As mentioned above, the Julia set can be found as the set of limit points of the set of pre-images of (essentially) any given point. So we can try to plot the Julia set of a given function as follows.

The Julia set is one of the best known examples of a fractal. It is a structure with an infinite amount of fine detail: you can zoom in on the edge of the fractal forever, and it will continue to …

The Julia sets, defined by the equation (\ref{julia}), can take all kinds of shapes, and a small change in $c$ can change the Julia set very greatly. In 1979, with the help of computer, B. B. …

Apr 12, 2025 · The "filled-in" Julia set is the set of points which do not approach infinity after is repeatedly applied (corresponding to a strange attractor). The true Julia set is the boundary of …

May 28, 2023 · The set we obtain with this equation is known as the Julia set. In fact, there is a different Julia set for almost every \(c\). Similarly as we did for the Mandelbrot set, we obtain a …

A Julia (named after G. Julia) set is the boundary of the sets of unbounded and bounded iterates of the family of functions \[f_a(x) = x^2 + a \tag{1} \label{eq1}\] where $a$ is fixed and $x_0$ …

Julia sets are certain fractal sets in the complex plane that arise from the dynamics of complex polynomials. These notes give a brief introduction to Julia sets and explore some of their basic …

The boundary of the set of points that do NOT escape to infinity is called the Julia set of the function f. Julia set may be a continuous curve, or totally disconnected set, depending on the …

The Julia sets, defined by the equation (\ref{julia}), can take all kinds of shapes, and a small change in $c$ can change the Julia set very greatly. In 1979, with the help of computer, B. B. …

Here are six Julia sets and their corresponding locations in the Mandelbrot set: Rendering Fractals. Of course we can zoom around and explore the fractal details of both Julia and …