Title: What about the "dust"? Post by: KRAFTWERK on December 18, 2009, 09:44:33 AM I am a real layman, both in mathematics and rendering/programming, I didn´t even know the difference between Pi and Phi until yesterday...
http://www.fractalforums.com/mandelbulb-renderings/degree-and960-mandelbulb/ :sad1: I am just an amazed explorer of this new world you found (must have been a thrilling journey for you...) therefore I ask the stupid questions... :) Could the dust that appears when you do a lot of iterations in reality be the true mandelbulb details you are looking for? Daniel White has two interesting examples of "dust" becoming details on his site: http://www.skytopia.com/project/fractal/mandelbulb.html (http://www.skytopia.com/project/fractal/new/q85/A-Slice-of-Mandelbrot-Gateaux-small.jpg) (http://www.skytopia.com/project/fractal/new/q50/Gateau7500-i2-small.jpg) Imagine Benoit Mandelbrot: (http://farm3.static.flickr.com/2569/4194803054_02cbd89dc0_m.jpg) The first attempt gave a lot of "dust" around the set, but if I do fewer iterations it looks much nicer: (http://farm3.static.flickr.com/2707/4194048077_504203276b_m.jpg) Am I too far out here? Newbee and layman and all... :) (May I propose a Philosophy-part in this forum, to prevent me and other laymen from polluting the Theory part? I sure have a lot of wonderings about this.) Title: Re: What about the "dust"? Post by: oftakofta on December 18, 2009, 11:53:08 AM Quote (May I propose a Philosophy-part in this forum, to prevent me and other laymen from poisoning the Theory part? I sure have a lot of wonderings about this.) I concur, a philosophy part would be a great addition to this forum. As far as I understand the logical foundations of mathematics, as outlined in Principia Mathematica, self-reference (and thereby paradoxes) is avoided by having a hierarchical structure of statements. That is, until Gödels incompleteness theorems proved otherwise. Douglas Hofstadter discusses this at length in his books "I am a Strange Loop" and "Gödel, Escher, Bach". These books are good if you have some basic philosophy training and can stand the pompous writing style of the author. No mathematics above high school level is needed to follow the arguments. Having said that, I am still convinced that mathematics is the only way to truly communicate objective truths about the nature of nature between pepole. It is just that it becomes a little strange when self-reference and infinities are involved. Sorry for drifting off topic. Title: Re: What about the "dust"? Post by: kram1032 on December 18, 2009, 04:46:23 PM Though it gets really interesting when maths in physics proof that subjectivity is an objective fact of nature. That's differently expressed in two theories which are searched to be unified :) Theory of relativity and Quantum mechanics :) |