What is the difference between Mandelbrot and Julia sets?

The Mandelbrot set is the set of all c for which the iteration z → z2 + c, starting from z = 0, does not diverge to infinity. Julia sets are either connected (one piece) or a dust of infinitely many points. The Mandelbrot set is those c for which the Julia set is connected.

What is the Mandelbrot set used for?

The term Mandelbrot set is used to refer both to a general class of fractal sets and to a particular instance of such a set. In general, a Mandelbrot set marks the set of points in the complex plane such that the corresponding Julia set is connected and not computable.

How is Mandelbrot calculated?

Remember that the formula for the Mandelbrot Set is Z^2+C. To calculate it, we start off with Z as 0 and we put our starting location into C. Then you take the result of the formula and put it in as Z and the original location as C. This is called an iteration.

Is there an end to the Mandelbrot?

Yet no matter how far you zoom in, there is no end in sight to the level of detail and intricacy contained in the fractal. The Mandelbrot set is the set of all complex numbers that do not “blow up” under iteration of the complex-valued function f(z) = z²+c, starting at z=0.

Is the Mandelbrot set infinite?

The Mandelbrot set puts some geometry into the fundamental observation above. Here is its precise definition: The Mandelbrot set consists of all of those (complex) c-values for which the corresponding orbit of 0 under x2 + c does not escape to infinity.

What is Julia set used for?

In general terms, a Julia set is the boundary between points in the complex number plane or the Riemann sphere (the complex number plane plus the point at infinity) that diverge to infinity and those that remain finite under repeated iteration of some mapping (function). The most famous example is the Mandelbrot set.

What are applications of fractals?

Fractals are used to model soil erosion and to analyze seismic patterns as well. Seeing that so many facets of mother nature exhibit fractal properties, maybe the whole world around us is a fractal after all! Actually, the most useful use of fractals in computer science is the fractal image compression.

Why is Julia a fractal set?

For Julia sets, c is the same complex number for all pixels, and there are many different Julia sets based on different values of c. By smoothly changing c we can transform from one Julia set to another over time, creating animated fractal shapes.