FOTD -- August 24, 2006 (Rating 6) Fractal visionaries and enthusiasts: Back in my naive teen-age years, when I was just becoming familiar with the scientific world of astronomy, weather, and atoms in particular, I often wondered what an atom looks like. I soon formed a picture of the atom as a miniature solar system, with electrons orbiting the nucleus like planets orbit their stars. The nucleus seemed to me to be a boiling mass of protons and neutrons somewhat resembling a pot of boiling liquid. It all made a kind of sense. When a radioactive atom decayed, it was because a proton had escaped the surface of the boiling nuclear liquid. I felt that if I could shrink myself small enough, I could actually observe these atomic things taking place. I wondered whether atoms actually might be miniature solar systems with galaxies, stars and planets, like in the story about a shrinking man which I read about that time. Then I started reading more serious books about the sub-atomic world and the quantum. I came to realize that whatever is actually down there is so far removed from our everyday experi- ence that it can be best described only approximately by math- ematical expressions. To attempt to picture a physical reality corresponding to the quantum math is a futile endeavor. I now know that protons and electrons are not 'things' in the sense that tables and chairs are things. They are ideas, mental models that happen to work reasonably well. In a sense, we create them along with their attributes when we describe them. This is well illustrated in the case of an electron, which is said to be both a potential wave and a potential particle with a spin of 1/2. Such a spin means it would need to undergo two complete 360-degree rotations before it would present the same face to a hypothetical observer. Unless an electron is some kind of single-sided Mobius object, which must be turned 720 degrees before it returns to its original position, the elec- tron's attributes would appear to be impossible. Electrons may appear impossible, but it would be interesting to see what a person would observe if an electron were enlarged to the size of a basketball. Of course, if electrons are mere points, enlargement is meaningless. By contrast, fractals most certainly are not only possible, but have actually been observed in full graphic representation. Unfortunately, so far at least, fractals such as the Mandelbrot set have been seen only as computer-generated photographs. Today's photographic image of a fractal has been named "Atomic Nucleus". The central midget reminds me of a nucleus, while the surrounding elements could be seen as electrons. The image is a scene in the parent fractal that results when Z^(-1.75) is subtracted from Z^(1.75) and (1/C) is added. In this case the parent fractal could more accurately be called the parent debris field. It is little more than a scattering of fractal debris. But that debris is filled with countless midgets, one of which lies peacefully at the center of today's frame. The rating of a 6 seems appropriate. Rendered as it is with the outside set to 'iter', the image does look a bit under-detailed, but in this case the under-detailed version is the best. The other outside options give so much detail that the result is more chaos than fractal semi-order. The image is a fast one, which renders in 2-1/2 minutes on my P200 machine. Equally brief if not briefer is the time spent downloading the finished image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> What a waste! We had another absolutely perfect day here at New Fractal Central on Wednesday and the new fractal cats didn't even care. They spent the day chasing each other up and down the hall and getting into other various and sundry trouble. My day was spent doing various odd jobs between the times I was doing fractals. If all goes well, and why should it not, the next FOTD will appear in 24 hours. Until then, take care, and don't be nucular, be nuclear. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Atomic_Nucleus { ; time=0:02:30.66--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.39532679744866780/+0.594877164365430\ 40/3.945085e+007/1/40/-1.05442878494538261e-006 params=1/1.75/-1/-1.75/0/0 float=y maxiter=500 inside=0 periodicity=10 colors=000sh2th2th2rg3qf3pe3od3mc3lb3ka3j`3h_3gZ3f\ Y3eY3eY3dX3bW3aV3`U3_T3YS3XR3WQ3VP3TO3SN3RN3QM3PL3\ NK3MJ3LI3KH3IG3HF3GE3FD3djKbhJagI`eH_dHZbGYaFX`FWZ\ EUYDPAmPAjPAgPAdKAaHAZDAWBAQAAMBAICBEDCAED5FE3k7tf\ 8mb9fZA_VAUQBNMCGID9GzzFxxFvvFutFsrFqpFpnFnlFljFkh\ FifFgdFfbFd`FbZFaXE_VEYTEXREVPETNESLEQJEOHENFELDEJ\ BEI9EG7EE5q`jmZfjXcgV_dTXaRUZPQWONTMJQKGNIDKG9HE6s\ rVrqUqpTpoTonSnmRmlRlkQkjQjiPihOhgOhgNgfNfeMedLdcL\ cbKbaKa`J`_I_ZIZYHZYHYXGXWFWVFVUEUTDTSDSRCRQCQPBPO\ AONAON9NM9ML8LK7KJ7JI6IH6HG5GF4FE4ED3zjYvgVrdTnbQj\ _OgXMcVJ_SHWQETNCPKALI7HF5s`7r_6q_6pZ6oZ6oY6nY6mX6\ lX6lX6kW6jW6iV6iV6hU5gU5fU5fT5eT5dS5cS5bR5bR5aQ5`Q\ 5_Q5_P5ZP5YO4XO4XN4WN4VN4UM4UM4TL4SL4RK4QK4QJ4PJ4O\ J4NI3NI3MH3LH3KG3KG3JG3IF3HF3HE3GE3FD3ED3YK7XJ6XJ6\ WJ6WJ6VJ6VJ6UI6UI6TI6TI6SI5SI5RH5RH5RH5QH5QH5PH5PG\ 5OG5OG5NG4NG4MG4MF4LF4LF4 } 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=========================================