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: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> 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 20.0 PAR-FORMULA 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 20.0 PAR-FORMULA FILE==================================