How do you make a Julia fractal?

Julia set fractals are normally generated by initializing a complex number z = x + yi where i2 = -1 and x and y are image pixel coordinates in the range of about -2 to 2. Then, z is repeatedly updated using: z = z2 + c where c is another complex number that gives a specific Julia set.

Is the Mandelbrot set a Julia set?

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 equation generates the Mandelbrot set?

The Mandelbrot set can be explained with the equation zn+1 = zn2 + c. In that equation, c and z are complex numbers and n is zero or a positive integer (natural number).

How do I generate a Mandelbrot or Julia set?

Switch: You can click anywhere on the image of the fractal to generate either a Mandelbrot or a Julia Set (based on your mouse coordinates; the fractal will resize to the default (original) x and y range every time a new fractal is generated).

What is the Mandelbrot set?

The Mandelbrot set is named after another French mathematician, Benoit Mandelbrot, who published an article on the complex dynamics of the iteration in 1980. The first visualizations had been produced two years earlier. There is a reason that the iteration starts at 0.

How are fractal images produced?

All fractal images produced by this application use either a Mandelbrot-style iteration or a Julia-style iteration, possibly with minor variations (for example, the Nova fractal is obtained by a Mandelbrot-style iteration, but with z0 = CONSTANT).

What is the Julia set of F?

One formal definition of the Julia set of f is that if f is an entire function (yep, Wiki link!), J (f) is the boundary of points that diverge to infinity under f. Therefore, values of c that head off to infinity are not part of this new set, but values which remain bounded are. When plotted, this set has a familiar form: