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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image bears the name "The True Beast". I gave it this name because it brings out the full beastly nature that was partly hidden in yesterday's image. Today's image shows the same midget that appeared yesterday, but the midget has been sliced in a different direction, one that is totally oblique to all six perpendicular planes of the four-dimensional Julibrot. In yesterday's image the spiral arms could be seen and followed as they multiplied and converged onto the midget. In today's image the arms are still there, but they are of a different number, and they no longer converge on the midget. Some arms have vanished entirely, leaving only traces where they almost appear. Others have morphed into horseshoe-like shapes, while still others have become concentric closed rings. I have kept the color palette and logmap from yesterday's image so that the corresponding parts can be more readily identified, but considerable stretching and skewing was necessary to restore the image to the same proportions. To see the area when it is unstretched, go the the 'z' screen, then the 'f6' screen and reset the 'x' mag factor to 1. Due to the skewing, the midget is some distance off the screen to the right, but it can easily be seen why stretching was necessary. The rating of a 6 might be a bit overdone, but today's image is still curious, amd well worth a look. The image may be viewed by running the attached parameter file or by downloading it, already rendered, from the FOTD web site at: When we left off the most recent burst of philosophy, we had reached the point where I had come to the conclusion that the mental images created by our senses are not a totally accurate representation of the actual outer world. It is at this point that I usually start getting flak from those who espouse the more materialistic sense-oriented world-views such as positivism and rationalism. But flak from those whose views differ does not make a world-view false. After much consideration, I chose the view that the hidden reality behind our sense-produced mental images is of a totally different and largely incomprehensible nature. I began my departure from accepted reality by noting that material objects are composed of atoms, and atoms are almost totally empty space. This means that the perceived solidity of the material world is something created in the mind. I pictured the world beyond the senses as consisting of ghostly objects, which would appear transparent and almost invisible if we could actually observe them. I next realized that color does not exist as an objective attribute. It does not appear until the mind interprets the impact of certain light frequencies on the retina of the eyes. This meant to me that those ghostly objects beyond the mental images are colorless as well as almost invisible. Not much remained of the solid world we assume we observe around us. I began to see the so-called 'real' world as more of a mental construct than an independently-existing objective thing. Then I considered the consequences of relativity. The theory of relativity states that time and space are different aspects of a single four-dimensional entity known as spacetime. In relativity, distances in space as well as intervals of time are not fixed, but vary according to relative velocity. The theory also states that matter is a condensed form of energy, and that mass is dependent on relative velocity. Relativity strengthened my conviction that things behind the scene are not as they appear in our mental image of them. Then I delved into the quantum theory, and read that in the subatomic realm, the most basic attributes we take for granted, such as the unchanging direction of time, and even existence and non-existence, begin to become fuzzy, and bear little resemblance to these well-defined attributes as they appear in the world we assume we observe around us. I had reached the point where I needed to make a decision. The entire discipline of science is based on the assumption that the images we observe in our minds are accurate representations of whatever is actually out there. I enjoyed science. I did not want to feel that it had lost its solid foundation, so I took the view that science is perfectly valid, but only when its investigations are limited to the perceived world of mental images. It followed that the apparently unsolvable problems, such as the origin of the conscious mind, arise because science sometimes unknowingly investigates phenomena whose source lies in the hyperreal world beyond the real world of our mental images. But what is this hyperreal world like? Is it a world much like the real world, filled with objects located in space? It cannot be exactly like the real world, for the attributes of solidity and color are creations of the mind, which do not exist in the hyperreal world. Is it a world with ghostly almost-invisible objects scattered about in space, while time passes linearly forward at an steady unchangeable rate? Most likely not. Time works differently in both the very large realm of relativity and the very small world of the quantum. Time works in its familiar manner only at the intuitive level of everyday experience, and the hyperreal world is far removed from the intuitive way we perceive a world around us. This left me with no choice but to accept that time as we know it most likely is also a creation of the mind, and does not exist in the hyperreal world. What then of space? Time and space are but two different ways of perceiving a single thing -- spacetime. I had to acknowledge that, most likely, space as we know it does not exist either in the hyperreal world, which must then be considered dimensionless and unchanging. We are left with a world with no solid objects, no color, no time and no space, for all these things are mental creations. And we have not yet included the quantum feature of probability. How does quantum probability affect the hyperreal world? More importantly, one might ask, does any of this crazy stuff I have pondered over the past few decades have any truth behind it, or have I totally gone off the deep end? My argument is still filled with holes, so stay tuned. The philosophy will continue in a few days. With warm sun and a temperature of 39F 3C, Monday was marred only by the soggy melting snow still covering the yard. The cats managed over an hour on the porch and even enjoyed a short trek to the holly thicket. When the day ended, they were happy enough so that no special treat was needed. This morning is starting the same as Monday. I assume the duo will have a similar day. For me the work is about average, which means that the next FOTD will appear in 24 hours as scheduled. Until then, take care, and be open minded but not too credulous. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
The_True_Beast { ; time=0:02:44.06--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=Slicejulibrot2 center-mag=+0.000005602\
47472017/+0.00000088644054031/846681.8/0.02445/\
171.009021891882384/-58.4065041085181846
params=195/2.76/81.96/-30.91/0.288136932805/0.4826\
45405409/0.288136932805/0.482645405409 float=y
maxiter=5000 inside=0 logmap=288 periodicity=10
colors=000SYsSXrSWqSVpSUoSTnSSmSQlTOkUMjVKiWIhXGgY\
Ef_CeaAdcAceAbgAaiA`kC_mEZoGYqIXrKWsMTrOSqQRpSQpUP\
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SzQWzN_zLczPgzUkzZozcszhvzmuzmwzmvzmvzmuzmuzmtzmtz\
mszmszmrzmrzmrzmqzmqzmpzmpzmozmozmnzmnzmmzmmzmmzml\
zmlzmkzmkzmjzmjzmizmizmiz }
frm:SliceJulibrot2 {; draws most slices of Julibrot
pix=pixel, u=real(pix), v=imag(pix),
a=pi*real(p1*0.0055555555555556),
b=pi*imag(p1*0.0055555555555556),
g=pi*real(p2*0.0055555555555556),
d=pi*imag(p2*0.0055555555555556),
ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
sg=sin(g), cd=cos(d), sd=sin(d),
p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
r=u*sg+v*ca*sb*cg, s=v*sin(a),
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=sqr(z)+c
|z|<=9 }
END PARAMETER FILE=========================================
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times.
