; Date: Tue, 12 May 2009 18:44:38 -0400 ; ; To: fractint@mailman.xmission.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 13-05-09 (Rectangle Holiday [8]) ; ; Id: <1.5.4.16.20090512184534.2a678c7a@pop.mindspring.com> ; --------- ; ; FOTD -- May 13, 2009 (Rating 8) ; ; Fractal visionaries and enthusiasts: ; ; There are very curious rectangles in one of the Julia sets of ; the Z^(2.003)+C Mandeloid. To see one of them, calculate the ; Julia set with a C-value of -1.7435 and check the Z-coordinates ; at 0.00019+0.07388i at a magnitude of 75. ; ; The orderly simplicity of the rectangle makes it an impressive ; fractal thing, especially when the surrounding railroad-track ; chaos is considered. And its fragility makes it all the more ; interesting. If imag(c) is changed even the slightest from ; zero, the rectangle distorts, fills with debris and disinte- ; grates like a soap bubble. And if the orientation within the ; Julibrot is changed by as much as one degree in any direction, ; the rectangle also distorts and disintegrates. ; ; Such rectangles are pure Julia objects . . . or this is what I ; thought until I found today's image, which shows a minibrot in ; the area of the 2.003 Mandeloid that corresponds to the Julia ; rectangle. To my surprise, I found that the area surrounding ; the minibrot is filled with rectangles exactly like those in the ; Julia set. In today's image, these rectangles appear as tiny ; open areas where the bulky arms appear to branch out into ; smaller arms. A single enlargement reveals them to be perfect ; rectangles however. ; ; I have not yet done much investigation of these Mandelbrot rec- ; tangles. Maybe some of them are not so perfect. Maybe some ; squares, trapezoids, parallelograms, or even more exotic figures ; with more than four sides, such as octagons, lie hidden in the ; scene. Too bad we're already near the limit of resolution. We ; may never find out. ; ; But I don't give up so easily, especially when it comes to ; fractals, and I have a funny feeling that many more surprises ; lie nearby. So I'll be doing a lot more exploration in the ; area. Stay tuned. Who knows what might turn up. ; ; I named the image "Rectangle Holiday" for the fun of it. I ; rated it at an 8 because I think it's pretty good. The calcula- ; tion time of 3-3/4 minutes will pass in a few flashes, or the ; flashes may be escaped by going to the FOTD web site at: ; ; ; ; and seeing the finished image posted there. ; ; Tuesday produced enough sun to keep the fractal cats happy. The ; temperature of 68F 20C was a little chilly for the date, but ; well within reason. My day was just eventful enough to prevent ; boredom. The next FOTD will be posted in 24 hours. Until then, ; take care, and when you find the ultimate truth, what will you ; do with it? ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Rectangle_Holiday { ; time=0:03:45.28-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrot4 passes=1 center-mag=+0.00002587319771205/+0.000021904280298\ 92/3.8e+010/1/67.5/0 params=0/0/0/0/-1.7435/0/0/0/\ 2.003/0 float=y maxiter=3600 bailout=10000 inside=0 logmap=516 periodicity=10 colors=00089K9AM9BO9CQADTAFVAGXBJZBL`BObCRdCUfCWhD\ ZjD`lD`nCboCeqCfsCguChwCixCjyCkwBlwBmwBnwBowBowBow\ BowBqzAqzAqzFqzKqzMqzOqzQqzSrzUrzWrzYrz_rzarzcrzer\ zgrzirzkrzmrznszotzpuzqvzrwzsxztyzuzzvzzwzzwzzwxzw\ vzurvsnrqjmofhnbdnZanVZnTWmPUmLRmHOmDLl9Ji9Kg9KiAK\ cALaAL`BL_BMZBMXCMWCMWCNVDNUDNTDOTEOSEOREPQFPQFPPF\ PUScZdr`cqabpbapcaod`ne_ng_mhZmiYljYkkXklWjmWjlXjl\ YjkZjk_jj`jjajibjicjhdjhejgfjggjghjfijfjjekjSziOzj\ KzkHzlGycFtWEoNDjFDe7HZBLSEPLH`IQlFYwDeqKhkQjfXl`b\ nVipQorKvtFzvEvwEpwEjwEdwJ`rNXnSUjWQf`Ma`JYaFUcCQg\ IRmQRr_RvdSwjSypSzwSzzYzzmzzz4zn3ph3fb3YX2OR2EL25G\ Agn2_q6`o9`nC`lFH`YvzI`iL`hOIKezLauRYnWUg`5M79PDDR\ JGlPKzVmz`U9kTEjTJiSNhSSgRXfmLJrONmQQcSTYVXVX_TZbV\ AFTOT0pz4nz7lzBjzEmzHrzLwzzzzzzzzzzzzzzzzzzzzzzzzd\ zzdzzezzezznzzlzzkzzjzzizzhWzgTzfdz7_zJVzVPzOQzURz\ _EzlLzhyzwsztmzqgznHzj9zi } frm:SliceJulibrot4 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(p5)+c |z|<=9 } ; END PARAMETER FILE========================================= ; ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint