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You are not logged in. #1 20121124 13:47:13
Newton FractalWill anyone expain me the basic principle behind the generation of Newton Fractals? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #2 20121124 16:17:00
Re: Newton FractalHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #3 20121124 17:11:31
Re: Newton FractalThey? Who are they? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #4 20121124 17:18:34
Re: Newton FractalGood question. Is there some function being iterated? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #5 20121124 17:24:00
Re: Newton FractalActually, this is not something I am being taught at school. 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #6 20121124 17:30:33
Re: Newton FractalHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #7 20121124 17:33:53
Re: Newton FractalNo! What's the name of the book? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #8 20121124 17:36:50
Re: Newton Fractal"Chaos Making a New Science" by James Gleick In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #9 20121124 18:36:37
Re: Newton FractalWhat is the basic principle behind generation of fractals? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #10 20121124 18:39:46
Re: Newton FractalThe instability of Newton's iteration is the main thing! In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11 20121124 18:45:01
Re: Newton FractalWhats "instable" about it? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #12 20121124 18:50:22
Re: Newton FractalWe would have to go over it to really understand that. But I can say that everyone is taught to use it as model of efficiency. Oh, the way it zooms in on the roots of the canned problems that are given it in books. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #13 20121124 20:08:04
Re: Newton FractalChaos is nice! 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #14 20121124 20:08:59
Re: Newton FractalNope! Chaos is a big mess. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #15 20121124 20:16:29
Re: Newton FractalWhy? Don't you enjoy randomness? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #16 20121124 20:30:17
Re: Newton FractalI am a numerical analyst. I consider that nothing but round off error, algorithm error. We try to eliminate it and Chaoticians are trying to show it, highlight it. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #17 20121124 22:02:52
Re: Newton FractalHi Bobby,
Yes, that's what happens with your towers problem if I use Newton's Method. Code:PROMPT "Enter approx. x (>33.886745 and <39.999999)";x$ x=VAL(x$) [loop] a=1/SQR(2500x^2)+1/SQR(1600x^2)1/10 IF ABS(az)<0.000000001 THEN PRINT "15digit approximation of x: ";USING("##.#############",x):END z=a b=x/(2500x^2)^(3/2)+x/(1600x^2)^(3/2) x=xa/b GOTO [loop] Output (for input between 33.886745 and 39.999999): "15digit approximation of x: 37.3550853341325" Last edited by phrontister (20121125 00:42:04) "The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do."  Ted Nelson #18 20121124 22:06:24
Re: Newton FractalHi;
In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #19 20121124 23:05:21
Re: Newton FractalHi Bobby,
"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do."  Ted Nelson #20 20121124 23:16:17
Re: Newton FractalRemember a while back with the loop that counted down from 1 to 0 by .1? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #21 20121124 23:33:49
Re: Newton FractalHmmmm......thinking........still thinking.........and.......nope! "The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do."  Ted Nelson #22 20121124 23:40:38
Re: Newton FractalThe comparison of two floating point numbers for equality is always dangerous. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #23 20121125 00:03:25
Re: Newton FractalAh...yes. I remember that now. *slaps forehead* "The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do."  Ted Nelson #24 20121125 00:05:08
Re: Newton FractalMaybe a FOR/NEXT loop? "The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do."  Ted Nelson #25 20121125 00:29:09
Re: Newton FractalHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. 