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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image, as do so many of my recent fractal images, features a scene in a fractal created by a whimsical formula: -0.4(Z^2)-2(Z^(-2))+(1/C). This formula draws a Mandeloid so grossly distorted that the period-12 buds are larger than the period-2 bud, which is almost lost. Today's scene lies on the north shore of the main bay, between the period-12 and period-13 buds. After studying the image for a few minutes and finding no satisfactory name, I thought to myself that the naming process was going nowhere. I immediately had my name -- "Fractal of Nowhere". Despite, or perhaps because of all its green and purple, I could rate the picture no higher than a 5. With a render time of 3-3/4 minutes, running the parameter file is marginally the best way of enjoying, (or disparaging), the image. The least efficient way to view the image is to wait 15 hours and download the GIF image file from the Usenet binary group: Today's partly sunny sky and mild temperature of 45F (7C) was ideal for fractal cats, but a brisk wind kept them skittish, limiting their outdoor adventure to a few minutes. They showed their frustration by getting into a spat, which left Thomas with a nicked ear and earned Tippy a claw trimming. All is now well however, since they made up and washed each other's faces soon after their spat. Once again, I had a successful day philosophizing. If the reader does not care for marginally on-topic ponderings, I recommend skipping to the last paragraph. In my afternoon philosophical ponderings I traveled back to my years at Saint Martin's Catholic Elementary school, which was taught by the Sisters of Charity, the nuns who at the time wore those starched white wings on their head. Since the school was a religious school, one of the subjects of study was the Catholic faith. We studied things such as the Holy Trinity, a mystery which I found intriguing; we learned some really big words such as 'transubstantiation'; we learned that we had souls, which, if we were good, would go to heaven when we died. (But of course if we were bad, our souls would go to the other place.) Being a studious student, I did reasonably well in my religion studies through the sixth grade, filling in the proper words on the religion tests. In the seventh and eighth grades however I began to think about some of the things I had been taught in religion class. The difficulties started when I began asking troublesome questions. Perhaps the first problem arose when I asked Sister Mary Thomas about the discrepancy between the age of the earth when she taught science and the age when she taught religion. When she taught science, she told the class that the earth was 4.5-billion years old; when she taught religion, she said the earth was 6-thousand years old. I asked her which age was right. The good nun replied by informing me that when she taught science, 4.5-billion years was the true age of the earth, and when she taught religion, 6-thousand years was the true age. When I protested that both could not be true, she told me to sit down and shut up. I heard similar phrases in religion class often the next year or so. When we were taught that we must believe in God to get to heaven, I asked why He makes belief so difficult by hiding Himself. The nun replied that if God were to make Himself visible, there would be no need for faith. When we were taught about life after death and heaven, I asked why I could find no science books about heaven or the soul. When we were taught about God's infinite mercy and kindness, I asked why, if we had died without having our mortal sins forgiven, He lost His mercy and became cruel, condemning us to eternal damnation because it was too late for us to be sorry. When we were told that good Christians would sit at the right hand of God, I commented on the huge crowd that would exist on his right side. I did not like crowds. I asked how eating meat on Fridays could be so evil that it was a sin worthy of eternal damnation. The nun told me that it was a precept of the church. Then I asked how almighty God could be forced to obey such arbitrary rules, which were set down by mere men. The nun told me to sit down. We learned about the missions to pagan lands. The Catholic Church teaches a type of salvation known as 'baptism of desire', which means that those who have had no chance to hear the Christian message can still get to heaven if they are good people. Once they have heard the Christian message however, these people must accept the message and be baptized before they can reach heaven. As I saw it, this situation meant that by traveling to pagan lands and spreading the Christian message, the missionaries had been actually causing the loss of the good souls who previously had been saved through the baptism of desire but then had been lost because they had heard the message but had not accepted it. When I pointed out that these people would have gone to heaven if the missionaries had not visited their land, and suggested that we should therefore stop sending missionaries, the nun lost her composure and gave me a scolding. After that episode I was a good quiet student, but I took religion lessons less and less seriously. Soon after leaving Saint Martin's School, I decided to try being an Atheist. As an Atheist I no longer needed to believe things that made no sense, but Atheism introduced a whole new set of problems. In a day or two I'll tell of my struggle and ultimate disillusionment with Atheism. For now it's lights out and shut-down time in the old fractal shoppe. Until tomorrow, take care, and to lose weight, exercise with a fractal. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Fractal_of_Nowhere { ; time=0:0X:XX.XX -- SF5 on a P200
reset=2001 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+11.46191326673826000/+12.729870818548550\
00/111.2787/1/162.499 params=0.2/2/1/-2/-3/0 float=y
maxiter=1500 inside=0 logmap=52 periodicity=10
colors=000K09I0BL0CM0EN0H<3>U0NW0PY0R_0T`0W<3>f2ah3c\
j3ek3f<3>Z9XWBUSBSPCPLENKFKHHIEIFBIE8KB5L92N60P50P30\
R20U1<4>1e01h01j02n02p02s02u00q50pR0pR0qR0qP0sP0sP0s\
P0uP0uP0wP0wN0yN<3>0zN0zN0zL0zL0zI0zL<7>0zK0zK0zK0zK\
0zI<3>0zI0zI0z00z00z00u00s00s00s00s00u00u00u00u00w00\
w00w00y0<3>0z20z20z20z30z30z30z5<3>0z60z60z60z8<3>0z\
90z90zB<3>0zC0zC0zE<3>0zF0zF0zH<3>0zI0zL0zU0za0uj0ps\
0jw0fw1fw1fw1fu1hu1hu0hu0hs0hs0js0js0jq0jq0lq<2>0lp0\
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0zZ0zZ0zX<3>0zW0zW0zW0zU0zU0zU0zU0zS<3>0zR0zR0zR0zR0\
zP0zP0zP0zN0zN0zN0zN0zL<4>0zK0zK0zK0zI0zI0zI0zK<10>0\
zL
}
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==================================
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times.
