; Date: Fri, 12 Mar 2004 09:28:55 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 12-03-04 (The African Veldt [6]) ; Id: <1.5.4.16.20040312093150.299f979c@pop.mindspring.com> ; --------- ; ; FOTD -- March 12, 2004 (Rating 6) ; ; Fractal visionaries and enthusiasts: ; ; There once was a time when I wandered freely through Fractal ; Land, roaming wherever my day's journey took me to study the ; surroundings. I was not on a search for any particular quarry. ; I photographed whatever was surrounding me in the place where I ; stopped for the day. Then something happened. I became fasci- ; nated with the so-called 'midgets' that I occasionally stumbled ; upon. I began seeking midgets, ignoring the sometimes spectacu- ; lar scenery that I passed by in my search. ; ; Midgets in fractals are higher-dimensional analogs of the maxi- ; mum or minimum stationary points so often found when the graphs ; of functions are plotted. And just as all stationary points ; have a similar parabolic shape, so do all midgets have a similar ; shape. With only a few hard-to-find exceptions, this shape is ; that of the classic Mandelbrot set. The familiar shape is some- ; times distorted beyond recognition, but even when unrecognizable ; the shape is there, and could be undistorted back into the M-set. ; ; It is hard to say why I became so fascinated with midgets, but ; this kind of thing seems to happen with fractals. Many become ; fascinated with spirals. When I come upon spirals, which I do ; many times in my search for midgets, I usually pass them by. ; They all look the same to me. It is curious that the same bore- ; dom has never arisen as I discover ever more of the super infi- ; nity of similarly shaped midgets that are out there, waiting to ; be found. ; ; Maybe I should devote a month or two to fractals without mid- ; gets. The discontinuity patterns in low-order fractional-power ; fractals can be quite interesting, and certainly deserve more ; exploration. The odd slices of the Z^2+C Julibrot can also be ; interesting. It is really surprising what Seahorse Valley looks ; like when viewed from some of the unfamiliar angles and double ; angles of four-dimensional space. Yes, I think I'll soon take a ; break from the endless stream of midgets, and have some fun with ; the other things found in the world of fractals. ; ; But that break from midgets does not appear in today's image, ; which is another adventure into the parent fractal of the two ; most recent FOTD's. I named the image "The African Veldt". I ; can give no reason for the name other than I think it sounds ex- ; citing. I also might have been thinking of an old story by Ray ; Bradbury named "The Veldt", which as I recall is about a house ; with animated walls that depict an African grassland scene. ; ; I rated today's image at a 6. Combined with the render time of ; 4 minutes, this gives an overall value of 142. The render time ; can be changed to a faster download time by visiting Paul's FOTD ; web site at: ; ; ; ; where the finished GIF image has been or soon will be posted. ; ; Thursday was quite a pleasant day here at Fractal Central. The ; warm sun, light winds and temperature of 56F 13C made conditions ; near ideal for an afternoon in the yard. The cats took advan- ; tage of the opportunity. This morning is starting sunny, but it ; is colder, and the wind is high. We'll see what the cats think ; of this. ; ; I'll think more of fractal things once I get the work behind me. ; Until the next FOTD appears, take care, and see you in the land ; of fractals. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE================================ The_African_Veldt { ; time=0:04:14.47--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.31518718326216360/+5.515004364619150\ 00/2.11448e+007/1/-17.5/3.45976670992897972e-008 params=0.55/-1.1/0.11/-3.1/0/0 float=y maxiter=600 inside=0 logmap=78 periodicity=10 colors=00000K00I01G05E08C0CA0F80J50M05T0FZ0Rc6ahDm\ mMxrTzx_zqTzjOueJsZDpR6lM1jF0gA0fH0gM6eT8bZAZeKXjU\ VmZVoXTqTTtRRvORxMJt_Cqm5mzzxczrqzozfRz53zACzDJrJQ\ eMXRQcDTJTX0hf1lq5oz6rzAvzCxz8mz6cz3Vz1Kx0At01r08q\ 0Fo1Mo3Tm5_l6fj8mj8rZMhMZ_AjQ0vH0oQ0jX0ee0_l0Vt0Qz\ 6JxVDvr8rz3qahc0zQ5zRDtRKfTTTT_HTROaJTjC_q3ez0lz0q\ z0lz0fq0ae0XV0RJ0M60H00D00Q00a00m10z80zD0zJFzTflcm\ aQtRCzH0rK8lMHeQQZR_RVhKXqJceHhTHoHFt5Fz06zfXhQvQ8\ z80cxrXxmOxhHxc8zX1zR0zM0zH0zC1z88z5Fz1Mz0Tz0_z0fz\ 0Mt03_D6OKe_TTeTJjV6oV0tX0xX0me0el5XrCOzHFzMQzR_zX\ hxarvfzrlzqHXe00T50HM05a0Dq0Mz0Vz0cz3az6azA_zD_xHZ\ tKZqMZmHTjDQf8Me5Ja0FZ0CX08j05v01z00z00h_05z03z01z\ 00z00t00o00h00c0ex5zzFozXJmm0Zz0Kz06t00o3DT6V80T00\ T00T0RxzMxzJytFzmAzf6z_3zVAzQFzMKzHQzDXzAaz5fz1lz0\ qz0vz0zz0zz0zz0zz0zz0zz0zz0zz6zzMzz_zzmzzjzzfzzecz\ FDz0Az06z03z00z30z6ozeezl } 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 PARAMETER FILE================================== ;