|
Fractal of the Day
by Jim Muth
|
|
Fractal enthusiasts and visionaries: Ah, the technological wonders of the internet. Everything was going good yesterday -- that is until the time came for me to log into Mindspring to post the FOTD. Then all hell broke loose when I did. I escaped with two copies of the Philofractal version of the FOTD and an incomplete copy of the Fractal-Art version actually appearing on the lists. I've never seen such strange responses from an ISP. No wonder that Mindspring, which only a month ago announced it was out to replace AOL as the nation's number-one online service, has just announced that it will soon be swallowed by Earthlink, just as it swallowed Pipeline a couple years ago. But that was yesterday; today has so far been uneventful -- no burrs in the fractal cats and no problems with the fractal ISP. I celebrated the uneventful day by returning to yesterday's fractal for further investigation. Today, I explored another of the off-center lobes, and came up with an image that I named "Candied Minibrot". I gave the picture this name when, after studying it for a few minutes, I got the urge for some brightly-colored candy. Not surprisingly, today's image bears a strong resemblance to yesterday's, the greatest difference being that today's picture is significantly deeper and therefore more intricate. The parameter file is pretty fast, but downloading the image file is equally fast and a bit less trouble. Regardless of the path you choose, the finished picture will be worth the minute or so invested in its re-creation. The JPEG'd image file can be found on Usenet at: The somewhat important weather was cloudy and rainy today here at Fractal Central, with about 1.6 inches (4cm) accumulating. But the temperature of 68F (20C) was perfect for finding fractals. On the philosophy front, I have still not presented my solution to the impossible question, "why am I myself and not someone else?" Today, I will approach that solution. IMO, there can be only one way to answer the puzzle, and that is to set the mind loose with no restraints. The answer I found is so bizarre as to be beyond belief, perhaps even beyond taking seriously. It may be considered, or rejected, or ignored (the highest form of rejection.) We already know that reason, which works so well when applied to the outer world of everyday experience, can never solve the mystery. What then, can solve it? I feel that the problem can be solved only by looking beyond our world-image. As I commented in a previous FOTD, the objective world that we are so familiar with is actually a series of sensory-produced images in our minds. To believe that the images are an exact duplicate of whatever is actually "out there" is an act of faith. When we observe another person, what we are actually experiencing is an image in our minds of a body behaving as though another intelligent awareness were animating it. Since we can know nothing of another person other than this moving image, can we truly say that the mental image is conscious in its own right? A 'yes' answer would open the way to many more questions. Sometimes in our dreams we meet and communicate intelligently with other people both living and dead. Where does the intelligence that animates these dream images come from? It comes from our own minds. When we talk with others in dreams, we are in effect talking with ourselves. Dreams show that our minds have the ability to create all the appearances of another intelligent human being. Sometimes these dream people actually give solutions to problems that have been perplexing us. And even when we are awake, we can be aware of other people only by the behavior of the images that their bodies produce in our minds. At this point, it would appear that I am next going to claim that solipsism is true, and my mind is the only thing that exists. I assure you that this is not the case, but the rather involved wrap-up will have to wait until tomorrow's FOTD. Well, looking out the fractal window, I see that dusk is starting to fall and the rain has stopped. Hopefully, this is a sign for a good week to come. The first fruits of that good week will appear tomorrow at this same time and place. Until then, take care, and be patient. Jim Muth jamth@mindspring.com |
START FORMULA==============================================
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 FORMULA================================================
START PARAMETER FILE=======================================
Candied_Minibrot { ; time=0:01:10.25 on a p233, SF5
reset=2000 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=ident passes=t
center-mag=-1.23310733902428400/+1.0503838471191590\
0/1.913303e+009/1/130 params=11/-11/1/1/0/0
float=y maxiter=300 bailout=25 inside=0 logmap=31
symmetry=none periodicity=10
colors=000CaHGjTqKw`Vmwm4cj`0142I48QGEYSJczKdmVkqzn\
zeUiVafLXsK`kzzziprFML<2>bZmobzWRhHGV35IAGFGRC<2>K8\
l<3>S8olmV<2>G6rHFnIOjPNdJXf9xYCs_Fw`IwbIwHJwTLwVDw\
kGwhIwe3w8CwOkwKdwPYwURwZMwlLwiKwfYwP<2>Nw`UwEQwNNw\
WCwdFwcIwc_wRSwNrwbfwcVwccwWUw_cw9UwPqwJ_w1<2>OwVlw\
`<2>Rwc1wx8wqEwj8wefw3VwMjwrwwCiwMXwV9wfwwzcwn2wX8w\
_Ewa8wM2wC<2>GwX`wh<2>OwdOwnmwu<2>Rwg4wXAw_FwaFw`Hw\
aJwbbwpSwI<2>MwZ`wP<2>Ow`mwG<2>RwYZwaoweqwjewgVweIw\
d<2>Kwcpwk_wghwr_wmSwhswd<2>Twciwj<2>QwdswVrwGfwOVw\
WRw9<2>LwX3wU9wYFw`ewT<2>Pwaow`gwCwwd<2>Uwcew`YwaRw\
brws`wkOwTMwZgwi_wgSwegw1_wESwRnwL<2>Rw_QwF<2>LwY8w\
pCwkGwgpwu_wlww9<2>UwXwwJcwUTwWOw_EwPGwUIwZswS6wp\
<2>HwfAwbFwc0wPAwXPw4MwM0wDAwRowHAwVOwaVwx<2>Mwh3\
we<2>GwcRwrOwmMwhew4VwM7wbEwcNwvLwl8w5
}
END PARAMETER FILE=========================================
START 19.6 PAR-FORMULA FILE================================
Candied_Minibrot { ; time=0:01:10.25 on a p233, SF5
reset=2000 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=ident passes=t
center-mag=-1.23310733902428400/+1.0503838471191590\
0/1.913303e+009/1/130 params=11/-11/1/1/0/0
float=y maxiter=300 bailout=25 inside=0 logmap=31
symmetry=none periodicity=10
colors=000CaHGjTqKw`Vmwm4cj`0142I48QGEYSJczKdmVkqzn\
zeUiVafLXsK`kzzziprFML<2>bZmobzWRhHGV35IAGFGRC<2>K8\
l<3>S8olmV<2>G6rHFnIOjPNdJXf9xYCs_Fw`IwbIwHJwTLwVDw\
kGwhIwe3w8CwOkwKdwPYwURwZMwlLwiKwfYwP<2>Nw`UwEQwNNw\
WCwdFwcIwc_wRSwNrwbfwcVwccwWUw_cw9UwPqwJ_w1<2>OwVlw\
`<2>Rwc1wx8wqEwj8wefw3VwMjwrwwCiwMXwV9wfwwzcwn2wX8w\
_Ewa8wM2wC<2>GwX`wh<2>OwdOwnmwu<2>Rwg4wXAw_FwaFw`Hw\
aJwbbwpSwI<2>MwZ`wP<2>Ow`mwG<2>RwYZwaoweqwjewgVweIw\
d<2>Kwcpwk_wghwr_wmSwhswd<2>Twciwj<2>QwdswVrwGfwOVw\
WRw9<2>LwX3wU9wYFw`ewT<2>Pwaow`gwCwwd<2>Uwcew`YwaRw\
brws`wkOwTMwZgwi_wgSwegw1_wESwRnwL<2>Rw_QwF<2>LwY8w\
pCwkGwgpwu_wlww9<2>UwXwwJcwUTwWOw_EwPGwUIwZswS6wp\
<2>HwfAwbFwc0wPAwXPw4MwM0wDAwRowHAwVOwaVwx<2>Mwh3\
we<2>GwcRwrOwmMwhew4VwM7wbEwcNwvLwl8w5
}
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 19.6 PAR-FORMULA FILE==================================
|
times.
