FOTD -- January 15, 2003 (Rating 8) Fractal visionaries and enthusiasts: Today's image is a lot like yesterday's, though I spent a bit more time on it and worked the coloring up to where the image earns a somewhat liberal 8. When I was finished, I named the image "Nest of Tachyons". Like the name I gave yesterday's FOTD, the name of today's image has little to do with the image's actual appearance. In fact, certain colorations that I tried and then discarded resulted in an image resembling rings of shark's teeth. Tachyons are hypothetical particles that travel faster than light. Perhaps it would be best to call such particles imaginary, for there is no evidence that they do exist and good reasons why they cannot exist. But if such particles did exist, they would travel backward in time. They would reach their destination before they left their point of departure. This attribute of tachyons might raise thoughts of backward time travel. We might latch on to a tachyon and go back in time to warn our earlier selves of all the mistakes we have made. If we could go back in time only a few hours, we could give ourselves the winning lottery numbers in time to buy a winning ticket. It's a good dream, but it will never happen. The natural world seems to treat backward travel in time as a taboo. Every time we discover a way we might do it, we soon find a reason why the way we have discovered will not work. No matter how clever our schemes, we are frustrated by some ineluctable law of nature. It reminds me of the situation we face with the uncertainty principle. If we try to determine both the position and momentum of an electron at the same time, we find the task impossible. The more accurately we know one, the vaguer the other becomes. Something always gets in our way. In this case, it is our assumption of the nature of the unmeasured electron that has led us to mistakenly look for something that does not exist. An electron is a wave of probability, with no definite attributes until we pin it down by our measurement. We naturally cannot measure what does not exist. I strongly suspect that when we contemplate the possibility of backward time travel, we make another wrong assumption. We assume time itself to be something that it is not. That 'grandfather' paradox could be trying to tell us something important. We often see black holes presented as possible means of time travel and faster-than-light travel. The problem with this method is that we could not survive the tidal forces as we pass the singularity. We also see multiple universes optimistically mentioned as a possible means of going backward in time. We have dark matter and dark energy which some say could be the gravity of these alternate worlds bleeding into our own universe. We have a cosmic repulsive force, which is said to result from the energy of the vacuum. We have many signs and theories that other worlds might exist, but no possible way of reaching them. We must face the fact that our one-way trip into the future, which actually is time travel, cannot be escaped. And I must face the fact that I have again wandered from the topic of fractals. I can see no way in which fractals could be a means of time travel, but stranger things have happened. With its 5-minute render time, today's image is mercifully fast. But even faster is the download from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> It was quite cold here at Fractal Central Tuesday, remaining just below freezing despite the strong sun. At this time of year the earth is about as close to the sun as it ever comes, yet the temperature is about as cold as it ever gets. Not concerned with astronomical trivialities, the dynamic ones (cats, that is) remained outside only a few minutes before getting their whiskers chilled and retiring indoors to their favorite heat sources. Today is starting cold again, and to make things worse, a fresh dusting of snow is on the ground. The fractal cats will not want to hear this. As for me, I always take whatever comes. (I have no other choice.) Until next time, take care, and never forget that we are made of tardyons. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ Nest_of_Tachyons { ; time=0:05:43.17--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-1.36800428773697500/+0.557337704952596\ 80/2.390289e+007/1/-37.5/-6.94211269788858054e-008 params=3.7/-0.85/0.1/-8.5/0/1e+100 float=y maxiter=120 inside=fmod proximity=0.5 periodicity=9 colors=0005zA5zA8zD8zD8zGAzGAzGAzIDzIDzLGzLGzOGzOI\ zOIzQIzQLzTLzTLzTOzWOzWQzYQzYQz_Uz_Uz_UzbWzbWzeWze\ YzgYzg`zg`zj`zjczmczmczoezoezoezrgzrgztjztjzvjzvmz\ vmzymzyozzozzmzzozzozzozzozyozyozyozyozvozvozvozto\ ztoztoztozrozrozrozrozoozoozoozmozmozmozmozjozjozj\ ozjozgozgozgozeozerzerzerzbrzbrzbrz_rz_rz_rz_wzYwz\ YwzYwzYwzWwzWwzWwzTwzTwzTwyTwyQwyQwyQwxQxxOyxOzxOz\ xLzxLzxLzxLzxIzxIzwIzwGzwIzxIzxLzxLzxOzxOyyQxyQwyT\ wyTwyWvzWuzYtzYsz_rzbqz_pz_oz_nz_mz_kz_iz_gz_ez_cz\ _az__zYYwYWwYUuYPuYKrYFpYApY5nY2kY2kY2hW2hW2fW2cW2\ bW2aW2`W2_W2YW2WW2UW2SV2RU2QT2PS2OR2NQ5MP5LO5KN5JM\ 5IL5HK5GJ5FI5EH5DG5CF5BE5AD59C58B57A56A55A54A53A82\ A81A80A80A80A80A80A80A80A80A80A80L80L80L80L80L80L8\ 0L80L80LA0OA0OA0QA0QA0TA0TA0WA0WA0YA0YA3_A8_ABaAGc\ AIeAKgAMiAOkAQmASoAUqAWsAYuA_wAaxAcyAezAgzAizAkzAm\ z8oz0qz0sz0uz0wz2xz2yz5zz } 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==================================