Julia set

So we can try to plot the Julia set of a given function as follows.

For some functions we can say beforehand that the Julia set is a fractal and not a simple curve.

In other words the Julia sets are locally similar around Misiurewicz points.

For these families, even maps with disconnected Julia sets may display nontrivial dynamics.

The complement of is the Julia set of .

Julia sets are also commonly defined in the study of dynamics in several complex variables.

At , the tip of the long spiky tail, the Julia set is a straight line segment.

Julia set of discrete nonlinear dynamical system with evolution function:

A Julia set is a fractal.

But all Julia sets will be self-similar in detail, and a change of scale does not significantly affect the complexity of the figure.

Julia sets hung thickly from the branches.

It is the Julia set of the meromorphic function which is given by Newton's method.

For the Julia set is the line segment between -2 and 2, and the iteration corresponds to in the unit interval.

As a Julia set is infinitely thin we cannot draw it effectively by backwards iteration from the pixels.

Note that certain parts of the Julia set are quite difficult to access with the reverse Julia algorithm.

At , the shorter, front toe of the forefoot, the Julia set looks like a branched lightning bolt.

Mandelbrot set and Julia set are locally asymptotically similar around Misiurewicz points.

For instance, a point is in the Mandelbrot set exactly when the corresponding Julia set is connected.

In other words, the filled-in Julia set is the complement of the unbounded Fatou component:

It is this property that causes the fractal structure of the Julia set (when the degree of the polynomial is larger than 2).

The filled Julia set consists of all points in the mapping plane whose images remain bounded under indefinitely repeated applications of .

For integer d, these sets are connectedness loci for the Julia sets built from the same formula.

This work grew from his earlier work with Julia sets and "Pickover biomorphs," the latter of which often resembled microbes.

For all but at most two points , the Julia set is the set of limit points of the full backwards orbit .

At the end of the 1980s, Pickover developed biological feedback organisms similar to Julia sets and the fractal Mandelbrot set.