QXmQWiTWdYYaa_YddTikPmqLrvIuxDyz9zz4zz0zz0xz0ru0jp\ 3dl4`i7VdAPaCMgFJoIGvJFvMCvO9vQ7vT4vV1vY0v`0va0vd0\ vi0vf0vd0vc0va0v`0vY1gX1TV3FT41S63Q74O96MA6LC7JC9I\ D9GFADGCCICAJD9LF7LF6II7GL9FO9DQACTCAXC9_D7`D4cF3f\ G1iG0lI0oJ0rJ0uL0vL0uJ0sI } frm:MandelbrotN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=z^(b)+c, |z| <= 16 } END 20.0 PAR-FORMULA FILE==================================

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Multifractal_8
by Albrecht.Niekamp＠t-online.de 12 Aug '03

12 Aug '03

Hi, Although Multifractal has become much longer there is hardly any slowdown due to some efficient speedups in the mainloop. The additional inputs p3, p4 and p5 can be used up to the maximum number of digits if only fractional values are concerned. If the total number is exceeded, the last digits are truncated. Three important changes this time. It now is possible to control the coloring using an alternative bailout which can be applied to one or two channels, imag(P2), last two digits of first input. Just type the number of the channel(s). The first alt-bailout is applied to the first choice, the second one is applied to the second choice. A high value - real(p3) or real(p3) 2nd input, digits 6-11 - compresses, a value lower then bailout expands the coloring of the concerned channel. Another way is to use iter-reset, which causes the iterationcounter to start from zero and so increases the number of iterations for the concerned channel, - coloring is modified in a more subtle way. This of course increases the calculation time, also the warp effect of the following channels is concerned. The second news is the real(p2) input, as now only the number of the frm is needed, no more double choices. This means if you call the "z" screen you can see at one glance which frms are used. The two reset commands and the warpeffect switch are combined in the real(p2) second input, last five digits, 1 digit for each channel. Scroll the text for explanation. (3) I have spend some efforts to get rid of distorted structures, so now I can reintroduce them, but on a controlled basis. This means the 3 inside channels (3-5) now can use bordervalues if wanted. The first digit, 2nd input, image(p4), real(p5), image (p5) controls use of maxiter or border values. The bordervalues can be used bothways, "in" or "out". "In" means that the concerned channel is switched on, if the border value is higher then the input and vv. If the selection is "7" or "8" both, maxiter and border-(both options) are used at the same time. This possibly will cause chaos, if the same part of the image is affected, but maybe thats ok in some cases. Testing this frm I again experienced some difficulties with that infamous fractint-bug (misreadings of the inputs under certain conditions). "Debugflag=322" is activated, but itïs not on my office computer, it does not make any difference. Btw against all rumours fractint runs perfectly under WindowsNT (Gforce2 videocard). Concerned is real(p2), first(!) input, where channel 2 (outside) was not read correctly if zeros follow. I fixed it adding"1" to the last digit and so avoid zero divisions. The second concerned input is real(p2) second input, last 5 digits. I already added 11111 to the input in multifractal_7, but I noticed that the last digit still was misread sometimes, so I used the "round" function for this digit. After many tests all inputs are executed correctly. The images : "House of the Helmets" is a four generations mandel and very beautiful, rather slow though as the "secant" frm used inorder to get rid of the tdis-sausages is very slow and I used iter reset to get the wanted coloring for the helmets. The part of the sausages to be eaten by secant is controlled by "image(p3)" 2nd input (outside border-in), a lower value eats more. "Mandel in the clouds" is an impressive zoom into this one, the new coloring expansion is used to generate the clouds. "Borderwatch" is another one, really extraordinary and worth waiting for. As this was generated under Winnt I cannot tell the actual time needed. "Ganymed" and "Islands" use the new inside border values, option1 (border-out). Btw Ganymed is the biggest Jupiter planet. "Ikebana" is a japanese ornamental floral arrangement. The many different shapes of the flowers are produced by the warp effect. Same goes for the "Jellyfish armada". Fractal Greetings, Al ---------------------------------------start-frm-------------------------- FRM:Multifractal_8 { ; Albrecht Niekamp 090803 ;p1 (spider)julia-seed ;real(p2) 5digits : (1)shape (2)outside (3)inside1 (4)inside2 (5)inside3 ; 0_off 1_secant 2_mand 3_bees 4_jul 5_m_mods 6_phoen 7_newt 8_spider ; input2 : 2digits_many-mods 2digits_phoenix 2digits_spider ; 5digits_reset : 0_no 1_z-reset 2_iter-reset 3_both +5_warp ;imag(p2)(-) 2-4digits : newton input (max 2000) ; 2digits : channel_alt-bailout1 channel_alt-bailout2 ; input2 : 4digits(-)_mand/jul 2digits_secant 4digits_bees ;real(p3) alt-bailout1, 5digits_bailout 6digits alt-bailout2 ;imag(p3) shape : factor (fn1), outside : border-in (5digits+fract.) ;real(p4) outside: factor (fn2), outside : border-out (5digits+fract.) ;imag(p4) inside1: maxit1, 1digit_use:1_maxit 2_bord-in 3_bord-out +5_both ; 5digits_factor1 (fn2) 4digits+fract_border1 ;real(p5) inside2: maxit2, 1digit_use:1_maxit 2_bord-in 3_bord-out +5_both ; 5digits_factor2 (fn3) 4digits+fract_border2 ;imag(p5) inside3: maxit3, 1digit_use:1_maxit 2_bord-in 3_bord-out +5_both ; 5digits_factor3 (fn4) 4digits+fract_border3 ;fn(1) shared by many-mods+bees ; da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+1 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==3)+(d==4)+(d==7)+(d==8) d4=(d3==0) vb=d>4 ab=(d==2)+(d==4)+(d==6)+(d==8) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>0 v1m=(d==5)+(d==6) v1j=d>6 dd1=(d==3)+(d==4)+v1j ab1=(d==2)+(d==4)+(d==6)+(d==8) d=trunc(dd/100) dd=dd-d*100 ex2=d>0 v2m=(d==5)+(d==6) v2j=d>6 dd2=(d==3)+(d==4)+v2j ab2=(d==2)+(d==4)+(d==6)+(d==8) d=trunc(dd/10) ex3=d>0 v3m=(d==5)+(d==6) v3j=d>6 dd3=(d==3)+(d==4)+v3j ab3=(d==2)+(d==4)+(d==6)+(d==8) d=dd-d*10 ex4=d>1 v4m=(d==6)+(d==7) v4j=d>7 dd4=(d==4)+(d==5)+v4j ab4=(d==3)+(d==5)+(d==7)+(d==9) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex0+ex1+ex2+ex3+ex4 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) d=round((d-dd)*10000000000) pp=trunc(dd/100)/10 dd=dd-1000*pp ba1=trunc(dd/10) ba2=dd-10*ba1 ; p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=real(p3) bb1=trunc(d) da=(d-bb1)*10000000000 ba=trunc(da/100000) bb2=da-100000*ba ; d=imag(p3) sfac=trunc(d) b1=(d-sfac)*100000 b0=b1/2 ; d=real(p4) ofac=trunc(d) b2=(d-ofac)*100000 ; d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=(d==3) fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=(d==3) fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 ; d=imag(p5) mi3=trunc(d) da=(d-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=(d==3) fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 ; mo=vb>ab mo1=v1m>ab1 mo2=v2m>ab2 mo3=v3m>ab3 mo4=v4m>ab4 ; sc=((ab+vb)==0) sc1=((ab1+v1m)==0) sc2=((ab2+v2m)==0) sc3=((ab3+v3m)==0) sc4=((ab4+v4m)==0) ; px=((ab+vb)==2) px1=((ab1+v1m)==2) px2=((ab2+v2m)==2) px3=((ab3+v3m)==2) px4=((ab4+v4m)==2) ; mb0=(ba1==1)+(ba2==1) mb1=(ba1==2)+(ba2==2) mb2=(ba1==3)+(ba2==3) mb3=(ba1==4)+(ba2==4) mb4=(ba1==5)+(ba2==5) ; if (d4) z=0 if (vb) if (mo) c=0.4*log(sqr(pixel^mm)) else c=pixel z=pixel endif else c=pixel z=pixel*sc endif else c=p1 z=pixel endif t=0 u=d3 bo=z p=pp z0=p7 zold=(0.0,0.0) cb=p9 bx=ba if (mb0) if (ba1==1) ba=bb1 else ba=bb2 endif else ba=bx endif : If (tt) t=t+1 if (ex0) if (bo>b0) u=2*(fn1(t/sfac)) if (d4) z=z*u if (mo) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else z=pixel cb=p9*u c=p1*u p=pp*u endif if (ir0) t=0 endif ex0=0 tt=tt-1 endif elseif ((ex1) && bo>b1) if (b2>bo) d3=dd1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif ab=ab1 if (d3) if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif vb=v1j else if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v1m if (mo1) c=0.4*log(sqr(pixel^mm)) endif endif if (mb1) if (ba1==2) ba=bb1 else ba=bb2 endif else ba=bx endif if (ir1) t=0 endif ex1=0 tt=tt-1 endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif ab=ab2 d3=dd2 if (d3) if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif vb=v2j else if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v2m if (mo2) c=0.4*log(sqr(pixel^mm)) endif endif if (mb2) if (ba1==3) ba=bb1 else ba=bb2 endif else ba=bx endif if (ir2) t=0 endif ex2=0 tt=tt-1 endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif ab=ab3 d3=dd3 if (d3) if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif vb=v3j else if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(pixel^mm)) endif endif if (mb3) if (ba1==4) ba=bb1 else ba=bb2 endif else ba=bx endif if (ir3) t=0 endif ex3=0 tt=tt-1 endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (mb4) if (ba1==5) ba=bb1 else ba=bb2 endif else ba=bx endif ab=ab4 d3=dd4 if (d3) if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif vb=v4j else if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v4m if (mo4) c=0.4*log(sqr(pixel^mm)) endif endif ex4=0 tt=0 endif endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Qusinewton Pusk s Istv n z2=p*z*z z=z-z1/z2 endif elseif (ab) zt=z*z+ph-0.5*zold ;Phoenix Mike Wareman zold=z z=zt else z2=fn1(z)+c ;Many_mods Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (d3) if (ab) z2=z*z ;Julia Pusk s Istv n z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) z2=z*z ;Mandel Pusk s Istv n z=z2*z2+p6*z2+c-p0 else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<=ba } ------------------------------------start-par------------------------------- Ganymed { ; Time 1.12.39.12 ; Albrecht Niekamp aug, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_8 function=sin/cosxx/cos/exp passes=t center-mag=+0.50549305714185240/-0.61811095723667920/704.0072/1/142.4999\ 99999998181/2.79927470092644626e-012 params=-0.02237006744590594/-0.07473982970671712/20685.64575300005/17053\ .0608020602/82048.03072420481/384.0000045/384.00024/128.3007680000451/25\ 6.300768002431/512.2007680082311 float=y maxiter=3072 inside=maxiter outside=tdis logmap=9 periodicity=0 rseed=-2436 colors=200034<23>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<13>UQFWSGYTH<3\ >e`LgbMidN<3>qjRslSunT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25\ >C00A00800<3>000<23>eeegggiiijjjlllnnn<2>sss<25>BBB999777<2>222000012 } Ikebana { ; Albrecht Niekamp Aug, 03 ; Time 0.49.15.81 ; ; ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_8 function=sin/cosxx/cos/sin passes=t center-mag=+1.01296887343957000/-0.25355247435077240/268.8172/1/104.9999\ 99999999417/4.71109262711877363e-013 params=-0.02237006744590594/-0.07473982970671712/20856.6459530051/5040.0\ 608020602/82048.02048000001/384.0000045/384.00024/128.1007682048001/184.\ 1007682048001/512.1007682048001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=11 periodicity=0 rseed=-2436 colors=2000NU<8>09C08A068<2>022000211<13>UQFWSGYTH<3>e`LgbMidN<3>qjRslSu\ nT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<25>\ iiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<15>0OW } Islands { ; Time 0.47.07.67 ; Albrecht Niekamp Aug,03 ; ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_8 function=sin/cosxx/cos/exp passes=t center-mag=+0.14743939138452520/-0.85700696310343770/988.7742/1/-177.500\ 000000000938/8.0188633511113494e-013 params=-0.02237006744590594/-0.07473982970671712/20685.64575300005/17053\ .0608020602/82048.03072420481/384.0000045/384.00024/128.3007680000451/25\ 6.300768002431/512.2007680082311 float=y maxiter=3072 inside=maxiter outside=tdis logmap=9 periodicity=0 rseed=-2436 colors=200222<22>eeegggiiijjjlllnnn<2>sss<25>BBB999777<2>222000012<24>0b\ o0cq0es<3>0kz<25>09C08A068<2>022000211<13>UQFWSGYTH<3>e`LgbMidN<3>qjRslS\ unT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<31>000 } Jellyfish_armada { ; Albrecht Niekamp Aug, 03 ; Time 0.46.44.55 ; ; ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_8 function=sin/cosxx/cos/sin passes=t center-mag=+1.05590865727923400/-0.26726304367583260/537.6344/1/-120.000\ 000000001336/1.0563286356735091e-012 params=-0.02237006744590594/-0.07473982970671712/20854.6459530051/5040.0\ 608020602/82048.02048000001/384.0000045/384.00024/128.1007682048001/184.\ 1007682048001/512.1007682048001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=11 periodicity=0 rseed=-2436 colors=2000NU<8>09C08A068<2>022000211<13>UQFWSGYTH<3>e`LgbMidN<3>qjRslSu\ nT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<25>\ iiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<15>0OW } Mandel_in_the { ; Clouds ; Albrecht Niekamp Aug, 03 ; Time 2.57.35.27 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_8 function=sin/exp/exp/sin passes=t center-mag=0.798692/0.00022867/24.61116/1/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/21222.32595700021/5025.05\ 06030602/89094.02048000094/384.0000545/384.00048/256.1007683001/512.1007\ 683001/768.1007683001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200444<21>fffgggiiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0c\ q0es<3>0kz<25>09C08A068<2>022000211<21>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A9\ 6875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000222 } Borderwatch { ; Albrecht Niekamp Aug, 03 ; ; ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_8 function=sin/exp/exp/sin passes=t center-mag=+0.76810386176090220/-0.04756578810250790/866.3365/1/90/-1.23\ 373533611470521e-014 params=-0.05825983458967864/0.3785210730307932/21222.32595700021/5025.05\ 06030602/89094.02048000094/384.0000545/384.00048/256.1007683001/512.1007\ 683001/768.1007683001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200444<21>fffgggiiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0c\ q0es<3>0kz<25>09C08A068<2>022000211<21>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A9\ 6875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000222 } House_of_the { ; Helmets ; Time 2.31.23.87 ; Albrecht Niekamp Aug,03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_8 function=sin/exp/exp/sin passes=t center-mag=0.332423/0.00308737/1.230666/1/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/21222.32595700021/5025.05\ 06030602/89094.02048049094/384.0000545/384.00048/256.1007683001/512.1007\ 683001/768.1007683001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200600<22>o00q00s00<3>z00<25>C00A00800<3>000<25>iiijjjlll<3>sss<2\ 5>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<21>i\ cNkeOmfP<3>unTwpVxqWzsX<25>CB7A96875<3>000400 } --------------------------------------end----------------------------------

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