; Date: Sat, 27 Mar 2004 10:10:02 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 27-03-04 (Fractal Nonsense [5]) ; Id: <1.5.4.16.20040327101308.2997d3bc@pop.mindspring.com> ; --------- ; ; FOTD -- March 27, 2004 (Rating 5) ; ; Fractal visionaries and enthusiasts: ; ; No, there is no mistake. That actually is a Mandeloid midget of ; the 6th order displayed in today's image. And the generating ; formula combines nothing other than Z^3 and Z^4. If this isn't ; nonsense, I have never seen it. ; ; Actually, the nonsense is deeper than what is immediately ; apparent. Check that large midget toward the northeast corner ; of the screen, and you will find that it most definitely is of ; the cubic variety. ; ; To make matters even sillier, the midgets located in the nodes ; of the filaments radiating from the large midget have no ; established shape whatever. They appear to be randomly shaped. ; But there is hope. ; ; Throughout the image, the deeper we search, the closer the ; midgets come to the expected quadratic shape, until finally, at ; a magnitude of around 0.000000001, order is restored and the ; world has once again become one we feel comfortable in. ; ; I'll leave it to the math geniuses to figure exactly what is ; going on in today's image. If it were explained, I probably ; would not understand it anyway. So for now, I'll simply call ; the apparent higher-order midgets in today's image 'pseudo- ; midgets' and let it go at that. ; ; It is this kind of unexpected stuff that keeps my fascination ; with fractals as strong as it was on the day I discovered them, ; which as I recall was in 1985. It is the same kind of ; unexpected stuff that makes modern physics almost as fascinating ; to me. ; ; We live in an intuitive world of sequential time, and three- ; dimensional space filled with objects. We feel comfortable in ; our well-ordered world. But the gurus of science tell us that ; this familiar comfort is built on a foundation of sub-atomic ; things (if they are things) that exist in a world totally beyond ; our comprehension. We fill our physics books with pages of ; abstruse mathematics and announce that we understand it all. ; But do we? It sometimes seems to me as if the whole sub-atomic ; world with its carefully contrived math is a human invention. ; If this is so, then maybe the comfortable 'intuitive' world ; around us is also a human invention. But we'll not start down ; that road at this time. Once this journey is begun, there is no ; turning back, and there are an infinity of fractals right here ; yet to find. ; ; I named today's image "Fractal Nonsense" and rated it at an ; average 5. When adjusted for the render time of 32 seconds, the ; overall value comes in at a whopping 918. It will take about as ; long to prepare this letter to be run as a parameter file as it ; will to download the finished GIF image from: ; ; ; ; A summer-like day here at Fractal Central on Friday, with warm ; sun and a temperature of 75F 24C, brought out what little kitten ; was left in the fractal cats. They actually romped in the yard, ; chasing each other about like they did so long ago when they ; were real kittens. When the end of the day came, they were ; exhausted and ready to settle down for a long rest. This ; morning is cloudy and light rain is falling. The cats will not ; have a repeat day. ; ; My task now is to do as little work as possible for the rest of ; the day. This will leave as much time as possible for a trip to ; fractal land. Unfortunately, with the warm weather comes yard ; work, so I might not find as much time for fractals as I would ; like. In any case, the next fractal will appear in 24 hours at ; this same spot. Until then, take care, and be sensible with ; nonsense. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE================================ Fractal_Nonsense { ; time=0:00:32.68--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident center-mag=-0.52300582159624930/0/276.6252 params=1/3/0.3553/4/0/0 float=y maxiter=1000 inside=0 logmap=14 symmetry=xaxis periodicity=10 colors=000SRhNWm_Zek`ZwbSveQvgOvjMvlKiXLYIMM3MEJP6\ YRCYWHY_KKHDID7G91F6AEAIDDQCHZBKfAOn9Rv8UnDVgHV`LV\ UPVNUWGYW9aW2eWBc_KacHRoEHzDJtCKnBMhANb9PX9QSBVWD_\ ZFdbHieJniLslPnkTjkXfj`ajdYihUikQikEPk35QCL5L`GmoN\ lqTlrZksdktOUyJxXKvWLuWMtVNsVOrVT0zX2y`4yd6xg8xkAw\ oCwsEvvFvmNweVxXbxPjyGrz8zzBttDnoFmjHmeOmNKmTHmYEm\ cBmh`mkPmDOmOOgZNiiNksLmuJonIqgHs`GuUFwNEyHCzOAzV9\ z`LzXWzTgzPrzLpzGnzBmz7gzQazhXzzZz1XzPVzkNzWFzHDzG\ CzGBzG5zkvzHszLqzPozTmzXkz`izdgzhaziWzjQzkKzlEzm8z\ m7zj7zg6zd6za5zZ5zX8zVAzTCzREzPGzNIzLKzJrzPNz4TzBZ\ zHczNdzOdzPezQezRezSfzTfzUfzVezVezUdzUczTbzTazSazS\ `zR_zQZzQZzPYzPXzOWzOVzNVzNUzMTzMSzLSzLRzKQzKPzJPz\ JOzIOzIOzIgzYizXkzWCzOLzTTzY`zbizgqzlyzqqznjzkbzhW\ zeOzbHz_AzYNza_zelziyzlxzixzgxzexzcxzaxzZxzXxzVwzT\ wzRwzOwzMwzKwzIwzGwzEszDozClzChzBdzBazAYzAUz9Rz8Nz\ 8Jz7Gz7Cz69z6czUfzSazYXzb } 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================================== ;