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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image is a Julia set of the fractal that results when both Z and C are raised to the power 1.4142 and multiplied together, and then C is added. It consists of gaudily colored but broken concentric circles with an interesting area of chaos toward the center. Most of the effect was achieved by calculating the formula with the outside set to 'tdis'. The chaotic parts of the image are filled with curious but hard-to-find Julia basins, one of which appeared two days ago as the 'Hairy Caterpillar' FOTD for January 25. I gave the image the name "Orb". The name was inspired by the nature of the image itself, which basically consists of nothing but circles. After a modicum of consideration, I rated it at a not-bad 7. The colors are a bit too brilliant, but still striking. The 'passes=b' option is fastest with this image, rendering the entire scene in only 11 seconds. This option often is the fastest, but it must be used with caution because it can easily miss important isolated features. The render time of under 11 seconds is true only when the image is rendered with the passes set to 'b'. I have discontinued the overall worth rating, which was weighted too heavily in favor of the render time. No one paid much attention to it anyway. The only important thing is the appearance of the completed image, which is covered in the rating that appears in the subject line of every FOTD. The image is a very fast one. By the time this letter is read, it should already be posted on the FOTD web site at: When we left off our philosophical ramblings, I had reached the point where I had realized that we do not actually observe an outer world. All we observe are signals sent to our mind by our sensory organs. Our mind then rectifies these nerve signals into a consistent series of mental images, which we learn early in life to take as an outer world existing totally apart from ourselves, in which we move about freely in space and move inexorably forward in time. This consistent set of images of an outer world is fascinating to observe and experiment with. It is what science examines in its investigations. But science, as productive as it may be, is still based on an assumption -- the assumption that the images our senses produce in our minds are exact reflections of the sources of the vibrations that strike our sensory organs and cause the neural signals to be sent to our minds. This does not invalidate the discipline of science, which remains perfectly valid as long as it is applied only to the mental images that we take to be the outer world. But men have insatiable curiosity, and their science, striving ever deeper into the mysteries of existence, is starting to transcend the image-world that we take for reality. We are entering the realm of the really real, which I call the hyperreal world -- the world that is sending the signals that impact our senses and cause the nerve signals to be sent to our minds, which then create the world-image that we know as the real world. The first hint of this transcendence appeared when the theory of relativity showed that the features of the large scale universe extend beyond the limits of our intuitive imagination. The quantum theory took us still farther into the hyperreal world, so far in fact that the world of the quantum no longer makes intuitive sense. But the most obvious place science is involved in the hyperreal world is the field of cognitive science, where it studies the brain in search of the source of the subjective things such as consciousness, thought, and emotion, which cause our outward behavior. The source of subjective things such as thought will never be found in the brain. We will find nothing there but the electrochemical processes that accompany, but do not cause, the subjective things we experience. We will never find how a chemical reaction or the firing of neurons in the brain can change into something with a totally different nature, such as a thought. This is because we are looking for the source of thought in the wrong place. The brain belongs to the so-called 'real' world. It is part of the mental image that we assume to be a world around us, while subjective things such as thought are a part of the hyperreal world, which is the source of the mental image of a 'real' world, but lies beyond the range of our senses and their instrumental extensions. It has long been known that a hyperreal world lies beneath the surface glitter of the 'real' world. Even Plato mentions it. There is an old puzzle -- if a tree fell in a forest and no one was there to hear it, would it make a sound?. This puzzle implies that the sensation known as sound is actually an aural image in the mind. The sensation of sound one would experience if they were there to hear the tree fall would not be the actual event. It would be only the sound of the event. In the same way, one might ask, 'if a tree fell in a forest and no one was there to see it fall, would any visual images of it exist'? The visual impressions one would experience if they were there would not be the actual event. They would be only the visual image of the event, which actually happened in the hyperreal world. True, if one were to arrive at the forest location one day after the tree fell, they would see that a tree had recently fallen. But the actual fall would have existed only in the hyperreal world, since no one would have been there to create the 'real' visual mental image in their mind. The ancient geologic events that our space probes are finding traces of on other planets, such as the surface water that once flowed on Mars, are in the same category. These ancient things are just now becoming real events. Until our probes revealed them, and the returned data created visual images in our minds, these other-planet events had existed only in the hyperreal world. I am going into such detail about the hyperreal world because in it lies the answers to the questions that science, limited as it is to the world of mental images, must be forever unable to answer. In the next outburst of wisdom (or foolishness -- take your choice), which will appear in a few days, I will go into my opinion of the nature of the hyperreal world. The sky was mostly cloudy, but the temperature reached a high of 47F 8C here at Fractal Central on Wednesday. Only the wet sloppy snow kept the fractal cats on the porch. Today is starting sunny but much colder. The temperature is down to 10F -12C, and the snow has frozen rock hard. I wonder what the dynamic duo will make of it. My only problem is where to find the next FOTD. The search will begin in a few hours. Until that next FOTD appears, take care, and be serene as a fractal. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Orb { ; time=0:00:10.82--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=mult-xy-zw-compjb function=ident/flip
center-mag=-0.00542788/-0.101983/0.1702254/1/40/\
-3.21104948186601e-011 params=90/90/1.4142/0/1.4\
142/0/0/0/-0.542983266/0.017693381 passes=b float=y
maxiter=5000 inside=255 outside=tdis periodicity=10
colors=000sCzqEzoGzmIzkKziMzfOycRx`UwYXvU_xRbwNdvK\
epLdnMbjM_fNXbNVZOSWOQSPNOPLKQIGSGDWFBaE9gF7kC5jH8\
hMAfRDdVFbYHeZFhZEkZDnZCqZBsZAUVG4RL8VKBYJF`IIcHMf\
GPiFQkHQlJRmLRnNSoPSpRSrTTsVTtXUuZUv`UwbSscQodOkeM\
gfKcgI_gGWhESiCOjAKk8Gk7Fj7Fi7Fh6Fg6Ff6Ee5Ed5Ed5Ec\
4Eb4Da4D`3D_3DZ3DY3DY9EWFFVLGURHSXHRbIQhJOnKNtKMsL\
OsLQsLSsLUsLWlRXeWYZ`YSeZLjZEo_7t_CrYHqWMpUQoSVnQ_\
mOclMhkKmjIqiHbaoeaqhaskau6Oi7Oo7OuCQtHStMTsQVsVXs\
_Yrd_rh`rbdmXhiRkdLo`FsW9vSLoZXieifogcleajc_gaYe_V\
bYT`WRYUPWSNTQKROIOMGMKEJG9IICHKFHMIGNLGPOFRRFTUEU\
XEW_DYbD_eC`hCbkBdnBfqALHRgsAdeCaTEWDFZGGaIHdLIgNJ\
jQKxNMlSL`WKQ`KEdJ3hJ8eKDcLHaLMZMQXMVVNeZTZTNTNHMH\
BGB5A50D72F83H94KA5MB6OC8RD9TEAVFBXGC_HIbHOeHUhH_k\
HenHkw8xpHpjQhcY`YfTSnMXhS`bXeXaiSgnMlrGqz7yvBvrEs\
nIpjLmfPjlOrcSgVVYMYOIOCE`EE`EEaEDaEDbEDbECcECcECd\
EBdEBeFBeFKKkKNiKQfKTdKWb }
frm:mult-XY-ZW-compjb {; draws 6 planes and rotations
;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J
;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J
a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994,
z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p4,
c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p5:
z=z^p2*(c^(p3-1))+c,
|z| < 400 }
END PARAMETER FILE=========================================
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times.
