3 Mandelbrot's Field
Definition

    The Mandelbrot's field is a case close to the Julia's one. It is described as:

    Instead of changing the initial value and check the convergence of the chain, Mandelbrot changed the value of the parameter and the initial value for z is fixed and equal to 0.

Plotting method

    It is quite the same method as Julia's except that the plotted value is nomore the initial value z0 but c. The test of convergence was done for a number of iterations of 30 and the constant M was equal to 2.

Matlab program

        Program: mandel.m

Results

    The form got with this calculation is a good example of fractals. Indeed the shape we have does not depend on the view scale.




    All the points that seem to be isolated, is in fact linked to the main figure. But these links cannot be seen at the view scale considered. The first calculation was done with an increase of the coordinates of 0.01. I decided to diminish the computing field and to use an increase of 0.001. I then discovered that this form that seems to be well defined graphically, was in fact composed of lots of parts. That makes better understand the idea of fractals.