FOTD -- April 23, 2011 (Rating 8) Fractal visionaries and enthusiasts: Today's image takes us back to the fantastic world of evaporation as seen through the MandNewt06a formula. The image consists mostly of inside stuff, though it appears to be a 50-50 inside-outside mixture. All that remains of the outside stuff in fact is the dots. The rest has pretty much evaporated away. I really like today's image, which I think deserves an honest rating of an 8. The name "Frosty Snowflakes" refers to the white dots scattered about parts of the scene. These dots are the remains of the outside stuff, which has all but totally evaporated away. The calculation time of 3-3/4 minutes is a bargain, considering that the result rates an 8. For the convenience of those who would rather not calculate the images, the finished image may be found on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> A hi-def version is posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original web site with all the bells and whistles is at: <http://www.Nahee.com/FOTD/> It is not up to date, though Paul has just posted a message to the Fractint list, letting us know he is still around. The formula that creates today's image appears to behave differently when used with different programs and math routines. So I cannot guarantee that the image generated on all systems will be identical to the image on the web sites. Some alternate renderings actually appear to be better than my own however. Recent messages on the list have my philosophical urges once again rising. I have read that the four greatest achievements of the human mind are the invention of Calculus, the theory of relativity, the theory of quantum mechanics, and the discovery of fractals. I pretty much agree. Each of these advances has expanded our view of the world we live in and at the same time raised new questions about the nature of reality. The Calculus demonstrated that, in some mysterious fashion, the laws and workings of the physical world can be encoded into the abstractions we call numbers. The encoding works so well that we can often learn more by working with the numerical models than we can by direct observation. Relativity demonstrated that time and space are not what they seem. According to relativity, time, space, mass, energy, acceleration, gravity, and so on are not the absolute fixed independent things they appear to be from our limited perspec- tive, but are united in higher dimensions into different aspects of a single thing. Relativity has so far passed all the tests devised to check it. Quantum mechanics has found that the sub-atomic particles making up the physical world do not appear as actual particles until we look to see them. When we are not looking, nothing exists but energy fields of varying strength that can be represented only as numbers. This raises the perplexing question of how things that exist only when someone is looking can be the building blocks of physical objects that are assumed to continue existing even when no one is looking. Quantum mechanics has also passed all the tests devised to check it. Unfortunately for the peace of mind of theoretical physicists, relativity and the quantum do not fit comfortably together. The two theories predict the existence of things that are incompat- ible with each other, and so far have defied all efforts to blended them into a single theory of everything except the self-awareness of those seeking the theory. Fractals demonstrate that simple everyday numbers are indeed capable of creating entire infinite universes. (We must remem- ber that complex numbers are made of simple numbers.) When we work with fractals, we see the behavior of reiterated complex numbers being transformed by machines into abstract shapes that have all the features of real physical objects except actual objective existence other than as pictures. This leads me to wonder whether much the same thing is happening in our everyday lives. Are our conscious minds like computers? Are our minds actually computing machines, constantly transform- ing the behavior of the far-more-complex quantum numbers into the mental images we take to be solid objects filling the four- dimensional spacetime world that we appear to live in? I'll have more to say about this stuff in upcoming discussions. And be assured that my ideas will respect no sacred cows of either science, religion or politics. Now on to the weather report. Friday began with clouds moving in here at Fractal Central. Rain moved in during the afternoon, while the temperature hovered around an unseasonably chilly 46F +8C. The fractal cats disapproved of the chilly wet conditions -- from the comfort of their indoor shelf of course. The humans' day was acceptable, though nothing to applaud. The next FOTD will be posted in 24 hours. Until then, take care, eat, drink and enjoy fractals, for tomorrow we . . . 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