FOTD -- February 04, 2005 (Rating 5) Fractal visionaries and enthusiasts: With today's image we return to the MandelbrotMix4 formula and the unlimited goodies therein. We examine the fractal that results when negative Z^1.5 is combined with Z^0.5 and straight C is added. This fractal is shaped much like a classic M-set that has been rotated 180 degrees, with the main exception being the area of East Valley, which is now on the west side of the main bay. Instead of jutting sharply into the bay, the valley has degenerated into a large area of chaos that extends some distance inland. This chaotic area is filled with quadratic- shaped midgets, one of which appears at the center of today's image. I named the image "The Drunkard's Walk". The midget at the center is surrounded by radiating filaments that remind me of a path a very tipsy drunkard might take when he leaves the bar and starts taking steps in random directions as he begins his walk hopefully toward home. This random path appears quite often in nature and is known to mathematicians as the drunkard's walk. A drunkard could never be expected to produce a worthy fractal simply by taking steps in random directions, but today's image rates a 5, and lesser images have made it to the lofty heights of Fractal of the Day. Our drunkard finally made it home, and does not appear in the image. The path he took on his trip is still visible however, and may be seen by running the included parameter file or by downloading the GIF image in completed form from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The latest chapter of philosophical musing appears in the philofractal version of today's FOTD discussion. Thursday failed to live up to its promise here at Fractal Central, as an unexpected wet snow began at 2:30pm and cut short the cats' time in the yard. Extra tuna was needed to ease their frustration. Today is again starting partly cloudy and mild. Hopefully, the day will turn out better than yesterday. For me it looks like a rather slow day coming up. This could mean a great fractal for tomorrow, or it could mean a lazy day for me. Regardless, the next FOTD will appear right here in 24 hours. Until then, take care, but don't forget the fun. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= The_Drunkards_Walk { ; time=0:02:50.93--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident center-mag=-0.86634515270768200/+0.265248736118700\ 60/1.378352e+009/1/-92.4997801961145996/-0.0003971\ 32291258053827 params=1/0.5/-1/1.5/0/0 float=y maxiter=500 inside=0 logmap=69 periodicity=10 colors=0004SP1QQ4PQ7OQAMPDLPFJOIGOLDMO9MS4LX1LaCIg\ MGfXKjfQomUsuYxzcszcpzZlxUiuPdpKalFYfDVaDQXFOSFLPF\ QTIX_JadMgjOmpPooMpmLrlJsjGsiFugDvfAxd9xc7vd4vf3vg\ 1vi0vj0vl0vm0vo0vp0vr0xs0yu0yv0zx0zy0zy0zz0zz0zz0z\ z0zz0yz0ux1ou6jr9foCYiLPdSI__9Vg1Po0Lv0Gz0Iz0Jz4Lz\ ALyGMxMOxSPvYPucQuiSsoTruTrfJoSAlD0i00gC7SMMCPPGQS\ JSVOTYQV`VXcYYfa_id`liaolcpodmmflmgiligljdllcjm`jm\ _joYipVirTgsQguPgvMfxLfxJfuIirGloGomFpjDsgDvfCxcAz\ `AzY9zX7zT7zQ6zP6zO9zMCzLFvJIoILiGOcFQXDTQCXLA_D9a\ 79c1QY7dODgSCiVAj_Ala9md7oi7rl6sp6us4vv3xz3yz1zz1s\ z7lzDdzJYzPSyVLx`Dvf6ul0sp0lv9sxPzxdzxuzxozyiuzcjz\ Y`zTSzOIzI7zC0z70zG0yPAsYLmdVgmfavpXzzQzzLzzMzzOzz\ PzzQzzSzzTzzVzzXzzYzz_zz`zz`uzamzcfzd`zfTzgMzgFzi9\ zj1zl0zm0zm0zf4z`DzVLzPTzI`zCiz6pz0xz0Xz74zL7zI9zF\ AzDDzAFz7Gz6Iz3Lz0Mz0Oz0Qz0Sz0Tz0Vz0Yz0`z0cz0fz1gz\ 4jz7mzCpzFrzIuzMxzPCzT7zT } 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=========================================