FOTD -- November 07, 2010 (No Rating) Fractal visionaries and enthusiasts: The lateness of today's image is due to a not-so-surprise antiquing expedition that arose not-so-unexpectedly on Saturday. But better late than never. Today's FOTD is the parent fractal of yesterday's 'Almighty Spiral' fractal. The actual spiral that filled yesterday's image lies humbly at the right edge of today's scene. Many other spirals fill the upper half of the image, which lies on the bud side of the Mandelbrot valley that is visible as the two brilliant wedges jutting across the center of the outer shape. The lower half of the image, which is the main-bay side, has no spirals at all. Today's image is not a Julia set, but it comes very close. It is double-rotated 0.04 and 0.04 degrees from the actual Julia orientation. (Double rotation is a mathematical abstraction most difficult to comprehend. Nothing at all like it exists in three-dimensional space.) But the orientation of today's image produces many Julia characteristics and also shows the position of the hairline spirals in relation to the Mandelbrot aspect of the area. With today's image being a near-repeat of yesterday's, I could give it no rating. The name "Home of the Spiral" needs no expla- nation however. The calculation time of almost 10 minutes will need to be endured in nail-biting impatience. I hear that Paul Lee has been in the hospital for over a week, and has been unable to update the FOTD web site. Fortunately, he appears to be on the road to recovery. But a trip to the FOTD web site that he has maintained for over 13 years and that holds the past FOTD images is always a lot of fun. The web site may be accessed at: <http://www.Nahee.com/FOTD/> Heavy scudding clouds, blustery north winds and a temperature of 43F +6C made Saturday quite brisk here at Fractal Central. The fractal cats had enough heat inside that they never noticed the outside chill. When the antiquing was over and done, my day was reasonably settled. The next FOTD will be posted in 24 hours. Until then, take care, and the answer may lie where least expected. Jim Muth jamth@mindspring.com START PARAMETER FILE======================================= Home_of_the_Spiral { ; time=0:09:52.49-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=1 center-mag=0/0/0.8503401/1/126/0 periodicity=6 params=89.96/0/89.96/0/0.3272613/0.0561252/0/0 float=y maxiter=150000 inside=0 logmap=yes colors=000REQSESUEUWEXYFZ_G`aHbcIeeJigKmiLqkMtmNwk\ OziPygQxeRwcSvaTu_UtYVqWWnUXkSYiQZfOZcMYaKXZIWWGVU\ EURCTOASM8RJ6QG4PE5OF5NF5MF5LF5KG5KG5KG5KG6KH6KH6K\ H6KH6KI6KI6KI6KI8KH9KGALGBNFDQEESEFUDGWDIZCJ`BKbBL\ dAMfAQbET_IWXMZUQbQTeNXhK`kHdnEgoFfoFepFdpGdqGcqGb\ rGarHasH`sH_sH_uL`vO`wR`xVayYaz`asaYlaUebRZbNScKLc\ GEdD7d91d5AdFFdPKeZUeccehmfhlfdiecfdbcca`b`Za_W`ZT\ _YQZWNYVLXUIWTFVSCUR9TQ7TPEXOL`OSdNZgNcdRMlCOpDMlC\ LiCMfCNcCO`CPYBQVBSSBUPBWMBYJB_GAaDAcAAc7Ac4Ac1Ac3\ Cc5Dc6Ec8Fc9HcBIZCJUEKPFMKHNFIOAKP5MR3NS3PT3QU3SW3\ TX4VY4W`4Yc4Zh4`m4ar4cv4ez4fz5iz5jz5lz5nz5oz5oz5pz\ 5pz5pz3qz5qz6qz8rz9rzBrzCszDszFszGtzItzJtzKuzMuzNu\ zPvzQvzSvzTwzUwzWwzXwzZwz_wz_wzawzbwzcwzdwzewzfwzh\ wziwzjwzkwzlwzmwzowzpwzqwzqwzqwzqwzqwzrwzrwzrwzrwz\ rwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrw\ zrwzrwzrwzrwzrwzrwzrwzrwz } frm:SliceJulibrot2 {; 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=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================