FOTD -- June 02, 2008 (Rating 8) Fractal visionaries and enthusiasts: Warning! Expect no answers in this discussion, only questions. There is a second fractal 'artist' here at F.C., one known as F.L., who usually prefers to lurk invisibly in the background, but sometimes says things that start an all-day line of thought going in my head. On Sunday she happened to catch a glance of today's image, and asked "why do the numbers you picked make a fractal that looks like a circle of eight owl's faces and not something like an icy tree?" I replied, "for the same reason that one plus one equals two and not three." But this is no answer at all. One plus one equals two because that's the way it is and it couldn't possibly be any other way. (I think it took B. Russell about 50 pages to prove that one plus one equals two, shortly before the whole point of his immense work was disproved by Godel.) But it's far different to state that one plus one must equal two than to state that today's fractal parameters must always equal a circle of eight figures vaguely resembling owl's faces. The first fact is intuitively obvious, the second must be accepted on the faith that the computer's fractal math routine calculates unambiguous truth. (Something I am not at all certain of.) During my no-longer-short life, I have 'wasted' countless hours trying to visualize the fourth dimension, and just as many hours wondering about things such as why I was born at a certain time to live a life as a U.S. citizen, and not 800 years ago to live a life as a nomad in Outer Mongolia or even as a deer to be devoured by a lion in central Africa. I also find it quite incredible that the universe should at this very moment be in the infinitesimal slice of time in which I will exist to observe and wonder about it. It must be true that a fool such as I can invent more questions than a wise man can answer. But this is not all. In addition, I have recently concluded that the perception of an outer universe (reality if you will) of three spatial dimensions is a function of the level of consciousness of humanity. As to why I am the person I am, and why the universe is in the infinitesimal period of time in which I will exist, it seems to be a matter of definition. How could it be any other way? Such an answer does not totally satisfy however. After all, does not the universe obey the mathematical laws of an objective three-dimensional space? But mathematics is a human invention, developed to be a symbolic statement of abstract human thought processes. Man certainly would never have developed a math that would be valid only in a perceived universe of four spatial dimensions. I now wonder whether our mathematics describes an objective reality at all, or if we intentionally designed and tweaked it to work with a three-dimensional space that we mentally create around us. The question of why the universe is in the tiny slice of time in which I exist might be a wrong question based on a wrong percep- tion. Relativity shows that there is no universal time which is true throughout the vast expanse of space. Each individual exists in his own unique present moment. We need to somehow re- phrase the question. I suspect that the question of why I am myself is also a wrong question, based on another misperception. So now, instead of searching for the correct answers, I find myself still searching for the proper questions. Perhaps it's time to turn to fractals. Today's image is named "Eight Hooting Owls" because that's what F.L. saw when she caught sight of it. It rates an 8 because I think it's a rather good image. The parent fractal is the same one that produced yesterday's image. But instead of lying at the edge of the fan, today's image lies almost at the dead center of the fan. The calculation time of 1-1/2 minutes is logical and provable. Just as logically provable is the fact that the image will soon be posted for viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Near perfect conditions prevailed here at Fractal Central on Sunday, with low humidity, lots of sunshine, gentle winds, puffy cumulus clouds, and a temperature of 79F 26C 299K 21R. The fractal cats, unconcerned about which temperature scale to use, (Celsius is probably the best), found their comfort in the sunniest window. My day was pleasant enough, though thanks to F.L., the nagging and unanswered questions simply would not go away. But despite this, the next FOTD will be posted in 24 hours. Until then, take care, and there must be aleph^(aleph) questions that never have been and never will be asked, much less answered. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Eight_Hooting_Owls { ; time=0:01:28.38-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+3.400279501439892/+0.0000082660249179/\ 3.599998e+010/1/-39/0 params=-11/-1.1/-1/-11/0/\ 525/0/0 float=y maxiter=1750 inside=0 logmap=165 periodicity=10 colors=0000Ob0Xe0zi0bm0zp0ig0kZ0dR0\ XI0TA2I0460820000T00b00z00z20z0Ma0xi0thErbTniimTxi\ zzgMzeozdGzdCzdAzd6xd4rd0md0gd0bd0Xd0Rd6IrM8z`0zX8\ zVEzTMzRRzOXvMdrKinInkGngGneGndEn`EnZELXEnTCnRCnPC\ QMCnKAnIAnEALCAVACQAEVAEVAGV8IV8KV8KV8MV8OV8PV8RV8\ TV8VV8XV8Zi8`i8zrvzptzprzppzpnzpmznkxnivngvnetndrn\ brm`pmZpmXnmVrtOvzGzz8zzAzzCzzEzzGzzGzzIzzKzzMzzOz\ zOzzPzvRzmTzgVzbVz`RzZOzZKzXGzXCxV8tV4pT0kT0gR0dR0\ gK0kE0m86p2Cr0Iv0Ox0Rz0`zCgzOnz`xzmzzxzzzzzzzzzttz\ nnzigzdbzZXzTRzOMzIEzC8z62z00z00z00z00z00z40tE0kO0\ bX0Ve0Mn0Cx04z08z0Az0Cz0Ex0Gv0It0Kr0Mp0On4Pm6RkK`m\ Ximgrntznbzpzxpxinz`2zb8zdEzeKxgOviTviZtkdrmgpnmnp\ rnpxmrzktzivzgxzgxzZzzRznIzZAzI0z00z00z04z0Az4GzAM\ zGRzMXzRbzXgzbmzgrzmkzkdziXzibzeezbkz`nzXtzVxzRzzO\ zzMzzIzzGrzdVzzRzxPzxMzxKzvGzvEzvAzt8zt4zt2zr0zr0z\ r0zp0zp0zp0zp0zn0zm0zk0zi0zg0ze0ze0zd0zb } frm:MandAutoCritInZ {; 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)+(p4)), 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=========================================