# Julia Sets: Periodic and Non-Periodic Points Explained

• Kortirion
In summary, Julia sets are a type of fractal set named after the French mathematician Gaston Julia. They are generated by a mathematical function and have been studied for their intricate patterns and connections to other mathematical concepts. There are two types of points on Julia sets - periodic and non-periodic, with the latter creating more complex patterns. The Mandelbrot set is a specific type of Julia set and is connected to the boundary of the Julia sets of the function z^2 + c. Julia sets have practical applications in computer graphics and can be visualized and explored using software programs and online tools that use complex number arithmetic and fractal algorithms.
Kortirion
I'm a little bewildered when reading about these Julia sets. From the definition a Julia set is the closure of all repelling periodic points of a complex map f.
However I read that a Julia set always contain periodic and non-periodic points. Wasn't the definition including only periodic points? What am I missing here.

The "Julia set" in the second definition is the closure of the "Julia set" of the first definition.

## 1. What are Julia sets?

Julia sets are a type of fractal set that is generated by a mathematical function. They are named after the French mathematician Gaston Julia and were first studied in the early 20th century.

## 2. What is the difference between periodic and non-periodic points in Julia sets?

Periodic points are points on a Julia set that repeat after a certain number of iterations of the mathematical function. Non-periodic points, on the other hand, do not repeat and create intricate patterns on the Julia set.

## 3. How are Julia sets related to the Mandelbrot set?

The Mandelbrot set is a specific type of Julia set that is generated by the function z^2 + c, where c is a complex number. The boundary of the Mandelbrot set consists of the points where the Julia sets of this function are connected.

## 4. What is the importance of studying Julia sets?

Julia sets have been studied for their complex and beautiful patterns, as well as their connections to other mathematical concepts such as chaos theory and dynamical systems. They also have practical applications in computer graphics and image compression.

## 5. How can Julia sets be visualized and explored?

There are various software programs and online tools that allow for the visualization and exploration of Julia sets. These tools use complex number arithmetic and fractal algorithms to generate images of the sets, allowing for a better understanding of their patterns and properties.

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