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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's fractal is named "Skimmers". There is nothing in the image that suggests such a name. I gave it this name because, after yesterday's 'dodo' image, I am still thinking of birds. At least skimmers, unlike dodos, are still quite plentiful and in no immediate danger of extinction. The parent fractal was created by combining various portions of Z^(-1.2) and Z^(1.2) before adding (1/C). It consists of a single large Mandeloid lying near the center of a vast expanse of chaos, which holds the usual infinity of other Mandeloids of all sizes and shapes. Today's scene lies in the chaos in the vicinity of East Valley of the large central Mandeloid. Most Mandelbrot midgets are surrounded by a symmetrical pattern of fractal elements, but the pattern around the midget at the center of today's image lacks this perfect symmetry. It does have a kind of symmetry however, which is somewhat spoiled by the unbalanced size of the corresponding parts of the pattern. The better-than-average coloring raises the rating to a 7. The render time of 11 minutes (on my tired old worn-out machine) is a bit slow, bordering on the boring. The rendering wait may be eliminated however by downloading the finished image from the FOTD web site at: I have no deep new philosophical revelations today, just a bit of rehashing of some stuff I have already written. The great enlightenment  will come later.There is an old TV episode (I think it is one of the 'Twilight Zone' episodes) about a man and woman deeply in love who have grown old together. Their old bodies are starting to fail, but there is a business in the area that sells android bodies into which aging people can be transferred. In these new android bodies, the old people can again live young, healthy and productive lives. As I recall, the aging couple has enough money to buy only one new body and they decide that the old man will be the one to get a new body. When the salesman transfers the old man into a new android body, the old man and his wife are over-joyed, but they soon realize that happiness will be impossible with only one of them young and vigorous. They finally decide that they both will remain old and die together. The old man tells the salesman to return him to his original body, which the salesman does, and the old man and his wife leave the store still in love and resigned to their old age. It's a touching, bittersweet story about social injustice in a future society, where money can bring youth itself. But the story also raises another big question -- what did the salesman transfer into the new body, and then put back into the original old body? He obviously transferred whatever that mysterious thing is that stays the same throughout our lives. A 'soul' would be a most satisfactory answer, but in the present-day world of science and reason, souls are assumed to be no more than wish-fulfilling fantasies that we no longer need to believe in. And even if the reality of souls were accepted, it would be quite difficult to imagine a physical procedure that could extract an immaterial soul from a physical body, hold onto it and insert it into a different body, which it would then take control of and in which it would feel perfectly at home. Since we have no immaterial soul to fall back on in our search for the old man's unchanging 'self', we must rely on material things. We cannot say it is the material of his physical body that stayed the same, for the body is a living organism that constantly changes the material of which it is composed. We cannot say it is the appearance of his body that remained the same, for his appearance also changed as he progressed through life. We cannot say it is the content of his mind; this is the most changeable part of all. We find ourselves reduced to speculation. In desperation, we assume that it must be some deep-seated, so far unrecognized, neural pattern of consciousness in his brain that stayed the same and was transferred into the android body. Let us assume that such a neural pattern is the correct answer. Using some vague electrically operated machine, the salesman simply copied the old man's neural pattern into the android, and presto, the old man found himself in a new body. But this assumption immediately leads to a huge problem. We now have the identical consciousness pattern in two places at the same time -- still in the original body and also in the android! Does the old man whose consciousness pattern has just been copied find himself in two places at the same time? If not, why not. And suppose the pattern were copied into a hundred androids? Why would the old man not be in a hundred places at the same time? The neural-pattern theory seems satisfactory enough on the surface, but it leads to paradoxes such as this that defy solution. Clearly, we need to search further for the answer to the question of what stays the same throughout our lives. We might conclude that such paradoxes show the impossibility of transferring the 'self' to another body without also transplanting the physical brain. This could well be true, but even if it is, it fails to tell us what stays the same through our lives. At this point, some might go to the extreme and declare that, since consciousness is not a material thing that can be put on a table and scientifically investigated, it does not really exist. It is all some kind of illusion. This also might be true, but if we claim this, we must then explain what if anything is experiencing the very convincing illusion that an enduring and conscious 'self' does exist. The paradoxes are deep and many, the answers few and unconvincing. We apparently need to set out in an entirely new direction if we hope to make headway. I will continue this philosophy in a few days. Progress toward a resolution may be slow, I may repeat things I have already said, but I will move inexorably in the direction of an answer. A high temperature of 93F 34C here at Fractal Central on Sunday made it a bit too warm for the fractal cats, but they still managed to enjoy over an hour in the shade of the holly thicket. A bit of extra tuna in the evening, combined with a bit of New York sharp cheddar cheese, ended their day satisfactorily. Today is starting sunny and a bit cooler. It should be a better day for the duo. For me, about three hours work is waiting, which I should be able to get through in plenty time to find a fractal worthy to be tomorrow's FOTD, and to do some serious philosophical pondering. Until then, take care, and sometimes it would be an advantage to be in many places at once. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Skimmers { ; time=0:10:57.24--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+0.801157791361965/+0.8200981387637338/\
935877.5/1/77.5/1.36488390208022725e-007
params=-1.34/-1.2/0.83/1.2/0/0 float=y maxiter=2000
inside=0 outside=imag logmap=195 periodicity=10
colors=000z_0ze0zpLzzrzzznwzatzSmzGfz6az8Wz8Vl8Ub8\
Oc8HZO8ld0pu0zr0zr0zp2zp4zp8znCznGznHzO_n0rL0z00p4\
0YC0GJ00S00_00h20WA2JHL8Qe0Yz0ez0Sz0GuC4jU0Yn0Lz0C\
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zAhz2ez0aG0G00000400C01J02S04_08h0Ap0Cz0Eh1JU6OECS\
1JW0Q_0Wd0nz0zz0lzCSuQ_Uah6np0pn0pn2plAplJpjSpjapj\
jz01A0z10z00j_zzCn04e00W00O00G400h0880e00h00j00l00\
n06p0Er0Hr0Lu0jz0_z2QuCGeL0OU6SWHUYUYYe__rdaz_Yzea\
zldzpezwjzzlzznzzpQzY16z0zG0rQ0dY0Qh0Ap00z00z0j_0e\
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Jz0Qz1Uz8lz1zz0uzClzWdzpOzu8zz0zz0zzGzzuzzzzuzzjzz\
_zzQ6zzOzQdz0CzeezGez2jz0 }
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=========================================
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times.
