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Sidney
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As a mathematician, what may you say are the beauties that you see in the Mandelbrot set??
For an implied definition of "fruitful" which is far from clear in this context ... it is a banned topic exactly because the discussions tend to be the opposite of fruitful in the sense of actually getting anywhere. One reason it tends not to go anywhere is the way people who prefer philosophical discussion keep missing out vital definitions like that and everyone ends up talking at cross purposes and then people get upset etc...Im sorry I am still coming to terms with the fact that philosophy (or some degree of it at least) is not allowed in a physics forum, i find the lines between the two a bit blurred and unconsciously most of the time i find myself leaning toward the philosophical side of physics..i feel that's where discussion is most fruitful..
What you are asking for here is basically the matter covered in a college course in fractals or chaos theory. That's a little big for this forum.Ok, can i rephrase that.. From "the beauty" to "the functionality (with respect to nature and the human sense experience ) and the mathematical significance of its discovery...
The Mandelbrot Set is a famous mathematical set discovered by mathematician Benoit Mandelbrot in 1979. It is a set of complex numbers that, when iterated through a specific mathematical formula, form a fractal shape that is infinitely complex and self-similar at different scales.
The Mandelbrot Set is a set of complex numbers, meaning numbers that have both a real and an imaginary part. The formula used to generate the Mandelbrot Set requires the use of complex numbers and their operations, such as addition, multiplication, and exponentiation.
The equation for generating the Mandelbrot Set is z_{n+1} = z_{n}^{2} + c, where z_{n} is a complex number and c is a constant value. This equation is iterated for each point in the complex plane, and depending on the behavior of the resulting value z_{n}, the point is either included in the Mandelbrot Set or not.
Yes, the Mandelbrot Set is often visualized as a colorful fractal pattern. The colors represent the behavior of the points in the complex plane, with points that are included in the set often colored black, and points that are not included colored differently based on how quickly they diverge from the set. Many computer programs and online tools are available for visualizing the Mandelbrot Set.
The Mandelbrot Set has many applications in various fields, including computer graphics, chaos theory, and even stock market analysis. It has also inspired artists and musicians, who have used its fractal patterns in their work. Additionally, studying the Mandelbrot Set has led to a deeper understanding of complex systems and their behavior.