FOTD -- October 01, 2002 (Rating 7) Fractal visionaries and enthusiasts: Today's fractal impresses me as a picture of a midget in the middle of a railway switching yard, surrounded by a maze of railroad tracks. I had little choice but to name the image "Midget in a Railyard". The formula behind the image is Z^2.001+2Z+C, a formula that draws virtually the same fractal as Z^2.001+C. But virtually is not the same as exactly, and there are small differences between the fractals drawn by the two formulae. When Z is added to Z^2 in a formula, the resulting fractal is a classic Mandelbrot set that has shifted its position but not changed its shape. But when Z is added to any other power of Z except 1, the resulting fractal changes shape as well as shifts its position. When the exponent is close to 2, as with the Z^2.001 of today's image, the change is small, but it is there. At first glance, the fractal created by the simple formula Z^2.001+C appears to be a normal M-set, but a closer examination of the negative stem will reveal that the stem has split into an infinitely divided series of filaments resembling curving railroad tracks. These track-like filaments are strung with midgets. In today's image, I have added 2Z to the simple Z^2.001, which further splits the filaments and works even more madness in the area of the negative stem. Today's midget lies on one of these track-like filaments. With a render time of 19 minutes, the parameter file of today's image is rather slow. Turbo speed can be found at the following web sites, where the completed image will soon be posted if it is not already waiting. <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Monday here at Fractal Central was once again near ideal. Warm sun and a temperature of 75F 24C lured the fractal cats once again into the yard, where they explored for an hour before retiring to their favorite chairs to enjoy the sun on the porch. As for me, now that I'm again on a daily FOTD schedule, I'll be writing mostly in the evening hours. Since it's now evening and the day's work is finished, I'll commence the shut-down of the fractal shoppe, turn out the lights, call it a night, and watch the end of the Ravens' football game. (We're winning!) Until tomorrow around this same time, take care, and never lose your sense of wonder. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ MidgetInA_Railyard { ; time=0:19:04.04--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-1.74390411923717100/-0.007465126522865\ 71/8.121706e+009/1/-90/3.88578058618804789e-016 params=1/2.001/2/1/0/0 float=y maxiter=2600 inside=0 logmap=421 periodicity=10 colors=000uayoavjaudar`apVamPajLaiFafAad4aa0a`1__3\ YY4VY6TX7SX9PVAOVCMTDJSFISGGQIDQJCPJAPLFOMIOOLOPOM\ PQMQTMSXMT_LTaLVfLXiJYlJ_oJ_sJ`xIazIczIczIazMazP`u\ T`oX_i__cc_`fYXiYSmXOpXJsVMxVTzX`zcguigmogfsg_xgSz\ gLzgDzg6zgFzg3zg6zg9xgCugFpgImgLlgOlgQjgTigYf``dTc\ aMf`FiY7lX0oT0pS0rP0sO0uM1rM4pM7oLAmLDlLIjLLjJOlJQ\ mJToJXpLVmLTjLTiLTfLTcMTaMTYMTTMTQMTMMTIOTFOTAOT6O\ T3OT0OT0MT0MT4LT7LTCJVFJXJIYOI_QGaVGcYGdaFffFiiDjm\ DlpCmuCpyArzAszAuzGizMYzSMzYAza0zc3zd6zd9zfAzgDzgG\ ziJyiLyjOxlQvlTvmVuoYso`spcrpdriuXazAcz7cz6cz4cz3c\ z1cz0cx0cv0cs0co0cl0ci0gf9lcQoagl_fjXdiXcgVafVadT`\ aT_`SY_SYYQXXPVVPTSOSQOSPMQOMPMLOLLOOIPPGPSFPTDPXC\ PYAQ`9Qa7Qd6Qf4Qg3Qj0Sl0So0Sr0Su0Sx0Tz0Tz0Tz0Tz0Tz\ 0Tz0Yz0az0fz0jz0oz0sz0xz0zz0zz0zz0zz0zz0zz0zz0zz0z\ z0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz1zzIzz9zz1zz1zz1zz1\ zz1zz1zz9zzFzzLzzSzzYzzcz } 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==================================