FOTD -- October 25, 2002 (Rating 7) Fractal visionaries and enthusiasts: Today's image continues the same theme as the most recent three images. One negative part of Z^(-14.14) was added to six negative parts of Z^(-1.414) before 1/C was added. The relation to the square root of 2 is intentional. The resulting parent fractal consists of the same large many-lobed Mandeloid as the past three FOTD's, but in this case, the enormous rings to the east are missing. The northern bay of the parent is partly obscured by two thick arms extending toward its mouth, which create the impression that the area is not critical and therefore no midgets will be found there. However, in the worlds created by the M-mix4 formula, things are not always as they first appear, and a closer examination of the eastern arm revealed suspiciously symmetrical areas. When I dove down into one of these areas, I did indeed find a perfect quadratic midget. The entire area is in a state that I call 'eroded', with the normally solid outside elements broken by numerous holes, which in many cases are larger than the midget itself. When the scene is calculated at the default bailout radius of 100, the holes are so numerous that they comprise the greater part of the scene. When this situation exists, the better fractals are often found when the remaining outside material is 'evaporated' by raising the bailout radius to one-googol, leaving only the ghost of the midget that was once there. It is this midget- ghost that is visible in today's image, which totally consists of trapped 'inside' points. The ghost is made manifest by the inside fill of bof61. With its 3-D effect, the ghost-midget rates a conservative 7, perhaps a liberal 8. I decided on the lesser rating; I could just as honestly have chosen the 8. (Is today's image really one whole rating beneath yesterday's?) I have no explanation for the name I gave the image -- "A Ringing Spectre", but the words have a poetic quality that rather matches the feeling of the blue and gold image. The 12-minute render time is somewhat slow, making the download the wiser but not quite as much fun choice. The download may be found at both Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Thursday was most unpleasant here at F.C., with heavy clouds, a raw northeast wind, occasional drizzle, and a temperature of 43F 6C. The dynamic cats were very undynamic as they passed the day in their favorite chairs, stirring only to look outside and eat. Today promises to be a gloomy repeat, so I guess it's a good chance to get ahead on some of the work I've been putting off. Until tomorrow, take care, and we have evaporated milk, why not evaporated fractals? Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ A_Ringing_Spectre { ; time=0:12:47.53--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.64824186856016940/+1.487023000176482\ 00/163749.5/1/-70/-3.00485698823127478e-010 params=-6/-1.414/-1/-14.14/0/1e+100 float=y maxiter=1800 inside=bof61 periodicity=10 colors=000lFW_FFPF0QK1RN4TQ9VVDWYIYaL_fQaiTalWbqad\ tdfxigzlizqkztlzynzznzzlzzFkzlzylxvkrtknrkiqkbnkYl\ iTkiNgiIfiDdi8bf9ddBdbDd_DdYFfWGfTGfRIfQKfNLgLLgFk\ zGPgFPgDQi9Ri8Ti6Ti2Vi1Wk0Wk0Yk0_k0_k0Yn0Wq0Wt0Yx0\ _y1az2bz4dz8fz9gzDizFkzGkzIgzIdyIatKYnKWiKTbKQWLNR\ LKLLIGLF9NB2N80N40N20K60I80G90DB0BF09G08I04K02L01O\ 00Q00Q00T0QV00Y0W_0Za0cb0cd0mo8ryImzRKza2z_2z_2zY2\ xY2rW2nW2iW6lY9n_DoaGibKtdNmdQxfTygWzi_zkbzlfzlizn\ lzoozqrzrvztyztxzoxzkvzfvzatzWtzRrzPrzKqzFqz9oz4oz\ 0oz0Wo9DTN06_16g86oF6vG4rI4oK2lK2iL2fN1bN1_P1WQ0TR\ 0QR0NT0KV0GV0DW09Y06Y04_19a4Fb8KdDPfGTgKWiPakRflVk\ n_oobrqfxrkztnzvqzvtzyvzzvzzvzzxzzxzzxzzxzzyzzyzzy\ zzyzzxvzxrzxnzvkzvfzvbztYztVztQzrNzrIzrFzq9zq6yq1x\ o0vo0to0to0oq0lq0gq0dr0_r0Wr0Tr0Pt0Lt0Gt0Dv08v04v0\ 1v00r00q00o00l00k00i00f00d00b00_00Y00W00_00a00d00f\ 00i00k00l00o00q02z0zFzxFn } 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 20.0 PAR-FORMULA FILE==================================