The Mandelbrot set is a mathematical set of points whose boundary is a distinctive and easily recognizable two-dimensional fractal shape. The set is closely related to Julia sets (which include similarly complex shapes), and is named after the mathematician Benoît Mandelbrot, who studied and popularized it.
Images of the Mandelbrot set are made by taking numbers on the complex plane, calculating whether it tends to infinity when the formula is iterated on the number, then using the number as X and Y coordinates in the picture and coloring the pixel depending on whether it tends to infinity or not. (see Computer drawings section of this article)
More precisely, the Mandelbrot set is the set of values of c in the complex plane for which the orbit of 0 under iteration of the complex quadratic polynomial zn+1 = zn2 + c remains bounded. That is, a complex number c is part of the Mandelbrot set if, when starting with z0 = 0 and applying the iteration repeatedly, the absolute value of zn remains bounded however large n gets.
For example, letting c = 1 gives the sequence 0, 1, 2, 5, 26,…, which tends to infinity. As this sequence is unbounded, 1 is not an element of the Mandelbrot set. On the other hand, c = i (where i is defined as i2 = −1) gives the sequence 0, i, (−1 + i), −i, (−1 + i), −i, …, which is bounded, and so i belongs to the Mandelbrot set.
I just thought it’s important for you to know this.
Merci pour cette information, mais, je ne comprends pas ces mots………
I stopped taking math courses at Calculus I when I begin studying integration.