For such an iteration the Julia set is not in general a simple curve, but is a fractal, and for some values of c it can take surprising shapes. See the pictures below.

The Julia set is named after the French mathematician Gaston Julia who investigated their properties in 1915 and culminated in his famous paper in 1918: Mémoire sur l’itération des fonctions rationnelles.

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 reveal ever-smaller details.

2025年1月31日 · 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 the filled-in set (the set of "exceptional points").

Julia set fractals are normally generated by initializing a complex number z = x + yi where i 2 = -1 and x and y are image pixel coordinates in the range of about -2 to 2. Then, z is repeatedly …

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 properties.

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 value of c.

Julia set fractals are fascinating mathematical objects that can be generated using complex numbers. These fractals are named after the French mathematician Gaston Julia, who studied them in the early 20th century.

The Julia set is named after the French mathematician Gaston Julia who investigated their properties in 1915 and culminated in his famous paper in 1918: Mémoire sur l’itération des fonctions rationnelles.

The Julia Set Fractal is a type of fractal defined by the behavior of a function that operates on input complex numbers. More explicitly, upon iterative updating of input complex number, the Julia Set Fractal represents the set of inputs whose resulting outputs either tend towards infinity or remain bounded.