; Date: Sat, 12 Feb 2005 10:25:18 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 12-02-05 (The Right Path [7]) ; Id: <1.5.4.16.20050212102535.2b47ff68@pop.mindspring.com> ; --------- ; ; FOTD -- February 12, 2005 (Rating 7) ; ; Fractal visionaries and enthusiasts: ; ; Yesterday's image was named "Most Unusual Midget", but it was ; not really all that unusual, and rated only a 5. Today's image, ; which is named "The Right Path", would have been better named if ; it had been given the name of yesterday's image. It is the more ; unusual of the two. ; ; Today's image is located far to the northeast of the main part ; of its parent fractal, which is the same fractal that has given ; us the most recent images. The scene is located in a cut-off ; bit of circular debris inside a large closed ring that ; terminates the most prominent filament leading from the main ; part of the fractal. ; ; The image got its name from the narrow, winding path that ; encircles the central midget like a beltway encircles a city. ; It is truly a path to nowhere. One could travel it forever and ; never arrive at an end, for, like infinity, it has no limits. ; ; The concept of infinity is a strange thing. It is so easy to ; see that if one were to start traveling along the path in ; today's image, they would never come to the end because no end ; exists. Yet if one tries to imagine a straight line with the ; same endlessness, they find that their mind cannot grasp the ; entirety of the thing. ; ; Even harder to imagine is a half-line, a straight line with only ; one end. Is it infinite or not? We can see that a straight ; line with no ends would be longer, for it would extend into ; regions where the half-line did not. The answer depends on the ; direction in which we view the line. In one direction it is ; infinite; in the other direction it has a certain, though ; unimaginably great length. ; ; This half line situation reminds me of a day in seventh grade ; religion class in a Catholic school, when the nun was re-re-re- ; telling of how our souls will be perfectly happy in heaven ; forever if we obey God's commandments in this life. I asked ; the good sister how heaven could be fair, since those good ; people who died long ago have already had more happy time than ; those now living, and no matter how long we are all in heaven ; the ones who went there first will always have had more ; happiness than the late-comers. The sister replied that we will ; be looking forward to our future happiness when we get to heaven ; and not back to the hardships of earth life. She explained that ; everyone will be in heaven forever and will therefore have the ; same infinite amount of perfect happiness. I started to say, ; "but . . .", and the sister told me to sit down and shut up. ; ; Infinity is strange indeed. Any quantity can be added or ; subtracted from it and it remains unchanged. It can be ; multiplied or divided by any quantity, even infinity, and it ; remains unchanged. It can be raised to any finite power and it ; remains unchanged. (If it is raised to the power of infinity it ; might become a higher order of infinity -- I am not sure.) ; ; Well, I see myself again wandering from the topic, so it's time ; to note that today's image rates a pretty good 7 and renders in ; 2-1/2 minutes. It is available for download on the FOTD web ; site at: ; ; ; ; Weak sun and chilling winds here at Fractal Central on Friday ; kept the fractal cats indoors most all day. They did manage a ; brief 20-minute sojourn to the holly thicket to check for ; intruders. When they found none, they hurried back inside to ; watch the world from their shelf by the window. An extra large ; treat of tuna in the evening eased their disappointment. Today ; is looking like it will be another blustery one. The duo is ; braced for more disappointment. ; ; For me it looks like an average day coming up. But sometimes ; average days can be quite interesting. Check back in 24 hours ; to see if anything of interest appears in before then. Until ; next FOTD, take care, and if only we knew which path is the ; right one. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= The_Right_Path { ; time=0:02:25.11--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+5.20383959978280900/+2.454715711010205\ 00/286974.9/1/55/5.08479132410588619e-009 params=5/-1.26/0.5/-12.6/0/0 float=y maxiter=900 inside=0 periodicity=10 colors=000KgOGhPCiQ8jR4kS7lT9lUBmUDmVFmVHnWJnWLoXN\ oXPoYRpYTpZVqZXq_Zq_XhZV`ZUSZSKZRCZkBtiCqgCnfCldCi\ bDgaDd_DbYD_WEYUEUSEPQEMOEKMDIKDGLCECCCDBAEBAGAAHA\ AJ9AK9AM8BN8CP7DQ7ES9FTAGVCHWDIYFJZGKaILcJMfLNhMOk\ OPmPPoRQqSRsTRuXPs`NqdLnhJjkImoGrsEvwDzzBzzzzzzzzz\ wzRrwWmr`omeqhjrcolZjgUfbPbYKZTIUOHQJGMEFI9EECFDEF\ CHGCJGBMGAOHARH9TH8WI8YI7`I6bJ6eJ5gJ5cN9_QDWTGSXKO\ _NKbRGfVCiY8la4od3oc3ob3oa3oa3o`3o_3o_2oZ2oY2oX2oX\ 2oW2oV2oV1oU1oT1oS1oS1oR1oQ1oQ5mT9lWDkZHi`LhcPgfTe\ hXdk`cndaph`sl_voZxm_yk`yjayhayfbyecyccybdy`eyZeyY\ fyWgzVhzThzRizQjzOjzNkzLlzJlzImzGnzFnzIlxKkwMivOhu\ QgtSesUdrWcpYao_`na_mdYlfXkhYjjZhl_gnafpceredtgcvi\ bxkavmbtobrqbpsbnuclwckyciycgzdezdczdazd_zeZzeXzeV\ zeTzfRzfPzfNzfMzfMzdMzcMzaaz5`z4_z6Zz7Yz8Xz9WzAVzC\ UzDTzESzFRzGQzHPzJOzKNzLMzMLzNKzPJzQIzRHzSGzTGzUJz\ RMzOPzMSzJVzHUzGTzFTzESzD } 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========================================= ; ;