October 2004 - Fractint - mailman.xmission.com

Variation on Jim Muth's Oct 26, '04 FOTD
by Hal Lane 26 Oct '04

26 Oct '04

########################################################### I was able to bring out some more detail in the four central brain mass-like blobs in Jim Muth's Oct 26,'04 FOTD using a variation of Damascena Korwen's Leather Gem color map. I modified her color map to remove some bright entries which gives it a more muted overall tone. A very nice fractal, Jim. - Hal Lane ######################### # hallane(a)earthlink.net # ######################### START PARAMETER FILE======================================= Iso-Iterations2 { ; Hal Lane Oct 26,'04 0:58 P400 ; 1024x768 ; Jim Muth's FOTD Oct 26,'04 with ; Damascena Korwen's Leather Gem ; color map (rotated). reset=2003 type=julia(fn||fn) function=sqr/tan passes=1 center-mag=-2.47062/2.15725/1.468253/1/-90/3.8857805\ 8618804789e-016 params=0.29/0.01/5.5 float=y maxiter=1200 bailout=9 inside=0 outside=summ logmap=yes periodicity=10 sound=off colors=YD0E`h<3>HgjIikJklKmm<8>CURBSOAQM<3>6GB5E86G9\ <9>EWHFYIGZJ<2>JdMKfNLhM<5>bmDenBhoA<3>ts3wt1sr2<5>Z\ f8Vd9SbA<3>DVF<4>CPCCNBCMA<2>BI9BH8BH8<3>AE79D6DE6<3\ >UI9YJAaLBeMCgODjQF<3>nXFoZGp`G<2>seG<15>dL4cK3bI2aH\ 1`F0`F0<5>UA0T90S80R80Q70P60<3>L30K30J20I10I10<16>UB\ 2UB2VC2<3>YE3<3>Q82O61M41<3>Q71R81S91fM5<3>iO5jP5kQ6\ <9>UB3S92Q82<3>I10931A00<3>VK0_P0dU0<3>zm0<3>zb0z_0z\ X0zU0<3>`F0UC0O80H40<2>A4773A73C<3>56K47M48O39Q2AS<1\ 3>DZf } END PARAMETER FILE========================================= ########################################################### --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.782 / Virus Database: 528 - Release Date: 10/22/04

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FOTD 26-10-04 (Iso-Iterations [7])
by Jim Muth 26 Oct '04

26 Oct '04

FOTD -- October 26, 2004 (Rating 7) Fractal visionaries and enthusiasts: For today's image we return for a second go at the julia(fn||fn) formula. I am giving the formula a second chance because I feel that yesterday's below-average image failed to do justice to it. For today's image I began by setting both functions to sqr, a setting that draws the familiar Z^2+C Julia sets. With an 'East Valley' Julia set on the screen, I changed the second function to 'tan' and reset the shift value to 5.5. The result was spectacular -- a fractal with more places of interest than a drop of water has molecules. The Julia set has been surrounded by rings and decorated with all kinds of gingerbread. In addition, spurious bits and pieces of very distorted J-sets have sprung up in the suburbs, where little would normally be expected. I chose a scene in one of these outlying areas, tried the various 'outside' options, chose the 'summ' option, and let the iterations roll. After only 35 seconds of rolling, today's image appeared on the screen. I took around 15 minutes working up a color palette that would bring out the multi-level image that I saw in the scene. The final result is today's Fractal of the Day. The formula undoubtedly has even better images in it, but at least, with today's image and its rating of a 7, I feel that justice has been done, and it is time to move on to the next formula. The very brief render time of 35 seconds results in an overall worth of 1195, and that rating is not to be sneezed at, especially in a time of flu vaccine shortage. I named today's image "Iso-Iterations", which means 'lines of equal iteration. I gave it this name before I set the outside to 'summ', a setting that creates bands in an entirely different manner. The image may be seen by running the included parameter file or by letting Paul run it and downloading the finished image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The clouds hung tough all day Monday here at Fractal Central. The fractal cats hung tough in their bad moods. Even the tuna left them a bit sullen. A lack of sun and a temperature of 57F 14C are not very pleasing to cats of the fractal variety. The clouds appear far less tenacious this morning, with even a few patches of blue showing through. If all goes well, we will have full sun and happy cats by noon. The next FOTD will appear in 24 hours. Until then, take care, and a fractal rating a whopping 9-1/2 will appear in 3 days. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Iso-Iterations { ; time=0:00:35.15--SF5 on a P200 reset=2003 type=julia(fn||fn) function=sqr/tan center-mag=-2.47062/2.15725/1.468253/1/-90/3.88578\ 058618804789e-016 params=0.29/0.01/5.5 float=y maxiter=1200 bailout=9 inside=0 outside=summ logmap=yes passes=1 periodicity=10 colors=000UA0c90cg0Oz0Ux0Zw0Ys0Yo0Xk0Xg0Xc0W_0WW0V\ S0VO0RK0TG0VC0X80ZE0aJAeNKhSUkX_n`eqeftjhwnizskzxl\ zzmzzkwxitvgruepsdnqbkoahnefkhdikbgnafq_ctYawW_zVZ\ zTXzRVzQUzURzXPz_NzbLzeIzhGzkEznCzhEzbGzXHzSJzMLzG\ MzAOz5Pz4Qz4Rz4Sz4Sz4Tz4Uz4Uz3Vz3Wz3Wz3Xz3Yz3Zz3Zz\ 3_z2`z2`z2az2bz2bz2cz2dz2dz4ez5fz6gz8hz9izAizCjzDk\ zElzFmzHnzInzJozLpzMqzNrzOszQszRtzSuzUvzVwzWxzXxzW\ vzWtzWrzWpzWnzWmzWmzWmzWmzWmzWmzWmzWmzWmzWmzWmzWmz\ WmzVmzVmzVmzUmzUmzUmzTmzTmzTmzSmzSmzSmzSmzUmzUmzUm\ zUmzUmzUmzUmzTmzQmzNmzJmzGmzDmz9mz6mz3mz2mz2mz2mz2\ mz2mz1mz1mz1mz1mz1mz1mz0mz0mz0mz0mz0mz0mz3mz6mz8mz\ BmzEmzGmzJmzLmzOmzRmzTmzWmzYmz`mzcmzemzhmzjmzimzhm\ zgmzfmzemzdmzcmzbmzamz`mz_mz_mzZmzYmzXmzWmzVmzUmzT\ mzSmzRmzQmzQmzOmzMmzKmzJmzHmzFmzDmzCmzAmz8mz7mzHmz\ Rmz`mzimzcmzZmzUmzPmzJmzEmz9mz4mz5mz6mz7mz7mzBmzEm\ zHmzKmzNmzRmzUmzXmz_mzbmz } END PARAMETER FILE=========================================

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FOTD 25-10-04 (The Big X [4])
by Jim Muth 25 Oct '04

25 Oct '04

FOTD -- October 25, 2004 (Rating 4) Fractal visionaries and enthusiasts: I almost gave up on the next formula in line, the julia(fn||fn) formula, a formula that uses the value of mod(Zn) to determine which function to apply to Zn+1. I spent nearly an hour trying different functions and different shift values, mostly getting nowhere. I found that when both functions are set to 'sqr', the well-known Z^2+C Julia sets result. It became immediately appar- ent that there could be no interesting function shifts when the two functions are identical. I kept trying different functions until I stumbled upon the 'recip-cos' combination while the shift value was set to 1 and the C parameter was set to 0.28, a point in East Valley of the Mandelbrot set. The resulting image was not great, but at least it was a fractal, so I searched it until I found a scene that barely makes the status of FOTD. That scene is today's image. I named the image "The Big X". When I chose the name, I might have been thinking of the movie 'It's a Mad, Mad, Mad, Mad World', where everyone was running around, looking for money buried under a mysterious 'big W'. The name is not totally un- justified. Some of the feathery elements actually do form a kind of big X on the right side of the image. I could rate the result at only a humble 4. The lowly rating is not the fault of the formula, which certainly has much more potential than I was able to find in it during the 3/4-hour or so that I worked with it. It is a complex formula that takes time to become familiar with. In fact, I am so certain that I have done the formula an injustice that I will use it again as the source of tomorrow's FOTD. Perhaps the best feature of the image is its very brief render time of 1-1/2 minutes, which combines with the rating of 4 to give an overall worth of 266 -- not such a bad value. And the minor task of rendering the image can be dispensed with entirely by downloading the finished GIF image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Off and on rain kept things wet and the fractal cats sullen here at Fractal Central on Sunday. The high temperature of 50F 10C helped not a bit. A generous treat of tuna and turkey was needed to make Thomas stop staring me in the eye blaming me for his bad day. Tippy merely hunkered down for a good sulk until the tuna and turkey appeared. This morning is starting cloudy and chilly, but dry. I have hopes for a better day among the cats. The fractals keep coming, and the next one, the second to be created by today's julia(fn||fn) formula, will appear at this same spot in 24 hours. It almost certainly will be a better one. Until that wonderful moment arrives, take care, and fractals not only spring eternal, they winter, summer and fall eternal as well. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Big_X { ; time=0:01:30.36--SF5 on a P200 reset=2003 type=julia(fn||fn) function=recip/cos passes=1 center-mag=-0.19876011638408430/+1.733781\ 852621153/38720.9/1/-60/3.05664410449324464e-010 params=0.28/0/1 float=y maxiter=1200 bailout=6400 inside=0 logmap=36 symmetry=none periodicity=10 colors=000YGK_IKaKKcMKeOKgQKiRKlSKoTKrUKuVKxWKzXKz\ dKzlKzrKzqKzoKzmKzkKziKzgKyeKxcUwacv`muZwtXzsVzrTz\ qRzpPzoNznLzmKzkNziQzgSzfVzdXzb_z`az_dzYfzWizVkzae\ zh_zoUzvOzzJzwLzrMzmOziPzdQz_SzVTzRUzMWzHXzDYzGZzJ\ ZzMZzP_zS_zV_zX`z_`zb`zeazhazkazmbzpbzsbzvczyczzcz\ zczzazz`zyZzwYzvWztVzrTzqSzoQznPzlNzjMziKzgJzfIzdI\ zbIz`IzZIzaLzcNzfPzhRzgSzgTzgUzgVzgWzgXzfYzfZzfZzf\ _zf`zfazebzeczedzeezefzefzfezgezhdzidzjczkczlbzmbz\ nbzoazpazq`zr`zs_zt_zuZzvZzwZzsWzoTzkQzgNzcKzePzgU\ ziZzkdzmdzndzpdzrdztdzvdzwdztdzqdzodzldzidzgdzddzb\ dz_dzXdzVdzSdzPdzNdzKdzIdzKdzMdzOdzQezSezUdzVdzXcz\ Zcz`bzbbzdazeazg`zi`zk_zm_zoZzpZzqYzqYzrXzrXzsXzsW\ ztWztWzuVzuVzvUzvUzwUzwTzxTzxTzySzySzySzxUzwWzvYzu\ _ztazsczrdzqdzpdzodzndzndzmdzldzkdzjdzidzhdzgdzfdz\ edzddzddzbdzadz_dzZdzYdzWdzVqzUnzSlzRizQfzOczN`zLZ\ zKWzJTzHQzGOzFLzDIzCFzBDz } END PARAMETER FILE=========================================

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FOTD 24-10-04 (A Fractal Primeval [6])
by Jim Muth 24 Oct '04

24 Oct '04

FOTD -- October 24, 2004 (Rating 6) Fractal visionaries and enthusiasts: The existence of Julia sets has been known for almost 100 years, though their exact appearance was not determined until modern computers were developed. And when computers finally opened the door to the world of fractals -- wow! were we surprised. The FOTD for today takes us on to the Julia version of the formula Z^2+C, a formula that draws perhaps the most basic and simplest of all fractals. This formula is so familiar and has been explored so thoroughly that it is a bit difficult to find anything new in it. But the fractals it produces are infinite in number, and infinity is inexhaustible. To find today's image, I chose a point in a basin of a midget deep in East Valley of the prominent midget on the negative X-axis of the Mandelbrot set, and checked its corresponding Julia set. The image I came up with is not excep- tional -- I have seen many similar images -- but it is different enough from what is normally pictured as a Julia set to qualify as the FOTD for today. I named the image "A Fractal Primeval". When I saw it, I was reminded of a scene deep in the primeval ocean of early earth, at a time when life had just evolved to the level of multicel- lular organisms. A few of these early creatures, if they can be considered creatures, are illustrated, complete with infinitely divided Cantor-style nuclei. I doubt that these early forms of life actually were colored the brilliant shade of red that I gave them, but the strong coloring is what raised the image to its rating of a 6. The rating of 6 might be a bit excessive for such an ordinary image. I feel the image is worth its rating however. And when the render time of under 10 seconds is figured in, the overall worth registers an amazing and grossly inflated 3681. The image may be seen by running the included parameter file and waiting a few seconds, or, if your computer is Fractint chal- lenged, by downloading the completed GIF image from the FOTD web site maintained by Paul Lee at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A fine sunny day here at Fractal Central on Saturday was kept from being perfect by a slightly-too-chilly temperature of 55F 13C. The cats did not seem to mind however, and spent most of the afternoon in the yard, doing what fractal cats do best. They came in at sunset as soon as they heard the food being opened, and enjoyed a treat of turkey and tuna. Today is starting not so sunny, with sprinkles of rain already falling. The day could go any way at all, so check back in 24 hours to see how the cats make out. The next glorious (IMO) fractal will also be available right here at that time. Until then, take care, and what a lovely bunch of fractals fills the cosmos. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Fractal_Primeval { ; time=0:00:09.78--SF5 on a P200 reset=2003 type=julia center-mag=-0.00000692960822\ 208/+0.05602788817859143/1599.23/1/-60/-3.94004273\ 651660242e-013 params=-1.749708627366082/3.2897258\ 61169113e-007 float=y maxiter=900 bailout=9 inside=255 logmap=232 symmetry=none periodicity=10 colors=000AKKAKKAKKAKKAKKAKKAKKAKKAKKAKKAKKBKKCKKD\ KKEKKDJNCIOBHSAHUCMXERZGVaIZeJbhLflNjoPnsRqvTszVuz\ XvzZwz`xzbyzdzzcxzZwucuvZrrUjmQehQ_cQXZQWUQXPNZKL_\ IIaIGbHEcGBeG9fF7gFEfKKePQdUWcZbcchbhnamt`rz`vw`nu\ `fr`Zp`Rm`Jk`BjcAje9ig9ij8ik8hl7hm7hn6go6gp5gq5_p6\ `qAaqKbqUcqUdqUeoUfkUggUhcUi_PjWKmSFpO8sK6tH5tJ4uL\ 3wN2wT2yT2wW2wX2rY2mZ2j_2j`2ja2jb9jcFjdLjeRcfPXgNR\ fLKeJDdH7bF8aT8`f8_sDZL7Y`2XoMWedVWwUMX`UW`ZV`cU`h\ U`lNbpGcs9ew3fzD`vMVrVQncKjlFgiEioEvpDzxDwrCpsCjkC\ mcCmWCmVBmUAmUAm9Ym9Nm9Dz8Hz8Lz8Pz8Sz7Wz7_z7cz7fzM\ _z_TzmNzRRz4UzIVzWWzhXzbazXfzRkzLpzGtzSezcSzEVpMUz\ UUz`TzwTzwTzjRzfQzbPzZOzUMzQLzMKzIJzFqzJmzMizPfzSb\ zV_zjbzydzsgzmizglzanzWqzRszhJzVEzH9zIqzFszDtzAvz8\ wz5yz3zzHozUdzZizcmzgqzluzpyzpszbezPTzCGzRSzdczejz\ fRzgKzhEzi7zi1z`7zTDzKJzCPz4VzAUzGUzLTzRTzXSzaSzgR\ zlRzgXzcaz_gzVlzRrzq`zqYz } END PARAMETER FILE=========================================

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FOTD 23-10-04 (Julia Tree-Rings [6])
by Jim Muth 23 Oct '04

23 Oct '04

FOTD -- October 23, 2004 (Rating 6) Fractal visionaries and enthusiasts: Today's image takes us to the julfn+zsqrd formula of Fractint, a formula that gave me a fight when I tried to wring a respectful fractal from it. I finally won the battle by investigating the Mandelbrot variations of the formula and finding the parameters likely to produce interesting Julia sets by noting the coordi- nates of the interesting places in the M-sets. Several functions produced interesting Mandelbrot sets. I decided to check the Julia sets associated with the shoreline of the M-set that results when the 'cabs' formula is applied. The first Julia set I checked was a winner. This winning set is an extension in the remaining two dimensions of a point on the the eastern shoreline of its M-set. The set is illustrated in today's image, which shows the entire Julia set, and looks sur- prisingly like yesterday's image. I named today's image "Julia Tree-Rings". I thought of tree rings the moment I saw the image. Such an easily created image can hardly be rated very far above average, but I put a bit of extra coloring effort into the image, and that coloring effort raises it to a slightly-above-average rating of 6. The rings that fill the inside of the Julia set appear very inte- resting as they are. It might appear that they would grow even more interesting as one zooms deeper, but a single inzoom will reveal that they are fractal in nature, and continue dividing into ever smaller similar rings. The rings are ultimately dis- appointing, but they do however produce some interesting patterns in the areas where they converge, and create images much like yesterday's 'moirefan' image. The render time of 6-3/4 seconds is unusually fast, and when com- bined with the rating of 6 results in an overall worth of a grossly inflated 5333. Those who are concerned about inflation can download the image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather remained cloudy here at Fractal Central on Friday, but the temperature warmed to 57F 14C and the wind was light, which made things pleasant enough for the fractal cats to enjoy several hours in the yard. Today is starting sunny, and we are promised more sun and warmer temperatures throughout the after- noon. I hope the good weather actually holds up. The cats do not like broken promises. I promised myself an actual day off this weekend, and with only one minor job on the shelf beside the desk, it looks like I'll keep that promise. Luckily, I do not consider playing with fractals to be work. The next playful image will appear right here in 24 hours. Until then, take care, and do palm trees have rings inside their trunks that tell the tree's age? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Julia_Tree-Rings { ; time=0:00:06.75--SF5 on a P200 reset=2003 type=julfn+zsqrd function=cabs center-mag=-1.249e-016/6.66134e-016/0.8090289/1/57\ .5/1.310757058448075e-014 params=-0.07/0.23 float=y maxiter=1200 bailout=9 inside=0 logmap=yes symmetry=none periodicity=10 colors=0000AN0FT0KZ0PeAUkKZqUckchdmmYvrSzzQmmPccNU\ UMPPKKKJELKIOLNRMRUNOXOM_PKbPHdQFgQDjRBlRIhVOdYV``\ `YcfUgmQjsMmyJpoQnfWlYakPhiGng7tf9ngAhhCbiDXjFRkGL\ kUM`gNQuOFsNGqNGoMGmMGkLGiLGhLGDzXChcBSjABq`Tvzizs\ juljqejmZjiTjeQgiNdmKapHZtFWwGVxHUxITyISyJRzKQzKPz\ QQuWRqaSmgTimUesVayVYJAiG9kD8mB8o87q67sUKTpX2kYAfZ\ IadHXiGSnFOdKKWOGMSCDW84_6AcFHbNNaVU`b__bY_bW_bV_b\ T_bR_bP_bN_bM_`EfZ7lXCkVGjTLiRPhPTgOYgMafKeeIjdGnc\ FrcGs_GsXGtUGtRHuNHuKHuHHvEIvAIw7Iw4Iw1Jv6JvBKvGKv\ LLvQLvVMu_MudNuiNunOusOuwnIKlLLjOMiQNgTNfWOdYPc`Qa\ bQ_eRZhSXjTWmTUpUTrVRuWQwWUqbXli`gpcbvbcubdubetbft\ bgtbhsbhsaisajrakralramqanqanqcondolfojgoghpejpckp\ alpZnpXoqVpqSrqQsqOtqMonOjkQehS`eUXcWS`YNY_IVaETbF\ WcGYcG_cHacHccIfcJhcJjdKldKndLqdMsdMudNwdNydQtbTp`\ WlZZhYadWd`UgXSiTRoCkkGjgKjcOj_SjWWjS_jOciKgiGkiCo\ i8si5wi7vk9ulAHb9MZ8RV7WR } END PARAMETER FILE=========================================

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FOTD 22-10-04 (Moire Fantasy [7])
by Jim Muth 22 Oct '04

22 Oct '04

FOTD -- October 22, 2004 (Rating 7) Fractal visionaries and enthusiasts: I named today's unusual image, which was created by the 'julfn+exp' formula, "Moire Fantasy" because of the Moire interference patterns that exist all through it. This means that the appearance of the image is partly created by the screen resolution, and the image will therefore appear slightly different at different resolutions. The passes=b option works unusually well with today's image. Not only is it the fastest, but it is by far the most interest- ing to watch in action. The banded effect was achieved by rendering the scene with the outside set to 'summ', an option that I rarely use, but like the passes=b, one that works quite well with today's image. The function I chose for today's image is the 'abs', which changes the negative and imaginary values to positive values. This particular function works best with the julfn+exp formula. I know of no other formula in which the absolute value function works best. The image is different enough from my usual type of fractals to rate a 7. I almost rated it at an 8, but when I could pin down nothing in it actually well above average, finally decided on the 7. When the short render time of 1-1/2 minutes is figured in, the overall worth registers an impressive 435. The completed GIF image is available at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A cloudy and drizzly day here at Fractal Central on Thursday, with a temperature of 50F 10C, kept the dynamic fractal cats stranded indoors for the second straight day. But once again their moods were surprisingly good, and no special treat was needed. Today is again starting cloudy and cool. I expect the cats to have a similar day. For me it looks like an average day, with enough work to keep me busy several hours before I can turn to the world of fractals. The next FOTD will appear tomorrow. Until then, take care, and believe what you will, but be sure to believe something. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Moire_Fantasy { ; time=0:01:36.50--SF5 on a P200 reset=2003 type=julfn+exp function=abs passes=b center-mag=-0.0958251/0.0660603/0.9908874/1/-87.5/\ -1.26836041669520228e-013 params=-1.6/0.42 float=y maxiter=1200 bailout=64 inside=255 outside=summ logmap=yes symmetry=none periodicity=0 colors=000jEekDelDdmCcmCcjBagB_eBZbBX_BWYBUVBTSBRQ\ BQNBOKBNIBLFBKCBIBDFABH9AI89JACIBEICHIDJIFMHGOHHQH\ ITHKVGLYGM_GNaGOdGQfFRiFSkFTmFVpEWrEXuEYwEZyEYwHXv\ JWuMWtOVsRUrTUqWTpYSo`SnbRmeQlgPkjPjlOioNhqNgtMfvL\ eyLdzKezJeyJexIewHfvHfuGftFfsFfrEgqDgpDgoCgnBhmBhl\ Ahk9hj9hj8gh8fe8eb8d_8cX7bV7aS7`P7_M7ZJ7ZHA`LDaPFc\ TIdXLf`NgcQhgTjkVkoYms`nwbozYruTtqRpsQmtPjuOgvMdxL\ ayKYzJVzHSzGPzFMzEJzIIzLHzOHzRGyUFxXFv_EucDsfDriCp\ lBooBmrAlu9jx9irBemCbhD_eCZbCY`BXYBWVBVTAUQAUNATL9\ SI9RF9QD8PA8O88OACPBGQDKREOSGSTHVUOYPV_KabFhdAof6k\ iEhkMemUaoaZqiWsqTuyWsvYrs_qpbpmdojfngildkkamjZpiW\ rhTtgQvfNseQpdTncWkcZhbafadc`g``jZ_mWZpUZsRaqPcoNe\ mLhkJjiKlgMoeOqcQsaSv_UxYWzXYyV_yUayScyReyPgyOiyNk\ yLmyKozIqzHszGuzHwzIxzJyzJzzKzzLzzLzzMzzNzzOzzOzzP\ zzQzzQzzMzzJzzGzzFzzEzzEzzDzzDzzGzzJzzMzzOzzRzzUzz\ WzzZzzazzczzfzzizzkzznhrz } END PARAMETER FILE=========================================

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FOTD 21-10-04 (Antarctic Fractal [6])
by Jim Muth 21 Oct '04

21 Oct '04

FOTD -- October 21, 2004 (Rating 6) Fractal visionaries and enthusiasts: Today's formula, the 'hypercomplexj', draws the Julia sets that correspond to the Mandelbrot sets drawn by the 'hypercomplex' formula. These formulas use 4-part hypercomplex numbers, which draw four-dimensional M-sets and J-sets. These two four-dimen- sional collections of sets are oriented so that they intersect in single points, with an entire 4-D Julia set corresponding to every individual point of the 4-D M-set. For this relation to be possible, fully eight dimensions are needed. So when we ex- plore with the 'hypercomplexj' formula, we are actually explor- ing an eight-dimensional Julibrot figure. In eight-dimensional space, there are six mutually-perpendicular directions that are at the same time perpendicular to a two- dimensional plane, such as that of the screen. All six direc- tions can be explored with the six variable parameters of the 'hypercomplexj' formula. (For some reason, the 'hypercomplex' formula ignores the 'warped' M-sets.) My dream formula would be one that draws every possible orientation through this 8-D Juli- brot. Unfortunately, my math ability is not up to the task of writing such a formula, so the formula will remain a dream. When I first saw today's image, it reminded me of something familiar that I could not quite recall. Then I recognized a resemblance to the continent of Antarctica, and named the image "Antarctic Fractal". The image is one of the Julia sets that corresponds to yester- day's 'Elephant-Seahorse' Mandelbrot image. In the 8-D Julibrot not all Julia set slices are symmetrical, as they are in the more familiar 4-D Julibrot. In today's image, which shows the entire Julia set, I emphasized this lack of symmetry. As was the case in yesterday's image, today's image has places where different elements overlap, and the lower-iteration ele- ments are obliterating the higher-iteration ones. What we have is two distinct Julia sets fighting to be displayed on the screen, with the lower parts of each set winning. It strikes me as much like human nature, where we know what is right but are prevented from doing it by our baser instincts. With so much calculating to do in each cycle and a maxiter of 27000, today's image is a slow one, taking an hour on my tired old workhorse 200mhz machine. (On the new 2200mhz machine, a test-rendering took 8 minutes, but that unit is for real work, not fun.) Today's image has much mathematical interest but lacks artistic beauty. I rated it at a 6, mostly for its math interest. When the one-hour render time is figured in, the overall worth equals a humble 10. My recommendation is to avoid such excessive humility by down- loading the completed GIF image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> But if your machine is a fast one and is Fractint compatible, be humble. Take a few minutes to enjoy the coming-into-existence of a tiny part of an unimaginable 8-dimensional world. And un- less I am mistaken, our universe is currently theorized to con- tain 11 dimensions. A chilly, dreary, misty day here at Fractal Central on Wednesday kept the fractal cats confined to their shelf by the window. For some unknown reason, their moods were not bad however. As a reward, they received extra tuna for their evening dinner. Today is again starting dreary and chilly. More tuna will be needed. In my department, the commercial work is still caught up, and the FOTD fractals will keep coming every day. The next one will appear, not quite by magic, at this same time and place 24 hours from now. Until that ecstatic moment, take care, and don't dis- turb the fractal peace with excess exuberance. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Antarctic_Fractal { ; time=0:12:09.08--SF5 on a P200 reset=2003 type=hypercomplexj function=sqr passes=t center-mag=-8.88178e-016/-0.132743/1.173709 params=-0.2218959949992792/-0.03077554360265753/0/\ 0.53/0.25/0 float=y maxiter=27000 bailout=9 logmap=yes symmetry=none periodicity=0 colors=000POePXeOZeO`eOdeNheOleOoeOqeWrd_sdctdeudf\ vefwgbwiZwkVwmRxpNxrKxsKwqKuoKsmKqkKoiKmgKkeKicKha\ Kh_FgYAgWDeUFcSHaQJ_OLYMOWLQUMSSMUQNWOOZMO`KPbIQdG\ QfERhDReCQcBPaBO_ANX9MV9LT8KR8JO7IM6HK6GI5FG5FH9JI\ CNIFRJIUKMYKPaLSeLVhMYgN_gNbgOdfOgfPifQleQneRqeRsd\ SvdSxdYugcriiokolnuipzfrzdtzeotejnfehgabhXXjSRkOLk\ JFjEAhACf9Dd8Eb7G`6HZ5IX4KV3LT2MR1NP0ON6PLCQKIRMOS\ NUTOUUPUWQVXRVYSVZTV_UW`VWaWWcXWdYXeZXf_Xg`XhaYibY\ kcYldYmeZnfZogZphZqi_sj_tk_ul_vm`wn`xo`ypazqayp`xn\ _vmZukYtjXsiWqgVpfUodUmcTlaSk`Rj_QhYPgXOfVNdUMcSMb\ RLaQK_OJZNIYLHWKGVIFUHESFDTGEUHEVHFWIFXIGYJGZKH_KH\ `LIaLIbMJcNJdNKeOKfOKgPLhQLiQMjRMkRNlSNmTOnTOoUPpU\ PqVQrWQsWRtXRuYRuZRt_9s`BraCqbEpcFodGmeIkfJigLghMe\ iNcjPakQ_lS_mR`nRanRboQcoQdoQfpPgpPhpPipPjqOkqOlqO\ nrNorNprNqsMrsMssMutNtsMtsMtsMtsMtsMtsMtrMtrMsrLsr\ LsrLsrLsqLsqLsqKsqKsqKsqK } END PARAMETER FILE=========================================

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FOTD 20-10-04 (Elephant-Seahorse [6])
by Jim Muth 20 Oct '04

20 Oct '04

FOTD -- October 20, 2004 (Rating 6) Fractal visionaries and enthusiasts: Today's FOTD takes us to the hypercomplex formula of Fractint, which draws a four-dimensional version of the Mandelbrot set. At one time I used this formula quite extensively, but since then I have written my own formula, the HyperMandelbrot, which draws all the same images plus many new images that the hyper- complex formula does not. The hypercomplex formula is not to be cast aside as outmoded however. It still draws some very interesting images, and it draws them faster than my own formula. In a case like today's, where the image takes over one hour to render, speed becomes quite important. In addition, the hypercomplex formula is the only one in which the various functions can be applied. Being four-dimensional, the overall shape of the hypercomplex Mandelbrot set is impossible to visualize, but when the function is 'sqr', it can be taken as two familiar Mandelbrot sets partly overlapping. The position of the overlapping sets is controlled by the Z parameter. The other functions produce different figures, but the figures behave in pretty much the same way. The most interesting parts of the fractals drawn by the hyper- complex formula are the places where different parts of the two overlapping M-sets intersect. One such place is seen in today's image, which shows an intersection of Elephant Valley and Seahorse Valley. When two elements intersect, the element with the lower itera- tion count always obliterates the higher. In today's image, Seahorse Valley appears as the brownish shaft shooting up the center of the frame, while the rest of the scene is a part of Elephant valley. Examine the brownish elephant-trunk features just above the center of the frame. The elephant spirals do not go on indefinitely, as would be expected. Instead, as their iteration count increases, they grow more diffuse as they grow smaller, until their iteration count finally becomes higher than the count of Seahorse Valley, which until now they have been obscuring, and they vanish entirely. The moral of all this is, 'once a point escapes, it is not coming back'. I named the image "Elephant-Seahorse", because it is a combina- tion of both valleys. I rated it at a 6, more for its mathema- tical interest than its artistic worth. The unusually slow render time of 1 hour 18 minutes reduces the overall worth to a pathetic 7.6. But that abysmal worth can be ignored by downloading the file of the completed GIF image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A chilly rain here at Fractal Central on Tuesday, with a temper- ature of 52F 11C, kept the dynamic duo of fractal cats indoors all day. They accepted their confinement stoically, though an extra treat of tuna was needed to help them find their stoicism. Today is starting chilly and cloudy, but at least it is dry. What the cats will make of this is anybody's guess. My guess is that the next FOTD will appear in 24 hours, and it is a pretty fair guess that the image will be memorable. Until that glorious moment arrives, take care, and search for the hidden meaning in fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Elephant-SeaHorse { ; time=1:18:35.73--SF5 on a P200 reset=2003 type=hypercomplex function=sqr passes=1 center-mag=-0.22062180436286390/-0.029775589430454\ 16/607.5435 params=0/0/0/0.53 float=y maxiter=27000 bailout=9 inside=0 logmap=25 periodicity=10 colors=000OSVPTVQUWRVWSWWUXWVYXWZXX_XY`XZaY_bYacYb\ dYceZdfZegZfhZgi_ij_jk_kl_lm`mn`no`opapqaop`nn_lmZ\ kkYjjXiiWggVffUedUccTbaSa`R`_QZYPYXOXVNVUMUSMTRLSQ\ KQOJPNIOLHMKGLIFKHEIFDJGEKHELHFMIFNIGOJGPKHQKHRLIS\ LITMJUNJVNKWOKXOKYPLZQL_QM`RMaRNbSNcTOdTOeUPfUPgVQ\ hWQiWRjXRkYRkZRj_9i`BhaCgbEfcFedGceIafJ_gLYhMWiNUj\ PSkQQlSQmRRnRSnRToQUoQVoQXpPYpPZpP_pP`qOaqObqOdrNe\ rNfrNgsMhsMisMktNjsMjsMjsMjsMjsMjsMjrMjrMirLirLirL\ irLiqLiqLiqLiqLhqKhqKhpKhpKhpKhpKhpKhpKhrIhpKhoMhm\ OhlQhjShiUhgVhfXhdZhc`habh`dhZehYghWihVkhTmhSohRpg\ SofTofToeUneUndVncVncWmbWmbXmaYmaYl`Zl_YmZXnYWoXVp\ WUqVTrUSsTRtSQuRPvQOwPNxOMyPLzPKzQJzQIzQHzRGzRGzSH\ zSIzTIzTJzTKzUKzULzVMzVMzWNzWOzWOzXPzXQyYQyYRyZSxZ\ SxZTx_Ux_Uw`Vw`Ww`Ww_VuZVtYUsXUrWTqVToUSnTSmTRlSRk\ RQiQQhPPgOPfNOeMOcLNbLNaKM`JM_ILYHLXGKWFKVEJUCISEJ\ TFKTGLTHMUINUJOUKPUMQVNRV } END PARAMETER FILE=========================================

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FOTD 19-10-04 (The Rage of Poseidon [6])
by Jim Muth 19 Oct '04

19 Oct '04

FOTD -- October 19, 2004 (Rating 6) Fractal visionaries and enthusiasts: Today we turn to the Halley formula of Fractint, which is one of my favorite formulas. It converges on roots of polynomials much like the Newton's formulas, but with much more control over the appearance of the images. The 'epsilon' parameter controls how close to the actual roots the points must come before calcula- tion is stopped. The 'relaxation' parameter has nothing to do with relaxing after a hard day's work. It controls the amount of chaos in the image. A value above one allows more chaos, while less than one keeps the chaos under tighter control. An imaginary value, such as I used in today's image, twists the entire scene. The colors are determined by the number of iterations needed to reach the point where the change is less than the value assigned 'epsilon'. The smaller this value, the more iterations will be needed, and the greater the opportunity for chaos to sneak in. Today's image uses a value of an extremely small 10^(-15), which brings out all potential chaos. In addition to total chaos between roots, some settings of the Halley parameters produce total chaos along the borders between areas of different numbers of iterations to the same root. This is the case in the purplish areas of today's image, where magni- fication will reveal that no two adjoining areas actually touch. Regardless of the magnitude, there is always chaos along the 'borders'. Though it usually consists of only two colors, this chaos is interesting in itself. Sometimes, as in today's image, it is totally chaotic, while at other times, unexpected geome- tric patterns appear. I am not sure whether this chaos is part of the formula or an artifact of the math routine, but it is curious nevertheless. One of the early versions of today's image was colored with a turquoise theme, and resembled an undersea scene, with air bubbles rising toward the surface. I named it "The Rage of Poseidon". (If I remember my mythology correctly, Poseidon is the god of the sea, who really had it in for Ulysses for blinding his cyclops son.) I have since totally changed the color scheme to something more like a view down into the pit of hell, but I have kept the angry oceanic name. I would have rated the image at a 7, but I have a certain aversion to spirals, of which today's image is a perfect exam- ple, so I could rate it no higher than a 6. When the brief render time of just under 4 minutes is considered, the overall worth equals a humdrum 153. The image may be rendered from the included parameter file or downloaded, already completed, from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather remained uneventful here at Fractal Central on Monday. The partly sunny skies and temperature of 59F 15C were barely good enough to meet the quality standards of the fractal cats, who spent less than an hour lounging testily in the yard. Things will be no better for the duo today, since it is starting wet and chilly. They will not like this. The next FOTD is but 24 hours away. Until then, take care, and don't surrender to fractal terrorism. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Rage_of_Poseidon { ; time=0:03:54.98--SF5 on a P200 reset=2003 type=halley passes=1 center-mag=14.1471\ /8.14196/0.03333333 params=12/0.9/1e-015/0.59 float=y maxiter=95 bailout=9 symmetry=none inside=bof61 logmap=yes periodicity=0 colors=000pfC_lPZkPXjQWhQVgQUeRTdRJeWScR_aMg`IeYLd\ VNcSQbPSaMV`JX_G_ZDaYAdX7fX2jW4hW6gW8fWAeWCdWEcVGb\ VIaVK`VM_VOZVQYVRXXSWZTV`UUbVTdWSfXRhYQjZQl_Pn`Opa\ NrbMtcLvdKxeJzeJxgIvhHtiGsjFrkEwlAzmKznUzoczpmzqwz\ zzzzzzzzzzzzzzzzwzzmzzczwUzrLzmMzhMzcNzcNzcNwYOtKO\ qEPnAOkANhANcAM_1LX4OW6QW8SXBVXEXYHZZLaZOc_Re_Vh`Y\ kaanafrbjudnzbox`owZovXotWosUorSoqQooOonNomLokJojH\ oiEqiGohHngJmfKleMjdNicPhbQgbSfaTd`Vc_WbZYaYZ_X`ZW\ aYWcXVdWUfUTgTSiSRjRQkQQiRPgRPeRPdRPbRP`RO_ROYROWR\ OVROTRNRRNQRNORNMRNLRNOSQRSSUSVXSX_S_bSa_U`XV`VW`S\ X`QY`NZ`L``Ia`Gb`Dc`Bd`8e`6f`5f`4fa3fa2fa2fa5g`7g_\ AhZChYEiXHiWJjWMjVOjUQkTTkSVlRYlRyqH_mQamPdnOfnNin\ MkoMmoLppKrpJuqIwqHfW7gX8gX8gX8gX8gY8hY8hY8hY8hY8h\ Z8hZ9iZ9iZ9iZ9i_9i_9j_9j_9j_9j`9j`9j`Ak`Ak`AkaAkaA\ kaAkaAlaAlbAlbAlbAlbBmbBmcBmcBmcBmcBmdBndBndBndBnd\ CneCneCoeCoeCoeCofCofCpfC } END PARAMETER FILE=========================================

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Fractint arbitrary precision
by Fractal Laboratory 18 Oct '04

18 Oct '04

Does anyone know if there is a translation of Fractint's arbitrary precision library into a Windows DLL? Thore Berntsen _________________________________________________________________ MSN Messenger http://www.msn.no/computing/messenger - Den korteste veien mellom deg og dine venner

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