Let us consider a map in the complex plane written as|
z n+1 = zn2 + c.
Depending on the value of the complex parameter c=(cr,ci), the trajectory zn from the initial condition z0=(x,y) converges to fixed points, periodic orbits, or chaotic orbits, but with some values of the initial condition, zn diverges to the infinity.
The initial point (x,y) for which the trajectory does not diverge is called as Julia set.
In the left field of this simulator, the Mandelbrot set is shown.
By clicking the Mandelbrot set with your mouse, the corresponding complex parameter c=(cr,ci) is set to the right field, and the Julia set would be drawn.
The set is colored with black, and the points which do not belong to it are colored depending on the time to diverge.
Both sets can be expanded by dragging the field with your mouse.