June 2003 - Fractint - mailman.xmission.com

[Fractint] re: Fractals Relate to Expansion-Contraction of the Universe
by Programmer Dude 27 Jun '03

27 Jun '03

Osher Doctorow (not Marleen Doctorow) writes: > I have been arguing [...] that fractals relate directly to > expansion-contraction of the universe. "Directly" perhaps remains to be seen. The idea of surfaces is interesting, though. I've read that some fractal "purists" only ever color the Mandlebrot in two colors: inside & outside. > The most unusual thing about expansion-contraction is that it differs > from ordinary curvilinear or linear motion in involving GLOBAL and > CONTROL properties... How does this really differ from ordinary movement, which also would seem to involve GLOBAL and CONTROL properties? For example, doesn't the earth's orbit involve properties "global" to the system (e.g. the earth's mass) as well as "control" properties (e.g. gravity)? It would seem that motion through space of an object where the object does not change form is distinct from motion involving a form change. In my experience, the term "orthogonal" is sometimes used to refer to properties that are not related. I would think that shape-changing movement is orthogonal with respect to non-shape-changing movement. Certainly some objects may do both. Throughout my life, my shape has changed (mostly gotten larger!), but I have also constantly moved through space (and time). > Fractals are BOUNDARY phenomena, and therefore are vitally related > to surfaces which are also boundaries of their insides and outsides > in 3 dimensions, or to projections of surfaces in 2 dimensions > (boundaries of continents, leaves, trees, etc.). There are many BOUNDARY phenomena, however. Is not the most salient aspect their fractal dimensionality? Do the expansion/contraction phenomena under study here demonstrate this? If not, I would question the connection. > It might be agreed by readers that Fractals are related to expansion- > contraction as surfaces,... The relation seems tenuous thus far. The fractal dimension aspect seems missing or not covered. Further, a given fractal seems static; neither expanding nor contracting. > Well, it turns out that there aren't that many types of objects in > the Universe which are expanding or contracting as their > characteristic motions. [grin] Yet your own list names some rather significant ones! After life, thought, energy and the entire universe, what's left? (Incidentally, I would add metals and water to that list.) > There is some prospect that not only can we generate fractals in the > above manner, but that ALL expansion-contraction objects obey similar > algebraic and calculus/analysis/differential equation formulas which > sharply distinguishes them from ordinary objects which only have > curvilinear or linear motion. I'll try to keep readers informed of > major developments as they occur. Okay! ;-) -- |_ CJSonnack <Chris(a)Sonnack.com> _____________| How's my programming? | |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL | |_____________________________________________|_______________________|

1 0

Fractals Relate to Expansion-Contraction of the Universe
by MARLENE DOCTOROW 26 Jun '03

26 Jun '03

>From Osher Doctorow (not Marleen Doctorow) I have been arguing on http://www.superstringtheory.com/forum, in the Strings/M Duality subforum of their Forum section, that fractals relate directly to expansion-contraction of the universe. In the cosmology branch of physics and mathematical physics (the latter is technically a branch of mathematics), where I spend much of my time, there is considerable interest in the expansion, contraction, and acceleration of the universe. The most unusual thing about expansion-contraction is that it differs from ordinary curvilinear or linear motion in involving GLOBAL and CONTROL properties - a whole bunch of coordinated parts of an object like a balloon expand or contract simultaneously, and theoretically different parts of an object can be controlled to expand at different rates. Up to this point in my posting, it doesn't look as though fractals and expansion-contraction have anything unusual about them, but now notice that the SURFACE of a balloon is critically involved in its expansion- contraction. The SURFACE, not just the volume, expands in coordination, and the surface reflects different rates of expansion. Fractals are BOUNDARY phenomena, and therefore are vitally related to surfaces which are also boundaries of their insides and outsides in 3 dimensions, or to projections of surfaces in 2 dimensions (boundaries of continents, leaves, trees, etc.). It might be agreed by readers that Fractals are related to expansion- contraction as surfaces, but what does this have to do with the Univese other than the fact that the Universe is supposed to be expanding? Well, it turns out that there aren't that many types of objects in the Universe which are expanding or contracting as their characteristic motions. Most things move curvilinearly (in a curve) or linearly (in a straight line). They don't blow up or contract like balloons. Here's a list of things in the Universe that do expand-contract as their characteristic motions. A. The whole universe itself as for example in the usual spherical model. B. Radiation (light, heat, etc.) from a source (a point or string) C. Biological life (growth, muscular movements, etc.) D. Human consciousness, memory, perception E. Galaxies (evolving with expansion or contraction from spiral to elliptic, etc.) F. Organic materials such as plastics which have viscoelasticity. David J. Wright (Oklahoma State) "Dynamical systems and fractals lecture notes," 8-19-96, www.math.oksate.edu/mathdept/dynamics/lecnotes/lecnotes.html, explains very clearly how fractals are generated by CONTRACTIONS of iterated function systems (IFS), either linear or hyperbolic. There is some prospect that not only can we generate fractals in the above manner, but that ALL expansion-contraction objects obey similar algebraic and calculus/analysis/differential equation formulas which sharply distinguishes them from ordinary objects which only have curvilinear or linear motion. I'll try to keep readers informed of major developments as they occur. Osher Doctorow Ph.D. One or More of California State Universities and Community Colleges

1 0

Re: HTML and web pages
by JackOTradez 26 Jun '03

26 Jun '03

Folks - I too have usually done my web page(s) initially with notepad; basic HTML is quite EZ 2 learn. However, I would enlighten you to a FREEware program I have just recently encountered, called HTML-kit. You can fetch it at http://www.chami.com/html-kit/ and it is fully functional and free. WHY someone gives away a good program like that free is a question for a better philosopher than I. It automatically inserts tags, has a friendly interface, can check coding format, and do a lot other things I can not begin to list here. It is quite sophisticated. Check it out! JoTz

4 3

FOTD 26-06-03 (Hers and His [6])
by Jim Muth 26 Jun '03

26 Jun '03

FOTD -- June 26, 2003 (Rating 6) Fractal visionaries and enthusiasts: Yesterday's FOTD picture was named "His and Hers". But because I inadvertently substituted a space band for an underscore between the words 'and' and 'hers', the word 'hers' did not appear when the parameter file was loaded into Fractint, and a great inequality was done to women. Since yesterday's image was named "His and Hers" for no reason at all, today's image can also be named for no reason at all. And so that justice might prevail, I have named today's image "Hers and His", with the feminine aspect in first place. The image is a scene in the parent fractal that results when 0.7 parts of Z and 0.7 parts of Z^5 are combined and C is added. This parent resembles a distorted M-set with its nose pointed southeast and its butt pointed northwest. Some distance beyond its butt lies a string of Julia-like open circles. Today's scene lies on a filament on the shore of one of the larger circles. To produce the strange effect, the scene was rendered with the outside set to 'fmod' and the inside set to 'bof61'. The inside part of the image consists of the interior of the central midget as well as the egg-shaped areas. I used these non-standard fills because when rendered in the normal manner, the image is downright dull. When the time arrived to rate the scene, I saw a picture that had been rescued from an abysmal rating of 3 or so and raised to an image that was actually a little above average. I rated today's image at a 6. The render time comes in at under 3 minutes on my tired-out fractal machine. It downloads in even less time from the FOTD web sites, which can be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Wednesday brought another typical 93F 34C summer day to Fractal Central. The sun was hot, the humidity was high, the wind was light, and the air was polluted. It was just the kind of day to bring out the laziness in the fractal cats, who spent the entire afternoon sleeping on the lawn chairs in the shade of the holly trees. Today will be a hotter repeat. It will also be a repeat for me. I don't have much work to finish, but the little bit I do have must be finished today. Until next FOTD, take care, and the world is filled with unseen fractal wonders. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Hers_and_His { ; time=0:02:54.61--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.610840504599416/+0.61145130410153/30\ 9223.4 params=0.7/1/0.7/5/0/0 float=y maxiter=800 inside=bof61 proximity=0.5 outside=fmod logmap=yes periodicity=10 colors=000otznszmrylqxkpwjovinuhmtg\ lsfkrejqdipchobgnafm`el_dkZcjYbiXahW`gV_fUZeTYdSXc\ RWbQVaPU`OT_NSZMRYLQXKPWJOVINUHMTGLSFKREJQDIPCHOBG\ NAFMAELBDKBCJEBIGAHHBGHBFJEELEBNGBPGBPGBRHBSHBUJBU\ JBWLBXLBZLB`NA`NAbPAdPAfRAfRAgRAiSAkSAlUAlUAnW7pW7\ rW7rX7sX7uZ7wZ7x`7x`7z`7zb7zb5zd5zd5zf5zf5zf5zg5zg\ 5zi5zi5zi5zg7zgAzgBzfBzfEzfGzdHzdHzdJzdLzbLzbNzbPz\ `Rz`Rx`SwZUwZUuZWuZXsXZsXZrX`pWbpWdnWdnWflUgkUgkUi\ iSkiSlgSlfRnfRpdRpdRrbPs`Pu`PuZNwZNxXNzXNzWLzULzUL\ zSJzSJzRJzPHzPHzNHzNHzLGzJGzJGzHEzHEzGEzAHzEGzGEzH\ BzJAzL7zN5zP4zR1zS0zW0zX0zZ0z`0zb0zd0zf0zg0zi0zi0z\ k0zk0zl0zl0zn0zn0zp0zp0zr0xr0ws0us0su0ru0pw0nw0kw0\ ix0gx0fz1dz4bz4`z5Zz5Wz7Uz7SzARzBPzBNzELzEJzGGzGEz\ HBzJAzJ7zL5zL4zN1zN0zP0zR0zR0zS0zS0zU0zZ0zW0zU0zS0\ zP0zN0zL0zH0zG0xE0uB0r70n51k44g05d07`0AZ0A`0B`0B`0\ B`0B`1B`4B`4Bb5Bb7BbABbABbBBbEBbEBbGBdHB } 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

Re: [Fractint] FOTD 21-06-03 (Beware the Lava Pit [5])
by gnome＠hawaii.rr.com 26 Jun '03

26 Jun '03

>Programmer Dude wrote: >> >> I cannot recommend highly enough "gvim", which is "GUI vim", which >> is a window version of vim, which is a charityware version of vi...on >> steroids! 100% compatible with vi (in all important respects), plus >> much, much more. It's been my primary editor for years! (You even >> find a lot of unix platforms that have aliased it for "vi".) >> >> Vim (Vi iMproved): http://www.vim.org/ >> > >Wha about Emacs ( http://www.gnu.org/software/emacs )? > >Ciao, >Danilo Emacs isn't just a text editor. Emacs can do so much more that it has become a religion! ;-) David an old vi user gnome(a)hawaii.rr.com

3 3

Re: FOTD 25-06-03 (His and Hers [7])
by Jim Muth 25 Jun '03

25 Jun '03

At 09:54 AM 6/25/03 -0500, Paul Lee wrote: >For those that save PAR files (and for Jim's FOTD CD), you >may wish to add another underscore to the 'name': >His_and_Hers > >Sincerely, >P.N.L. I caught the mistake as soon as I sent the FOTD. Since the PAR file still renders correctly, and the error is obvious, I did not repost it. Murphy's law says that every FOTD I check before posting will be correct, while those that I do not check will all have errors. :-) Jim M.

1 0

FOTD 25-06-03 (His and Hers [7])
by Jim Muth 25 Jun '03

25 Jun '03

FOTD -- June 25, 2003 (Rating 7) Fractal visionaries and enthusiasts: Adding Z to Z^3 changes the entire shape of the resulting fractal. Adding Z to Z^2 merely shifts the position of the fractal without changing its overall shape. When the exponent is between 2 and 3, the closer to 3 the greater the change. For today's image I varied the exponent between 2 and 3 to observe the gradual change. I settled on Z+Z^2.05+C because I noticed a lot of interesting chaos along the splitting negative X-axis. Today's image is located in this chaos. Most of the artistic effect is created by the 'fmod' option, which was applied to the outside parts of the image. Don't ask me why I chose the name "His and Hers". I can see nothing whatever in the picture to justify such a name. But even though the name makes little sense, the image is still worth a 7. The render time of 5 minutes is reasonable for the above-average result. And the completed GIF image is available on the internet for download at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> A perfect summer day with lots of sun and a temperature of 91F 33C on Tuesday here at Fractal Central made for perfectly happy cats who spent several hours on guard in the yard. When the cat from two doors down appeared in the brush, Tippy was ready to attack. Luckily for someone, the cat backed off and no force was needed. Thomas slept through the danger. The similar forecast for today should bring similar conditions. And if I finish the necessary work early enough, I might find some time to enjoy the day myself. Until next time, take care, and search for that lost fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ His_and Hers { ; time=0:05:02.98--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-1.57498835838500200/+0.013976629359833\ 04/1.084695e+011/1/80/-0.0922994127536091724 params=1/2.05/1/1/0/0 float=y maxiter=650 inside=0 proximity=0.25 outside=fmod logmap=yes symmetry=none periodicity=10 colors=000SGdRGdQHcQHcPIcOIbNJbNJbMKaLKaKL`KL`JM`I\ M_HN_GQYHN_HLaIJcIHeIFgJDhJBjJ9lK7nK5pL0qK2qK3qJ4q\ J5qJ6qI7qI9qIAqHBqHCqHDqGEqGGqGHqFIqFJqFKqELqENqDO\ qDPqDQqCRqCSqCUqBVqBWqBXqAYqAZqA`q9aq9bq9cq8dq8eq8\ er8fq8fp8fo8fn8fn8gm8gl8gk8gj8gj8hi8hh8hg8hf8hf8he\ 8id8ic8ib8ib8ia8j`8j_8j_8jZ8jY8kX8kW8kW8kV8kU8kT8l\ S8lS8lR8lQ8lP8mO8mO8mN8mM8mL8mLAnNCnODnPFoQGoRIoSJ\ pTLpUMpVOqWPqXRqYSrZUr_Vr`XsbYsc_sd`tebtfctgeuhhui\ kujnvkqvltvmwwnzwozwpzxuyxswwquuostmqskoqimpgkoeim\ cglaej_ciYahW_fUYeSWdQUbOSaMQ_KOZIMYGKWEIVCHU9HTAF\ SBDRBBQCAPD8OD6NE4MF2LD3KE3JF3IG3HH3GI3FJ3EK3FK3GL\ 3HM3JN3KO3LP3MQ3NR3OR3PS3QT3RU3SV4UW4VX4WY4XY4YZ4Z\ _4_`4`a4ab5bcAddFedKfePgfUhgZihdjijkjolkumjxmkulkp\ lkjkkejk_jlVilPhlKhlFgl8fl7fm7em7dm7dm8cm8bm8bn8an\ 9`n9`n9_n9ZnAZoAYoAXoAXoBWoBVoBVpBUpCTpCTpCSp6Uw9T\ sCSpFRmHRiWDfVEfUEeTFeTFe } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

2 1

FOTD 24-06-03 (Good Fortune [6])
by Jim Muth 24 Jun '03

24 Jun '03

FOTD -- June 24, 2003 (Rating 6) Fractal visionaries and enthusiasts: The formula that created today's image is one of the simplest -- Z+Z^3+C. Yet it creates a parent with scenes that rate at least a 6, as in today's picture, and likely with scenes that would rate a 9, if only they could be found. Curiously, adding Z to Z^2 makes no change in the appearance of the Mandelbrot image, though it does move it to the west, but adding Z to Z^3 totally changes the appearance of the resulting fractal. The parent fractal of today's scene consists of an obvious Mandelbrot set standing on its nose, with much interesting detail beyond its East (or North) Valley, and an almost completely obscured Mandelbrot set hidden beneath the detail beyond the first Mandeloid's East Valley. This second M-set is visible only with carefully chosen coloring. Today's image is located in a spiral in a valley near the northern extremity of the parent. The unusually-well-defined pattern surrounding the midget is a result of the coloring. With other palettes the pattern vanishes. I named today's image "Good Fortune". When I gave it this name, I had an idea in mind, but whatever it was, it has eluded me. So let's just say the scene in the image is very lucky to have been found. The odds against it ever having seen the light of day are at least one-googol-to-one. The image takes 1/2 hour to render on my machine. This is a bit of a drag for busy fractalists. So I recommend 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> Summer weather finally arrived at Fractal Central on Monday, as the temperature reached 89F 32C and the hot sun beamed down on the fractal cats, who were pleased with the turn of events and showed their pleasure by playing like kittens. Tippy actually scampered up a holly tree, while Thomas watched with amusement. No tuna was needed. Since today will be a repeat, I expect a repeat performance from the dynamic duo. I'll do my part by finishing the work early. But to finish the work, I must first start it, so until next FOTD, take care, and wait until the fractals come home. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Good_Fortune { ; time=0:29:42.99--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.00290337839407/+1.12763603161069/6.4\ 25424e+008/1/-177.5/-0.00023613749 params=1/1/1/3/\ 0/0 float=y maxiter=4200 inside=0 periodicity=10 colors=000AVK8TK6TM6RM4PM2PM0OM0MM0MM0KM0IM0GI0IM0\ IO0IP4IR6ITAIVCIXGIYIIbMIdOIeRIgTIiXIkYIlbIndIpgIs\ iIulIwnIxrIzsIzwIzxIzzIzzIzzIzzIzzIzzIzzIzzIzzIzzI\ zzKzzMzzOzwPzpRziTzbVzVXzOYzG_z4XzA_zGdzKgzPkzVnzY\ rzduzixwlzunwwpswrpwslwuiwwewx_wzXwzTwzPwzMwzIwzCw\ z8wz4wz0wz0wz0wz0sz0wz0xz0zs8zkEzbKzTRzKXzCbzI_zMY\ zPXzTVxXTu_RrePniOllMipKesIbwG_zEXzCTzAPz8Oz6Kz4Gz\ 2Cz2Az08z06z06z04z02z02x00u00p00l00i00e00_00X00T00\ P00K00G00C008006006006004004204602A02C02G02K00O00P\ 00T00X00Y00b00e00i00k00n00r00u00w00z00z00z00z00z00\ z00z04z4IsEVgPgXYsKgz6rz0zz0zz0zz0zz0zz0xz0uz0sz0p\ x0nu0kr0in2ek4dg6_d8Y_AXXCTTERPGOMIMIKIEMGAOC6PA2R\ 60T40V00X00Y00_00b00_00Y00X00V00V22T46R6AP8COAGOCK\ MEOKGRIIVGKYGMbEOdCPgARk8Tn8Vr6Xu4Yx2_z0bz0dz0iz0n\ z0sz0xz0zz0zz0zz0zz0zz2zw6zrCzlGzgKzbOzXRzRVzM_zGd\ zAgz4kz0nz0rzG_KEYKCXKCXK } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

1 0

FOTD 23-06-03 (More of the Brush [7])
by Jim Muth 23 Jun '03

23 Jun '03

FOTD -- June 23, 2003 (Rating 7) Fractal visionaries and enthusiasts: To start the day, I downloaded the usual hundred or so junk e-mails. Before deleting them, and being certain I was off- line, I checked the content of one e-mail, which had an unusually clever subject line about an old friend who had just found me. Not surprisingly, the letter was not from an old friend, but from one of those questionable on-line pharmacies with doctors who prescribe prescription drugs without an examina- tion. It would have been just another unwanted piece of junk had it not been for the line that read, "if you act now, your order can be shipped by January". No wonder only one recipient in ten-thousand replies to such letters. Fractals are far more reasonable. Today's image has been created by an entirely different formula than yesterday's, but the same brush-like shape is there. Whereas I decided that yesterday's image rated a 6 and then lowered it to a 5 at the last minute, today's image rates a firm 7. I named the image "More of the Brush" in recognition of the fact that its basic shape closely resemble the brush shape of yesterday's image. The formula behind today's image is Z^10-Z^9+C. This formula produces a parent fractal that is little more than an circle with broken bays around its perimeter. It displays critical characteristics only in the area of its 'East Valley', which is where today's scene is located. The outside parts of today's image were rendered by the 'fmod' option, which in this case does a better job than the standard equal-iteration-bands method. The brilliant turquoise color of the inside of the central midget is a departure from my standard dead black inside color, used today because it works well. The 5-minute render time is within reason, but the 1-minute-or- less download time is even more reasonable. The GIF image can be found, ready for download at either one of the two FOTD web sites: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The clouds hung around most of Sunday at Fractal Central while we were away on the shopping trip. When we returned at 6pm, the sun was trying to break through, the temperature was 79F 26C, and the cats were ready to romp. They enjoyed the yard for over two hours before hunger brought them inside to eat. Today is sunny and warmer -- the kind of weather fractal cats approve of. I've got a bit of work to do before I re-enter the world of fractals, and the sooner I get started, the sooner I'll finish. So until next FOTD, take care, and don't lose the faith. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ More_of_the_Brush { ; time=0:05:24.29--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=ident passes=1 center-mag=+1.00172680834191900/-0.000089662866518\ 10/8255452/1/-147.5/1.85261191e-007 params=1/10/-1\ /9/0/0/0/0 float=y maxiter=850 inside=255 proximity=0.7 outside=fmod logmap=yes periodicity=10 colors=000zzwyztxzqwznuzkszhqzhozhmzhkzhizhgzieyic\ xiawi_viZuiYtiXsiWrjVqiUpiTohSnhRmgQlgPkgOjfNifMhe\ LgeKfeKedKddJccJbcJabJ`bI_bIZaIYaIX`HW`HV`HU_HS_GR\ ZGQZGOYFNYFMYFKXFJXEIWEGWEFWEEVDCVDBUDAUD9UE8VF8WG\ 8WG8XH8YI8YI8ZJ8ZK8_K8`L8`M8aM8aN8bO8cO8cP8dQ8dR8e\ R8fS8fT8gT8hU8hV8iV8iW8jX7kX7kY7lZ7lZ7m_7n`7n`7oa7\ ob7pc7qc7qd7re7se7sf7tg7tg7uh7vi7vi7wj7xk7yk7zl7zm\ 7zm7zl9zlAzlCzkDzkEzkFzjGzjHzjIziJziKziLzhMzhNzhOz\ gPzgQzgRzgSzfTzfUzfVzeWzeXzeYzdZzd_zd`zcazcbzcczbd\ zbezbfzbgzahzaizajz`kz`lz`mz_nz_oz_pzZqzZrzZszYtzY\ uyYvxYwwXxvXxuXwtWvsWurWtqVspVroVqnUpmUolUnkTmjTli\ TkhSjgSifSheSgdRfcRebRdaQc`Qb_QaZP`YP_YPZXOYWOXVOW\ UNVTNUSNTRMSQMRPMQOMPNLOMLNLLMKKLJKKIKJHJJGJIFJHEI\ GDIFCIEBHDAHC9HB8HB8HFBHJDHMFHQHHUJHXLH`NHdQHgSHkU\ HoWHrYHv_Gz`HyaHxaIwaIvbJubJubKtcKscKrcLqcLpdMpdNg\ fNhfNhfNifNigNjgNjgNkg0zz } 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==================================

1 0

FOTD 22-06-03 (Haidinger's Brush [5])
by Jim Muth 22 Jun '03

22 Jun '03

FOTD -- June 22, 2001 (Rating 5) Fractal visionaries and enthusiasts: Today's image reminds me of Haidinger's brush, and that is what I named it. Haidinger's brush is not a cleaning device or scrubbing device; it is almost like a fractal. The brush is not a real brush at all; it is a figure seen at the center of the field of vision when gazing at a smooth and polarized source of light, such as the clear blue sky at 90 degrees from the sun. This ability of the unaided human eye to detect polarized light is little known, but most certainly does exist and can be scientifically demonstrated. Though it is not actually a sixth sense, it comes rather close. A far more complete discussion can be found on the internet at: <http://polarization.com/haidinger/haidinger.html> As a fractal, today's image rates a 6. It was created by subtracting 1.2 parts of Z^(-0.93) from 1.2 parts of Z^(0.93) and adding (1/C) instead of plain C. The resulting parent fractal has a large bay with a very extended, drawn-out shore- line dotted with tiny bays. Today's scene is located on one of the arms of a 'star' at the tip of the filament extending from one of these bays. The image is not all that different from what would be found in the classic Mandelbrot set at a similar location. Therefore, I could rate it no higher than an average 5. But this is the *FOTD* average. And the FOTD average is well above the average of all fractals :-) so the image is worth a quick look, if not the 23-minute render time. That quick look may be found at Paul's web site: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or at Scott's site: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Scattered thunder-showers started popping up in the local area around 4pm on Saturday, finally joining together into one monster storm at 7pm, which flooded many sections on the east side of town. Fractal Central, which is on the east side, escaped with only a puddle of water in the basement; others were not so lucky. Before the rain arrived, the temperature reached 73F 23C, and there was enough sun to give the cats a satisfac- tory day in the grass. The forecast for today is for improved conditions. We'll see what happens . . . Today I find myself going on another of those trips to examine the old junque that others have discarded. Departure time is in an hour, so until next FOTD, take care, and the best is yet to come. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Haidingers_Brush { ; time=0:23:23.32--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=-1.97873106110103800/+1.880302311215394\ 00/486402.7/1/-30/1.06422635703928847e-008 params=1/0.93/-1/-0.93/0.2/-30/0/0 float=y maxiter=3200 inside=0 logmap=347 periodicity=10 colors=000UKUXY_TZaP_cLcgIgkFjoBns8rw5uzG_gQFQBHRD\ JQFKQHMQJNQLOQNQQORPQSPSUPUVPWWPYYPZZP`_ObaOdbOfcO\ heOjfOkgNmiNojNqkNsmNuoNwqQvoNukKtfHsaErZBqU8pM5jP\ AdSEZVJTXNN_SHbWBe`6gd8eb9c`BaZC_XDYVFWTGVRHTPJRNK\ PLLNJNLHOJFPIDRGBSE9TC7VA5W83X71Y93YA5YB7YC9YEBYFD\ YGFYHHYJJYKLYLNYMPYORYPTYQVYRWZSV_SU`TTaTTcUSdVReV\ QfWPhWOiXNjXNkYMlZLnZKo_Jp_Iq`Hr`Hq_Iq_Jq_Kq_KqZLp\ ZMpZNpZNpZOpYPpYPoYQoYRoYSoXSoXTnXUnXVnWVnWWnWXnWX\ mWYmVZmV_mV_mV`lValUblUblUclUdmSclUdlWelXelZfk_gka\ gkchkdijfijgjjikjkkillinmiomiqnirngslfskesjdsicsga\ sf`se_sdZscYsaWs`Vs_UsZTtXStWRtVPtUOtTNtRMtQLtPJtO\ ItMHtLGtKFtJCvJEtIFrIHpHInHKlGLjGNhFOfFQdERbETaEU_\ DWYDXWCZUC_SBaQBbOAdMAeK9gI9jE8hH9fJ9dL9bOA`QA_SAY\ VBWXBUZBS`BQcCPeCNgCLjDJlDKmDMnDOoEQpESqFUrFWsGYtG\ _uGavHcwHexIgyIizIkzJmzJozKqzKrzLszLtzLuzMvzMwzNxz\ NyzNzzNzzNzzNzzQzzSzzUzzW } 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==================================

1 0