FOTD -- July 08, 2002 (Rating 7) Fractal visionaries and enthusiasts: Fractals are infinite -- which is why they are called fractals. They are infinite in many ways. But what is infinity. At one time I thought that infinity was the largest possible number. Somewhat later, I realized that if infinity were the largest number, that number could be represented by the letter X and increased by any desired amount by adding another number to it as in X+Y=Z. Of course, the new number represented by Z could be given the same treatment, and the process continued forever, demonstrating that no largest number exists. Infinity is not a number, it is a condition -- the condition of being without limit. This condition is quite easy to see in a case such as a toy train track arranged in a circle. The track has no limit, and a toy train running along it will travel a trip without a limit. As a basic concept, infinity is easy to understand. Paradoxes arise however when we begin asking meaningless questions about infinity. The toy train going in a circle is a simple concept, but if we ask how many circuits of the track will the train eventually make if nothing ever stops it and nothing wears out, or how many days will the train continue running before it comes to the end of the line, we find ourselves faced with questions without answers. In our everyday lives we ask such questions, often without realizing it. Questions about the beginning and end of time and space are puzzling for the same reason that questions involving the end of the toy-train line are puzzling -- we are trying to introduce into our intuitive world-view something that does not exist. I admit that it is fun to wonder about what happened 'before' the 'big-bang', (if the bang itself actually happened), but being able to perceive time intuitively only as an infinite straight line with no imaginable beginning or end, I know that I will never find an answer that appears intuitively correct. And speaking of infinity, today's fractal contains infinite detail, an infinitesimal part of which appears in today's image. I named the scene "A Blue Creation", though I have not decided whether I created it when I entered the parameters, or merely discovered it. Regardless of its origin, the image rates a 7, which makes it almost worth the 6 minutes required to render it from the parameter file. As always, the completed image is available on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and on Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Sunday here at Fractal Central was smoky. Smoke from forest fires in Canada blew in on north winds and gave us a day with a dull grey sky and visibility of less than 1km. The smell of burning timber was quite noticeable, which may be why the dynamic duo remained outdoors only a few minutes. The temperature of 81F 27C was quite pleasant but hard to enjoy with the smoke totally obscuring the sun. If I'm lucky, I'll get done the things that need to be done, and have enough time left over to enjoy part of the afternoon. But before I hope to finish, I must begin. Until next time on July 10, take care, and before we can know the truth we must know the question. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ A_Blue_Creation { ; time=0:06:15.52--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-1.164418403483855/-0.00416714065635447\ /4.784102e+008/1/-7.5/-1.34769670230433514e-005 params=1.75/0.8/0.175/-8/0/0 float=y maxiter=750 inside=0 logmap=111 periodicity=10 colors=0000005E46D38B0990z0zr0nl0hc0`W3ZQ6YJ9YBDY5\ J_4K`4Lb4Oa3Pb3Qc3Rd2Se2Tf2Ug0Vh0Wj0Xl0Ym0Xq0Vt3St\ 5Op9KkBIfEHcKHbKIYKJUQKRTLPWMLZNJaOGdMEfMBiQFjTIkV\ KnZMo`PpcTsfVtiYul_xoayqezthzxjzzlzzozypzvqztszptz\ nuzkvyhxyexxcyx_zvYzuVzuRztPztMzhflYzVTxPPvJKuDGs6\ Bq08p0Bk0Fh3Jd6M_AQWEUTIYPL`KQdGUhDYk8`o4ds0hv0kq3\ jn8ijEheJfaPeZUeUZdQdcMiaIo`Et_Ay_FscKlePhhUajZYlc\ RphMslGuqBxv5zz0zx2xu3tt3oq4ko4fn5ck5Zi6Vh6Qe8Mc8I\ a9E_99YA5WA2`DAdEJiFRlI_qJhuKpyLxsIynEzhBzc8zZ5zYA\ vYFpYKjYPdYTZTVaPWeLYhG_kD`o9aqFWtLQuQKxWEy`8zf2zk\ 0zl3zn8xoDuoIqpMoqRlqWis`ftedtjavk_xkZykYzkWzkVznV\ ypVysVxuVxvVvyVuzVuzVtzVtzVazeLzo4zy3xv2qu0ks0eq0_\ o0Un0Ok0JjfJihGkhFlhEnhDohAqh9sh8th6u`DsVJqPPoJVnD\ `l6fj0li0sh6piIniTkjcijnfjkjaioUjqkqxuyzzxzzxzxxzu\ vzsvzpvznuzjuzhuzetzctz`tzZtzWkzUdzTYzQQzPIzOAzL3z\ K0zJ0zG0zF0zE0zB2zA3z93z8 } 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==================================