; Date: Fri, 25 Jan 2008 19:05:41 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 26-01-08 (Pentagon Heptagon [8]) ; Id: <1.5.4.16.20080125185540.0da72ece@pop.mindspring.com> ; --------- ; ; FOTD -- January 26, 2008 (Rating 8) ; ; Fractal visionaries and enthusiasts: ; ; NEW FORMULA ALERT! ; ; Today's image uses a new formula, which is simply yesterday's ; formula with initial 'b' generalized rather than set to 0,0. ; This might give a little more variety to the images it draws. ; I named the new formula HyperMandelbrot2. ; ; Today's image is named "Pentagon Heptagon" because of the very ; prominent pentagon. And there is also a heptagon, much smaller ; and closer to the center. And yes, the series of polygons with ; an odd number of sides does continue indefinitely. An outzoom ; will reveal a triangle, while a couple inzooms will reveal a ; nonagon, a hendecagon, and a tridecagon. (I think these are the ; right names for polygons of 9, 11 and 13 sides.) How far the ; series goes beyond this point is anybody's guess, but I suspect ; that, like so much else in the world of fractals, it continues ; without limit. ; ; I have made no effort to figure out the number series of the ; arms stretching between the polygons, though it probably has a ; logical order. But at the same time, I see that the arms within ; the pentagon are unevenly distributed. Two of the pentagon ; vertexes have arms connecting with them from within, while the ; other three are cut off from the center. ; ; Today's coordinates define a blank area in the classic Mandel- ; brot set. If real(p3) and real(p4) are set to zero, the result ; is a flat black screen. The area actually lies somewhat inside ; the main bay of the M-set. ; ; Even though I have no idea how today's image ranks among Sea- ; horse Valley images of the HyperMandelbrot set, I have rated it ; at an 8. Its mathematical interest is enough to be worth at ; least that rating. ; ; The calculation time of 4-1/4 minutes is fast enough to keep ; impatience at bay. And if it is not, the finished image will ; soon be available on the FOTD web site at: ; ; ; ; Friday was bright and sunny here at Fractal Central, but it was ; also cold and blustery, making it a rather unpleasant day to be ; outside. The high temperature of 27F -3C fely cold even in the ; strongest sun. With numerous sources of heat inside F.C., the ; fractal cats had their problem deciding where to spend the day. ; ; I had no such problem however. I spent the day working, then ; searching for a FOTD. As today's image shows, I was successful. ; And the next FOTD image will be posted in 24 hours. Until then, ; take care, and where's it at? ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Pentagon-Heptagon { ; time=0:04:14.05-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot2 passes=t center-mag=-0.749480813398176/+0.031703452082799/\ 3.321327e+010/1/89/0 params=0/0/0/0/0.2/0/1e-020/0 float=y maxiter=3600 inside=0 periodicity=0 colors=000mL6lM9lNBlODlPFlQIlRKlSMlTOlURlVTlWVlXXk\ `_lYZmWYnUXnSXoQWpOVpMVqKUrITtCTrGTqJToMTnPTlSTkVT\ iYTh`TfcTjcYecT`cPXcKScGNcBMc4Jc7HcAEcCCcF9cI7cK4d\ N2cQ0cSgcaXcZKcVNcXQcZSc`VcbYcc_cebdgefigikjklmnno\ pzrszuuzzzzvtzvrzupvunrtkmtihsgcse`sbYr`VrZTqXQqUN\ pSLpQIpOGrJPsFYuBev7nt9Bw3vu4ss5pq6mo7jm8gk9di9agA\ ZeBWcCTaDQ_ENa7GZEKWKOURSRXWzz_zzczzfzzbzzZzzVzzRz\ zOifKndGrcCva8z`5tb6oc7ie8df9ZhAUiBOkCJlDDnE8oEAnF\ CmFEmGGlGIlHKkHMkIOjIUiJZiJchKhhKmgLrgLvkMwkMwlRwq\ NwrJwwGwxCws8wt6vt5rp4mp3hq7cmAZmKUnUPmcKmmFlvAnz5\ oz3pz3qz4lz4gm4bc5ZZ5UZ6UY6dY7dY7dY5sa7nY9jVBfRDaO\ FYKDUFGUHJUILUKOULQUNTUOVUQYUR_UTbUUdUWgUXiUYkRalO\ dnLgoJjlMeiOagRYdTUaWP_YLX`HUbDPb8Sd9VeAXgB_hCbiDd\ kEglFjmBimFijIhgLhcOg`RgYVfUYfR`eOceKfdHjdEmcApc7s\ c4va5r`5o_6kY6hX6dW7aV7YT7VS8RR8OV4RQ8LLBGGFA8H2CI\ 5GI8KIBNJERJHVJKZJNaKQeKT } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } ; END PARAMETER FILE========================================= ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint