FOTD -- September 04, 2002 (Rating 6) Fractal visionaries and enthusiasts: The parent fractal of today's image mixes some Z^3 with some Z and produces a Mandelbrot set with a new open area caught in the act of opening on the X-axis some distance to the west. (This new area is quite sensitive to small changes in the real(p3) parameter.) The Mandelbrot set part of the parent holds pretty much the same features as the classic M-set, but the newly-opened area to the west contains some entirely new features. One of these new features is a double valley. In the classic M-set, Double valleys usually indicate a non-critical environment, but in the world of the M-Mix4 formula there are no hard and fast rules, so I decided to take a look into one of the several arms in this double valley, where I found an interesting environment, better viewed than described. Today's scene is located in the suburbs of a larger midget near the end of a filament in the double valley. The trip down, which is rather interesting, can be seen in reverse by changing the logmap setting to 0 and doing multiple outzooms. Unlike I do in most of my FOTD's, I did not rotate today's image to the normal position, with the main stem of the midget facing west. The reason is simple -- though I know it is there, I have never seen the midget at the center. Unfortunately, the midget is beyond resolution. The invisibility of the midget inspired the name "The Unseen Midget". The rating of 6, based on the pattern around the midget alone, seems fair. All is not lost however, for as the pattern indicates, today's midget lies in the suburbs of a larger midget, and this larger midget is nearly exactly the same as the unseen midget in today's image. (I can tell by the pattern.) So a trip out to see the larger midget will give a good idea of the appearance of today's unseen midget. The drawback to all this exploration is the slowness of the image, which takes nearly an hour to render on my machine, but if the passes is reset to <g> and the exploration is done at thumbnail size, the trip is do-able. As always, the completed GIF image will soon be available on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and on Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Tuesday was summer-like here at Fractal Cen- tral. The hot sun and temperature of 88F 31C kept the dynamic cats satisfied, though not as active as they still occasionally are. In the evening, I found the remains of a half-eaten bird at the foot of the porch stairs. Both Thomas and Tippy pleaded innocent, so I have no idea how the bird got there. But I have a very good idea of how I'll get from busy to idle -- and that is to finish the work that needs to be done. And if I hope to finish, I must begin. So until the next FOTD on Friday September 6, take care, and accept no FOTD substitutes. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ The_Unseen_Midget { ; time=0:55:10.80--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+0.00245214023728272/+1.268076105879121 /1.714617e+011/1/90/3.88578058618804789e-016 params=1/3/1/1/-0.195/0 float=y maxiter=3600 inside=0 logmap=-1138 periodicity=10 colors=000H0_F0aD0cA0e80g60i80kA0mB0oD0qE1sG2uH3wJ\ 4yL5zM5zO4zP4zR3zS3zR6zRAzRDzRGzRKzRNzRQzRTmQXeQ_Y\ QbWQeTQiQQlNQoKQrIToGVmFXkEZhCafBcdAea8g_7jY6lV4nT\ 3pR2YhQ_gNagRehUhr_yzDxwGxwJxrMwmPwhSwcVvZYvU`vPcu\ KdtFesFfrIgqKhpNioPjnSjmVklXlk_mjanidohfpgiqfkq`gm\ WdjQ`fLYcGV`FS_EPZDMYCKXBHWAEV9CU89T76S74R95SB6TD7\ UF8UH9VJ9WLAXMBXOCYQDZSD_UE_WF`YGa_Hb`Hb_Ga_Ga_G`_\ F`_F__F__EZ_EZ_EZZGXZIWZKVZLTYNSYPRYRPYSOXUNXWLXYK\ XZJW`HWbGWdFWeER`HMXJHSMDOO8NR4NU0NW3PV6QV8SVBTUEV\ UGWUJYTMZTO`TRaSUcSWdSSeVOeYKf`GfcCgf8gi4hl1ho2di2\ ac2YZ2VT2RN2OI2KC2H62E1EQGQ`UalhlwvdtlXrbPpTHnJAl9\ FiJKgSPdaUbjZ`sKj`5sI8tLBuNDvPGwRIwTMtVPrWSoXVmZYj\ _ah`debgccj`dmZel`bka`jbZidXheVhfSggQfiOejMdkKdlIN\ h1KaX8YLbeE`bH_`JZZLYXNWUQVSSUQUTOWRLZQJ`PHbOFdMCg\ LAiK8kJ6mDNb7bS1rH3lK5gN6aP8XS9SUBMXDH_EBaG6dH1fLd\ SSgQYjPVgTTdWRaZOZaMWdKTg } 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==================================