; Date: Fri, 04 Feb 2005 09:53:24 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 04-02-05 (The Drunkard's Walk [5]) ; Id: <1.5.4.16.20050204095551.2b77ff62@pop.mindspring.com> ; --------- ; ; 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: ; ; ; ; 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========================================= ; ;