; Date: Fri, 18 Feb 2011 18:03:59 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 19-02-11 (Lost And Found [No Rating]) ; Id: <1.5.4.16.20110218180405.135f219a@pop.mindspring.com> ; --------- ; ; FOTD -- February 19, 2011 (No Rating) ; ; Fractal visionaries and enthusiasts: ; ; Today's image is quite a discovery, at least as far as I am ; concerned. The object at the center of the screen is a minibrot ; in the Z^(-2)+C Mandeloid. Yes, I know, or rather, I have ; assumed that minibrots can not exist in Mandeloids with single ; negative exponents of Z. It turns out that I was mistaken. ; ; As today's image shows, minibrots do exist in such Mandeloids. ; And they have the expected number of lobes -- one less than the ; exponent of Z. In today's image, the exponent of Z is minus 2. ; One less than minus two is minus three. Therefore we find minus ; three lobes in the minibrot. I'm not sure what a negative lobe ; is supposed to look like, it might appear as a peninsula, but ; why question such a reasonable explanation? ; ; Quite a bit of trickery was needed to bring out the minibrot in ; today's image. To begin, I raised the bailout radius to the ; point where nearly the entire fractal had evaporated. Then I ; rendered the remaining scene with the inside set to 'atan'. ; Finally, I set the periodicity to its most aggressive setting, ; which causes the stuff that would normally fill the interior of ; the minibrot to be skipped over and show up as black. ; ; The resulting image is not exactly correct, but it does show ; what I assume to be a minibrot lying in a fractal with a single ; negative exponent of Z. ; ; Since the image is almost entirely of mathematical interest, I ; could give it no rating. The name "Lost And Found" describes ; the adventures of all such negative minibrots. ; ; The calculation time of 2-1/4 minutes is reasonable. Viewing ; the finished image on the FOTD web site at: ; ; ; ; will save a bit of effort. ; ; The original FOTD web site may be accessed at: ; ; ; ; A preview of spring visited Fractal Central on Friday. The warm ; sun and temperature of 68F 20C made it feel more like mid-April ; than mid-February. The fractal cats did not bother themselves ; with time-of-year details however. They spent the day on their ; shelf in the sun. ; ; My day was moderately busy, while FL had a slower day. The next ; FOTD is due in 24 hours. Only an unexpected antiquing trip ; could delay it. Until next time, take care, and look for the ; bright side of the darkness. ; ; ; Jim Muth ; jamth@mindspring.com ; ; ; START PARAMETER FILE======================================= Lost_And_Found { ; time=0:02:16.06-SF5 on P4-2000 reset=2004 type=manzpower passes=1 center-mag=-0.900448534/0/7843.38 params=0/0/-2/0 float=y maxiter=1500 bailout=10000000 inside=atan symmetry=xaxis periodicity=yes colors=000000elJZdGSZDLz9CzJ9zI6aG3bF1bEBUHLLKSANV\ DMYFL_IKbKJeNI000jSGoSHlUGiVGfXGdYGa_FZ`FXbFUcFReF\ OfEMhEJiEGkECkCElEFlFGlG000JmIKmJLnKMnLOnNPnOQoPRo\ QToRUpSVpTWpUXpVXdZXTaZFeXHdVIdTJc000QMcONbMPbLQaJ\ RaHTaGU`EV`CX_AY_9Z_7`Z5aZ4bZ2jY1rX0yW5sTAnR000JdM\ O_KSUIXPGaKDeFBjA9n57m49l4Ak4Cj3Dj3Ei3Gh2Hg2Jg2Kf1\ Le1N000d1Ph1Lk1Hn1Dq19t15w12NiMOmtQjsRgrTdqUapWZoX\ XoZUn_RmaOlbLkcJkeHmgFniDpkBqm9ro7tq5ur3vq7wqAwqDw\ qGwqJwqMwqPwpSwpVwpYwp`wpcwpfwpiwplwhiw`gwTdwLbwMc\ tMcrNdpNdnNdlOejOehPffPfdPfbQg`QgZRhXRhVRhTTjQUkOV\ lMWnKYoHZpF_rD`sBbt8cv6dw4ex2fy0crC`zOYz_VzkTzwPzp\ MziJzbGzXDzSBzN9zI6zEWzv4z92z4v4aozXhzTbzPWzLQzGJz\ CDz86z4yz5nz4dz3Vz2Kz1Az0dzM`zKYzzUzzRzzNzzKzzHzzD\ zzAzz6zz3zz1zz0zz0zz0zz0zz0zzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzz0zz6zz5zz5zz4zz4zz4zz3z\ z3zz2zz2zz2zz1zz1zz0zz000 } ; END PARAMETER FILE========================================= ; ; ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint ;